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papers/0AYosSFETw/metadata.json

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+{
+  "id": "0AYosSFETw",
+  "title": "Towards human-like spoken dialogue generation between AI agents from written dialogue",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-21",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=0AYosSFETw"
+}

papers/0AYosSFETw/paper.md

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+# TOWARDS HUMAN-LIKE SPOKEN DIALOGUE GENERA-TION BETWEEN AI AGENTS FROM WRITTEN DIALOGUE
+
+Anonymous authors
+
+Paper under double-blind review
+
+# ABSTRACT
+
+The advent of large language models (LLMs) has made it possible to generate natural written dialogues between two agents. However, generating human-like spoken dialogues from these written dialogues remains challenging. Spoken dialogues have several unique characteristics: they frequently include backchannels and laughter, and the smoothness of turn-taking significantly influences the fluidity of conversation. This study proposes *CHATS* — CHatty Agents Text-to-Speech — a discrete token-based system designed to generate spoken dialogues based on written dialogues. Our system can generate speech for both the speaker side and the listener side simultaneously, using only the transcription from the speaker side, which eliminates the need for transcriptions of backchannels or laughter. Moreover, CHATS facilitates natural turn-taking; it determines the appropriate duration of silence after each utterance in the absence of overlap, and it initiates the generation of overlapping speech based on the phoneme sequence of the next utterance in case of overlap. Experimental evaluations indicate that CHATS outperforms the text-to-speech baseline, producing spoken dialogues that are more interactive and fluid while retaining clarity and intelligibility.
+
+# 1 INTRODUCTION
+
+Large Language Models (LLMs) have profoundly influenced the field of natural language processing (NLP) and artificial intelligence (AI) [\(Zhao et al., 2023\)](#page-11-0). LLMs, with their capacity to generate coherent and contextually relevant content, have enabled more natural text-based dialogues between humans and computers and paved the way for inter-computer communication. The recently proposed concept of Generative Agents [\(Park et al., 2023\)](#page-10-0) underscores the potential of LLMs, where emulated agents within the model engage in autonomous dialogues, store information, and initiate actions. This emerging paradigm of agent-to-agent communication offers vast potential across various sectors, from entertainment to facilitating human-to-human information exchange. However, considering the dominance of spoken communication in human interactions, integrating voice into machine dialogues can provide a richer expression of individuality and emotion, offering a more genuine experience. A significant challenge then emerges: how can we transform written dialogues, whether generated by LLMs or humans, into human-like spoken conversations?
+
+Although both written and spoken dialogues serve as mediums for communication, their characteristics and effects on the audience differ significantly. Spoken dialogues are imbued with unique elements such as backchannels, laughter, and smooth transitions between speakers. These are rarely captured fully in written form. For instance, a nod or a simple "uh-huh" serves as a backchannel in spoken dialogues, subtly indicating the listener's engagement and understanding [\(Yngve, 1970\)](#page-11-1). Similarly, laughter can convey amusement, act as a bridge between topics, and ease potential tensions [\(Adelsward, 1989\)](#page-9-0). The smoothness of turn-takings in spoken dialogues, wherein one speaker ¨ naturally yields the floor to another, introduces a rhythm and fluidity that is challenging to reproduce in text [\(Stivers et al., 2009\)](#page-11-2). Several approaches have been proposed to model these backchannels [\(Kawahara et al., 2016;](#page-9-1) [Lala et al., 2017;](#page-10-1) [Adiba et al., 2021;](#page-9-2) [Lala et al., 2022\)](#page-10-2), laughter [\(Mori](#page-10-3) [et al., 2019;](#page-10-3) [Tits et al., 2020;](#page-11-3) [Bayramoglu et al., 2021;](#page-9-3) [Xin et al., 2023;](#page-11-4) [Mori & Kimura, 2023\)](#page-10-4), and ˘ turn-taking [\(Lala et al., 2017;](#page-10-1) [Hara et al., 2018;](#page-9-4) [Sakuma et al., 2023\)](#page-11-5). However, most have focused on human-to-agent conversation or the task itself (e.g., laughter synthesis) and the agent-to-agent situation has not been evaluated.
+
+A straightforward approach for transforming written dialogues into spoken dialogues involves employing a text-to-speech (TTS) system. Advancements in TTS have facilitated the generation of individual utterances at a quality comparable to human voice [\(Kim et al., 2021;](#page-9-5) [Tan et al., 2022\)](#page-11-6). Certain studies have focused on generating conversational speech by considering linguistic or acoustic contexts [\(Guo et al., 2021;](#page-9-6) [Cong et al., 2021;](#page-9-7) [Li et al., 2022;](#page-10-5) [Mitsui et al., 2022;](#page-10-6) [Xue et al., 2023\)](#page-11-7). Furthermore, certain studies have equipped LLMs with TTS and automatic speech recognition to facilitate human-to-agent speech communication [\(Huang et al., 2023;](#page-9-8) [Zhang et al., 2023;](#page-11-8) [Wang](#page-11-9) [et al., 2023;](#page-11-9) [Rubenstein et al., 2023\)](#page-11-10). However, these systems are fully turn-based, where each speaker utters alternatively, and the characteristics of spoken dialogues such as backchannels and turn-taking are neglected. Recently, SoundStorm [\(Borsos et al., 2023\)](#page-9-9) has succeeded in generating high-quality spoken dialogue; however, it requires transcriptions for backchannels and is subject to a 30-s length constraint. Another approach introduced the dialogue generative spoken language modeling (dGSLM), which generates two-channel audio autoregressively, achieving realistic vocal interactions, laughter generation, and turn-taking [\(Nguyen et al., 2023\)](#page-10-7). Although dGSLM's operation based solely on audio is revolutionary, it cannot control utterance content via text. Moreover, as reported in section [4.4,](#page-8-0) generating meaningful content with dGSLM requires a vast dataset.
+
+This study proposes CHATS (CHatty Agents Text-to-Speech), a system for transforming written dialogue into spoken dialogue, whose content is coherent with the input written dialogue but generated with backchannels, laughter, and smooth turn-taking. By conditioning dGSLM on the phonetic transcription of speaker's utterance, our system can generate meaningful and contextually proper utterances on the speaker side. Simultaneously, it generates various backchannels and laughter without transcription on the listener side. The proposed system is designed to overcome the limitations of existing methods, including the turn-based nature of TTS systems and content control constraints of textless models. A collection of audio samples can be accessed through <https://anonresearch81.github.io/research/publications/CHATS/>.
+
+Our contributions are multi-fold:
+
+- Exploration of Dual-Tower Transformer Architecture: Our system is built on top of dGSLM, whose core comprises a dual-tower Transformer to generate discrete acoustic tokens. We condition dGSLM with phonemes and investigate the effect of pre-training in TTS tasks on the textual fidelity. Furthermore, we introduce a pitch representation following [Kharitonov et al.](#page-9-10) [\(2022\)](#page-9-10) and analyze its effects on both textual fidelity and prosody.
+- Introduction of a Turn-Taking Mechanism: A novel mechanism for predicting the timing of spoken dialogues is introduced. This encompasses both the duration of pauses after utterances and instances where subsequent utterances overlapped with preceding ones, echoing the organic rhythm and fluidity of human conversations.
+- Extensive Investigation of Generated Spoken Dialogue Characteristics: We conduct a comprehensive analysis of the characteristics of generated spoken dialogue, comparing its closeness to human dialogue across various dimensions. These include the quality of utterances, the frequency and content of backchannels, the duration of turn-taking events, and the subjective perception of dialogue naturalness.
+
+# <span id="page-1-0"></span>2 BACKGROUND
+
+### 2.1 GENERATIVE SPOKEN LANGUAGE MODELING
+
+Generative Spoken Language Modeling (GSLM) is a framework introduced by [Lakhotia et al.](#page-10-8) [\(2021\)](#page-10-8) to capture both acoustic and linguistic characteristics of spoken language directly from raw audio, without relying on text or labels. One of the main challenges in raw audio modeling is its excessive information; for instance, a typical audio file contains tens of thousands of samples per second (e.g., 16,000 in 16 kHz audio) and includes various non-linguistic factors like speaker identity and background noise. To effectively process this, GSLM employs a pipelined architecture as shown in Figure [1.](#page-2-0) The first step involves encoding the raw audio into a sequence of discrete *Units*. This encoding aims to reduce information density (as units are typically at 50 Hz) and to discard nonlinguistic information. These units are automatically discovered by clustering the hidden features of a pre-trained self-supervised learning (SSL) model. The module responsible for this conversion is collectively referred to as the speech-to-unit (s2u) module. Subsequently, a unit Language Model
+
+<span id="page-2-0"></span>![](figures/_page_2_Figure_1.jpeg)
+
+![](figures/_page_2_Figure_2.jpeg)
+
+Figure 1: Overview of GSLM pipeline
+
+Figure 2: DLM architecture
+
+(uLM) is trained on these discrete units. Similar to language models used for NLP, the uLM employs the standard Transformer architecture and can generate continuations of existing unit sequences once it has been trained. The final step involves the unit-to-speech (u2s) module, which transforms these units back into raw audio. Originally, the u2s module combined a TTS model, Tacotron 2 [\(Shen](#page-11-11) [et al., 2018\)](#page-11-11), with a neural vocoder, WaveGlow [\(Prenger et al., 2019\)](#page-10-9). However, recent studies [\(Kharitonov et al., 2022;](#page-9-10) [Nguyen et al., 2023\)](#page-10-7) have replaced these with a single neural vocoder, HiFi-GAN [\(Kong et al., 2020\)](#page-9-11).
+
+# <span id="page-2-1"></span>2.2 DIALOGUE GENERATIVE SPOKEN LANGUAGE MODELING
+
+[Nguyen et al.](#page-10-7) [\(2023\)](#page-10-7) applied the GSLM framework to model spoken dialogues directly, wherein two speakers' voices were recorded separately in two-channel audio. This framework is referred to as dialogue Generative Spoken Language Modeling (dGSLM). While the s2u and u2s modules were remained similar to the original GSLM, a novel architecture for uLM called Dialogue Transformer Language Model (DLM) was proposed to handle two channels of units simultaneously, as illustrated in Figure [2.](#page-2-0) DLM comprises two towers of Transformers that share their weights, allowing for interactions between two-channel units. In addition, DLM introduces *Edge Unit Prediction* and *Delayed Duration Prediction* objectives to efficiently model the repeating units (e.g. 96, 96, 52, 52, 52, . . . ). The edge unit prediction forces the model to predict the next unit only if it differs from the current one (i.e. edge unit). The delayed duration prediction allows the model to predict the duration of an edge unit at time step t with a one-step delay (i.e. at time step t + 1).
+
+# 3 CHATS
+
+### 3.1 SYSTEM ARCHITECTURE
+
+Our system aims to generate spoken dialogues wherein the spoken content aligns with input written dialogues but listener's responses (e.g. backchannels and laughter) are automatically generated. To address this challenging task, we adopt the pipeline architecture of GSLM [\(Lakhotia et al., 2021\)](#page-10-8), comprising three primary modules: s2u module, uLM, and u2s module.
+
+### 3.1.1 SPEECH-TO-UNIT (S2U) MODULE
+
+The s2u module extracts a concise representation from speech signals, operating on the entirety of a spoken dialogue. It (1) facilitates easy modeling by the uLM and (2) retains the necessary detail for the u2s module to reconstruct a high-fidelity waveform. Following [Kharitonov et al.](#page-9-10) [\(2022\)](#page-9-10), our s2u module extracts two distinct representations: *Content Units* and *Pitch Units*. The content units, which are identical to the "units" described in section [2,](#page-1-0) are used to capture the spoken content information. It is obtained using a combination of a pre-trained Hidden-Unit BERT (HuBERT) [\(Hsu](#page-9-12) [et al., 2021\)](#page-9-12) and a k-means clustering [\(MacQueen, 1967\)](#page-10-10). The pitch units are used to capture the prosody of speech, which is often discarded in content units. It is obtained by quantizing the speaker-
+
+<span id="page-3-0"></span>![](figures/_page_3_Figure_1.jpeg)
+
+Figure 3: Overview of MS-DLM. It processes content and pitch streams to predict subsequent units and their delayed durations. Each stream comprises a speaker ID, phonemes of current and next utterances, context units, and units to be generated. Each channel corresponds to a different speaker. Phonemes are replaced with listening (LIS) tokens when the utterance is made by the other speaker.
+
+normalized logarithm of the fundamental frequency ( $\log F_0$ ). For the notation, these units are referred to as  $u_{n,t}^{c,k}$  or simply  $u_t^{c,k}$  when the *n*th utterance need not be highlighted, where *n* is the utterance index, *t* is the timestep, *c* is the audio channel, and *k* is the codebook index associated with the content and pitch units, respectively. We assume  $c, k \in \{1, 2\}$  in this study.
+
+#### <span id="page-3-1"></span>3.1.2 Unit Language Model (uLM)
+
+The uLM is designed to generate content and pitch units for two channels based on written dialogue. In contrast to s2u and u2s modules, the uLM focuses on individual utterances, rather than entire dialogues, owing to inherent sequence length limitations. However, our uLM only requires the text of the current and next utterances to generate the current speech, thus facilitating sequential production of spoken dialogues without waiting for the generation of the entire written dialogue.
+
+**Model Architecture:** The uLM architecture is based on the DLM (Nguyen et al., 2023) described in section 2.2, which comprises two decoder-only Transformer towers that share parameters. We propose a novel *Multi-Stream DLM (MS-DLM)* architecture for handling multiple streams. We extend the DLM to include two input and output projection layers associated with the *content* and *pitch streams*, respectively, wherein the content and pitch unit sequences are prefixed with the tokens described in the subsequent paragraph. The detailed architecture is depicted in appendix A.1.
+
+**Prefix tokens:** We meticulously design the input sequences of our uLM to facilitate the text-based control over spoken content. The proposed sequences, as illustrated in Figure 3, are as follows:
+
+$$\text{BOS}, s^c, p^c_{n,1}, \dots, p^c_{n,M_n}, \text{NXT}, p^c_{n+1,1}, \dots, p^c_{n+1,M_{n+1}}, \text{CTX}, u^{c,k}_{t-C}, \dots, u^{c,k}_{t-1}, \text{SEP} \qquad (1)$$
+
+where  $s^c$  is the speaker ID of channel c,  $M_n$  is the number of phonemes in the nth utterance, C is the predetermined context length, and  $p_{n,m}^c$  is the mth phoneme of the nth utterance if uttered by speaker  $s^c$ , and otherwise substituted with listening (LIS) token. BOS, NXT, CTX, SEP tokens represent beginning of sentence, phonemes of the next utterance, context units, and separator, respectively. Building on the practices from Kharitonov et al. (2022), the uLM delays the pitch stream by one step considering their high correlation with content stream. Positions without tokens owing to this delay are filled with padding (PAD) tokens. Additionally, the target sequence obtained by shifting the input sequence by one step is appended with an end-of-sentence (EOS) token.
+
+The conditioning of the uLM on the speaker ID compensates for the context length constraint, ensuring that the model retains each speaker's unique characteristics. Further, phonemes of the n+1th utterance are essential for handling overlaps, particularly if the n+1th utterance disrupts the nth one. With these prefix tokens, our uLM generates speaker's unit sequences from phonemes conditionally, and listener's unit sequences (may contain backchannels and laughter) unconditionally.
+
+**Training Objective:** The model adopts both the edge unit prediction and delayed duration prediction techniques, proposed by Nguyen et al. (2023), for both content and pitch streams. Full details can be found in appendix A.2.
+
+```
+0.000 1.500 A: Hey, thinking of seeing that new movie this weekend.
+ 1.800 3.000 B: "Time's Mirage"?
+ 3.300 5.000 A: Yeah, that one. Coworker said it's good.
+ 5.000 5.300 B: Uh-huh.
+ 5.100 6.500 A: Mentioned something about great visuals.
+ 7.300 8.000 B: And the music?
+ 8.200 10.100 A: Right! They loved the soundtrack. Made them dance 
+                     in their seat, apparently.
+ 9.400 10.200 B: Hahaha!
+10.500 12.000 B: Sounds fun. Let's go together.
+                                                                          A: Hey, thinking of seeing that new movie this weekend.
+                                                                          B: "Time's Mirage"?
+                                                                          A: Yeah, that one. Coworker said it's good. Mentioned 
+                                                                             something about great visuals.
+                                                                          B: And the music?
+                                                                          A: Right! They loved the soundtrack. Made them dance 
+                                                                             in their seat, apparently.
+                                                                          B: Sounds fun. Let's go together.
+```
+
+Figure 4: Comparison of (a) raw spoken dialogue transcription and (b) typical written dialogue.
+
+(b) Written dialogue
+
+# 3.1.3 UNIT-TO-SPEECH (U2S) MODULE
+
+(a) Spoken dialogue transcription
+
+The u2s module is developed to solve an inverse problem of s2u module. It is trained to reconstruct the original waveform given content and pitch units extracted using the s2u module. As content and pitch units contain minimal speaker information, the u2s module also accepts a speaker embedding. Following [Kharitonov et al.](#page-9-10) [\(2022\)](#page-9-10), we adapt the discrete unit-based HiFi-GAN [\(Polyak et al., 2021\)](#page-10-11).
+
+## 3.2 PREPROCESSING AND MODELING TECHNIQUES FOR SPOKEN DIALOGUE
+
+# <span id="page-4-1"></span>3.2.1 WRITTEN DIALOGUE PREPARATION VIA BACKCHANNEL EXCLUSION
+
+We consider a dataset comprising recordings of spontaneous dialogues between two speakers, each accompanied by its transcription (Figure [4](#page-4-0) (a)). These transcriptions inherently contain elements not usually present in standard written dialogues (Figure [4](#page-4-0) (b)), such as timestamps and listener responses, including backchannels and laughter. Training CHATS directly on these raw transcriptions would be suboptimal, as the system might then fail to replicate these spontaneous behaviors when processing typical written dialogue inputs. To address this, we remove elements like backchannels and laughter from the transcriptions using a combination of rule-based and machine learning approaches. This modification ensures that the system learns to autonomously generate these behaviors in the listener's responses.
+
+First, we omit the temporal metadata and retain only the verbal content. In this process, successive utterances from an identical speaker are merged if they are separated by a silence of < 200 ms, and are referred to as inter-pausal units (IPUs). Subsequently, we remove the listener's IPUs, which correspond to backchannels and laughter, from the transcription through the following steps:
+
+- Step 1 If one speaker's IPU encompasses another's, it is termed the *speaker IPU* (*s-IPU*), while the latter is termed the *listener IPU* (*l-IPU*). Any IPUs not fitting these definitions are labeled as *undefined IPU*s (*u-IPU*s).
+- Step 2 A binary classifier , hereinafter referred to as *IPU classifier*, is trained to determine whether a given IPU is an *s-IPU* or *l-IPU* based on its content units. The training is conducted using speech segments corresponding to *s-IPU*s and *l-IPU*s identified in step 1.
+- Step 3 The classifier trained in step 2 is then applied to categorize the *u-IPU*s.
+- Step 4 IPUs identified as *l-IPU*s in steps 1 or 3 are excluded from the transcription.
+
+Consequently, the resulting written dialogues are composed exclusively of *s-IPU*s. Hereinafter, "utterance" denotes an *s-IPU* unless otherwise specified.
+
+## 3.2.2 TURN-TAKING MECHANISM (TTM)
+
+To simulate natural turn-taking, which includes overlapping speech, the uLM is trained using a simple and effective approach. Considering two successive utterances, turn-taking can be bifurcated into two scenarios: *no overlap* and *overlap*. These are shown in the top section of Figure [5.](#page-5-0) Let a<sup>n</sup> and b<sup>n</sup> be the start and end times of the nth utterance, respectively. The conditions for *no overlap* and *overlap* can be described by b<sup>n</sup> ≤ an+1 and b<sup>n</sup> > an+1, respectively. These start and end times are modified as follows:
+
+$$\hat{b}_n = \hat{a}_{n+1} = \max(b_n, a_{n+1}) = \begin{cases} b_n & (overlap) \\ a_{n+1} & (no \ overlap) \end{cases} . \tag{2}$$
+
+<span id="page-5-0"></span>![](figures/_page_5_Figure_1.jpeg)
+
+Figure 5: Two scenarios of turn-taking, (a) no overlap and (b) overlap.
+
+The modified time boundaries are shown in the bottom section of Figure 5. Following these alterations, our uLM is trained to predict the duration of trailing silence in the *no overlap* scenario, and pinpoint the onset of overlap in the *overlap* scenario. In the *Overlap* scenario, the uLM must generate the first  $b_n - a_{n+1}$  seconds of the n+1th utterance concurrently with the nth utterance; thus we condition our uLM with the phonemes of the n+1th utterance. Moreover, the uLM is tasked with the continuation of the n+1th utterance in the *overlap* scenario, justifying our decision to condition the uLM using context units.
+
+#### 3.2.3 Data augmentation by context reduction
+
+Although context units are included in the prefix tokens, they are not available during the initial steps of inference, which leads to suboptimal generation quality at the start of the dialogue. To address this, data augmentation is proposed, wherein the context is either removed or shortened. We augment the dataset by modifying the context length to  $C' = \{0, 0.1C, 0.2C, ..., 0.9C\}$  for each training example. This augmentation is only performed for utterances that do not overlap with previous utterances, as the uLM must generate continuations of context units in the *overlap* scenario.
+
+#### 3.3 Inference procedure
+
+Considering a written dialogue comprising N utterances and speaker pair information  $(s^1,s^2)$ , a corresponding spoken dialogue can be generated as follows. For each utterance indexed by  $n=1,\ldots,N$ , first, the prefix tokens are acquired. The phonemes of the nth and n+1th utterances are derived using a grapheme-to-phoneme tool, while the context units are sourced from the units generated in previous steps. Then, the content and pitch units of the nth utterance are generated autoregressively using the uLM. The process concludes when the EOS token is chosen as the content unit for any channel. Thereafter, the delayed pitch units are synchronized with the content units and concatenated to the units that were produced in the earlier steps. Subsequently, the two desired waveform channels are derived using the u2s module. Notably, since our system does not rely on input sentences that extend beyond two sentences ahead, it can facilitate continuous spoken dialogue generation when integrated with an LLM. Illustrative explanation is provided in appendix A.3.
+
+#### 4 EXPERIMENTS
+
+#### 4.1 SETUP
+
+**Datasets:** We used internal spoken dialogue dataset comprising 74 h of two-channel speech signals (equivalent to 147 h of single-channel speech signals). It includes 538 dialogues conducted by 32 pairs with 54 Japanese speakers (certain speakers appeared in multiple pairs) with their transcriptions. Additionally, we utilized the Corpus of Spontaneous Japanese (CSJ) (Maekawa, 2003) to pre-train our uLM. It contains single-channel speech signals with their phoneme-level transcriptions. All of these were utilized, excluding dialogue data, resulting in 523 h from 3,244 speakers. A detail of our internal dataset and complete procedure of preprocessing are described in appendix B.1.
+
+**Model, training, and inference:** A simple 3-layer bidirectional LSTM was used for the IPU classifier described in section 3.2.1. For the s2u module, we utilized a pre-trained japanese-hubert-base<sup>1</sup> model for content unit extraction, and the WORLD vocoder (Morise et al., 2016) for pitch
+
+<span id="page-5-1"></span><sup>1</sup>https://huggingface.co/rinna/japanese-hubert-base
+
+unit extraction. For the uLM model, a Transformer model comprising 6 layers, 4 of which were cross-attention layers, with 8 attention heads per layer and an embedding size of 512 was considered [\(Nguyen et al., 2023\)](#page-10-7). This uLM was developed atop the DLM implementation found in the fairseq library[2](#page-6-0) [\(Ott et al., 2019\)](#page-10-14). A single-channel variant of our uLM was pre-trained on the CSJ dataset. Subsequently, we finetuned a two-channel uLM on all of the *s-IPU*s from our spoken dialogue dataset. Model optimization was performed over 100k steps on two A100 80GB GPUs with a batch size of 30k tokens per GPU, requiring approximately 5 h for pre-training and 11 h for finetuning. During inference, nucleus sampling [\(Holtzman et al., 2020\)](#page-9-13) with p = 0.9 was adopted. The u2s module utilized the discrete unit-based HiFi-GAN [\(Kong et al., 2020;](#page-9-11) [Polyak et al., 2021\)](#page-10-11) with minor adjustments. This model was optimized over 500k steps on a single A100 80GB GPU with a batch size of 16 0.5-second speech segments, requiring approximately 32 h. Further details are provided in appendix [B.2.](#page-14-1)
+
+## <span id="page-6-2"></span>4.2 UTTERANCE-LEVEL EVALUATION
+
+First, we focused on the utterance-level generation quality of the proposed system. The fidelity of the generated speech to the input text was investigated by evaluating our system in the TTS setting. We generated speech waveform corresponding to all 4,896 utterances in the test set separately and measured their phoneme error rate (PER). To perform phoneme recognition, we finetuned japanese-hubert-base model with the CSJ dataset. We compared the performance of the proposed system (*Proposed*) with other systems, including 1) *Ground Truth*, the ground-truth recordings, 2) *Resynthesized*, where we combined s2u and u2s modules to resynthesize the original waveform, and 3) *Baseline*, a single-channel counterpart of *Proposed* trained without phonemes of next sentence and the turntaking mechanism. Additionally, we ablated several components including pre-training on CSJ dataset (*w/o pre-training*), data augmentation by context reduction (*w/o augmentation*), context units (*w/o context*), and phonemes of next sentence
+
+<span id="page-6-1"></span>Table 1: PER measured in TTS setting. The lowest PER in each section are bolded.
+
+| METHOD            | PER ↓ |
+|-------------------|-------|
+| Ground Truth      | 8.95  |
+| Resynthesized     | 11.49 |
+| Baseline          | 12.13 |
+| w/o pretraining   | 14.10 |
+| Proposed          | 13.03 |
+| w/o pretraining   | 15.32 |
+| w/o augmentation  | 59.35 |
+| w/o context units | 14.12 |
+| w/o next sentence | 12.79 |
+
+(*w/o next sentence*). PERs for *Ground Truth* and *Resynthesized* include both grapheme-to-phoneme error and phoneme recognition error, while *Baseline* and *Proposed* include only the latter.
+
+The results are summarized in Table [1.](#page-6-1) Although the PER for the *Proposed* system was slightly worse than for *Baseline*, the degradation was minute considering that it performed other tasks in addition to basic TTS, including generating the listener's speech and predicting turn-taking. Pretraining and use of the context units were effective, and data augmentation was crucial because no context was given in the TTS setting. The *Proposed w/o next sentence* marginally outperformed *Proposed* in TTS setting; however, it often generated unnatural or meaningless content as overlapping segment. We investigated the effect of introducing pitch units in appendix [C.](#page-15-0)
+
+# 4.3 DIALOGUE-LEVEL EVALUATION
+
+Next, we evaluated the spoken dialogue generation quality of the proposed system. We quantified how close the generated spoken dialogues were to the recorded ones from two aspects: listener's and turn-taking events. For comparison, we prepared a *Baseline* system, the same system described in section [4.2](#page-6-2) but operated alternatively to generate spoken dialogue, as well as *dGSLM* [\(Nguyen et al.,](#page-10-7) [2023\)](#page-10-7). As *Baseline* cannot generate the listener's tokens, we filled them with the most frequently used content and pitch units corresponding to unvoiced frames. Furthermore, *Proposed w/o TTM* was evaluated to investigate the effectiveness of our turn-taking mechanism.
+
+We created written dialogues that excluded listener's events for the test set as detailed in section [3.2.1.](#page-4-1) Next, we generated the entire spoken dialogues from those written dialogues. For *dGSLM*, we utilized 30 s of speech prompts from the test set to generate the subsequent 90 s. As the resulting dialogues for *dGSLM* were three times longer than the original test set, we divided the results (e.g., backchannel frequency and duration) by three.
+
+<span id="page-6-0"></span><sup>2</sup><https://github.com/facebookresearch/fairseq>
+
+# 4.3.1 LISTENER'S EVENT EVALUATION
+
+We applied the Silero Voice Activity Detector (VAD)[3](#page-7-0) to the generated spoken dialogues and performed hybrid IPU classification for each IPU as in section [3.2.1.](#page-4-1) We then counted the number of backchannels qBC and all utterances qALL along with their durations dBC and dALL. The results are summarized in Table [2.](#page-7-1) Although the backchannel frequency and duration for *Proposed* were lower than for *Ground Truth*, the proportion of backchannels in all utterances was closest to the *Ground Truth* in terms of both frequency and duration. *dGSLM* tended to produce too many backchannels, whereas *Baseline* produced too few. Further, *Proposed w/o TTM* produced excessive backchannels. We conjecture that the uLM generates overlapped segments twice without the TTM (as the last part of the nth utterance and the first part of the n + 1th utterance), resulting in unwanted backchannels. Further investigation of backchannel content and speaker-specific characteristics, as well as laughter frequency and duration, is described in appendix [D.](#page-16-0)
+
+| METHOD       | qBC  | qALL | 100 × qBC/qALL | dBC<br>[s] | dALL<br>[s] | 100 × dBC/dALL |
+|--------------|------|------|----------------|------------|-------------|----------------|
+| Ground Truth | 1854 | 9453 | 19.61          | 1518       | 16588       | 9.15           |
+| dGSLM        | 1710 | 6141 | 27.84          | 1678       | 12378       | 13.56          |
+| Baseline     | 76   | 3656 | 2.08           | 151        | 11713       | 1.29           |
+| Proposed     | 1535 | 6668 | 23.02          | 1322       | 14001       | 9.44           |
+| w/o TTM      | 1756 | 5273 | 33.30          | 1480       | 14052       | 10.53          |
+
+<span id="page-7-1"></span>Table 2: Backchannel frequency q and duration d. Ratios closest to the *Ground Truth* are bolded.
+
+# 4.3.2 TURN-TAKING EVENT EVALUATION
+
+Following [Nguyen et al.](#page-10-7) [\(2023\)](#page-10-7), we examined the distribution of four turn-taking events: 1) *IPU*, a speech segment in one speaker's channel delimited by a VAD silence of ≥ 200 ms on both sides, 2) *overlap*, a section with voice signals on both channels, 3) *pause*, a silence segment between two IPUs of the same speaker, and 4) *gap*, a silence segment between two IPUs by distinct speakers. The results are summarized in Figure [6.](#page-7-2) Both *dGSLM* and *Proposed* exhibited similar distribution to the *Ground Truth*, confirming that the proposed system could mimic human-like turn-taking. The distribution of *Baseline*, particularly for overlaps, deviated significantly from that of the *Ground Truth* because theoretically it cannot generate any overlaps. The durations of pauses and gaps were underestimated for *Proposed w/o TTM*, which is congruent with the idea that the TTM is helpful for estimating appropriate silence durations following each utterance. Speaker-specific characteristics of turn-taking events are investigated in appendix [E.](#page-17-0)
+
+<span id="page-7-2"></span>![](figures/_page_7_Figure_7.jpeg)
+
+Figure 6: Distributions of turn-taking event durations.
+
+<span id="page-7-0"></span><sup>3</sup><https://github.com/snakers4/silero-vad>
+
+# <span id="page-8-0"></span>4.4 HUMAN EVALUATION
+
+Finally, we measured the subjective quality of the generated spoken dialogue. For each speaker pair, we randomly extracted two 10-turn dialogues, each lasting 15–45 seconds, from the test set, leading to a total of 64 dialogues. We generated the corresponding spoken dialogue segments using the *Baseline* and *Proposed* systems. For *dGSLM*, we used 30 s of the recorded speech segments preceding these dialogues as prompts and generated 30 s continuations for each one. Each dialogue segment was assessed based on three distinct criteria: 1) *Dialogue Naturalness*, evaluating the fluidity of the dialogue and the naturalness of the interaction, 2) *Meaningfulness*, determining the comprehensibility of what is spoken, and 3) *Sound Quality*, checking for noise or distortion in the speech signal. Each item was rated on a 5-point scale from 1–5 (bad to excellent). Twenty-four workers participated in the evaluation and each rated 25 samples. The instructions and dialogue examples actually used for the evaluation are presented in appendices [F](#page-19-0) and [G,](#page-19-1) respectively.
+
+The results are presented in Table [3.](#page-8-1) The *Proposed* system outscored both the *dGSLM* and *Baseline* systems across all metrics. Particularly, it recorded a significantly higher score in Dialogue Naturalness compared to the *Baseline* system (p = 0.038 in the Student's t-test). Thus, features such as backchannels, laughter, and seamless turn-taking, rendered possible by the proposed system, are vital for generating natural spoken dialogues. Interestingly, *dGSLM* had low scores in both Meaningfulness and Dialogue Naturalness. This finding is at odds with the results from a previous study [\(Nguyen et al., 2023\)](#page-10-7). We hypothesize that this decline in performance was owing to the smaller dataset used (2,000 h in the previous study vs. 74 h in this study). However, considering that Meaningfulness of *dGSLM* was low in the previous study as well, our system's text conditioning capability proves to be highly effective for generating meaningful spoken dialogue.
+
+While our findings indicate advancements in spoken dialogue generation, certain areas require further refinement to match human-level performance. Notably, the Sound Quality of the *Resynthesized* is behind that of the *Ground Truth*, suggesting the necessity for improved s2u and u2s modules with enhanced speech coding. Moreover, the *Proposed* system trails in Dialogue Naturalness when compared to both the *Ground Truth* and *Resynthesized*. Thus, our future efforts will focus on accumulating a more extensive dialogue dataset and refining our method accordingly.
+
+<span id="page-8-1"></span>
+
+| METHOD        | Dialogue Naturalness | Meaningfulness | Sound Quality |
+|---------------|----------------------|----------------|---------------|
+| Ground Truth  | 4.85±0.08            | 4.81±0.09      | 4.75±0.09     |
+| Resynthesized | 4.48±0.12            | 4.55±0.12      | 3.82±0.18     |
+| dGSLM         | 2.68±0.24            | 1.18±0.07      | 2.93±0.20     |
+| Baseline      | 3.01±0.20            | 3.43±0.18      | 3.22±0.18     |
+| Proposed      | 3.30±0.18            | 3.58±0.17      | 3.38±0.18     |
+
+Table 3: Human evaluation results.
+
+# 5 CONCLUSION
+
+This study proposed CHATS, a system that generates spoken dialogues from written ones. We proposed conditioning uLM with speaker, text, and past speech to achieve coherent spoken dialogue. Additionally, we proposed a mechanism for handling the timing for turn-taking or speech continuation explicitly. We performed a detailed analysis on the generated spoken dialogue, which showed that the proposed system reproduced the ground-truth distribution of backchannel frequency and turn-taking event durations well. Further, the results of our human evaluations demonstrated that the proposed system produced more natural dialogue than the baseline system, which used a TTS model to generate spoken dialogue. We verified that the innovative capability of the proposed system to generate backchannels and laughter without transcriptions was effective in mimicking human dialogue and creating natural spoken dialogue. However, there is still ample room for improvement. To further bridge the divide between human and generated dialogues, we plan to expand our study to a larger dataset for better naturalness and sound quality. Additionally, we will explore the advantages of conditioning our model on raw text to better understand the context of written dialogues. Furthermore, evaluating our system from the aspect of speaking style consistency and expressiveness is a valuable research direction.
+
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+
+# A MS-DLM DETAILS
+
+#### <span id="page-12-0"></span>A.1 MODEL ARCHITECTURE
+
+![](figures/_page_12_Figure_3.jpeg)
+
+Figure A.1: MS-DLM architecture. All weights are shared across two Transformer towers.
+
+### <span id="page-12-1"></span>A.2 TRAINING OBJECTIVE
+
+MS-DLM predicts the unit  $u_{n,t}^{c,k}$  and its duration  $d_{n,t}^{c,k}$  only when  $u_{n,t}^{c,k} \neq u_{n,t-1}^{c,k}$  (i.e.  $u_{n,t}^{c,k}$  is the edge unit). It is trained by minimizing the sum of edge unit prediction and edge duration prediction losses:
+
+$$\mathcal{L}_{uLM} = \sum_{n=1}^{N} (\mathcal{L}_{EU}^{n} + \mathcal{L}_{ED}^{n})$$
+(3)
+
+$$\mathcal{L}_{EU}^{n} = \sum_{c=1}^{2} \sum_{k=1}^{2} \sum_{\substack{u^{c,k} \neq u^{c,k} \\ u^{c,k} \neq u^{c,k}}} \log P(u_{n,t}^{c,k} | u_{n,1:t-1}^{*,k}; \Lambda, \Theta)$$
+(4)
+
+$$\mathcal{L}_{ED}^{n} = \sum_{c=1}^{2} \sum_{k=1}^{2} \sum_{\substack{t \ u_{n,t}^{c,k} \neq u_{n,t-1}^{c,k}}} \left| d_{n,t}^{c,k} - \hat{d}_{n,t}^{c,k}(u_{n,1:t}^{*,k}; \Lambda, \Theta) \right|$$
+ (5)
+
+where N is the total number of utterances in a dialogue,  $\hat{d}_{n,t}^{c,k}$  is the continuous duration prediction, and  $\Lambda,\Theta$  are prefix tokens and model parameters, respectively.
+
+### <span id="page-13-0"></span>A.3 INFERENCE PROCEDURE
+
+An example of MS-DLM inference steps, where the total number of utterances N=3 and the context length C=4, is illustrated in Figure A.2. The inference proceeds as follows:
+
+- n=1 The phonemes of the first and second sentences are obtained using a grapheme-to-phoneme tool. Since the first sentence will be uttered by speaker A, its phonemes on channel 2 are replaced with LIS tokens. Similarly, the phonemes of second sentence on channel 1 are replaced with LIS tokens. The prefix tokens are then prepared by combining these phonemes with speaker IDs and some special tokens. Note that the context units may be absent or shorter than the context length C for small n. The content and pitch units of the first utterance are generated in an autoregressive manner until the EOS token is selected as the content unit for any channel.
+- n=2 The phonemes of the second and third sentences are obtained in the same manner. Prefix tokens are prepared by incorporating the units generated at n=1 as context units. Then, the content and pitch units of the second utterance are similarly generated.
+- n=3 Since the inference ends at n=3, phonemes of the n+1th sentence is not used in this step. The content and pitch units generated in the second step are used as context units. Note that since the context length C=4 exceeds the length of units from the previous step (only three units are generated in n=2), context units are additionally derived from the previous context units.
+
+Each step does not rely on input sentences that extend beyond two sentences ahead. For instance, the generation of the first utterance does not rely on the third sentence. This feature facilitates continuous spoken dialogue generation when integrated with an LLM.
+
+<span id="page-13-1"></span>![](figures/_page_13_Figure_7.jpeg)
+
+Figure A.2: Conceptual diagram of inference steps with total number of utterances N=3 and context length C=4.
+
+### B EXPERIMENTAL SETUP DETAILS
+
+#### <span id="page-14-0"></span>B.1 DATASET AND PREPROCESSING
+
+We collected audio recordings of 74 h comprising 538 dialogues conducted by 32 pairs with 54 Japanese speakers (certain speakers appeared in multiple pairs). These dialogues were divided into 474/32/32 for train/valid/test sets, respectively (valid and test sets included all speaker pairs). For the recording sessions, two speakers entered separate soundproof rooms, where they could see and hear each other through glass and via headphones, respectively. Conversations occurred freely and captured in two-channel 96 kHz/24 bit audio.
+
+The recorded 538 dialogues yielded  $538 \times 2 = 1,076$  audio files, which were downsampled to 16 and 24 kHz for the s2u and u2s modules, respectively. To eliminate volume discrepancies between different channels and speaker pairs, we calculated the average dBFS of each audio file, and used these averages to normalize the volume levels. Subsequently, the Silero VAD<sup>4</sup> was employed for voice activity detection. Further, we utilized the large model of whisper<sup>5</sup>(Radford et al., 2023) for automatic speech recognition on the detected speech segments. Manual corrections for start times, end times, and transcriptions were made for 645 of 1,076 files. Transcripts were automatically converted into phonemes using Open JTalk<sup>6</sup>.
+
+#### <span id="page-14-1"></span>B.2 MODEL, TRAINING, AND INFERENCE
+
+**IPU Classifier:** For the IPU classification task, we employed a 3-layer bidirectional LSTM with the input embedding and hidden dimensions of 256 and 512, respectively. Training was conducted on a single A100 80GB GPU with a batch size of 8,192 tokens, using the Adam optimizer (Kingma & Ba, 2015) with an initial learning rate of  $1 \times 10^{-4}$  and betas of  $\beta_1 = 0.9$  and  $\beta_2 = 0.98$ . Our training set comprised 49,339 *s-IPUs* and 27,794 *l-IPUs*, and the model was trained over 20k steps. The checkpoint with the lowest validation loss was selected for final use. When tested on an evaluation set containing 2,604 *s-IPUs* and 1,930 *l-IPUs*, our classifier achieved an accuracy of 87.83%.
+
+**s2u module:** For the s2u module, we used japanese-hubert-base<sup>7</sup> model, a pre-trained HuBERT base model trained on 19k h of Japanese speech, as a frontend for the content unit extractor. It encodes 16 kHz speech into 768-dimensional continuous vectors at 50 Hz. The k-means++ (Arthur & Vassilvitskii, 2007) clustering model was trained on our spoken dialogue dataset described in appendix B.1. In line with Nguyen et al. (2023), the number of clusters was set to 500. The number of bins for pitch unit extraction was 32, one of which was designated for unvoiced frames. The WORLD vocoder (Morise et al., 2016) was used to extract pitch every 20 ms, yielding pitch units at 50 Hz.
+
+**uLM:** We adopted the same hyperparameters as described by Nguyen et al. (2023), utilizing a Transformer model comprising 6 layers, 4 of which were cross-attention layers, with 8 attention heads per layer and an embedding size of 512. The context length C was 500, corresponding to a 10-s waveform. The uLM's vocabulary included 500 content units (with 32 shared with pitch units), 39 phonemes, 9 special tokens, and a combined total of 3,298 speaker IDs (comprising 54+3,244 entries). Special tokens included BOS, EOS, PAD, NXT, CTX, SEP, LIS, as described in section 3.1.2, UNK for unknown input, and LAU for explicitly including laughter in the phoneme sequences. However, outputs are limited to the content/pitch units, PAD, and EOS tokens by setting the output probabilities for other tokens to zero.
+
+A single-channel variant of our uLM was pre-trained on the CSJ dataset, where we simplified the prefix tokens by omitting the phonemes of the next utterance and context units. The refined prefix tokens took the following form:
+
+BOS, 
+$$s^c, p_{n,1}^c, \dots, p_{n,M_n}^c$$
+, SEP. (6)
+
+<span id="page-14-2"></span><sup>4</sup>https://github.com/snakers4/silero-vad
+
+<span id="page-14-3"></span><sup>5</sup>https://github.com/openai/whisper
+
+<span id="page-14-4"></span><sup>6</sup>https://open-jtalk.sourceforge.net/
+
+<span id="page-14-5"></span><sup>&</sup>lt;sup>7</sup>https://huggingface.co/rinna/japanese-hubert-base
+
+Consequently, this phase of pre-training can be regarded as a conventional text-to-speech training. This pre-training employed two A100 80GB GPUs, each managing a batch size of 30,000 tokens. Optimization was performed over 100k steps using an Adam optimizer (Kingma & Ba, 2015) with an inverse square root learning rate schedule, whose initial learning rate was set to  $1\times10^{-7}$ , warmup steps to 10k steps, and maximum learning rate to  $5\times10^{-4}$ . This required approximately 5 h.
+
+Subsequently, we finetuned a two-channel uLM on all of the *s-IPU*s present in our spoken dialogue dataset, which contained 82,060 utterances. As our uLM shares the weight across two Transformer towers, two-channel uLM were warm-started with the pre-trained single-channel uLM weights. Finetuning was conducted in the same configuration as pre-training; however, the maximum learning rate was  $1 \times 10^{-4}$ , requiring approximately 11 h.
+
+For decoding, we adopted nucleus sampling (Holtzman et al., 2020) with p=0.9. Through empirical observation, we discerned that the top-20 sampling, as utilized for dGSLM (Nguyen et al., 2023), produced speech signals misaligned with the input phonemes. This misalignment likely stems from units with marginally lower probabilities, such as the top-19 or top-20 units, correlating with pronunciations incongruent with the desired phoneme.
+
+**u2s module:** Our u2s module received a global speaker ID with 50 Hz content and pitch units. These discrete values were embedded into 128-dimensional continuous vectors, which were then summed to produce 50 Hz input features. These features were subsequently upsampled by factors of [10,6,4,2] to obtain a 24 kHz waveform. Following Kong et al. (2020), we trained our u2s module with the Adam optimizer, setting an initial learning rate to  $2 \times 10^{-4}$  and betas at  $\beta_1 = 0.8$  and  $\beta_2 = 0.99$ . The model was optimized over 500k steps on a single A100 80GB GPU with a batch size of 16 0.5-second speech segments, requiring approximately 32 h. Our training set consisted all of the VAD speech segments from our spoken dialogue dataset, totalling 130,050 utterances. During inference, we decoded the waveform for each channel and utterance individually, as excessive GPU memory would be required to process the entire 5–10 minute dialogue at once.
+
+### <span id="page-15-0"></span>C EFFECTS OF INTRODUCING PITCH UNITS
+
+To explore the effect of the pitch units, we calculated PER for systems without pitch units in the same manner as described in section 4.2. Additionally, we extracted  $F_0$  values from the generated speech using the WORLD vocoder, calculated the mean and variance of the voiced frames, and averaged them across all utterances. The results are summarized in Table C.1. Interestingly, the removal of pitch units worsened the PER for *Resynthesized*, whereas it improved the PER for *Baseline* and *Proposed* systems. Thus, the requirement to predict the pitch units rendered it difficult to predict the accurate pronunciation, which is mostly determined by the content units. However, the  $F_0$  statistics of systems with pitch units were consistently closer to those of *Ground Truth* than their pitch-ablated counterparts, indicating that the pitch units were effective for generating expressive speech uttered in spoken dialogues.
+
+<span id="page-15-1"></span>Table C.1: PER and pitch statistics measured in TTS setting. The lowest PER and  $F_0$  statistics closest to the Ground Truth in each section are highlighted in bold.
+
+| METHOD                        | PER ↓                 | $F_0$ mean [Hz]    | $F_0$ var [Hz <sup>2</sup> ] |
+|-------------------------------|-----------------------|--------------------|------------------------------|
+| Ground Truth                  | 8.95                  | 191.6              | 2831.6                       |
+| Resynthesized w/o pitch units | <b>11.49</b> 12.20    | <b>189.2</b> 177.0 | <b>2509.8</b> 2202.8         |
+| Baseline<br>w/o pitch units   | 12.13<br><b>11.61</b> | <b>181.8</b> 173.7 | <b>2271.1</b> 1802.5         |
+| Proposed w/o pitch units      | 13.03<br><b>11.17</b> | <b>186.2</b> 178.1 | <b>2639.4</b> 2234.4         |
+
+### <span id="page-16-0"></span>D BACKCHANNEL AND LAUGHTER EVALUATION
+
+#### D.1 BACKCHANNEL CONTENT EVALUATION
+
+We transcribed all backchannels in the Ground Truth and generated spoken dialogues using the large model of whisper (Radford et al., 2023). Subsequently, we removed the trailing symbols ("!", "...", ", etc.) and sorted them by their frequency. The results are shown in Table D.1. These results indicate that our system is capable of appropriately generating backchannels used in actual conversations.
+
+<span id="page-16-1"></span>Table D.1: Top-20 frequently used backchannels in Ground Truth and generated spoken dialogues. Each Japanese transcripts were translated into English to match the meaning as closely as possible.
+
+| Ground Truth |            |               |             | Propose | d (Generated) |               |                 |
+|--------------|------------|---------------|-------------|---------|---------------|---------------|-----------------|
+| Freq.        | Transcript | Pronunciation | Translation | Freq.   | Transcript    | Pronunciation | Translation     |
+| 261          | うん         | un            | Uh-huh      | 148     | うん            | un            | Uh-huh          |
+| 87           | んー         | nn            | Mm-hm       | 117     | $\lambda$     | n             | Mm              |
+| 58           | はい         | hai           | Yes         | 77      | んんん           | nnn           | Mmm             |
+| 47           | そう         | sou           | I see       | 62      | んんっ           | nn            | Mm!             |
+| 43           | んんん        | nnn           | Mmm         | 26      | んんんん          | nnnn          | Mm-hmm          |
+| 43           | $\lambda$  | n             | Mm          | 25      | んん            | nn            | Mm-mm           |
+| 32           | うんうん       | unun          | Yeah yeah   | 24      | んー            | nn            | Mm-hm           |
+| 25           | んんんん       | nnnn          | Mm-mm       | 24      | はい            | hai           | Yes             |
+| 23           | あーー        | aaa           | Ah          | 14      | ふぅ            | fuu           | (sigh)          |
+| 21           | うーん        | uun           | Hmm         | 12      | そう            | sou           | I see           |
+| 20           | www        | (laugh)       | (laugh)     | 11      | はいはい          | haihai        | Yes yes         |
+| 17           | はぁ         | ha            | Oh          | 11      | うんうん          | unun          | Yeah yeah       |
+| 16           | そうそうそう     | sousousou     | Exactly     | 10      | あ、そうなんだ       | a, sounanda   | Oh, is that so? |
+| 14           | こんふ        | fufu          | (chuckle)   | 8       | フフフフフフフ       | fufufufufufu  | (laugh)         |
+| 11           | ねえ         | nee           | Hey         | 7       | はぁ            | ha            | (sigh)          |
+| 11           | wwww       | (laugh)       | (laugh)     | 6       | そうそうそう        | sousousou     | Exactly         |
+| 11           | んんっ        | nn            | Mm!         | 6       | そうなんだ         | sounanda      | Oh, really?     |
+| 10           | んふふふ       | nfufufu       | (giggle)    | 6       | んふふふ          | nfufufu       | (giggle)        |
+| 9            | はいはいはい     | haihaihai     | Yes yes yes | 6       | そうだね          | soudane       | That's right    |
+| 9            | んーー        | nnn           | Mm-hmm      | 5       | www           | (laugh)       | (laugh)         |
+
+#### <span id="page-16-3"></span>D.2 Speaker-specific characteristics of backchannels
+
+While the overall frequency of backchannels is summarized in Table 2, it actually varies from speaker to speaker. To further probe the speaker characteristics, we computed the proportion of backchannels  $100 \times q_{\rm BC}/q_{\rm ALL}$  for each speaker. The mean absolute error (MAE) and Pearson correlation coefficient r between the *Ground Truth* and generated dialogues were calculated. The results are listed in Table D.2. *Proposed* achieved the lowest MAE and exhibited a positive correlation with *Ground Truth*. These results demonstrate that the proposed system can produce backchannels in appropriate frequency, and the speaker characteristics are preserved in the generated spoken dialogues.
+
+<span id="page-16-2"></span>Table D.2: Detailed comparison of backchannel frequency for individual speakers between the reference and generated dialogues. Values closest to the *Ground Truth* are bolded. Significance levels of r are shown by  $^{\dagger}(^{\ddagger}p < 0.01, ^{\dagger}p < 0.05)$ .
+
+| METHOD       | $MAE\downarrow$ | $r\uparrow$       |
+|--------------|-----------------|-------------------|
+| Ground Truth | 0.00            | $1.00^{\ddagger}$ |
+| dGSLM        | 0.09            | 0.63 <sup>‡</sup> |
+| Baseline     | 0.18            | $0.40^{\ddagger}$ |
+| Proposed     | 0.07            | $0.54^{\ddagger}$ |
+| w/o TTM      | 0.14            | $0.54^{\ddagger}$ |
+
+### D.3 LAUGHTER EVALUATION
+
+We applied an open-source laughter detection model<sup>8</sup> (Gillick et al., 2021) to the generated spoken dialogues. We then counted the instances of laughter and calculated their total duration. The results are summarized in Table D.3. The frequency and duration of laughter generated by the proposed system were closer to those of the *Ground Truth* compared to those of the *Baseline* and *dGSLM* regardless of the existence of a turn-taking mechanism. Note that the *Baseline*, which cannot generate laughter on the listener side, generated a certain amount of laughter because the input written dialogue often contained laughter. *dGSLM* could not utilize such written information, which led to an underestimation of laughter frequency.
+
+<span id="page-17-2"></span>
+
+| Table D.3: Laughter frequency and duration | . Values closest to the <i>Ground Truth</i> are bolded. |
+|--------------------------------------------|---------------------------------------------------------|
+|--------------------------------------------|---------------------------------------------------------|
+
+| METHOD       | Frequency | Duration |
+|--------------|-----------|----------|
+| Ground Truth | 1268      | 2975     |
+| dGSLM        | 998       | 2443     |
+| Baseline     | 1011      | 2373     |
+| Proposed     | 1275      | 2810     |
+| w/o TTM      | 1280      | 3010     |
+
+# <span id="page-17-0"></span>E SPEAKER-SPECIFIC CHARACTERISTICS OF TURN-TAKING EVENTS
+
+We analyzed the speaker-specific characteristics of turn-taking event durations following the procedure detailed in appendix D.2. For each speaker, we calculated the median durations of the four turn-taking events, IPU, pause, overlap, and gap. The results are presented in Figure E.1 with their regression lines. The values from dGSLM and Proposed demonstrate positive correlations between the reference and generated dialogues, indicating the preservation of speaker-specific characteristics. Subsequently, we determined the MAE and Pearson's r values between Ground Truth and each system. The results are listed in Table E.1. The performance of Proposed was consistently superior to Baseline and Proposed w/o TTM, and it achieved comparable results to dGSLM. Moreover, dGSLM leveraged 30 s of recorded speech, whereas Proposed did not. Therefore, we conclude that the proposed system effectively utilized the speaker information in the prompt tokens, facilitating the reproduction of the general aspects of turn-taking and the specific characteristics of each individual speaker.
+
+<span id="page-17-3"></span>Table E.1: Detailed comparison of turn-taking event durations for individual speakers between the reference and generated dialogues. Values closest to the *Ground Truth* are bolded. Significance levels of r are shown by  $^{\dagger}(^{\dagger}p < 0.01, ^{\dagger}p < 0.05)$ .
+
+| METHOD       | IPU             |                   | PAUSE            |                   | OVERLAP         |                   | GAP             |                   |
+|--------------|-----------------|-------------------|------------------|-------------------|-----------------|-------------------|-----------------|-------------------|
+| METHOD       | $MAE\downarrow$ | $r\uparrow$       | $MAE \downarrow$ | $r\uparrow$       | $MAE\downarrow$ | $r\uparrow$       | $MAE\downarrow$ | $r\uparrow$       |
+| Ground Truth | 0.00            | 1.00‡             | 0.00             | 1.00 <sup>‡</sup> | 0.00            | 1.00‡             | 0.00            | 1.00 <sup>‡</sup> |
+| dGSLM        | 0.25            | $0.35^{\dagger}$  | 0.09             | $0.42^{\ddagger}$ | 0.13            | $0.50^{\ddagger}$ | 0.06            | 0.42 <sup>‡</sup> |
+| Baseline     | 1.40            | $0.38^{\ddagger}$ | 0.14             | 0.16              | 0.32            | 0.04              | 0.33            | 0.01              |
+| Proposed     | 0.24            | $0.63^{\ddagger}$ | 0.08             | $0.42^{\ddagger}$ | 0.10            | $0.42^{\ddagger}$ | 0.08            | $0.34^{\dagger}$  |
+| w/o TTM      | 0.34            | $0.52^{\ddagger}$ | 0.16             | -0.09             | 0.11            | $0.35^{\ddagger}$ | 0.12            | 0.21              |
+
+<span id="page-17-1"></span><sup>8</sup>https://github.com/jrgillick/laughter-detection
+
+<span id="page-18-0"></span>![](figures/_page_18_Figure_1.jpeg)
+
+Figure E.1: Scatter plot and regression line of the median duration of each speaker's turn-taking events, with the 95% confidence intervals indicated by the shaded region. Each point indicates a different speaker.
+
+#### <span id="page-19-0"></span>F HUMAN EVALUATION CRITERIA
+
+For better reproducibility, the instruction used in our human evaluation is presented below. Please note that this instruction is translated from Japanese.
+
+Please listen to the following audio of friends chatting casually through headphones and evaluate its quality based on these three criteria:
+
+- Dialogue Naturalness: Are backchannels and laughter appropriately included to create a human-like interaction? Is there a seamless transition between the speaker and listener at the right moments? Does the conversation flow smoothly?
+- Meaningfulness: Does the dialogue have meaningful content, and is it possible to understand what is being said?
+- Sound Quality: Is the sound clear and easy to hear, free from noise or other distractions?
+
+Please rate each item on a scale of 1 (bad) to 5 (excellent). When evaluating each criterion, do not consider the other criteria. For example, if the content is incomprehensible but the interaction sounds human-like, rate Dialogue Naturalness highly.
+
+## <span id="page-19-1"></span>G GENERATION CASE STUDIES
+
+We present examples of written dialogues (Table G.1, Table G.2) and the generated spoken dialogues using the proposed system (Figure G.1, Figure G.2). These examples correspond to the test-set sample 1 and 2 of our demo page<sup>9</sup>. Although the original dialogues are in Japanese, we provide their English translation for better readability. As we expected, the entire spoken dialogue closely follows the input written dialogue, with appropriate generation of backchannels and laughter on the listener side. Additionally, some utterances slightly overlap with previous ones, facilitating natural turn-taking. Furthermore, our system can generate laughter on the speaker side by explicitly including a laughter tag (LAU) in the written dialogue, as demonstrated in the sixth segment of Figure G.2. However, upon closer examination of the fourth utterance of Figure G.2, it is observed that the laughter from speaker B is not generated, and instead, the generation of speaker A's utterance begins. This indicates areas for improvement such as ensuring accurate synthesis of the input text content and addressing the issue of too rapid onset of utterance overlap.
+
+Table G.1: The first example of a written dialogue input with utterance index n.
+
+<span id="page-19-2"></span>
+
+| n  | Original Script                                                        | Translated Script                                                                                                                     |
+|----|------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------|
+| 1  | A: 見たりしますね                                                             | A: I do watch it.                                                                                                                     |
+| 2  | B: え、すごい、実写かぁ、えっ、エフェクトつ<br>ける                                          | B: Oh, that's cool, it's live-action, huh, with effects.                                                                              |
+| 3  | B: ってことはあれだよねー、あのー、編集して、実際の                                            | B: So that means, um, editing it, the actual                                                                                          |
+| 4  | B: 動きは人間がやって、                                                          | B: movements are done by humans,                                                                                                      |
+| 5  | B: なんかやってみた感                                                           | B: kind of giving it a try.                                                                                                           |
+| 6  | A: もうなんかこう、光をこう、ラケットとボールが当たる瞬間にこう入れてみたりとか                              | A: I just, like, tried adding light, like, at the moment the racket hits the ball,                                                    |
+| 7  | A: なんかそのー、ボールがそのー、えー、コートに着地した時に、その着地したところが崩れるエフェクトがあって、なんか穴がコートに開くみたいな | A: like, when the ball, um, lands on the court, there's an effect where the landing spot crumbles, like a hole opens up in the court. |
+| 8  | B: うわっ                                                                 | B: Woah                                                                                                                               |
+| 9  | B: そこまでやっちゃうんだ                                                         | B: You go that far.                                                                                                                   |
+| 10 | A: そうなんですよ                                                             | A: Yes, that's right.                                                                                                                 |
+
+<span id="page-19-3"></span><sup>9</sup>https://anonresearch81.github.io/research/publications/CHATS/
+
+<span id="page-20-1"></span>![](figures/_page_20_Figure_1.jpeg)
+
+Figure G.1: The first example of a generated spoken dialogue. Dashed lines indicate the boundaries of each utterance, and the numbers from 1 to 10 indicate the indices of the utterances.
+
+Table G.2: The second example of a written dialogue input with utterance index n.
+
+<span id="page-20-0"></span>
+
+| n  | Original Script                                                    | Translated Script                                                                                                           |
+|----|--------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------|
+| 1  | B: なかなかないよね                                                        | B: It's pretty rare, isn't it?                                                                                              |
+| 2  | A: ふーん、自分で行く、よね、それこそファー                                            | A: Hmm, you'd go there yourself, right, especially for                                                                      |
+| 3  | ストフード<br>A: くらい、よ                                                  | fast food.<br>A: At least, right.                                                                                           |
+| 4  | B: (LAU)                                                           | B: (LAU)                                                                                                                    |
+| 5  | A: お安い、回転寿司の方が落ち着くし                                                | A: It's cheaper, and I feel more at ease at conveyor belt<br>sushi places.                                                  |
+| 6  | A: ねー、いっぱい食べれるしね(LAU)、そうなの<br>よ、結局ね、結局そうなんですよ、結局、そう<br>なる、そこに行くんです | A: Right? You can eat a lot (LAU), exactly, in the end,<br>that's what it comes down to, eventually, that's where<br>we go. |
+| 7  | A: やっぱりすごいです                                                       | A: It's really amazing.                                                                                                     |
+| 8  | B: うん、チェーン店は、偉大ということで                                              | B: Yeah, chain stores are, in a sense, remarkable.                                                                          |
+| 9  | B: はい、一旦これで、おわりでいい?                                                | B: Alright, can we conclude this for now?                                                                                   |
+| 10 | A: はい、いいですかね                                                       | A: Yes, is that okay?                                                                                                       |
+
+<span id="page-20-2"></span>![](figures/_page_20_Figure_5.jpeg)
+
+Figure G.2: The second example of a generated spoken dialogue. Dashed lines indicate the boundaries of each utterance, and the numbers from 1 to 10 indicate the indices of the utterances.

papers/0AYosSFETw/review.json

@@ -0,0 +1,70 @@
+{
+  "id": "0AYosSFETw",
+  "title": "Towards human-like spoken dialogue generation between AI agents from written dialogue",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "2qgRBrOuYh",
+      "rating": 6,
+      "content": {
+        "summary": "This paper tackles the task of generating spoken dialogues between 2 parties using autoregressive models. It follows the earlier work on DLM (dialogue language model), and tries to extend it for better turn-taking and pause modeling. This results in more natural generated dialogs. The authors train all models from scratch.",
+        "soundness": "4 excellent",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "It makes sense to incorporate pitch and content units in a multi-stream dialog language model for spoken dialog generation. The authors also build secondary models for turn taking and pause modeling. These are very critical for a more natural sounding dialog generation, and are lacking in textual dialogs. Especially the audio samples with overlapping speech are impressive.",
+        "weaknesses": "I had a hard time to understand the concept of \"units\" and has to read Kharitonov. The paper should do a better job explaining what they are with motivation. Furthermore I had a hard time understanding uLM and had to read the DLM paper. The authors should first explain DLM. But after reading these 2 papers, it is clear that the contribution is actually not that significant, but still very creative idea, applied to Japanese data.",
+        "questions": "dGSLM is trained with 2000 hours of English data. In this paper authors use only 74 hours of Japanese data. And they train the dGSLM models from scratch using that 74 hours. The experimental results show inferior comprehensiveness compared to the original dGSLM paper. This begs the question of authors replicating the experiments for English with larger training set. In other words, we do not know whether their improvements will disappear with more data.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "I had a hard time to understand the concept of \"units\" and has to read Kharitonov. The paper should do a better job explaining what they are with motivation. Furthermore I had a hard time understanding uLM and had to read the DLM paper. The authors should first explain DLM. But after reading these 2 papers, it is clear that the contribution is actually not that significant, but still very creative idea, applied to Japanese data. The core idea of incorporating pitch and content units into a multi-stream dialog language model is not novel, and the specific implementation details of the turn-taking and pause modeling, while important, do not represent a major leap in the field. The improvements, while noticeable in the provided audio samples, appear to be incremental rather than transformative. The lack of a thorough ablation study further obscures the individual contributions of each component. It is unclear how much each of the proposed modifications contributes to the overall performance gains.",
+        "suggestions": "The paper needs to provide a more detailed explanation of the 'units' used in the GSLM framework. The authors should clearly define what these units represent (e.g., sub-word units, phonemes, etc.), how they are extracted from the speech signal, and why they are chosen over other possible representations. A concrete example of how the speech-to-unit (s2u) module operates would be beneficial. Furthermore, the authors should explain the motivation behind using these units in the context of spoken dialogue generation, as opposed to directly modeling waveforms or other speech representations. A more thorough explanation of the unit language model (uLM) is also necessary, including its architecture, training procedure, and how it interacts with the other components of the system. The relationship between uLM and the original DLM needs to be clearly articulated, highlighting the differences and improvements introduced in this work. Without this foundational understanding, it is difficult to assess the true novelty and impact of the proposed approach.\n\nThe paper should include a more rigorous experimental evaluation to substantiate the claims of improved turn-taking and pause modeling. The current evaluation lacks a detailed ablation study that isolates the impact of each proposed modification. For example, the authors should compare the performance of the full model against versions without the turn-taking model, the pause model, and the multi-stream architecture. This would allow for a better understanding of the contribution of each component. Additionally, the evaluation should include quantitative metrics that specifically measure the quality of turn-taking and pause modeling, beyond just the overall comprehensiveness of the generated dialogues. Metrics such as the frequency of overlapping speech, the duration of pauses, and the naturalness of turn transitions would be valuable. The authors should also compare their approach against existing state-of-the-art methods for spoken dialogue generation, not just the original dGSLM. This would provide a more comprehensive assessment of the proposed method's performance.\n\nFinally, the paper should address the limitations of the current experimental setup, particularly the relatively small size of the Japanese dataset (74 hours) compared to the dataset used for training the original dGSLM (2000 hours). The authors should acknowledge that the inferior comprehensiveness compared to the original dGSLM might be due to the limited training data. While the authors mention the language-independent design of the GSLM pipeline, they should provide more evidence to support this claim. This could include experiments on other languages or a detailed analysis of the model's ability to generalize across different languages. The paper should also discuss the potential challenges of applying the proposed method to languages with different phonetic structures and prosodic patterns. A more thorough discussion of the limitations and future research directions would greatly enhance the paper's overall impact."
+      }
+    },
+    {
+      "id": "0Ubl1s0DWb",
+      "rating": 8,
+      "content": {
+        "summary": "The paper proposes a method to generate natural overlapping spoken dialogue with the listener cues like backchannels and laughter only using the written transcripts (that lack the rich spoken dialog modes). This system generates speech for both the speaker and the listener simultaneously, using only the transcription from the speaker side by finetuning the modified dGSLM model with careful curation and pre-processing of natural dialog. The overall pipeline is similar to the one used by the dGSLM system; however using the careful finetuning process delivers very strong results and a practical tool for enriching the dialogs with natural spoken dialog properties. \n\nThe model has extensive experiments to show that the utterance quality is good, the dialog segments contain high quality of close to ground truth backchannels and pauses and the turn taking events also resemble the ground truth. Most important, the qualitative human evaluation experiments also show very good naturalness, meaningfulness and sound quality.",
+        "soundness": "4 excellent",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "- There are many Dialog generation LLMs available today. These are currently not very natural generation systems, meaning, they cannot mimic human-to-human conversations that contain rich elements like laughter, backchannel, fluid turn-taking, etc. This paper aims to solve this problem and generates natural spoken dialog and presents methods including how to prepare datasets, create context properly in the training data and predict turn-taking events using the dual-transformer architecture (dGSLM). \n- The methods also shows how smaller datasets (74 hr of 2 channel speech) can be used to train a high quality spoken dialog generator (using a pre-trained uLM model). \n- Ablations show that data augmentation, next sentence objectives, turn-taking mechanism were all important pieces of the architecture and pipeline are all important for getting the overall natural dialog output.",
+        "weaknesses": "- the paper presents the overall system very well, however, it is not clear if the original contribution of the work is significant. It seems like a straightforward extension of the dGSLM model where it has been fine-tuned to create this improved version of natural dialog corpora. \n- there is no comparison to any other baseline system that is described in the paper. \n- human evaluation does not try to assess the content and quality of generated backchannels. \n- Also, it is not clear how the generation will transfer to various other data domains.",
+        "questions": "- it is not clear how many backchannel tokens are in the vocabulary (like laughter, ums, etc).",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": " - the paper presents the overall system very well, however, it is not clear if the original contribution of the work is significant. It seems like a straightforward extension of the dGSLM model where it has been fine-tuned to create this improved version of natural dialog corpora. \n- there is no comparison to any other baseline system that is described in the paper. \n- human evaluation does not try to assess the content and quality of generated backchannels. \n- Also, it is not clear how the generation will transfer to various other data domains.",
+        "suggestions": "The paper would benefit from a more rigorous justification of its novelty beyond a simple fine-tuning of the dGSLM model. While the results are promising, the core contribution needs to be more clearly articulated. The authors should explicitly compare their approach to other relevant methods, even if those methods do not directly address the same problem. For example, they could compare against a pipeline approach where a separate backchannel generation model is used in conjunction with a standard text-to-speech system. This would help to isolate the benefits of their end-to-end approach. Furthermore, the authors should provide a more detailed analysis of the generated backchannels, perhaps using metrics that quantify the appropriateness and diversity of these cues. This could involve analyzing the distribution of different backchannel types (e.g., 'uh-huh', 'mm-hm', laughter) and their placement within the dialogue. It would also be useful to investigate the correlation between the generated backchannels and the speaker's utterances, to determine if the model is capturing the subtle cues that drive natural human conversation. \n\nTo address the lack of comparison to other baseline systems, the authors should consider implementing a simple baseline that combines a standard text-to-speech (TTS) system with a rule-based or statistical model for backchannel generation. This baseline could serve as a point of comparison to demonstrate the advantages of the proposed end-to-end approach. For instance, a simple rule-based system could insert backchannels at fixed intervals or based on pauses in the speaker's utterances. A statistical model could be trained to predict backchannel locations based on features extracted from the speaker's text. Comparing the proposed system against such baselines would provide a more comprehensive evaluation of its performance and highlight its unique contributions. The authors should also consider using more objective metrics to evaluate the quality of the generated speech, such as word error rate (WER) or perceptual evaluation of speech quality (PESQ), in addition to the subjective human evaluation. This would provide a more quantitative assessment of the system's performance.\n\nFinally, the paper needs to address the issue of domain transferability. The authors should acknowledge that the current system is trained on a specific dataset and may not generalize well to other domains. They could explore techniques for domain adaptation, such as fine-tuning the model on data from a different domain or using domain-specific features. In addition, the authors should discuss the limitations of their approach and identify potential areas for future research. For example, they could investigate how the system performs in noisy environments or with speakers who have different accents or speaking styles. The authors should also consider the ethical implications of their work, such as the potential for misuse of the technology to create realistic but fabricated conversations."
+      }
+    },
+    {
+      "id": "5YdY7AKDmz",
+      "rating": 5,
+      "content": {
+        "summary": "This paper proposes CHATS (CHatty Agents Text-to-Speech), a system for transforming written dialogue into spoken dialogue, whose content is coherent with the input written dialogue but generated with backchannels, laughter, and smooth turn-taking. Several contributions are announced: a method to prepare written dialogue by excluding backchannels, a mechanism for taking turns in conversation, and a Multi-Stream Dialogue Transformer Language Model. Paper builds upon previous work, such as dGSLM and Dialogue Transformer Language Model by Nguyen et al. in 2023 and it provides evaluations for different parts of the proposed system, including the dialog model, turn-taking model, and back-channeling model. \n\nWhen I take a closer look, it's clear that paper has too much stuff in it. There are many models and evaluations crammed together in one document w/o enough details of each of them. This makes it hard to read and understand the paper. It's unfortunate because this is an ambitious and relevant research objective that is described here. Current version of the paper needs a big re-organization to make it clearer and maybe each problem addressed should correspond to a single paper with deeper / more detailed description and evaluation; that would allow reader/reviewer to better understand and appreciate the valuable insights it offers.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "3 good",
+        "strengths": "-This research is ambitious because it explores how people talk in real conversations, not just in written text.\n\n-It introduces a Turn-Taking and Backchanneling Mechanism, which is important for making better autonomous spoken conversational agents.\n\n-The Multi-Stream Dialogue Transformer Language Model (MS-DLM) seems the main contribution and is definitely an interesting architecture",
+        "weaknesses": "* It's unfortunate that the spoken dialog examples on GitHub are not in English. This makes it challenging for me to evaluate, and it limits its accessibility since only Japanese speakers can understand it. English examples would have been more universal.\n\n- In the contributions mentioned in the paper, it is not clear why \"Conversion from Spoken to Written Dialogue\" is valuable or innovative. Authors mention using both rule-based and machine learning approaches to identify backchannels and exclude them from written dialogues, but the paper lacks detail on the challenges this addresses. Is it mainly about data preprocessing?\n\n- As said above, the paper's structure needs improvement, as it tries to cover too many topics in one document.\n\n- The paper builds on the work of dGSLM (Nguyen et al., 2023) and the Dialogue Transformer language model (DLM) (Nguyen et al., 2023), but it doesn't provide enough information about these previous models to make this paper self-understandable\n\n- Section 3.1.2 seems to be a core part, but it's too brief to fully understand its significance.",
+        "questions": "see main remarks above +\n not clear was is the challenge in the part \"Conversion from Spoken to Written Dialogue\"",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " It's clear that paper has too much stuff in it. There are many models and evaluations crammed together in one document w/o enough details of each of them. This makes it hard to read and understand the paper. It's unfortunate because this is an ambitious and relevant research objective that is described here. Current version of the paper needs a big re-organization to make it clearer and maybe each problem addressed should correspond to a single paper with deeper / more detailed description and evaluation; that would allow reader/reviewer to better understand and appreciate the valuable insights it offers.\n\n * It's unfortunate that the spoken dialog examples on GitHub are not in English. This makes it challenging for me to evaluate, and it limits its accessibility since only Japanese speakers can understand it. English examples would have been more universal.\n\n- In the contributions mentioned in the paper, it is not clear why \"Conversion from Spoken to Written Dialogue\" is valuable or innovative. Authors mention using both rule-based and machine learning approaches to identify backchannels and exclude them from written dialogues, but the paper lacks detail on the challenges this addresses. Is it mainly about data preprocessing?\n\n- As said above, the paper's structure needs improvement, as it tries to cover too many topics in one document.\n\n- The paper builds on the work of dGSLM (Nguyen et al., 2023) and the Dialogue Transformer language model (DLM) (Nguyen et al., 2023), but it doesn't provide enough information about these previous models to make this paper self-understandable\n\n- Section 3.1.2 seems to be a core part, but it's too brief to fully understand its significance.",
+        "suggestions": "The paper attempts to tackle a very complex problem, which is admirable, but the current presentation makes it difficult to assess the individual contributions. The core issue is that the paper tries to do too much at once, lacking sufficient depth in each area. For example, the 'Conversion from Spoken to Written Dialogue' is presented as a key step, but the challenges and nuances of this process are not clearly explained. Is it simply about removing backchannels and laughter, or are there more subtle aspects of spoken language that need to be addressed? The paper should either focus on a single aspect of the problem, or provide a much more detailed explanation of each component, including the specific challenges and solutions for each step. This would require a significant restructuring of the paper, possibly into multiple papers, each focusing on a specific aspect of the proposed system.\n\nFurthermore, the lack of detail on the dGSLM and DLM models makes it hard to understand the novelty of the proposed Multi-Stream Dialogue Transformer Language Model (MS-DLM). The paper mentions that it builds upon these previous models, but without a clear explanation of their architectures and limitations, it's difficult to appreciate the advancements made by the MS-DLM. A more detailed explanation of the conventional DLM and how the MS-DLM differs in terms of architecture, input/output sequences, and training objectives is essential. This would help the reader understand the specific contributions of the proposed model and its advantages over existing approaches. The paper should include a dedicated section or appendix that provides a comprehensive overview of these foundational models.\n\nFinally, the absence of English examples on the demo page is a significant limitation. While the authors mention the language-independent nature of their system, the lack of English examples makes it difficult for a large part of the research community to evaluate the system's performance. The visual representation of backchannels, laughter, and overlaps is a good start, but it doesn't replace the need for actual audio examples in a widely understood language. The authors should prioritize the creation of an English dataset or adapt their system to an existing English dataset to provide more accessible and comprehensive evaluation examples. This would significantly enhance the impact and accessibility of their work."
+      }
+    }
+  ]
+}

papers/0QAzIMq32X/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "0QAzIMq32X",
+  "title": "Inner Classifier-Free Guidance and Its Taylor Expansion for Diffusion Models",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Accept",
+  "date": "2023-09-16",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=0QAzIMq32X"
+}

papers/0QAzIMq32X/paper.md

@@ -0,0 +1,574 @@
+# INNER CLASSIFIER-FREE GUIDANCE AND ITS TAYLOR EXPANSION FOR DIFFUSION MODELS
+
+Shikun Sun<sup>1,2</sup>, Longhui Wei<sup>3</sup>, Zhicai Wang<sup>4</sup>, Zixuan Wang<sup>1,2</sup>, Junliang Xing<sup>1,2</sup>, Jia Jia<sup>1,2\*</sup> & Qi Tian<sup>3\*</sup>
+
+ $^1\text{Tsinghua University}, ^2\text{BNRist}, ^3\text{Huawei Inc.}, ^4\text{University of Science and Technology of China} \\ \{\text{ssk21,wangzixu21}\} \\ \{\text{mails.tsinghua.edu.cn}, \text{weilh2568@gmail.com wangzhic@mail.ustc.edu.cn}, \\ \{\text{jlxing, jjia}\} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qi1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qu1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qu1@huawei.com}\} \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qu1@huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu1@huawei.com}] \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \} \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn}, \text{tian.qu2~huawei.com}] \\ \{\text{tsinghua.edu.cn},$ 
+
+#### **ABSTRACT**
+
+Classifier-free guidance (CFG) is a pivotal technique for balancing the diversity and fidelity of samples in conditional diffusion models. This approach involves utilizing a single model to jointly optimize the conditional score predictor and unconditional score predictor, eliminating the need for additional classifiers. It delivers impressive results and can be employed for continuous and discrete condition representations. However, when the condition is continuous, it prompts the question of whether the trade-off can be further enhanced. Our proposed inner classifier-free guidance (ICFG) provides an alternative perspective on the CFG method when the condition has a specific structure, demonstrating that CFG represents a first-order case of ICFG. Additionally, we offer a second-order implementation, highlighting that even without altering the training policy, our second-order approach can introduce new valuable information and achieve an improved balance between fidelity and diversity for Stable Diffusion.
+
+### 1 Introduction
+
+Diffusion models have garnered significant achievements in tasks involving image and audio generation (Sohl-Dickstein et al., 2015; Ho et al., 2020; Rombach et al., 2022; Podell et al., 2023; Huang et al., 2023; Wang et al., 2024). These models exhibit comparable, and in some cases, superior performance to GAN-based models (Brock et al., 2019) and autoregressive models (Razavi et al., 2019) regarding diversity and fidelity. Notably, text-based image generation models have emerged as particularly successful examples, including Stable Diffusion (Rombach et al., 2022), SDXL (Podell et al., 2023), DALL·E 2 (Ramesh et al., 2022).
+
+There are primarily two approaches to introducing or enhancing guidance in diffusion models: using classifiers (Dhariwal & Nichol, 2021) and employing classifier-free guidance (Ho & Salimans, 2022) (CFG). In the case of classifiers, an external trained classifier is employed to guide the diffusion model at each timestep towards achieving a higher probability according to the classifier's judgment, which is also be extended to energy-based guidance (Zhao et al., 2022; Lu et al., 2023; Sun et al., 2023). On the other hand, classifier-free guidance involves utilizing a single model to optimize the conditional score predictor and unconditional score predictor jointly. The discrepancy between these predictors is then employed as guidance, which is subsequently added to the score function. This approach eliminates the need for additional classifiers and has delivered impressive results (Ho & Salimans, 2022).
+
+Nevertheless, none of these methods impose specific constraints on the condition space, resulting in the underutilization of the benefits of continuity when the condition space is continuous. Our focus lies in exploring whether the nature of continuity can be effectively applied to CFG. Moreover, in the case of widely used text-based image diffusion models like Stable Diffusion (Rombach et al., 2022), the complexity of the text encoder (Radford et al., 2021) raises the question of whether a structured continuous space exists. This space could potentially enhance the balance between fidelity and diversity in generated samples.
+
+<sup>\*</sup>Corresponding author
+
+To address these concerns, we propose a novel interpretation of CFG. Our approach assumes that the condition space possesses a (local) cone structure. Under this assumption, CFG can be seen as a first-order Taylor expansion of our proposed inner classifier-free guidance (ICFG) method. Building on this interpretation, we further introduce a second-order Taylor expansion of ICFG and reveal an alternative energy-based formulation. Surprisingly, we discover that the second-order Taylor expansion of ICFG yields enhancements for Stable Diffusion, even without modifying the training policy. This finding suggests the existence of a structured continuous condition space that has the potential to enhance the sample performance of Stable Diffusion further.
+
+To summarize, our main contributions are three-fold as follows:
+
+- We introduce ICFG and analyze the convergence of its Taylor expansion under specific conditions.
+- We demonstrate that CFG can be regarded as a first-order ICFG and propose a second-order Taylor expansion for our ICFG.
+- We apply the second-order ICFG to the Stable Diffusion model and observe that, remarkably, our new formulation yields valuable information and enhances the trade-off between fidelity and diversity, even without modifying the training policy.
+
+#### 2 BACKGROUND
+
+#### 2.1 DIFFUSION MODELS
+
+Diffusion models encompass various formulations, and we will provide a brief overview of score-based diffusion models (Song & Ermon, 2019; Song et al., 2021b;a; Sun et al., 2023; Ni et al., 2023) (SBDMs) as they offer a solid foundation for guidance methods. SBDMs employ a stochastic differential equation (SDE) to diffuse the data distributions towards known distributions, typically Gaussian distributions. By learning the necessary information to reverse the diffusion process while preserving the marginal distribution, we can sample from the known distribution and subsequently reverse the SDE. This process is equivalent to sampling directly from the data distribution.
+
+Denote the unknown dataset distribution as  $q(\mathbf{x}_0)$ , where  $\mathbf{x}_0 \in \mathbb{R}^d$ . We aim to sample from  $q(\mathbf{x}_0)$ . We also have the terminal distribution  $q(\mathbf{x}_T)$ , where  $\mathbf{x}_T \in \mathbb{R}^d$ . To connect these two distributions, we introduce a forward diffusion process  $\{\mathbf{x}_t\}_{t\in[0,T]}$ , where  $q(\mathbf{x}_t)$  or  $q_t(\mathbf{x})$  represents the distribution of  $\mathbf{x}_t$ . We assume that this diffusion process follows a SDE:
+
+<span id="page-1-0"></span>
+$$d\mathbf{x} = \mathbf{f}(\mathbf{x}, t)dt + q(t)d\mathbf{w},\tag{1}$$
+
+where  $\mathbf{f}(\mathbf{x},t)$  is the drift term, g(t) is the diffusion coefficient, and  $\mathbf{w}$  is the standard Wiener process. In the work by Song et al. (2021b), it has been shown that to reverse the SDE while maintaining the marginal distribution, the score function  $\mathbf{s}(\mathbf{x},t)$  is the only required information. The score function is defined as follows:
+
+$$\mathbf{s}(\mathbf{x}, t) = \nabla_{\mathbf{x}_t} \log q(\mathbf{x}_t). \tag{2}$$
+
+Then, the reverse-time SDE is:
+
+$$d\mathbf{x} = [\mathbf{f}(\mathbf{x}, t) - g(t)^{2} \mathbf{s}(\mathbf{x}, t)] dt + g(t) d\overline{\mathbf{w}},$$
+(3)
+
+where the symbol  $\overline{\mathbf{w}}$  represents another standard Wiener process that is independent of the Wiener process  $\mathbf{w}$  in the forward diffusion process. The reverse-time SDE is equivalent to the reverse-time diffusion process  $\{\mathbf{x}_t\}_{t\in[T,0]}$ . Then we can sample from the known distribution  $q(\mathbf{x}_T)$ , and reverse the SDE to get the sample from the data distribution  $q(\mathbf{x}_0)$ .
+
+The works of Vincent (2011); Song et al. (2021b) present a feasible method to estimate the score functions of complex datasets using a neural network  $\mathbf{s}^{\theta}(\mathbf{x},t)$ . The optimization objective is defined as follows:
+
+$$\theta^* = \arg\min_{\theta} \int_0^T \mathbb{E}_{q(\mathbf{x}_0)q_{0t}(\mathbf{x}_t|\mathbf{x}_0)} \left[ \lambda(t) \left\| \mathbf{s}^{\theta}(\mathbf{x}_t, t) - \nabla_{\mathbf{x}_t} \log q_{0t}(\mathbf{x}_t|\mathbf{x}_0) \right\|^2 \right] dt, \tag{4}$$
+
+where  $\lambda(t)$  is a weighting function, and  $q_{0t}(\mathbf{x}_t|\mathbf{x}_0)$  is the transition probability from  $\mathbf{x}_0$  to  $\mathbf{x}_t$ .
+
+Furthermore, consider Eq. (1) where we have  $\mathbf{x}_t = \alpha_t \mathbf{x}_0 + \beta_t \mathbf{z}$ , with  $\mathbf{z}$  being a standard Gaussian distribution, and  $\alpha_t$  and  $\beta_t$  representing the corresponding coefficients. In many scenarios, the diffusion score is parameterized as  $\epsilon^{\theta}(\mathbf{x},t) = -\beta_t \mathbf{s}^{\theta}(\mathbf{x},t)$ . Moreover, in the case of conditional diffusion models, where the data  $\mathbf{x}$  is accompanied by a conditioning variable  $\mathbf{c}$ , the only modification is to include  $\mathbf{c}$  as an input to  $\epsilon^{\theta}$ , resulting in  $\epsilon^{\theta}(\mathbf{x},\mathbf{c},t)$ .
+
+#### 2.2 Classifier guidance for diffusion models
+
+Dhariwal & Nichol (2021) introduce classifier guidance for diffusion models to enhance control over conditions. Assume that the learned conditional diffusion score is denoted as  $\epsilon^{\theta}(\mathbf{x}, \mathbf{c}, t)$ , and we have a set of classifiers  $p_t^{\theta}(\mathbf{c}|\mathbf{x}_t)$  that predict the condition  $\mathbf{c}$  based on the diffused data  $\mathbf{x}_t$  at various time steps t. In this case, we can modify the diffusion score as follows:
+
+$$\widetilde{\epsilon}^{\theta}(\mathbf{x}_{t}, \mathbf{c}, t) = \epsilon^{\theta}(\mathbf{x}_{t}, \mathbf{c}, t) - w\beta_{t}\nabla_{\mathbf{x}_{t}}\log p_{t}^{\theta}(\mathbf{c}|\mathbf{x}_{t}) = -\beta_{t}\nabla_{\mathbf{x}_{t}}\left[\log q^{\theta}(\mathbf{x}_{t}|\mathbf{c}) + w\log p_{t}^{\theta}(\mathbf{c}|\mathbf{x}_{t})\right],$$
+(5)
+
+where w represents a weighting factor that controls the strength of the guidance. The modified diffusion score, denoted as  $\tilde{\epsilon}^{\theta}(\mathbf{x}_t, \mathbf{c}, t)$ , replaces the original diffusion score  $\epsilon^{\theta}(\mathbf{x}_t, \mathbf{c}, t)$  in the sampling process. At each time step t,  $\tilde{\epsilon}^{\theta}(\mathbf{x}_t, \mathbf{c}, t)$  serves as the diffusion score for a new conditional distribution.
+
+$$\widetilde{q}^{\theta}(\mathbf{x}_t|\mathbf{c}) \propto q^{\theta}(\mathbf{x}_t|\mathbf{c})p_t^{\theta}(\mathbf{c}|\mathbf{x}_t)^w.$$
+ (6)
+
+It can be observed that  $\tilde{q}^{\theta}(\mathbf{x}_{t}|\mathbf{c})$  can be seen as the conditional distribution  $q^{\theta}(\mathbf{x}_{t}|\mathbf{c})$  multiplied by  $p_{t}^{\theta}(\mathbf{c}|\mathbf{x}_{t})^{w}$ . This indicates that the modified diffusion score assigns a higher probability to the data  $\mathbf{x}_{t}$  that is more likely to be associated with the condition  $\mathbf{c}$ . Consequently, the modified diffusion score allows for a trade-off between sample diversity and sample fidelity.
+
+The classifier guidance can also be applied to an unconditional diffusion score. For the unconditional diffusion score  $\epsilon^{\theta}(\mathbf{x},t)$ , using the same set of classifiers, the modified diffusion score is given by:
+
+<span id="page-2-0"></span>
+$$\hat{\epsilon}^{\theta}(\mathbf{x}_{t}, \mathbf{c}, t) = \epsilon^{\theta}(\mathbf{x}_{t}, t) - (w+1)\beta_{t}\nabla_{\mathbf{x}_{t}}\log p_{t}^{\theta}(\mathbf{c}|\mathbf{x}_{t}) = -\beta_{t}\nabla_{\mathbf{x}_{t}}\left[\log q^{\theta}(\mathbf{x}_{t}) + (w+1)\log p_{t}^{\theta}(\mathbf{c}|\mathbf{x}_{t})\right].$$
+(7)
+
+The corresponding guided intermediate distribution is:
+
+<span id="page-2-1"></span>
+$$\widetilde{q}^{\theta}(\mathbf{x}_t|\mathbf{c}) \propto q^{\theta}(\mathbf{x}_t)p_t^{\theta}(\mathbf{c}|\mathbf{x}_t)^{w+1}.$$
+ (8)
+
+While the experiments on guiding the unconditional diffusion score may not have yielded as remarkable results as the conditional case initially (Dhariwal & Nichol, 2021), this formula can still be further connected to the concept of classifier-free guidance.
+
+#### 2.3 CLASSIFIER-FREE GUIDANCE FOR DIFFUSION MODELS
+
+To avoid training classifiers, Ho & Salimans (2022) propose an alternative approach called classifier-free guidance (CFG) for diffusion models. The main idea behind CFG is to use a single model to simultaneously fit both the conditional score predictor and the unconditional score predictor. This is achieved by randomly replacing the condition  $\mathbf{c}$  with  $\varnothing$  (an empty value). By doing so, one can obtain the conditional score predictor  $\epsilon^{\theta}(\mathbf{x}, \mathbf{c}, t)$  and the unconditional score predictor  $\epsilon^{\theta}(\mathbf{x}, t)$ , which is equivalent to  $\epsilon^{\theta}(\mathbf{x}, \varnothing, t)$ . Then, because
+
+$$\nabla_{\mathbf{x}_{t}} \left[ \log p_{t}(\mathbf{c}|\mathbf{x}_{t}) \right] = \nabla_{\mathbf{x}_{t}} \left[ \log q(\mathbf{x}_{t}|\mathbf{c}) - \log q(\mathbf{x}_{t}) + \log p(\mathbf{c}) \right]$$
+
+$$= \nabla_{\mathbf{x}_{t}} \left[ \log q(\mathbf{x}_{t}|\mathbf{c}) - \log q(\mathbf{x}_{t}) \right], \tag{9}$$
+
+which indicates that after applying the operator  $\nabla_{\mathbf{x}_t}$ , we can replace the last term of Equation (7) with  $\log q^{\theta}(\mathbf{x}_t|\mathbf{c}) - \log q^{\theta}(\mathbf{x}_t)$  to achieve a similar effect. Then we get the enhanced diffusion score:
+
+$$\hat{\epsilon}^{\theta}(\mathbf{x}_{t}, \mathbf{c}, t) = (w+1)\epsilon^{\theta}(\mathbf{x}_{t}, \mathbf{c}, t) - w\epsilon^{\theta}(\mathbf{x}_{t}, t)$$
+
+$$= -\beta_{t}\nabla_{\mathbf{x}_{t}} \left[ \log q^{\theta}(\mathbf{x}_{t}|\mathbf{c}) + w(\log q^{\theta}(\mathbf{x}_{t}|\mathbf{c}) - \log q^{\theta}(\mathbf{x}_{t})) \right]$$
+
+$$= -\beta_{t}\nabla_{\mathbf{x}_{t}} \left[ \log q^{\theta}(\mathbf{x}_{t}) + (w+1)(\log q^{\theta}(\mathbf{x}_{t}|\mathbf{c}) - \log q^{\theta}(\mathbf{x}_{t})) \right],$$
+(10)
+
+whose enhanced intermediate distribution is:
+
+<span id="page-2-2"></span>
+$$\hat{q}^{\theta}(\mathbf{x}_t|\mathbf{c}) \propto q^{\theta}(\mathbf{x}_t) \left[ \frac{q^{\theta}(\mathbf{x}_t|\mathbf{c})}{q^{\theta}(\mathbf{x}_t)} \right]^{w+1}$$
+ (11)
+
+It is worth noting that both of these guidance methods can be regarded as a more general form of energy-based guidance (Zhao et al., 2022; Lu et al., 2023). In this case, the formulation of the intermediate time distribution is:
+
+$$\overline{q}^{\theta}(\mathbf{x}_t|\mathbf{c}) \propto q^{\theta}(\mathbf{x}_t)e^{-(w+1)\beta(\mathbf{x}_t)},$$
+ (12)
+
+where  $\beta(\mathbf{x}_t)$  is an arbitrary energy function.
+
+#### 3 INNER CLASSIFIER-FREE GUIDANCE
+
+Firstly, consider the enhanced intermediate distribution  $\overline{q}^{\theta}(\mathbf{x}_t|\mathbf{c})$  obtained by Eq. (8) or Eq. (11), given the condition  $\mathbf{c}$ . The question is whether these enhanced distributions follow the same diffusion forward process as the original intermediate distribution  $q^{\theta}(\mathbf{x}_t)$ . We have:
+
+<span id="page-3-0"></span>**Theorem 3.1.** Given condition  $\mathbf{c}$ , the enhanced transition kernel  $\overline{q}_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c})$  by Eq. (8) or Eq. (11) equals to the original transition kernel  $q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c}) = q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0)$  does not hold trivially. Specifically, when w = 0, the equation holds.
+
+The proof and discussions of Theorem 3.1 is in the Appendix A. Theorem 3.1 suggests that in the majority of cases, the enhanced intermediate distribution  $\overline{q}^{\theta}(\mathbf{x}_t|\mathbf{c})$  at different timesteps t does not adhere to the same SDE as the original intermediate distribution  $q^{\theta}(\mathbf{x}_t)$  or the original conditional intermediate distribution  $q^{\theta}(\mathbf{x}_t|\mathbf{c})$ , which is also mentioned in the work of Lu et al. (2023); Du et al. (2023).
+
+There are two important clarifications to make regarding Theorem 3.1:
+
+- $q^{\theta}(\mathbf{x}_0|\mathbf{x}_t)$  appears to never be a  $\delta$  distribution. However, under certain conditions, such as a low noise level or when  $\mathbf{x}_0$  is sparse, it can be approximately close to a  $\delta$  distribution.
+- Even if  $\overline{q}_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c})$  deviates from the original diffusion process, The sampling process may still be effective based on the underlying principles of Langevin dynamics.
+
+To address this issue, we incorporate the guidance strength w and represent the enhanced intermediate distribution in a more clear form as  $q^{\theta}(\mathbf{x}_t|\mathbf{c},w+1)$ . For instance, in the context of CFG, we can express  $q^{\theta}(\mathbf{x}_t|\mathbf{c},w+1) \propto q^{\theta}(\mathbf{x}_t) \left[\frac{q^{\theta}(\mathbf{x}_t|\mathbf{c})}{q^{\theta}(\mathbf{x}_t)}\right]^{w+1}$ .
+
+Let  $\beta=w+1$ . It is worth noting that in Theorem 3.1, when  $\beta=1$ , we have  $q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c},\beta)=q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0)$ . The question arises: Can we always ensure that  $\beta=1$ ? In other words, can we treat  $\beta$  and  $\mathbf{c}$  as the same variable, such that  $q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c},\beta)=q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0)$  holds consistently? By doing so, we incorporate the condition strength into the condition variable itself, and we refer to this approach as inner classifier-free guidance (ICFG).
+
+To establish a well-defined ICFG, it is necessary to impose certain structural assumptions on the space C of the condition c. The following assumptions are made:
+
+#### <span id="page-3-1"></span>**Assumption 3.1.**
+
+- C is a cone, which means  $\forall \beta \in \mathbb{R}^+, \forall \mathbf{c} \in C, \beta \mathbf{c} \in C$ .
+- For each  $c \in C$ ,  $\|c\|$  represents the guidance strength and  $\frac{c}{\|c\|}$  represents the guidance direction.
+
+For implementation purposes, as the origin  $\mathcal C$  does not inherently form a cone, it is common practice to extend the existing meaningful space  $\mathcal C$  to conform to a cone structure. This extended space is denoted as  $\overline{\mathcal C} = \{\mathbf c_0 + \beta(\mathbf c - \mathbf c_0) | \beta \in \mathbb R^+, \mathbf c \in \mathcal C\}$ , where the vertex of the cone  $\mathbf c_0$  is not necessarily 0. Further details can be found in Appendix D.
+
+Under Assumption 3.1, we define  $\bar{q}^{\theta}(x_t|c) = q^{\theta}(\mathbf{x}_t|\mathbf{c},\beta) \triangleq q^{\theta}(\mathbf{x}_t|\beta\mathbf{c})$ . Based on this definition, we can state the following Corollary 3.1.1:
+
+<span id="page-3-2"></span>**Corollary 3.1.1.** Given condition c and the guidance strength  $\beta = w + 1$ , we have:
+
+$$q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c},\beta) = q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0).$$
+
+Corollary 3.1.1 indicates that for ICFG, the forward diffusion process consistently remains the same as the original forward diffusion process, given condition c and guidance strength  $\beta$ .
+
+We propose a training policy that allows the model to assess the guidance strength based on a correlation metric  $r(\mathbf{x}, \mathbf{c})$ , which measures the relationship between the condition and the data. The training policy is outlined in Algorithm 1.
+
+```
+Algorithm 1 Training policy for ICFG
+```
+
+```
+Require: r(\mathbf{x}, \mathbf{c}): similarity metric
+
+Require: p_{uncond}: probability of unconditional training
+
+1: \overline{r} = \mathbb{E}_{\mathbf{x}, \mathbf{c}} r(\mathbf{x}, \mathbf{c})
+
+2: repeat
+
+3: (\mathbf{x}, \mathbf{c}) \sim p(\mathbf{x}, \mathbf{c})
+
+4: \overline{\mathbf{c}} = \mathbf{c}/r(\mathbf{x}, \mathbf{c}) * \overline{r}
+
+5: \overline{\mathbf{c}} \leftarrow \varnothing with probability p_{uncond}
+
+6: t \sim U[0, T]
+
+7: \epsilon \sim \mathcal{N}(\mathbf{0}, \mathbf{I})
+
+8: \mathbf{x}_t = \alpha_t \mathbf{x}_0 + \beta_t \epsilon
+
+9: Take gradient step on \nabla_{\theta} \| \epsilon^{\theta}(\mathbf{x}_t, \overline{\mathbf{c}}) - \epsilon \|^2
+
+10: until converged
+```
+
+#### 4 TAYLOR EXPANSION OF ICFG AND ITS CONVERGENCE
+
+In most cases, we use the extended cone  $\overline{\mathcal{C}} = \{\beta \mathbf{c} | \beta \in \mathbb{R}^+, \mathbf{c} \in \mathcal{C}\}$ . Consequently, we need to consider the Taylor expansion of ICFG at  $\beta = 1$  to estimate the score under conditions within  $\overline{\mathcal{C}}/\mathcal{C}$ . The n-th order Taylor expansion of  $\overline{\epsilon}^{\theta}(\mathbf{x}_t | \beta \mathbf{c})$  at  $\beta = 1$  is given by:
+
+<span id="page-4-1"></span>
+$$\overline{\epsilon}^{\theta}(\mathbf{x}_{t}|\beta\mathbf{c}) = \overline{\epsilon}^{\theta}(\mathbf{x}_{t}|\mathbf{c}) + \sum_{k=1}^{n} \frac{1}{k!} \frac{\partial^{k} \overline{\epsilon}^{\theta}(\mathbf{x}_{t}|\beta\mathbf{c})}{\partial \beta^{k}} \bigg|_{\beta=1} (\beta - 1)^{k} + R_{n}(\beta), \tag{13}$$
+
+where  $R_n(\beta)$  represents the remainder term. It is evident that CFG is a first-order Taylor expansion of ICFG at  $\beta = 1$  without  $R_1(\beta)$  and with the following estimation:
+
+$$\frac{\partial \overline{\epsilon}^{\theta}(\mathbf{x}_{t}|\beta\mathbf{c})}{\partial \beta}\bigg|_{\beta=1} \approx \overline{\epsilon}^{\theta}(\mathbf{x}_{t}|\mathbf{c}) - \overline{\epsilon}^{\theta}(\mathbf{x}_{t}|\mathbf{0}) = \overline{\epsilon}^{\theta}(\mathbf{x}_{t}|\mathbf{c}) - \overline{\epsilon}^{\theta}(\mathbf{x}_{t})$$
+(14)
+
+Then we will discuss the convergence of the Taylor expansion of ICFG in Eq. (13).
+
+Firstly, considering this problem from the model space  $\mathcal{S} = \{\overline{\epsilon}^{\theta}(\mathbf{x}_t|\beta\mathbf{c})|\forall\theta,\forall\mathbf{x},\forall\mathbf{c}\}$ , if we judiciously choose the components of the neural network such that the function  $\overline{\epsilon}^{\theta}(\mathbf{x}_t|\beta\mathbf{c})$  becomes analytic with respect to  $\beta$ , then the convergence of the Taylor expansion near  $\beta=1$  is guaranteed trivially.
+
+Secondly, if we desire a bound for  $R_n(\beta)$  for any  $\beta \in [0,B]$ , certain assumptions must be introduced. Before that, consider the specific quantitative relationships of Stable Diffusion, as depicted in Figure 1. It becomes apparent that the estimation of  $\frac{\partial \bar{\epsilon}^{\theta}(\mathbf{x}_t | \beta \mathbf{c})}{\partial \beta}\big|_{\beta=1}$  is relatively small. Consequently, we propose the following Assumption:
+
+<span id="page-4-2"></span>**Assumption 4.1.** For all  $k \in \mathbb{N}^+$ , the k-th order partial derivative  $\frac{\partial^k \overline{\epsilon}^{\theta}(\mathbf{x}_t | \beta \mathbf{c})}{\partial \beta^k}$  at  $\beta \in [0, B]$  is bounded by  $M_k$ .
+
+Then, we have:
+
+<span id="page-4-3"></span>**Theorem 4.1.** Under Assumption 4.1, the remainder term  $R_n(\beta)$  of the n-th order taylor expansion of  $\bar{\epsilon}^{\theta}(\mathbf{x}_t|\beta\mathbf{c})$  at  $\beta=1$  is bounded by  $\frac{M_{n+1}}{(n+1)!}B^{n+1}$ . This bound converges to 0 when the sequence  $M_{n+1}\sim o\left(\sqrt{n+1}\left[\frac{n+1}{eB}\right]^{n+1}\right)$ .
+
+By Stirling's formula, the proof will be discussed in the Appendix B.
+
+![](figures/_page_5_Figure_1.jpeg)
+
+<span id="page-5-0"></span>Figure 1: The quantitative relationships of Stable Diffusion during sampling. These figures show the relationship between the norm of the predicted score  $\bar{\epsilon}^{\theta}(\mathbf{x}_t|\mathbf{c})$ ,  $\bar{\epsilon}^{\theta}(\mathbf{x}_t)$  and the distance norm between them during the 50 sampling timesteps of CFG. The guidance strength for the first two figures is set to 3, while the last two figures have a guidance strength of 80. The caption for all figures states, "A photograph of an astronaut riding a horse."
+
+#### 5 IMPLEMENTATION OF SECOND-ORDER ICFG FOR STABLE DIFFUSION
+
+For the pretrained popular Stable Diffusion, we present two approaches to implement the second-order ICFG. The first method follows a straightforward Taylor expansion, as outlined in Algorithm 2. Notably, when we use  $\frac{y_2-y_1}{x_2-x_1}$  of two points  $(x_1,y_1),(x_2,y_2)$  to estimate the gradient at  $\frac{x_1+x_2}{2}$ , the second-order term is unique. Further details will be discussed in the Appendix C.
+
+```
+Algorithm 2 Strict sample algorithm for second-order ICFG
+
+Require: m: middle point for estimate second-order term
+
+Require: w: guidance strength on conditional score predictor
+
+Require: \mathbf{c}: condition for sampling
+
+Require: Require \{t_1, t_2, ..., t_N\} increasing timestep sequence of sampling
+
+Require: Sample(\mathbf{z}_t, \epsilon_t): sample algorithm for diffusion models given \mathbf{z}_t and \epsilon_t
+
+1: \mathbf{z}_N \sim \mathcal{N}(\mathbf{0}, \mathbf{I})
+
+2: \mathbf{for}\ i = N, ..., 1\ \mathbf{do}
+
+3: \bar{\epsilon}_t = \epsilon^{\theta}(\mathbf{z}_i, \mathbf{c}) + w(\epsilon^{\theta}(\mathbf{z}_i, \mathbf{c}) - \epsilon^{\theta}(\mathbf{z}_i))
++w^2 \frac{1}{m(1-m)} \left( (1-m)\epsilon^{\theta}(\mathbf{z}_i) + m\epsilon^{\theta}(\mathbf{z}_i, \mathbf{c}) - \epsilon^{\theta}(\mathbf{z}_i, m\mathbf{c}) \right)
+
+4: \mathbf{z}_{i-1} = Sample(\mathbf{z}_i, \bar{\epsilon}_t)
+
+5: end for
+
+6: return \mathbf{z}_0
+```
+
+However, in practical scenarios, the second-order term may suffer from a large bias due to the unchanged training policy, and this bias is further amplified by the coefficient  $w^2$ . To address this issue, we propose an alternative approach called the non-strict sample algorithm, presented in Algorithm 3. This algorithm offers a practical solution and can be effectively applied to mitigate the aforementioned problem.
+
+The only distinction between Algorithm 3 and Algorithm 2 lies in assigning a completely unrestricted hyperparameter v to the second-order term. This modification allows for more flexible control over the second-order term.
+
+#### 6 EXPERIMENTS
+
+The primary motivation behind our experiments is twofold. Firstly, we seek to showcase the efficacy of our new sampling algorithm in leveraging the continuity of  $\mathcal C$  and incorporating valuable information to achieve an improved balance between diversity and fidelity, even in cases where  $\mathcal C$  does not exhibit a "cone" structure apparently. Secondly, we aim to demonstrate that our new training policy enables the model to capture better the inherent "cone" structure of  $\mathcal C$ . To accomplish the first objective, we utilize the pretrained Stable Diffusion v1.5 model and apply our Algorithm 3 to generate sampled images. More implementation details are in Appendix D. Nevertheless, our second-order ICFG continues to demonstrate its advantages in these experiments. For the second target, we ex-
+
+```
+Algorithm 3 Non-strict sample algorithm for second-order ICFG
+Require: m: middle point for estimate second-order term
+Require: w: first-order guidance strength on conditional score predictor
+Require: v: second-order guidance strength on conditional score predictor
+Require: c: condition for sampling
+Require: Require {t1, t2, ..., tN } increasing timestep sequence of sampling
+Require: Sample(zt, ϵt): sample algorithm for diffusion models given zt and ϵt
+ 1: zN ∼ N (0, I)
+ 2: for i = N, ..., 1 do
+ 3: ϵt = ϵ
+              θ
+               (zi
+                  , c) + w(ϵ
+                            θ
+                             (zi
+                                , c) − ϵ
+                                        θ
+                                         (zi))
+           +v
+               m(1−m)
+
+                        (1 − m)ϵ
+                                  θ
+                                   (zi) + mϵθ
+                                              (zi
+                                                 , c) − ϵ
+                                                         θ
+                                                          (zi
+                                                             , mc)
+
+ 4: zi−1 = Sample(zi
+                           , ϵt)
+ 5: end for
+ 6: return z0
+```
+
+<span id="page-6-1"></span>Table 1: The results of varying the guidance strength and the condition space on the MS-COCO validation set.
+
+| Model&Settings      | FID ↓             | CLIP Score (%)↑   |
+|---------------------|-------------------|-------------------|
+| CFG                 |                   |                   |
+| w = 1.0             | 17.24             | 25.03             |
+| w = 2.0             | 15.42             | 25.80             |
+| w = 3.0             | 16.68             | 26.12             |
+| w = 4.0             | 18.18             | 26.34             |
+| w = 5.0             | 19.53             | 26.45             |
+| Ours                |                   | v = 0.25/0.5/1.0  |
+| w = 1.0, C = Call   | 16.40/17.34/20.70 | 25.46/25.71/25.86 |
+| w = 2.0, C = Call   | 15.28/15.42/16.34 | 26.11/26.30/26.52 |
+| w = 3.0, C = Call   | 16.59/16.69/16.88 | 26.37/26.54/26.73 |
+| w = 4.0, C = Call   | 17.98/18.06/18.20 | 26.51/26.64/26.81 |
+| w = 5.0, C = Call   | 19.35/19.32/19.45 | 26.59/26.69/26.86 |
+| w = 1.0, C = Cnouns | 16.33/17.24/21.78 | 25.02/24.88/24.23 |
+| w = 2.0, C = Cnouns | 15.22/15.23/15.71 | 25.86/25.81/25.61 |
+| w = 3.0, C = Cnouns | 16.59/16.60/16.61 | 26.19/26.18/26.09 |
+| w = 4.0, C = Cnouns | 18.08/18.07/18.02 | 26.36/26.37/26.30 |
+| w = 5.0, C = Cnouns | 19.33/19.31/19.47 | 26.48/26.49/26.44 |
+
+clusively fine-tune the U-Net [\(Ronneberger et al.,](#page-10-12) [2015\)](#page-10-12) of Stable Diffusion v1.5 [\(Rombach et al.,](#page-10-1) [2022\)](#page-10-1) with Low-Rank Adaptation [\(Hu et al.,](#page-9-9) [2022;](#page-9-9) [Ruiz et al.,](#page-10-13) [2023\)](#page-10-13).
+
+## 6.1 SAMPLING WITH SECOND-ORDER ICFG
+
+We employ the pretrained Stable Diffusion v1.5 model directly and utilize our Algorithm [3](#page-6-0) to generate sampled images. The settings we follow are consistent with those provided in the official repository of Stable Diffusion v1.5. The sampling algorithm employed is PNDM [\(Liu et al.,](#page-9-10) [2022\)](#page-9-10), and the default number of timesteps is 50. The evaluation of the results, presented in Table [1,](#page-6-1) Table [2](#page-7-0) and Table [3](#page-8-0) is based on two metrics: the Frechet Inception Distance (FID) ( ´ [Heusel et al.,](#page-9-11) [2017\)](#page-9-11) and the CLIP Score [\(Radford et al.,](#page-10-7) [2021\)](#page-10-7). The FID metric is calculated by comparing 10,000 generated images with the MS-COCO [\(Lin et al.,](#page-9-12) [2014\)](#page-9-12) validation dataset, measuring the distance between the distribution of generated images and the distribution of the validation dataset. On the other hand, the CLIP Score is computed between the 10,000 generated images and their corresponding captions by the model ViT-L/14 [\(Radford et al.,](#page-10-7) [2021\)](#page-10-7), reflecting the similarity between the images and the textual descriptions. In our tables, the default configuration is set to w = 2.0, v = 0.25, m = 1.1. We systematically vary the guidance strength w and v, the middle point m, and the condition space C to observe the impact of the second-order term. The designs of Call and Cnouns are in Appendix [D.](#page-13-0)
+
+![](figures/_page_7_Figure_1.jpeg)
+
+Figure 2: The FID-CLIP Score of varying w, v and C.
+
+<span id="page-7-0"></span>Table 2: The results of varying the middle points on the MS-COCO validation set. Here v = 0.5, C = Call.
+
+| Middle points | FID ↓ | CLIP Score (%)↑ |
+|---------------|-------|-----------------|
+| m = 0.5       | 15.59 | 26.02           |
+| m = 0.8       | 15.58 | 26.28           |
+| m = 0.9       | 15.54 | 26.27           |
+| m = 1.05      | 15.47 | 26.31           |
+| m = 1.1       | 15.42 | 26.30           |
+| m = 1.2       | 15.43 | 26.28           |
+
+#### 6.1.1 VARYING THE GUIDANCE STRENGTH AND THE SPACE OF CONDITION
+
+Here we experimentally validate the first primary claim in this paper: that second-order ICFG can improve the balance between FID and CLIP Score. By varying the guidance strength and space of condition, We determine that the optimal balance between FID and CLIP Score is achieved at w = 2.0, v = 0.25. The best w is the same as many other diffusion models [\(Bao et al.,](#page-9-13) [2023b\)](#page-9-13) Beyond this point, we observe a discernible trade-off between FID and CLIP Score as w increases. In the condition space Call, we note the presence of a trade-off between FID and CLIP Score as v increases. However, such a trade-off is not evident in the conditional space Cnouns. Additionally, we observe that while the best FID score is obtained in Cnouns, a superior balance between FID and CLIP Score is achieved in Call. This finding suggests that the condition space Call exhibits a more favorable "cone" structure for processing.
+
+#### 6.1.2 VARYING THE MIDDLE POINTS
+
+One of the key hyperparameters in the second-order ICFG is the selection of middle point, which is utilized to estimate the second-order term. Two primary factors influence the outcome in this regard. Firstly, if the chosen points are too close to each other, the estimated second-order term fails to capture long-term changes adequately. Secondly, if the middle points are relatively distant from either 0 or 1, the model struggles to estimate the corresponding score. The observed "U" shape of the FID results presented in Table [2](#page-7-0) serves to validate our analysis.
+
+#### 6.1.3 VARYING THE NUMBER OF SAMPLING STEPS
+
+The number of sampling steps also influences the quality of the generated samples. We have observed that the CLIP Score remains relatively stable across different numbers of sampling steps, while the FID score improves as the number of sampling steps increases. This suggests that the sample quality improves with an increase in the number of sampling steps. However, it is worth
+
+<span id="page-8-0"></span>
+
+| Table 3: The results | of varving the san | ipling steps on the M | IS-COCO validation set. |
+|----------------------|--------------------|-----------------------|-------------------------|
+|                      |                    |                       |                         |
+
+| Model&Settings | FID ↓               | CLIP Score (%)↑                                            |
+|----------------|---------------------|------------------------------------------------------------|
+| Ours           | $\mathcal{C} =$     | $\overline{\mathcal{C}_{\rm all}/\mathcal{C}_{\rm nouns}}$ |
+| T = 10         | 15.80/15.86         | 26.13/25.87                                                |
+| T = 20         | 15.39/15.40         | <b>26.15</b> /25.86                                        |
+| T = 30         | 15.29/15.28         | 26.13/25.86                                                |
+| T = 40         | 15.29/15.23         | 26.11/25.86                                                |
+| T = 50         | 15.28/ <b>15.22</b> | 26.11/25.86                                                |
+
+noting that even with a small number of sampling steps, the initial matching degree between the generated text and the image is already quite good.
+
+#### 6.2 Few-shot fine-tuning for Stable Diffusion
+
+To validate the efficacy of our training algorithm, we employ a fine-tuning process on the pretrained Stable Diffusion v1.5 model using Algorithm 1. We then compare the outcomes with those obtained through traditional fine-tuning. By generating cases with varying inner  $\beta$  values, we aim to assess the capacity of the model to capture the inherent "cone" structure of  $\mathcal{C}$ . The results, presented in the Appendix E, demonstrate that our training algorithm yields improved tolerance when coupled with more substantial inner guidance.
+
+#### 7 DISCUSSION
+
+ICFG offers a novel perspective for comprehending CFG and can be seen as an extension of CFG. One significant advantage of our ICFG approach is its simplicity in implementation. Furthermore, integrating second-order ICFG into complex conditions in trained diffusion models is straightforward, involving adding a few lines of code. By selecting a suitable space to exploit continuity, we can effectively implement second-order ICFG. In cases where the condition space  $\mathcal C$  exhibits a well-defined structure, extending the second-order ICFG to higher-order ICFG becomes feasible.
+
+We also offer an intuitive explanation of how the Taylor expansion operates. When we extend the CFG to a higher-order Taylor expansion of ICFG, the corresponding enhanced transition kernel  $\overline{q}_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c})$  gradually aligns with the original transition kernel more smoothly. In simpler terms, the enhanced transition kernel  $\overline{q}_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c})$  becomes increasingly similar to the original transition kernel  $q_{0t}^{\theta}(\mathbf{x}_t|\mathbf{x}_0)$ . This explains why the second-order ICFG can enhance the FID and CLIP Score balance.
+
+Despite its advantages, ICFG also has a few potential disadvantages. Firstly, the training policy of ICFG relies on more precise data pairs to accurately capture the guidance strength during training. However, this requirement can be alleviated by incorporating the similarity function  $r(\mathbf{x}, \mathbf{c})$ . Secondly, the second-order ICFG necessitates three forward passes of the diffusion model to estimate the second-order term, which can lead to increased sampling time. Nevertheless, this issue can be mitigated by reusing the points for the pre-order term, thereby reducing the computational overhead.
+
+#### 8 Conclusion
+
+We introduce ICFG, a novel perspective on CFG. ICFG is an extension of CFG and can be readily implemented in training and sampling processes. We further propose the Taylor expansion of ICFG and analyze its convergence properties. By incorporating second-order ICFG, we mitigate the mismatch issue in the diffusion process that arises from CFG. Through our experiments on Stable Diffusion, we validate the efficacy of our second-order approach. In future work, we intend to investigate higher-order ICFG and anticipate further investigations into the application of ICFG in a wide array of diffusion models across diverse data modalities.
+
+## 9 ACKNOWLEDGEMENTS
+
+This work is supported by the National Key R&D Program of China under Grant No.2021QY1500.
+
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+
+#### <span id="page-11-0"></span>A PROOF OF THEOREM 3.1 AND COROLLARY 3.1.1
+
+#### A.1 Proof of Theorem 3.1
+
+*Proof.* Firstly, we ignore the symbol  $\theta$ . Classifier guidance and CFG with guidance strength w have the following enhanced conditional probability:
+
+$$\overline{q}(\mathbf{x}_t|\mathbf{c}) = \frac{1}{Z_t} q(\mathbf{x}_t) q(\mathbf{c}|\mathbf{x}_t)^{w+1}, \tag{15}$$
+
+where  $Z_t = \int q(\mathbf{x}_t)q(\mathbf{c}|\mathbf{x}_t)^{w+1}d\mathbf{x}_t$ .
+
+Suppose the enhanced transition kernel  $\overline{q}_{0t}(\mathbf{x}_t|\mathbf{x}_0,\mathbf{c})$  equals the original transition kernel  $q_{0t}(\mathbf{x}_t|\mathbf{x}_0)$ , we have:
+
+$$\overline{q}_{t}(\mathbf{x}_{t}|\mathbf{c}) = \int \overline{q}_{0t}(\mathbf{x}_{t}|\mathbf{x}_{0}, \mathbf{c})\overline{q}_{0}(\mathbf{x}_{0}|\mathbf{c})d\mathbf{x}_{0} 
+= \int q_{0t}(\mathbf{x}_{t}|\mathbf{x}_{0})\overline{q}_{0}(\mathbf{x}_{0}|\mathbf{c})d\mathbf{x}_{0} 
+= \frac{1}{Z_{0}} \int q_{0t}(\mathbf{x}_{t}|\mathbf{x}_{0})q_{0}(\mathbf{x}_{0})q(\mathbf{c}|\mathbf{x}_{0})^{w+1}d\mathbf{x}_{0} 
+= \frac{1}{Z_{0}} \int q(\mathbf{x}_{t}, \mathbf{x}_{0})q(\mathbf{c}|\mathbf{x}_{0})^{w+1}d\mathbf{x}_{0} 
+= \frac{1}{Z_{0}} q(\mathbf{x}_{t}) \int q(\mathbf{x}_{0}|\mathbf{x}_{t})q(\mathbf{c}|\mathbf{x}_{0})^{w+1}d\mathbf{x}_{0} 
+= \frac{1}{Z_{t}} q(\mathbf{x}_{t})q(\mathbf{c}|\mathbf{x}_{t})^{w+1}.$$
+(16)
+
+Because  $q(\mathbf{c}|\mathbf{x}_t) = \int q(\mathbf{x}_0|\mathbf{x}_t)q(\mathbf{c}|\mathbf{x}_0)d\mathbf{x}_0$ . We take the last two terms and then get the following equation:
+
+<span id="page-11-1"></span>
+$$\frac{1}{Z_0} \int q(\mathbf{x}_0|\mathbf{x}_t) q(\mathbf{c}|\mathbf{x}_0)^{w+1} d\mathbf{x}_0 = \frac{1}{Z_t} \left[ \int q(\mathbf{x}_0|\mathbf{x}_t) q(\mathbf{c}|\mathbf{x}_0) d\mathbf{x}_0 \right]^{w+1} .$$
+
+$$\Leftrightarrow \frac{\int q(\mathbf{x}_0|\mathbf{x}_t) q(\mathbf{c}|\mathbf{x}_0)^{w+1} d\mathbf{x}_0}{\left[ \int q(\mathbf{x}_0|\mathbf{x}_t) q(\mathbf{c}|\mathbf{x}_0) d\mathbf{x}_0 \right]^{w+1}} = \frac{Z_0}{Z_t}$$
+
+$$\Leftrightarrow \frac{\mathbb{E}_{\mathbf{x}_0 \sim q(\mathbf{x}_0|\mathbf{x}_t)} q(\mathbf{c}|\mathbf{x}_0)^{w+1}}{\left[ \mathbb{E}_{\mathbf{x}_0 \sim q(\mathbf{x}_0|\mathbf{x}_t)} q(\mathbf{c}|\mathbf{x}_0) \right]^{w+1}} = \frac{Z_0}{Z_t}.$$
+(17)
+
+To enhance clarity, let's consider a straightforward scenario. Suppose  $\mathbf{x}_0$  comprises only  $\mathbf{x}_0^1$  with label  $\mathbf{c}^1$  and  $\mathbf{x}_0^2$  with label  $\mathbf{c}^2$ . Given  $\mathbf{c} = \mathbf{c}^1$ , the left side of Eq. (17) is as follows:
+
+$$L = \frac{\frac{1}{e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} + e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{2}\|^{2}/(\beta_{t}^{2})}}{\left[\frac{1}{e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} \left(e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} q(\mathbf{c}^{1}|\mathbf{x}_{0}^{1})^{w+1} + e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{2}\|^{2}/(\beta_{t}^{2})} q(\mathbf{c}^{1}|\mathbf{x}_{0}^{2})^{w+1}\right)}}$$
+
+$$= \frac{\frac{1}{e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} + e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{2}\|^{2}/(\beta_{t}^{2})}}}{\left[\frac{1}{e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} + e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{2}\|^{2}/(\beta_{t}^{2})}}}{\left(e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} \times 1 + e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{2}\|^{2}/(\beta_{t}^{2})} \times 0\right)}\right]^{w+1}}$$
+
+$$= \left[\frac{1}{e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} + e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{2}\|^{2}/(\beta_{t}^{2})}}}{e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})}}\right]^{w}},$$
+
+$$(18)$$
+
+which is a function of  $x_t$ .
+
+For a more general situation: We have N data pairs  $(\mathbf{x}_0^i, \mathbf{c}^i)$ . Given  $\mathbf{c} = \mathbf{c}^1$ , then the left side of Eq. (17) is
+
+$$L = \frac{\frac{1}{\sum_{i=1}^{N} e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{i}\|^{2}/(\beta_{t}^{2})}} \left(\sum_{i=1}^{N} e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{i}\|^{2}/(\beta_{t}^{2})} q(\mathbf{c}^{1} | \mathbf{x}_{0}^{i})^{w+1}\right)}{\left[\frac{1}{\sum_{i=1}^{N} e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{i}\|^{2}/(\beta_{t}^{2})}} \left(\sum_{i=1}^{N} e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{i}\|^{2}/(\beta_{t}^{2})} q(\mathbf{c}^{1} | \mathbf{x}_{0}^{i})^{w+1}\right)\right]^{w+1}}$$
+
+$$= \frac{\frac{1}{\sum_{i=1}^{N} e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{i}\|^{2}/(\beta_{t}^{2})}} \left(e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} \times 1\right)}{\left[\frac{1}{\sum_{i=1}^{N} e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{i}\|^{2}/(\beta_{t}^{2})}} \left(e^{-\|\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})} \times 1\right)\right]^{w+1}}$$
+
+$$= \left[\frac{\sum_{i=1}^{N} e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{i}\|^{2}/(\beta_{t}^{2})}}{e^{\|-\mathbf{x}_{t} - \alpha_{t} \mathbf{x}_{0}^{1}\|^{2}/(\beta_{t}^{2})}}\right]^{w}.$$
+(19)
+
+And the radio of two enhanced intermediate distributions is
+
+$$\frac{Z_t}{Z_0} \left[ \frac{\sum_{i=1}^N e^{\|-\mathbf{x}_t - \alpha_t \mathbf{x}_0^i\|^2 / (\beta_t^2)}}{e^{\|-\mathbf{x}_t - \alpha_t \mathbf{x}_0^1\|^2 / (\beta_t^2)}} \right]^w . \tag{20}$$
+
+Then reconsider the context of Eq. (17), it is observed that the equation does not maintain universal validity. A contradiction between the two sides becomes apparent, as the left side is a function of the stochastic variable  $\mathbf{x}_t$ , while the right side remains a constant. However, it is easy to check the equation holds when w=0, because when w=0, the left side and the right side of the last line of Eq. (17) are 1.
+
+We specifically discuss the case of  $q(\mathbf{x}_0|\mathbf{x}_t)$  being a  $\delta$  distribution because  $q(\mathbf{x}_0|\mathbf{x}_t) = \frac{e^{-\|\mathbf{x}_t - \alpha_t \mathbf{x}_0\|^2}}{\int e^{-\|\mathbf{x}_t - \alpha_t \mathbf{x}_0\|^2} \mathrm{d}\mathbf{x}_0}$ , which approaches an approximation of a  $\delta$  distribution when t is small or when the values of  $\mathbf{x}_0$  are highly sparse.
+
+#### A.2 PROOF OF COROLLARY 3.1.1
+
+*Proof.* In this case, we have:
+
+$$\overline{q}(\mathbf{x}_t|\mathbf{c}) = q(\mathbf{x}_t|\beta, \mathbf{c}) 
+= q(\mathbf{x}_t|\beta\mathbf{c}).$$
+(21)
+
+Treat the  $\beta c$  as an entire  $\bar{c}$ , which is a special case of w = 0 in Theorem 3.1.
+
+#### <span id="page-12-0"></span>B Proof of Theorem 4.1
+
+*Proof.* Consider the Lagrange form of  $R_n(\beta)$ :
+
+$$R_k(\beta) = \frac{\frac{\partial^{k+1} \varepsilon^{\theta}(\mathbf{x}_t | \beta \mathbf{c})}{\partial \beta^{k+1}} \Big|_{\beta = \xi}}{(k+1)!} (\beta - 1)^{k+1}, \tag{22}$$
+
+where  $\xi \in [0, \beta]$ . Then we can get the upper bound of  $||R_n(\beta)||$ :
+
+<span id="page-12-1"></span>
+$$||R_n(\beta)|| \le \frac{M_{n+1}}{(n+1)!} (B-1)^{n+1}$$
+
+$$\le \frac{M_{n+1}}{(n+1)!} B^{n+1}.$$
+(23)
+
+To establish a more relaxed condition for the convergence of the sequence  $\{M_n \mid n \in \mathbb{N}\}$ , we utilize Stirling's formula in Eq. (23) to obtain:
+
+$$\frac{M_{n+1}}{(n+1)!}B^{n+1} \sim \frac{M_{n+1}}{\sqrt{n+1}} \left[ \frac{eB}{n+1} \right]^{n+1},\tag{24}$$
+
+which indicates when  $n \to +\infty$ , the sequence  $\{R_n(\beta) \mid n \in \mathbb{N}\}\$  converges to 0 if
+
+$$M_{n+1} \sim o\left(\sqrt{n+1}\left[\frac{n+1}{eB}\right]^{n+1}\right).$$
+
+## <span id="page-13-1"></span>C THE UNIQUENESS OF THE SECOND-ORDER TERM
+
+*Proof.* When we use  $\frac{y_2-y_1}{x_2-x_1}$  of two points  $(x_1,y_1),(x_2,y_2)$  to estimate the gradient at  $\frac{x_1+x_2}{2}$ , For three data pairs  $(x_0,y_0),(x_1,y_1),(x_2,y_2)$ , where  $(x_1-x_0)(x_2-x_1)(x_0-x_2)\neq 0$ , no matter how we organize them, the estimated second-order gradient is uniquely determined as:
+
+$$2\frac{x_0y_2 + x_1y_0 + x_2y_1 - x_0y_1 - x_1y_2 - x_2y_0}{(x_1 - x_0)(x_2 - x_1)(x_0 - x_2)}.$$
+
+Let us define  $x_0 = 0$ ,  $x_1 = m$ , and  $x_2 = 1$ . With these values, we can proceed to estimate the second-order gradient, which is given by:
+
+$$\frac{2}{m(1-m)}((1-m)y_0+my_2-y_1).$$
+
+#### <span id="page-13-0"></span>D IMPLEMENTATION DETAILS
+
+#### D.1 THE CONDITION SPACE $\mathcal{C}$
+
+In this paper, we have designed two "cone" structures for the conditions of Stable Diffusion. All two kinds C are extended from the tensors after CLIP model, whose dimension is  $77 \times 768$ .
+
+- $\mathcal{C}_{all}$ : We use the pretrained CLIP model to extract the text embedding  $\mathbf{c}_{text}$  of the captions. We also get the extract embedding  $\mathbf{c}_{\varnothing}$  of empty caption, then with the inner coefficient  $\beta$ , we get the enhanced embedding  $\mathbf{c}_{\varnothing} + \beta(\mathbf{c}_{text} \mathbf{c}_{\varnothing})$
+- $\mathcal{C}_{nouns}$ : We utilize the pretrained CLIP model to extract the text embedding  $\mathbf{c}_{text}$  from the captions. Additionally, we obtain the embedding  $\mathbf{c}_{\varnothing}$  for an empty caption. By incorporating the inner coefficient  $\beta$  and the indicator function  $\mathbf{1}_{nouns}$ , we can modify the embedding. Specifically, we set the values corresponding to the positions of nouns to 1 in  $\mathbf{1}_{nouns}$ , while the remaining values are set to 0. The resulting enhanced embedding is given by  $\mathbf{c}_{\varnothing} + \beta \mathbf{1}_{nouns}(\mathbf{c}_{text} \mathbf{c}_{\varnothing})$ .
+
+#### D.2 DETAILS OF FIN-TUNING PROCESS
+
+We set rank = 4 and apply the Low-Rank Adaptation (Hu et al., 2022; Ruiz et al., 2023) to modify the attention layers of the U-Net (Ronneberger et al., 2015) of Stable Diffusion v1.5 (Rombach et al., 2022). We use the Adam optimizer with a learning rate of 1e - 4 and a batch size of 8. We fine-tune the model for 300 epochs on a small part of MS-COCO (Lin et al., 2014) dataset, which contains 30 images and their corresponding captions. We use the pretrained Stable Diffusion v1.5 model as the initialization of the U-Net. We compare our fine-tuning policy with default fine-tuning policy.
+
+#### <span id="page-13-2"></span>E SAMPLES AFTER FINE-TUNING
+
+After the fine-tuning process, we proceed to compare the samples generated using different training policies. The corresponding results are presented in Figure 3 and Figure 4. Each sample is generated with the caption "a brown and white giraffe in a field of grass" and arranged from left to right, with values of inner  $\beta$  set to 1.0, 1.2, 1.4, and 1.6. Notably, our training policy demonstrates superior performance compared to the default training policy when  $\beta$  assumes relatively larger values. This observation suggests that our training policy effectively captures the inherent "cone" structure of  $\mathcal{C}$ .
+
+![](figures/_page_14_Picture_1.jpeg)
+
+Figure 3: Generated images of different inner β of our training policy.
+
+<span id="page-14-1"></span><span id="page-14-0"></span>![](figures/_page_14_Picture_3.jpeg)
+
+Figure 4: Generated images of different inner β of default training policy.
+
+<span id="page-15-0"></span>Table 4: FID results on U-ViT of CFG and ICFG.
+
+| Steps | 5w                                                                                       | 10w | 15w | 20w |  |  |  |  | 25w 30w 35w 40w 45w 50w 55w 60w 65w 70w 75w 80w |  |  |
+|-------|------------------------------------------------------------------------------------------|-----|-----|-----|--|--|--|--|-------------------------------------------------|--|--|
+|       | CFG 34.23 13.64 11.26 10.38 9.78 8.98 8.98 8.76 8.58 8.52 8.37 8.37 8.27 8.32 8.39 8.10  |     |     |     |  |  |  |  |                                                 |  |  |
+|       | ICFG 24.69 13.51 11.00 10.13 9.69 9.09 8.82 8.68 8.54 8.41 8.35 8.21 8.29 8.15 8.10 7.92 |     |     |     |  |  |  |  |                                                 |  |  |
+
+<span id="page-15-1"></span>Table 5: Experiments about the speedup.
+
+| Method                 | Time (seconds) | Extra Time | U-Net Computation | FID   | CLIP Score |
+|------------------------|----------------|------------|-------------------|-------|------------|
+| CFG                    | 10.43 ± 0.23   | 0%         | 100%              | 15.42 | 25.80      |
+| 2nd-order ICFG         | 15.01 ± 0.31   | 43.91%     | 150%              | 15.28 | 26.11      |
+| 0.2-0.8 2nd-order ICFG | 13.17 ± 0.26   | 26.27%     | 130%              | 15.29 | 26.03      |
+
+## F VISUAL RESULTS COMPARISON
+
+We conducted a comparison between CFG and second-order ICFG with w = 5.0 and v = 0.25. The visual comparisons are presented in Figure [5.](#page-16-0) It is evident from the images that second-order ICFG outperforms CFG, producing images with better-rendered hands and closer alignment to the provided prompts.
+
+## G EXPERIMENTS ON ANOTHER FRAMEWORK
+
+we train another framework, U-ViT [\(Bao et al.,](#page-9-14) [2023a\)](#page-9-14), with a resolution of 256x256 on the COCO dataset from scratch to fully explore the capabilities of our ICFG. The FID results are listed in Table [4.](#page-15-0)
+
+## H EXPERIMENTS ABOUT THE SPEEDUP
+
+We conducted our experiments on an NVIDIA GeForce RTX 3090, using a batch size of 4. We performed 100 samplings to calculate the timings and utilized 10,000 images for the computation of FID and CLIP scores, The results are shown in Table [5.](#page-15-1)
+
+We have the following findings.
+
+- Due to the text encoder and VAE decoder, the real-time consumption of the 2nd-order ICFG is less than the estimated extra computation of the U-Net.
+- Through a preliminary selection of key timesteps (0.2-0.8) for applying the 2nd-order ICFG, we achieve nearly full FID benefits and a 74% improvement in CLIP scores, with a reduced extra inference time of 26.27%. We anticipate further enhancements in extra inference time by refining the selection of key timesteps.
+
+![](figures/_page_16_Figure_1.jpeg)
+
+<span id="page-16-0"></span>Figure 5: The generated images presented here compare the outputs of CFG and second-order ICFG with w = 5.0 and v = 0.25, utilizing the model anything-v4.0 (https://huggingface.co/xynai/anything-v4.0). In the first two rows, it is evident that our second-order ICFG produces superior results in hand generation. In the last row, our second-order ICFG generates images that align more closely with the provided prompts.

papers/0QAzIMq32X/review.json

@@ -0,0 +1,91 @@
+{
+  "id": "0QAzIMq32X",
+  "title": "Inner Classifier-Free Guidance and Its Taylor Expansion for Diffusion Models",
+  "decision": "Accept",
+  "reviews": [
+    {
+      "id": "0JDy5bGcUt",
+      "rating": 5,
+      "content": {
+        "summary": "This work presents a new perspective on classifier-free guidance (CFG) for diffusion models imposing specific assumptions on the space of condition. Assuming that the condition space has a cone structure, the previous CFG can be seen as the first-order Taylor expansion of the proposed ICFG, and this work further presents a second-order ICFG that improves the Stable Diffusion model.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "- The observation that there exists a mismatch between the transition distribution of the original forward process and the conditional forward process is new to the best of my knowledge. \n\n- The idea that the mismatch is alleviated when assuming that the condition space has a cone structure is interesting.",
+        "weaknesses": "- The contribution of the proposed ICFG is not clear: Although the authors state that the second-order ICFG introduces new valuable information, it is not clear which additional information it provides, and further the experimental results show a marginal improvement over previous CFG, e.g., FID improvement from 15.42 (CFG) to 15.22 (ICFG) and CLIP Score from 26.45 (CFG) to 26.86 (ICFG), on only single dataset (MS-COCO). Especially, ICFG does not seem to provide an improved balance between FID and CLIP Score. What is the main reason we should use ICFG instead of CFG?\n\n- As the main motivation of this work is the mismatch between the transition kernels (in Theorem 3.1), this should be further analyzed, for example, how much difference in these kernels and how much it affects the generation quality. The proposed method should be evaluated after these validations.\n\n- The assumptions (Assumptions 3.1 and 4.1) made to achieve the proposed method do not seem realistic and were not verified in the experiments.",
+        "questions": "- What is the main reason we should use ICFG instead of CFG?\n\n- How much does the enhanced transition kernel deviate from the original transition kernel (as in Theorem 3.1?) How much does the deviation affect the generation quality?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " - The contribution of the proposed ICFG is not clear: Although the authors state that the second-order ICFG introduces new valuable information, it is not clear which additional information it provides, and further the experimental results show a marginal improvement over previous CFG, e.g., FID improvement from 15.42 (CFG) to 15.22 (ICFG) and CLIP Score from 26.45 (CFG) to 26.86 (ICFG), on only single dataset (MS-COCO). Especially, ICFG does not seem to provide an improved balance between FID and CLIP Score. What is the main reason we should use ICFG instead of CFG?\n\n- As the main motivation of this work is the mismatch between the transition kernels (in Theorem 3.1), this should be further analyzed, for example, how much difference in these kernels and how much it affects the generation quality. The proposed method should be evaluated after these validations.\n\n- The assumptions (Assumptions 3.1 and 4.1) made to achieve the proposed method do not seem realistic and were not verified in the experiments.",
+        "suggestions": "The paper introduces an interesting perspective on classifier-free guidance (CFG) by framing it as a first-order Taylor expansion within a cone-structured condition space, and further proposes a second-order extension (ICFG). However, the experimental validation of ICFG's advantages remains limited. The reported improvements in FID and CLIP scores are marginal, and the paper lacks a clear explanation of the specific additional information provided by the second-order term. To strengthen the claims, the authors should provide a more detailed analysis of the enhanced intermediate distributions, showing how the second-order term leads to more consistent distributions across different time steps. Furthermore, the experiments should include a more comprehensive comparison of CFG and ICFG under various conditions, including different guidance strengths and datasets. It is essential to demonstrate that ICFG consistently outperforms CFG, not just in isolated cases.\n\nTo address the concerns regarding the mismatch between transition kernels, the authors should provide a more thorough analysis of the differences between the original and conditional forward processes. This should include a quantitative assessment of the deviation between the transition kernels, as well as an analysis of how this deviation affects the generation quality. The theoretical analysis should be complemented by empirical evidence, for example, by visualizing the enhanced intermediate distributions and quantifying the differences between them. It is also important to clarify the practical implications of the cone assumption. The authors should explain how the condition space is extended to form a cone and provide evidence that the score predictor can adapt to this extended space. The experiments should include a validation of the cone assumption, showing that the proposed method works well within the assumed structure.\n\nFinally, the authors should avoid overclaiming the benefits of ICFG. The current experimental results do not show a clear and consistent improvement over CFG, and the authors should acknowledge the limitations of their approach. The paper should also include a more detailed discussion of the limitations of the assumptions made to achieve the proposed method. It is important to provide a more realistic perspective on the applicability of the method and to avoid making claims that are not supported by the experimental results. The authors should also consider comparing their method with other existing approaches for improving diffusion models, to better contextualize the contribution of their work."
+      }
+    },
+    {
+      "id": "RMV9cTzYc7",
+      "rating": 8,
+      "content": {
+        "summary": "This paper generalizes CFG for diffusion model guidance by adapting the guidance strength according to the relevance between the condition and a given sample. Conditions more relevant to a sample require weaker guidance strength.",
+        "soundness": "4 excellent",
+        "presentation": "4 excellent",
+        "contribution": "3 good",
+        "strengths": "The paper identifies an issue with the deviating SDE when guidance is added and proposes a solution with clearly defined assumptions. The paper strikes a good balance between theoretical analysis and empirical results. The theories are relevant to the technique and justify the design choice. Extensive ablation studies on hyperparameters of the method yield insight to the adoption of the technique in practice.",
+        "weaknesses": "**Cone assumption**\n\nIt seems like the key point of ICFG working is for the conditional space to be a cone. Is there any method to check whether a conditional space is a cone beforehand for practioners to decide whether ICFG should be adopted? Are there any metrics for characterizing how cone-shaped a conditional space is?\n\n**Algorithm 3 relaxing 2nd order term**\n\nThe relaxation of the 2nd order term is concerning. The argument for ICFG with 2nd order Tayler Expansion working better than typical CFG is the additional information provided by the 2nd order term. However, if an additional hyperparmeter is introduced and optimized over, does this argument still hold? Does the performance gain of ICFG truly come from the 2nd order information or is it the mere additional of another tuning knob $v$?\n\n**3 forward passes for naive 2nd order ICFG implementation**\n\nThe last paragraph of the discussion section mentions one major drawback of 2nd-order ICFG, which would require 3 forward passes to estimate the 2nd order term. The authors mention a solution of \"reusing the points for the pre-order term\". Elaboration on how exactly this can be done is crucial for actual adoption of this technique. Paying a computation penalty of 3 forward passes is definitely not feasible. The authors should also compare theoretically and/or empirically how this approximation would affect the efficacy of ICFG.",
+        "questions": "(see weaknesses)\n\nWilling to increase score if issues are adequately handled.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " \n**Cone assumption**\n\nIt seems like the key point of ICFG working is for the conditional space to be a cone. Is there any method to check whether a conditional space is a cone beforehand for practioners to decide whether ICFG should be adopted? Are there any metrics for characterizing how cone-shaped a conditional space is?\n\n**Algorithm 3 relaxing 2nd order term**\n\nThe relaxation of the 2nd order term is concerning. The argument for ICFG with 2nd order Tayler Expansion working better than typical CFG is the additional information provided by the 2nd order term. However, if an additional hyperparmeter is introduced and optimized over, does this argument still hold? Does the performance gain of ICFG truly come from the 2nd order information or is it the mere additional of another tuning knob $v$?\n\n**3 forward passes for naive 2nd order ICFG implementation**\n\nThe last paragraph of the discussion section mentions one major drawback of 2nd-order ICFG, which would require 3 forward passes to estimate the 2nd order term. The authors mention a solution of \"reusing the points for the pre-order term\". Elaboration on how exactly this can be done is crucial for actual adoption of this technique. Paying a computation penalty of 3 forward passes is definitely not feasible. The authors should also compare theoretically and/or empirically how this approximation would affect the efficacy of ICFG.\n",
+        "suggestions": "The paper introduces an interesting approach to diffusion model guidance by adapting the guidance strength based on the relevance between the condition and the sample. While the theoretical analysis is sound, some practical aspects of the proposed method require further clarification. Specifically, the cone assumption, while theoretically motivated, lacks a clear method for practitioners to verify its applicability to their specific conditional spaces. A more concrete example, such as the CLIP embedding space, should be included early in the paper to illustrate how this assumption is met in practice. Furthermore, the paper should provide a more detailed discussion on how to assess the suitability of a given conditional space for the cone assumption, possibly by introducing metrics that quantify the 'cone-shapedness' of the space. This would greatly improve the practical usability of the proposed method.\n\nThe introduction of the hyperparameter $v$ in Algorithm 3 raises questions about the true source of performance gains. While the authors argue that the second-order term provides crucial directional information, the need for a tunable parameter to scale this term suggests that the raw second-order estimate might not be reliable. The paper should include a more thorough analysis of the sensitivity of the method to the choice of $v$, possibly through a sweep of values. This would help to determine if the performance improvement is genuinely due to the second-order information or simply the result of adding another degree of freedom to the model. Furthermore, a heuristic for selecting a good value of $v$ would be beneficial for practitioners.\n\nFinally, the computational cost of the 2nd-order ICFG is a significant concern. While the authors mention reusing points to reduce the number of forward passes, a more detailed explanation of this process is needed. The paper should provide a clear algorithm or pseudocode illustrating how the points are reused and how this affects the accuracy of the second-order estimate. Additionally, the suggested approach of applying the 2nd-order ICFG only during key timesteps needs empirical validation. The authors should provide experimental results demonstrating the efficacy of this approach and quantify the resulting speedup in practice. Without these details, the practical feasibility of the method remains questionable."
+      }
+    },
+    {
+      "id": "xkqbvcRjXN",
+      "rating": 6,
+      "content": {
+        "summary": "This paper presents a generalized version of classifier-free guidance (CFG), i.e., inner classifier-free guidance. By exploiting the continuity of the generation condition, the author propose an interesting taylor expansion formulation to interpret CFG, where the classic CFG is viewed as the first order case of the proposed formulation. Given such novel formulation, the author proposed higher order version of CFG to achieve better image generation results.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "1. The proposed formulation is novel and insightful.\n2. The paper is easy-to-follow.\n3. The hyper-parameters introduced by the method is well-studied.",
+        "weaknesses": "1) In the reviewer's viewpoint, the major weakness of the current submission is that the empirical validation is not sufficient. More qualitative results should be provided to justify the effectiveness of the method. One example is that it would be better if the provided qualitative samples could corroborate with the numerical experimental results. Another example is that the author could provided some examples showing that ICFG can resolve some of the well-known failure cases of Stable Diffusion.\n\n2) In addition, it would be good to show the effectiveness of ICFG on other fine-tuned variation of Stable Diffusion such as anything-V4 (https://huggingface.co/xyn-ai/anything-v4.0), etc.",
+        "questions": "1. Is the few-shot training of ICFG on a small dataset generalizable to large scale setting? For example, as I understand, in this work, the authors trained with the ICFG policy on COCO dataset. I was wondering if this trained LoRA is readily available for generation beyond COCO dataset (e.g., on laion-level dataset)?\n\n2. Is the proposed ICFG applicable on other fine-tuned variation of Stable Diffusion such as anything-V4 (https://huggingface.co/xyn-ai/anything-v4.0), etc.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1) In the reviewer's viewpoint, the major weakness of the current submission is that the empirical validation is not sufficient. More qualitative results should be provided to justify the effectiveness of the method. One example is that it would be better if the provided qualitative samples could corroborate with the numerical experimental results. Another example is that the author could provided some examples showing that ICFG can resolve some of the well-known failure cases of Stable Diffusion.\n\n2) In addition, it would be good to show the effectiveness of ICFG on other fine-tuned variation of Stable Diffusion such as anything-V4 (https://huggingface.co/xyn-ai/anything-v4.0), etc.",
+        "suggestions": "The paper introduces an interesting Taylor expansion formulation for classifier-free guidance (CFG), which is a novel perspective. However, the empirical validation needs to be significantly strengthened to fully support the claims. Specifically, the qualitative results should be more comprehensive and directly linked to the quantitative findings. For instance, if the numerical results show a specific improvement in FID or CLIP score, the qualitative samples should visually demonstrate this improvement, perhaps by showing side-by-side comparisons of images generated with and without the proposed higher-order guidance. Furthermore, it would be beneficial to showcase examples where the proposed method addresses known failure modes of Stable Diffusion, such as distorted faces or unnatural object interactions. This would provide more compelling evidence of the practical advantages of the proposed approach.\n\nTo further enhance the empirical evaluation, the authors should explore the performance of their method on a wider range of fine-tuned Stable Diffusion models, not just the base model. Given the popularity of models like anything-V4, it is crucial to demonstrate that the proposed method is not only effective on the base model but also generalizable to other fine-tuned variations. This would involve not only reporting quantitative metrics like CLIP scores but also providing qualitative examples that showcase the visual quality and prompt alignment on these different models. It would be particularly insightful to see if the higher-order guidance can address specific issues that arise in these fine-tuned models, such as style transfer or specific object generation. This would provide a more robust and comprehensive evaluation of the method's applicability.\n\nFinally, the paper should include a more detailed analysis of the computational cost associated with the proposed higher-order guidance. While the paper mentions the hyper-parameters, it does not discuss the computational overhead of computing the higher-order terms. It would be valuable to include a comparison of the computational cost of the proposed method with the standard CFG, including the time required for both training and inference. This analysis should also consider the impact of different hyper-parameter settings on the computational cost. Such an analysis would provide a more complete picture of the practical trade-offs associated with the proposed method and would help practitioners make informed decisions about its applicability in real-world scenarios."
+      }
+    },
+    {
+      "id": "0zH6TJ4hGc",
+      "rating": 5,
+      "content": {
+        "summary": "This paper introduces an enhancement of classifier-free guidance (CFG) for diffusion models, called inner classifier-free guidance (ICFG). The paper claims that CFG can be extended to ICFG when the condition is continuous, leading to further improvements. They provide a theoretical analysis based on the condition space assumption and Taylor expansion. They present the experimental results comparing CFG and ICFG.",
+        "soundness": "1 poor",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "The idea of combining the guidance strength and condition is interesting because adjusting guidance strength is the effect of a trade-off between image fidelity and condition information.",
+        "weaknesses": "1. Concerns about the theoretical analysis in Section 3\n* In the proof of Theorem 3.1, there is doubt about the validity of the third equality in Eq. 16. It seems that it may come from Eq. 15, which might change the equality to the proportion.\n* Additionally, the relationship between the last two terms in Eq. 16 is the proportional relationship, but I'm not sure why these two terms are equal after the logarithm, as shown in Eq. 17.\n* In the proof of Theorem 3.1, it would be helpful to provide a detailed explanation of why there is a contradiction unless $w=0$ or $q(x_0|x_t)$ is a Dirac delta distribution.\n* Theorem 3.1 claims necessary and sufficient conditions, but the proof only demonstrates one direction.\n* In the paper, all cases of the enhanced intermediate distribution are denoted $\\bar{q}$. (In addition, $\\beta(x_t)$ in Eq. (12) is not defined.) This is confusing, especially for the definition $\\bar{q}(x_t|c,\\beta):=\\bar{q}(x_t|\\beta c)$.\n* In the proof of Corollary 3.1.1, it is unclear whether the first proportion holds. It seems that $q$ is modified by $\\bar{q}$. Detailed derivation and explanation would be helpful.\n\n2. Not significant experimental results\n* The quantitative results suggest that the performance gain is marginal, and this may require very careful hyperparameter tuning. It would be beneficial to include results from other datasets to assess the tuning problem.\n* The implementation of ICFG in Algorithms 2 and 3 requires three network evaluations for each timestep ($\\epsilon(z_i), \\epsilon(z_i,c), \\epsilon(z_i,mc)$), which is 1.5 times more network evaluations than CFG. Consequently, ICFG has 1.5 times higher sampling cost compared to CFG.",
+        "questions": "Please answer the questions in the Weaknesses section.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. Concerns about the theoretical analysis in Section 3\n* In the proof of Theorem 3.1, there is doubt about the validity of the third equality in Eq. 16. It seems that it may come from Eq. 15, which might change the equality to the proportion. Specifically, the transition from a joint distribution to a conditional distribution seems to be missing a normalization factor, which would change the equality to a proportionality. This needs to be explicitly addressed. \n* Additionally, the relationship between the last two terms in Eq. 16 is the proportional relationship, but I'm not sure why these two terms are equal after the logarithm, as shown in Eq. 17. The logarithm operation should not transform a proportional relationship into an equality without additional assumptions or justifications. The authors need to clarify this step. \n* In the proof of Theorem 3.1, it would be helpful to provide a detailed explanation of why there is a contradiction unless $w=0$ or $q(x_0|x_t)$ is a Dirac delta distribution. This contradiction is not immediately obvious and requires a more thorough explanation of the underlying probabilistic arguments. The current explanation is too brief.\n* Theorem 3.1 claims necessary and sufficient conditions, but the proof only demonstrates one direction. The proof needs to show both directions to fully justify the claim. The current proof is incomplete. \n* In the paper, all cases of the enhanced intermediate distribution are denoted $\\bar{q}$. (In addition, $\\beta(x_t)$ in Eq. (12) is not defined.) This is confusing, especially for the definition $\\bar{q}(x_t|c,\\beta):=\\bar{q}(x_t|\\beta c)$. The notation is inconsistent and makes it difficult to follow the mathematical derivations. The authors should use a more precise notation to avoid ambiguity. The definition of $\\beta(x_t)$ is also missing, which is crucial for understanding the formulation.\n* In the proof of Corollary 3.1.1, it is unclear whether the first proportion holds. It seems that $q$ is modified by $\\bar{q}$. Detailed derivation and explanation would be helpful. The relationship between the original distribution $q$ and the modified distribution $\\bar{q}$ needs to be clearly defined and justified. The current explanation is insufficient.\n\n2. Not significant experimental results\n* The quantitative results suggest that the performance gain is marginal, and this may require very careful hyperparameter tuning. It would be beneficial to include results from other datasets to assess the tuning problem. The current results do not strongly support the claim of significant improvement. The lack of results on diverse datasets makes it difficult to generalize the findings. \n* The implementation of ICFG in Algorithms 2 and 3 requires three network evaluations for each timestep ($\\epsilon(z_i), \\epsilon(z_i,c), \\epsilon(z_i,mc)$), which is 1.5 times more network evaluations than CFG. Consequently, ICFG has 1.5 times higher sampling cost compared to CFG. The increased computational cost is a significant drawback that needs to be addressed.",
+        "suggestions": "The theoretical analysis in Section 3 needs significant clarification and expansion. Specifically, the proof of Theorem 3.1 requires a more detailed explanation of the transition from Eq. 15 to Eq. 16, explicitly addressing the normalization factor and the change from equality to proportionality. The subsequent logarithmic transformation in Eq. 17 also needs a rigorous justification, as it is not clear why a proportional relationship becomes an equality after applying the logarithm. Furthermore, the contradiction argument in the proof needs to be elaborated upon, providing a step-by-step explanation of why the conditions must hold. The proof of Theorem 3.1 should also be completed by showing both necessary and sufficient conditions, rather than just one direction. The notation for the enhanced intermediate distribution, $\\bar{q}$, needs to be more precise, and the definition of $\\beta(x_t)$ in Eq. 12 must be explicitly provided. Finally, the derivation of Corollary 3.1.1 needs to be clarified, with a detailed explanation of the relationship between the original and modified distributions.\n\nThe experimental results need to be more robust and comprehensive. The current quantitative results show only marginal improvements, which are not convincing enough to claim a significant performance gain. The authors should include results on a wider range of datasets to demonstrate the generalizability of their method and to assess the sensitivity of the method to hyperparameter tuning. The current results are limited to a single dataset, which makes it difficult to draw any general conclusions. The authors should also provide a more detailed analysis of the hyperparameter tuning process, including the range of values explored and the impact of different settings on the performance of the method. The lack of such analysis makes it difficult to assess the practical applicability of the proposed method.\n\nFinally, the increased computational cost of ICFG compared to CFG is a major concern. The authors need to address this issue by either proposing a more efficient implementation or by demonstrating that the performance gains justify the additional cost. The current implementation requires 1.5 times more network evaluations, which is a significant overhead. The authors should explore techniques to reduce this computational burden, such as selective application of the second-order ICFG or other optimization strategies. Without addressing this computational cost, the practical value of the proposed method is limited. The authors should also provide a more detailed analysis of the computational complexity of their method and compare it with existing approaches."
+      }
+    }
+  ]
+}

papers/0SOhDO7xI0/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "0SOhDO7xI0",
+  "title": "DeepDRK: Deep Dependency Regularized Knockoff for Feature Selection",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-22",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=0SOhDO7xI0"
+}

papers/0SOhDO7xI0/review.json

@@ -0,0 +1,93 @@
+{
+  "id": "0SOhDO7xI0",
+  "title": "DeepDRK: Deep Dependency Regularized Knockoff for Feature Selection",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "tEQX45duoz",
+      "rating": 6,
+      "content": {
+        "summary": "This paper investigates the problem of feature selection from the perspective of Model-X knockoff owing to its guarantee of false discovery rate (FDR) control.  Realizing the diminished selection power caused by the swap property that knockoffs need, the authors proposed a  Deep Dependency Regularized Knockoff (DeepDRK), which is a distribution-free deep learning method that strikes a balance between FDR and power.  Experiments on synthetic, semi-synthetic, and real-world data verify the effectiveness of the proposed DeepDRK method.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1. This paper is well-written and easy to follow.\n2. This paper has a clear motivation for diminished selection power caused by the swap property that knockoffs need.\n3. Comprehensive experiments on synthetic, semi-synthetic, and real-world data are conducted, which verify the effectiveness of the proposed DeepDRK method.\n4. To me, such a distribution-free deep learning method that strikes a balance between FDR and power is new and novel.",
+        "weaknesses": "I don't see any major weakness in this work.",
+        "questions": "I have no more questions. I am not an expert in this field, but I feel this paper is good from the perspective of general machine learning.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "details_of_ethics_concerns": "No ethics review is needed.",
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "I don't see any major weakness in this work.",
+        "suggestions": "While the paper is well-written and the method seems promising, further exploration of the practical limitations and computational costs would be beneficial. Specifically, the authors should investigate the scalability of the DeepDRK method with respect to the number of features and the size of the dataset. Deep learning methods can be computationally expensive, and it is important to understand how the performance of DeepDRK degrades as the problem size increases. It would also be useful to compare the computational cost of DeepDRK with other feature selection methods, such as traditional knockoff methods or other deep learning-based feature selection techniques. This analysis would provide a more comprehensive understanding of the trade-offs between the statistical power and computational efficiency of the proposed method.\n\nFurthermore, the paper could benefit from a more detailed analysis of the hyperparameter sensitivity of the DeepDRK method. Deep learning models are often sensitive to the choice of hyperparameters, and it is important to understand how the performance of DeepDRK is affected by different hyperparameter settings. The authors should conduct a thorough sensitivity analysis to identify the key hyperparameters that have a significant impact on the performance of the method. This analysis would provide practical guidance for users on how to tune the hyperparameters of DeepDRK for optimal performance. It would also be helpful to provide some guidelines or heuristics for selecting the appropriate hyperparameters for different types of datasets. For example, the authors could investigate how the optimal hyperparameters vary with the dimensionality of the data or the level of noise.\n\nFinally, while the experiments on synthetic, semi-synthetic, and real-world data are comprehensive, it would be valuable to include a more detailed analysis of the types of datasets where DeepDRK performs particularly well or poorly. This analysis would help to identify the strengths and weaknesses of the method and provide guidance on when it is most appropriate to use DeepDRK. For example, the authors could investigate how the performance of DeepDRK varies with the correlation structure of the features or the presence of non-linear relationships between the features and the response variable. This analysis would provide a more nuanced understanding of the applicability of the proposed method and help to identify areas for future research."
+      }
+    },
+    {
+      "id": "zp8w7WbTvN",
+      "rating": 6,
+      "content": {
+        "summary": "The paper proposed “Deep Dependency Regularized Knockoff (DeepDRK)”, a distribution-free deep learning method that strikes a balance between FDR and power. It leverages transformer architecture and several loss functions for training to generate Knockoff.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1. It introduces knockoff Transformer to generate knockoff with different regularizations. And it uses multi-swappers to ensure to swap property of generated knockoff.\n2. Experimental results show the effectiveness of the proposed method compared to other deep model based knockoff methods.",
+        "weaknesses": "1. Some arguments of the proposed method is not validated with corresponding experimental results. For example, “multi-swapper” is used to better achieve swap property. But there are no experiments to justify the how swap property changes when changing from single swapper to multi-swapper. I think authors should also introduce how to empirically measure the swap property. Since the proposed method relies on regularization to enforce the swap property, which is not guaranteed by design.\n2. The proposed method uses many regularization terms. Some of the regularization terms have ablation studies, but others are not. For example, L_swapper and L_ED are not included. The effect of $\\alpha$ in Eq.~(9) is also not investigated. Moreover, there are four hyperparameters require tuning, making the proposed method hard to tune. \n3. The regularization terms largely come from existing papers; I think authors should better justify what is their contribution on top of existing papers.",
+        "questions": "Since most dataset is not very large, but the model size is quite large. Did authors try to change the model size to see how it impacts the performance? Maybe the model could be smaller.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. Some arguments of the proposed method is not validated with corresponding experimental results. For example, “multi-swapper” is used to better achieve swap property. But there are no experiments to justify the how swap property changes when changing from single swapper to multi-swapper. I think authors should also introduce how to empirically measure the swap property. Since the proposed method relies on regularization to enforce the swap property, which is not guaranteed by design.\n2. The proposed method uses many regularization terms. Some of the regularization terms have ablation studies, but others are not. For example, L_swapper and L_ED are not included. The effect of $\\alpha$ in Eq.~(9) is also not investigated. Moreover, there are four hyperparameters require tuning, making the proposed method hard to tune. \n3. The regularization terms largely come from existing papers; I think authors should better justify what is their contribution on top of existing papers.",
+        "suggestions": "The authors should provide a more rigorous analysis of the swap property achieved by their method. Specifically, they should introduce a quantitative metric to measure the degree to which the generated knockoffs satisfy the swap property. This could involve calculating the empirical probability of a feature and its knockoff being swapped in a given sample, and then averaging this probability across the dataset. Furthermore, the authors should conduct experiments to show how this swap property metric changes when using a single swapper versus multiple swappers. This would provide empirical evidence for the claim that multi-swappers are beneficial. Without this, the claim remains unsubstantiated and the reader is left to wonder if the added complexity of multi-swappers is truly necessary.\n\nRegarding the regularization terms, a more thorough ablation study is needed. The authors should systematically evaluate the impact of each regularization term, including L_swapper and L_ED, on both the swap property and the final feature selection performance (FDR and power). This should include varying the weights of each term and observing the resulting changes in performance. Furthermore, the effect of the hyperparameter $\\alpha$ in Eq.(9) needs to be investigated more thoroughly. The authors should provide a plot showing how the FDR and power change as a function of $\\alpha$. This will help the reader understand the trade-offs involved in choosing the value of $\\alpha$. The authors should also discuss the sensitivity of the method to the choice of these hyperparameters and provide guidance on how to tune them effectively. Without a clear understanding of the impact of each hyperparameter, the method may be difficult to apply in practice.\n\nFinally, the authors need to better articulate the novelty of their approach in the context of existing work. While the regularization terms may be borrowed from other papers, the authors should emphasize how they are combined and adapted for the specific task of knockoff generation. They should also clearly explain how their method differs from existing deep learning-based knockoff methods. This should include a detailed comparison of the architectural choices, loss functions, and regularization techniques used in their method versus those used in other methods. This will help the reader understand the unique contributions of their work and justify the need for a new method."
+      }
+    },
+    {
+      "id": "tWbuOUTe2U",
+      "rating": 6,
+      "content": {
+        "summary": "This paper proposes DeepDRK, a new model-X knockoff based methods which adopts a two-stage framework to generate knockoff variables. A ViT (called knockoff transformer in the paper) is trained by minimizing a swap loss plus a dependency regularization loss in the training stage, while its output is further perturb through a row-permuted version of the original covariate to reduce the dependency between knockoffs and original covaraites. Experiments on synthetic, semi-synthetic and real data demonstrates the effectiveness of DeepDRK.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "1. Writing is good and it is easy to follow\n2. The idea of leveraging distribution-free methods while avoiding overfitting is well motivated.\n3. Experiment results are impressive.",
+        "weaknesses": "1. Ablation study is not very thorough. \n- The loss in DeepDRK contains five terms, SWD, REx, cosine similarity w.r.t. swappers, SWC and the entry-wise decorrelation term. The necessity of introducing these five losses is under-explored in the paper.\n- The necessity of DRP is unclear. There lacks comparison of $\\tilde{X}_{\\theta}$ and $\\tilde{X}_{\\theta}^{DRP}$ in empirical performance.\n2. Experiments need further analysis and explanation. \n- It is clear that DeepDRK performs better than other baseline methods. But the reason has not been analyzed clearly and adding some intermediate results will be helpful. It is unclear how well the knockoffs generated by DeepDRK following the swap property and avoid overfitting compared to baseline methods.\n- The results w.r.t. the Gaussian mixture seems inconsistent with that in the original DDLK paper (DDLK performs the worst in this paper while it performs better than deep knockoffs and knockoffgan in the original paper).",
+        "questions": "To avoid overfitting, why introducing a post-training perturbation instead of modifying training strategy like early stopping or tuning hypermeters?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "details_of_ethics_concerns": "None",
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. Ablation study is not very thorough. \n- The loss in DeepDRK contains five terms, SWD, REx, cosine similarity w.r.t. swappers, SWC and the entry-wise decorrelation term. The necessity of introducing these five losses is under-explored in the paper. Specifically, while the SWD term is presented as crucial for the swap property, the precise contribution of the other four terms, particularly REx, cosine similarity, SWC, and the decorrelation term, remains unclear. It is not evident how each of these terms independently affects the quality of the generated knockoffs and the overall performance of the method. A more detailed analysis of the impact of removing or modifying each term is needed to justify their inclusion.\n- The necessity of DRP is unclear. There lacks comparison of $\\tilde{X}_{\\theta}$ and $\\tilde{X}_{\\theta}^{DRP}$ in empirical performance. The paper introduces DRP as a post-training perturbation to reduce dependency, but it is not clear how much this perturbation contributes to the final performance. A direct comparison of the knockoffs generated with and without DRP is needed to quantify the benefit of this step. The current presentation does not provide sufficient evidence to justify the added complexity of this step.\n2. Experiments need further analysis and explanation. \n- It is clear that DeepDRK performs better than other baseline methods. But the reason has not been analyzed clearly and adding some intermediate results will be helpful. It is unclear how well the knockoffs generated by DeepDRK following the swap property and avoid overfitting compared to baseline methods. The paper claims that DeepDRK avoids overfitting, but it lacks a direct evaluation of the swap property of the generated knockoffs. It is necessary to show how well the generated knockoffs satisfy the swap property, and how this property relates to the performance in feature selection. Furthermore, the paper should provide a more detailed analysis of how the training process avoids overfitting, beyond simply stating that early stopping is used. \n- The results w.r.t. the Gaussian mixture seems inconsistent with that in the original DDLK paper (DDLK performs the worst in this paper while it performs better than deep knockoffs and knockoffgan in the original paper). The paper should address this discrepancy by either providing a clear explanation of the differences in experimental setup or by re-evaluating the performance of DDLK under the same conditions as the original paper.",
+        "suggestions": "The ablation study needs to be significantly expanded to justify the inclusion of all five loss terms in DeepDRK. Specifically, the paper should include experiments where each of the REx, cosine similarity, SWC, and the entry-wise decorrelation terms are individually removed or modified. This would help to quantify the contribution of each term to the overall performance and to understand their individual roles in the knockoff generation process. For example, the paper could show how the performance changes when the cosine similarity term is removed, or when the decorrelation term is weakened. This would provide a more nuanced understanding of the model's behavior and justify the complexity of the loss function. Furthermore, the paper should provide a more detailed analysis of the DRP step. It is necessary to show how the performance of the knockoffs changes with different levels of perturbation, and to compare the performance of the knockoffs generated with and without DRP. This could be done by varying the parameter that controls the amount of perturbation and showing how this affects the FDR and power. This would help to determine the optimal level of perturbation and to justify the inclusion of this step in the model.\n\nTo better understand why DeepDRK performs better than the baseline methods, the paper should include intermediate results that demonstrate how well the generated knockoffs satisfy the swap property. This could be done by measuring the mean discrepancy distance with the linear kernel, and sliced Wasserstein distances, as these metrics can quantify the sample-level swap property. The paper should also provide a more detailed analysis of how the training process avoids overfitting, beyond simply stating that early stopping is used. This could include showing the training and validation loss curves, and discussing how the early stopping criteria were chosen. This would help to demonstrate that the model is not overfitting and that the performance gains are not due to memorization. It is also important to clarify the discrepancy in the Gaussian mixture results compared to the original DDLK paper. The paper should either provide a clear explanation of the differences in the experimental setup, such as the signal strength, or re-evaluate the performance of DDLK under the same conditions as the original paper. This would help to ensure that the results are consistent with the existing literature and that the conclusions are valid.\n\nFinally, the paper would benefit from a more thorough discussion of the limitations of the proposed method. For example, the paper could discuss the computational cost of training the model, or the sensitivity of the model to the choice of hyperparameters. This would help to provide a more balanced view of the method and to identify areas for future research. The paper should also discuss the potential impact of the choice of the ViT architecture on the performance of the method. While the ViT architecture has shown good performance in other domains, it is not clear if it is the optimal choice for this task. The paper could explore the use of other architectures, or provide a justification for the choice of ViT. Addressing these points would significantly strengthen the paper and make it more impactful."
+      }
+    },
+    {
+      "id": "8SxH0lQZcB",
+      "rating": 5,
+      "content": {
+        "summary": "The authors develop a distribution-free deep learning method for knockoff generation which strikes a balance between FDR and power, called “Deep Dependency Regularized Knockoff” (DeepDRK). In DeepDRK, a “multi-swapper” adversarial training procedure is proposed to enforce the swap property, while a sliced-Wasserstein-based dependency regularization (together with a novel perturbation technique) is introduced to reduce reconstructability. Experiments on real, synthetic, and semi-synthetic datasets are carried out to show the good performance.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1) Proposed a distribution-free deep learning method for knockoff generation which strikes a balance between FDR and power.\n2) A DeepDRK pipeline is provided to increase readability.\n3) A number of experimental results are provided on simulated, semi-simulated and real datasets to illustrate the performance of the proposed method.",
+        "weaknesses": "1) Though it enjoys theoretical result that a no free lunch situation for selection power when there is exact reconstructability in Appendix B, it seem that there is no theoretical guarantees on the power or explanations for that how the sliced-Wasserstein-based dependency regularization together with a novel perturbation technique introduced to reduce reconstructability can promote selection power.\n2) It is not clear that how to enforce the swap property by the “multi-swapper” adversarial training procedure.\n3) The motivation behind feature selection is high-dimensional data settings, which in my understanding means that the number of features is larger than the number of examples in the dataset. However, none of the simulated experiments include such scenario. \n\nExamples of writing problems:\n-“Similar observations can be found in Figure 4.” seems to be “Similar observations can be found in Figure 5.” in the paragraph “Results” of section 4.4.\n-“Among them, model-specific ones such as AEknockoff (Liu & Zheng, 2018) Hidden Markov Model (HMM), knockoff (Sesia et al., 2017)” seems to be “Among them, model-specific ones such as AEknockoff (Liu & Zheng, 2018), Hidden Markov Model (HMM) knockoff (Sesia et al., 2017)” in the first paragraph of section 2.2.",
+        "questions": "(1) More explanations for the proposed method striking a balance between FDR and power.\n(2)The diagram of DeepDRK pipeline and code library are given, but the algorithm for training objective (4) is not provided.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1) Though it enjoys theoretical result that a no free lunch situation for selection power when there is exact reconstructability in Appendix B, it seem that there is no theoretical guarantees on the power or explanations for that how the sliced-Wasserstein-based dependency regularization together with a novel perturbation technique introduced to reduce reconstructability can promote selection power. Specifically, while the authors argue that reducing reconstructability is important, the mechanism by which the sliced-Wasserstein distance and the perturbation specifically contribute to improved power, beyond a general intuition, is not rigorously established. The connection between the degree of reconstructability and the resulting selection power remains unclear, requiring more formal justification.\n2) It is not clear that how to enforce the swap property by the “multi-swapper” adversarial training procedure. The description of the swapper mechanism lacks sufficient detail to understand how it effectively enforces the swap property. The adversarial training process, particularly how the swappers interact with the knockoff generator to achieve the desired property, needs further clarification. The optimization process and how the multi-swappers contribute to the overall objective function requires a more detailed explanation.\n3) The motivation behind feature selection is high-dimensional data settings, which in my understanding means that the number of features is larger than the number of examples in the dataset. However, none of the simulated experiments include such scenario. The experimental validation does not adequately address the method's performance in high-dimensional settings, which is a key motivation for feature selection. The absence of experiments where the number of features exceeds the number of samples raises concerns about the practical applicability of the proposed method in the intended high-dimensional context.\n\nExamples of writing problems:\n-“Similar observations can be found in Figure 4.” seems to be “Similar observations can be found in Figure 5.” in the paragraph “Results” of section 4.4.\n-“Among them, model-specific ones such as AEknockoff (Liu & Zheng, 2018) Hidden Markov Model (HMM), knockoff (Sesia et al., 2017)” seems to be “Among them, model-specific ones such as AEknockoff (Liu & Zheng, 2018), Hidden Markov Model (HMM) knockoff (Sesia et al., 2017)” in the first paragraph of section 2.2.",
+        "suggestions": "The paper would benefit from a more rigorous theoretical analysis of the proposed method's power. While the authors mention a trade-off between FDR and power, a more formal treatment is needed to understand how the sliced-Wasserstein-based dependency regularization and the perturbation technique specifically influence the selection power. It would be beneficial to explore the theoretical underpinnings of this relationship, possibly by analyzing the properties of the generated knockoffs under different levels of reconstructability. For example, a theoretical analysis could investigate how the sliced-Wasserstein distance affects the covariance structure of the knockoffs and how this, in turn, impacts the power of the feature selection procedure. Furthermore, the authors should provide a more detailed explanation of the perturbation technique and its effect on the knockoff generation process. A deeper analysis of how the perturbation interacts with the sliced-Wasserstein regularization to achieve the desired balance between FDR and power is needed.\n\nTo clarify the multi-swapper adversarial training procedure, the authors should include a more detailed description of the swapper design and its role in enforcing the swap property. The explanation should include the specific optimization steps and how the swappers interact with the knockoff transformer. A more detailed explanation of how the Gumbel-softmax random variable is used to sample indices and how these indices are used to perform the swaps is necessary. The authors should also clarify how the swap property is enforced by maximizing the SWD with respect to the swapper weights while minimizing it with respect to the knockoff generator. A more detailed description of the optimization process, including the specific loss function and the gradient updates, would be beneficial. Furthermore, it would be helpful to provide a visual representation of the multi-swapper architecture and its interaction with the knockoff generator.\n\nFinally, the authors should include experiments that explicitly address the high-dimensional setting where the number of features exceeds the number of samples. This is crucial to validate the method's applicability in the intended context. The authors could consider using synthetic datasets with a larger number of features than samples or using real-world high-dimensional datasets, such as gene expression data. The experimental results should clearly demonstrate the method's performance in such settings, including metrics such as FDR and power. It is also important to analyze the computational complexity of the method in high-dimensional settings and discuss any potential limitations. The authors should also discuss the practical implications of their method in high-dimensional data analysis and provide guidance on how to apply it effectively in such scenarios."
+      }
+    }
+  ]
+}

papers/1OP4crhgkD/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "1OP4crhgkD",
+  "title": "Semantically Aligned Task Decomposition in Multi-Agent Reinforcement Learning",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-18",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=1OP4crhgkD"
+}

papers/1OP4crhgkD/review.json

@@ -0,0 +1,92 @@
+{
+  "id": "1OP4crhgkD",
+  "title": "Semantically Aligned Task Decomposition in Multi-Agent Reinforcement Learning",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "VkDV0AAUh3",
+      "rating": 6,
+      "content": {
+        "summary": "This paper proposes the Semantically Aligned task decomposition (SAMA) framework, which aims to solve the sparse reward problem in multi-agent reinforcement learning. SAMA prompts pre-trained language models with chain-of-thought that can suggest potential goals, provide suitable goal decomposition and subgoal allocation as well as self-reflection-based replanning. Each agent's subgoal-conditioned policy is trained by the language-grounded RL method. Compared with the traditional automatic subgoal generation method, SAMA can have higher sample efficiency. This paper verifies the performance of SAMA on Overcooked and MiniRTS.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1. The paper has a clear structure, introduces the proposed method step by step, and the figures are clear and easy to understand.\n2. Experimental details are given in the appendix, which makes it easy to reproduce the experimental results. Relevant prompts are also given in the appendix, making the contribution and experimental results more convincing.\n3. The testbed chosen in this paper is very representative and challenging. The tasks in Overcooked and MiniRTS can be decomposed by common sense, and their status is relatively easy to translate into natural language. This allows the paper to better focus on how to decompose tasks and allocate subtasks.\n4. It can be seen from the experimental results that SAMA can indeed reach or exceed the performance of existing baselines, and the sample efficiency is indeed significantly higher than other baselines.",
+        "weaknesses": "1. Currently, SAMA may not be applicable to an environment where human rationality is immaterial or inexpressible in language or when state information is not inherently encoded as a natural language sequence. For example, when the state space is continuous, it is difficult for SAMA to complete the state and action translation stage.\n2. PLM still has some flaws, which sometimes hinder the normal progress of the entire SAMA process. In addition, using PLM will bring additional time costs and economic costs.\n3. In some scenarios (such as Coordination Ring), although SAMA learns very quickly in the early stage, the final convergence results are still not as good as some baselines.\n4. Although in the task manual generation stage, SAMA automatically extracts critical information from the latex file or code through PLM, this is undoubtedly a relatively cumbersome process, so the cost of this stage cannot be ignored.",
+        "questions": "1. Is the introduction of the self-reflection mechanism unfair to other baselines? Because other methods do not have this ability similar to \"regret.\"\n2. As can be seen from Figures 4 and 5, although SAMA has a very high sample efficiency in the early stages of training, it often converges to a local optimal solution. What is the reason for this result? Is it because the interval $k$ is too large? Do different $k$ values have different effects on the algorithm's performance?\n3. How to ensure the accuracy of PLM in the Task Manual Generation stage or the generated code snippet for assessing sub-goal completion?\n4. Is the wall time for the agent to complete a round in SAMA much different from other baselines? What is the number of tokens that need to be input to PLM in one episode?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "details_of_ethics_concerns": "N/A",
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. Currently, SAMA may not be applicable to an environment where human rationality is immaterial or inexpressible in language or when state information is not inherently encoded as a natural language sequence. For example, when the state space is continuous, it is difficult for SAMA to complete the state and action translation stage.\n2. PLM still has some flaws, which sometimes hinder the normal progress of the entire SAMA process. In addition, using PLM will bring additional time costs and economic costs.\n3. In some scenarios (such as Coordination Ring), although SAMA learns very quickly in the early stage, the final convergence results are still not as good as some baselines.\n4. Although in the task manual generation stage, SAMA automatically extracts critical information from the latex file or code through PLM, this is undoubtedly a relatively cumbersome process, so the cost of this stage cannot be ignored.",
+        "suggestions": "The core limitation of the SAMA framework lies in its reliance on language as the primary interface for task decomposition and agent interaction. This dependence restricts its applicability to environments where state and action spaces are not easily translatable into natural language, such as continuous control tasks or scenarios with complex, non-verbalizable dynamics. For instance, consider a robotic manipulation task where the robot's state is defined by joint angles and sensor readings, and actions involve continuous motor commands. Translating these continuous values into a meaningful language representation for the PLM to process would be a significant challenge, requiring a potentially lossy discretization or a complex encoding scheme. Moreover, the inherent ambiguity and potential for misinterpretation in language could introduce further noise into the system, hindering effective planning and execution. Future work could explore methods for bridging the gap between continuous state and action spaces and language-based representations, possibly through the use of learned embeddings or multimodal models that incorporate both visual and textual information.\n\nFurthermore, the performance of SAMA is intrinsically tied to the capabilities of the underlying PLM. While PLMs have shown impressive abilities in various natural language tasks, their performance in specific, niche domains can be inconsistent and unreliable. The reliance on a general-purpose PLM without any task-specific fine-tuning can lead to suboptimal task decompositions, inaccurate subgoal assignments, and flawed self-reflection processes. For example, in a complex multi-agent environment, the PLM might struggle to generate optimal subgoals or to accurately assess subgoal completion, leading to inefficient exploration and suboptimal policies. Moreover, the computational cost and latency associated with querying PLMs can be a bottleneck, especially in real-time applications. The authors should explore the possibility of fine-tuning the PLM on task-specific data to improve its performance and reduce computational overhead. Additionally, investigating methods for caching or reusing PLM outputs could help to mitigate the latency issue.\n\nFinally, the task manual generation stage, which involves extracting information from LaTeX files or code, introduces an additional layer of complexity and potential failure points. The accuracy of the PLM in this stage is crucial for the overall performance of the SAMA framework. Errors in extracting task-relevant information or in generating accurate reward functions could propagate through the system, leading to poor performance. The authors should investigate methods for verifying the correctness of the generated task manuals and reward functions, possibly through human-in-the-loop validation or automated testing procedures. Furthermore, the cost of this stage, both in terms of time and computational resources, should be carefully considered. The authors should explore alternative methods for task specification that are less cumbersome and more efficient, such as using structured data formats or domain-specific languages."
+      }
+    },
+    {
+      "id": "GMu7ztrlUe",
+      "rating": 3,
+      "content": {
+        "summary": "The authors propose Semantically Aligned task decomposition in MARL (SAMA), a method that aims to generate subgoals for MARL tasks with sparse reward signals. By taking advantage of pretrained language models, the proposed method shows to be more sample efficient during MARL training.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "Generally, the paper is well written and well organized.\n\nThis paper:\n* proposes a complex method to integrate language models and MARL from a task decomposition perspective\n* shows that using prior knowledge from language models improves sample efficiency in MARL\n* provides detailed analysis regarding the language learned for the tasks",
+        "weaknesses": "* Overall, there is a big limitation from the proposed method: the approach introduced requires the prior existence of the required resources to create an accurate task manual and state action translations. This is indeed pointed by the authors in section 3.1: \"Nevertheless, linguistic task manuals still need to be made available for general multi-agent tasks. Furthermore, except for a handful of text-based tasks, typical multi-agent environment interfaces cannot provide text-based representations of environmental or agent state information and action information.\"; this makes this method very limiting\n* It is stated that the language task manual is generated from the latex code of the paper of the multi-agent task. Once again, this sounds very limiting.\n* While the proposed method shows to reduce the required samples in the tasks (Fig. 5), it requires very complex prior preprocessing to create the required text-based rules and manuals. This makes me think that it possible that the method becomes even more costly, in general, after all of this processing, despite the sample efficiency in the task.\n* From my understanding, the goal decomposition is made prior to the task, meaning that a lot of prior knowledge is required (as mentioned before). Other methods such as MASER [1] or [3] decompose the tasks on a more flexible manner, which saves a lot of potential preprocessing.\n* Throughout the paper, the authors claim several times that their method does not need to learn how to split subgoals or to generate them on the go as other methods do, reducing the sample complexity. However, the preprocessing carried needed to achieve this seems very complex and requires a lot of prior knowledge and carefuly engineered features. I wonder again whether this is really more advantageous than following the standard approaches.\n* I have concerns regarding the claims that this method addresses the credit assignment problem. Also since the authors test is environments with only two agents, this can be difficult to analyse (overcooked with 2 agents and MINIRTS with 2 agents; in related works environments with many more agents such as SMAC [2] are used).\n* In the conclusion it is stated as a limitation: \"where human rationality is immaterial or inexpressible in language or when state information is not inherently encoded as a natural language sequence.\"; Yet i believe this is a very interesting remark and would be interesting to see how a method such SAMA can be used to tackle these problems, instead of having a preset of convenient \"manuals\".\n* The authors mention throughout the paper (introduction and Fig. 2, for example) the potential for generalizability of the proposed method. However, this is not shown or further discussed, and due to the required preprocessing I fail to understand how generalization to different environments/tasks can be easily done.\n\nOverall, I think that the proposed way of integrating language models with MARL from a task decomposition perspective is interesting and can contribute to the explainability of MARL systems. However, I feel that the proposed method in this paper has several limitations and requires a very complex preprocessing. If the manuals cannot be properly generated, then it is not possible to tackle the problems. I also wonder whether the shown sample efficiency is really worth it since it needs all this preprocessing.\n\n[1] https://arxiv.org/abs/2206.10607\n\n[2] https://arxiv.org/abs/1902.04043\n\n[3] https://ieeexplore.ieee.org/document/9119863\n\n\nMinor:\n- in section 2:  \"endeavoring to parse it into N distinct sub-goals g1k, · · · , gN\"; missing brackets\n- in section 3.1: \"illustrate the process in the yellow line of Figure 2\" the word figure shouldnt be in yellow; same here (purple line in Figure 2) and in the others that follow in the paper",
+        "questions": "1. To extend the proposed method to other cases, would it be possible to create a task manual and state action translation for environments that do not follow the conventions presented in this paper? For instance, in more complex environments such as SMAC [2].\n2. In section 3.1: \"For each paragraph $S^i_{para}$, we filter paragraphs for relevance and retain only those deemed relevant by at least one prompt from $Q_{rel}$.\"; how is the filtering of the relevant paragraphs done? Are they manually filtered?\n3. In overcooked, despite the method being more sample efficient during training (figure 5) we can see in figure 4-right that the testing performance of the proposed method stays below other sota methods. Is this because MARL might not be good enough for this environment?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "3: reject, not good enough",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": " * Overall, there is a big limitation from the proposed method: the approach introduced requires the prior existence of the required resources to create an accurate task manual and state action translations. This is indeed pointed by the authors in section 3.1: \"Nevertheless, linguistic task manuals still need to be made available for general multi-agent tasks. Furthermore, except for a handful of text-based tasks, typical multi-agent environment interfaces cannot provide text-based representations of environmental or agent state information and action information.\"; this makes this method very limiting\n* It is stated that the language task manual is generated from the latex code of the paper of the multi-agent task. Once again, this sounds very limiting. The reliance on LaTeX source code for task manual generation severely restricts the applicability of this method to environments where such resources are not readily available or standardized. This dependency introduces a significant bottleneck, as many real-world and even simulated environments lack accompanying LaTeX documentation.\n* While the proposed method shows to reduce the required samples in the tasks (Fig. 5), it requires very complex prior preprocessing to create the required text-based rules and manuals. This makes me think that it possible that the method becomes even more costly, in general, after all of this processing, despite the sample efficiency in the task. The preprocessing steps, involving the extraction of information from LaTeX documents, the generation of task manuals, and the creation of state-action translations, introduce a substantial overhead. The computational cost and time required for these preprocessing stages may outweigh the benefits gained from reduced sample complexity during the actual MARL training, especially when considering the potential for errors in the automated extraction and translation processes.\n* From my understanding, the goal decomposition is made prior to the task, meaning that a lot of prior knowledge is required (as mentioned before). Other methods such as MASER [1] or [3] decompose the tasks on a more flexible manner, which saves a lot of potential preprocessing. The rigid, pre-task decomposition of goals contrasts with more adaptive methods that dynamically adjust the decomposition based on the current state of the environment and the agents' learning progress. This inflexibility limits the method's ability to handle unforeseen situations or changes in the task dynamics, potentially leading to suboptimal performance in complex or uncertain environments.\n* Throughout the paper, the authors claim several times that their method does not need to learn how to split subgoals or to generate them on the go as other methods do, reducing the sample complexity. However, the preprocessing carried needed to achieve this seems very complex and requires a lot of prior knowledge and carefully engineered features. I wonder again whether this is really more advantageous than following the standard approaches. The claim of reduced sample complexity is undermined by the extensive preprocessing required, which involves significant manual effort and domain expertise. The need for carefully engineered features and prior knowledge raises concerns about the method's scalability and ease of use in diverse MARL scenarios.\n* I have concerns regarding the claims that this method addresses the credit assignment problem. Also since the authors test is environments with only two agents, this can be difficult to analyse (overcooked with 2 agents and MINIRTS with 2 agents; in related works environments with many more agents such as SMAC [2] are used). The limited evaluation on two-agent environments raises questions about the method's ability to handle more complex scenarios with a larger number of agents. The credit assignment problem, which is particularly challenging in multi-agent systems, may not be adequately addressed by the proposed approach, especially in environments with more agents and complex interactions.\n* In the conclusion it is stated as a limitation: \"where human rationality is immaterial or inexpressible in language or when state information is not inherently encoded as a natural language sequence.\"; Yet i believe this is a very interesting remark and would be interesting to see how a method such SAMA can be used to tackle these problems, instead of having a preset of convenient \"manuals\". The method's reliance on human-interpretable task manuals and natural language state representations limits its applicability to scenarios where human rationality is not a factor or where state information is not easily translated into natural language. This constraint restricts the method's ability to tackle a wide range of MARL problems, particularly those involving complex, non-intuitive dynamics.\n* The authors mention throughout the paper (introduction and Fig. 2, for example) the potential for generalizability of the proposed method. However, this is not shown or further discussed, and due to the required preprocessing I fail to understand how generalization to different environments/tasks can be easily done. The lack of empirical evidence supporting the method's generalizability to diverse environments and tasks is a significant concern. The extensive preprocessing and reliance on task-specific manuals raise doubts about the method's ability to adapt to new, unseen scenarios without substantial modifications and manual intervention.",
+        "suggestions": "The paper presents an interesting approach to integrating language models with MARL for task decomposition, but several aspects require further consideration to enhance its practical applicability and generalizability. First, the method's dependence on pre-existing resources, such as LaTeX source code and detailed task manuals, severely limits its applicability to a broader range of MARL problems. To address this, the authors could explore alternative methods for generating task manuals and state-action translations that do not rely on such specific resources. For instance, they could investigate techniques for automatically extracting task-relevant information from diverse sources, such as simulation logs or environment descriptions, or explore the use of multimodal models to directly process visual or sensory inputs from the environment. This would make the method more versatile and adaptable to environments where detailed documentation is not readily available.\n\nSecond, the extensive preprocessing required by the proposed method raises concerns about its overall efficiency and scalability. While the authors claim that the method reduces sample complexity during MARL training, the computational cost and time required for preprocessing may negate these benefits. To mitigate this, the authors could explore more efficient preprocessing techniques, such as using lightweight language models or developing more streamlined extraction and translation algorithms. Additionally, they could investigate methods for reusing or adapting preprocessed information across different tasks or environments, reducing the need for extensive preprocessing for each new problem. This would make the method more practical for real-world applications where computational resources and time are often limited.\n\nFinally, the paper's evaluation is limited to two-agent environments, which raises questions about the method's ability to handle more complex scenarios with a larger number of agents and more intricate interactions. To address this, the authors should conduct more extensive evaluations on diverse MARL environments with varying numbers of agents and task complexities. This would provide a more comprehensive understanding of the method's strengths and limitations, as well as its ability to handle the challenges of credit assignment and coordination in more complex multi-agent systems. Furthermore, the authors should explore how the method can be extended to handle scenarios where human rationality is not a factor or where state information is not easily translated into natural language, potentially by incorporating learning mechanisms that can adapt to different types of environments and tasks."
+      }
+    },
+    {
+      "id": "ifae4SBWt6",
+      "rating": 5,
+      "content": {
+        "summary": "This paper investigates long-horizon, sparse reward tasks in cooperative multi-agent RL problems. The proposed method is to use the pre-trained large language model and pre-trained language-ground RL agent. The method prompts the pre-trained language model to generate potential goals, decompose the goal into sub-goals, assign sub-goals to each agent in the multi-agent setting, and replan when the pre-trained RL agents fail to achieve the goal. \n\nThe experiments are conducted on two challenging benchmarks for MARL, Overcooked and MiniRTS. The proposed method outperforms the SOTA baselines.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "The problem of long-horizon, sparse reward tasks in multi-agent RL is super challenging and significant.\n\nIt is well-motivated to apply the large-language model, to use prior knowledge and common sense for goal generation and task planning.\n\nEmpirically, the proposed method outperforms the SOTA.",
+        "weaknesses": "In general, the presentation can be improved. Since there are too many components in the pipeline, it will be better to emphasize and explain the most novel and important part in detail, rather than briefly mention each component within space limit.\n\nThe proposed method is not fully analyzed. For example, as for the reward design part, how is it accurate to determine task completion? About the pre-trained language-grounded RL agent, how does it perform the training and validation set of states and sub-goals? In the self-reflection phase, how does the task planning evolve?",
+        "questions": "Could you please clarify in Figure 5, which component of the proposed method is updated as environment steps increase? If the language-grounded RL agent is trained here, why is it called pre-trained?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "In general, the presentation can be improved. Since there are too many components in the pipeline, it will be better to emphasize and explain the most novel and important part in detail, rather than briefly mention each component within space limit.\n\nThe proposed method is not fully analyzed. For example, as for the reward design part, how is it accurate to determine task completion? About the pre-trained language-grounded RL agent, how does it perform the training and validation set of states and sub-goals? In the self-reflection phase, how does the task planning evolve?",
+        "suggestions": "The paper introduces a complex pipeline involving multiple components, including a pre-trained language model for goal generation and decomposition, a language-grounded RL agent, and a self-reflection mechanism. While the integration of these components is interesting, the paper would benefit from a more focused presentation that emphasizes the most novel aspects of the approach. Instead of providing a brief overview of each component, the authors should dedicate more space to explaining the core innovations and their impact on the overall performance. For instance, the self-reflection mechanism, which is crucial for adapting to failures and refining the task planning, is not explained in sufficient detail. A more thorough analysis of how this mechanism works, including specific examples of how it modifies goals and sub-goals based on past failures, would significantly enhance the paper's clarity and impact. Furthermore, the paper should clarify how the different components interact and contribute to the overall performance of the system. A detailed ablation study could be beneficial to evaluate the contribution of each component.\n\nRegarding the reward design, the paper lacks a detailed explanation of how task completion is accurately determined. The reward function is critical for guiding the RL agent towards the desired behavior, and it is essential to understand how the reward is structured to ensure that it accurately reflects task completion. The authors should provide a more thorough analysis of the reward function, including how it is generated and how it is used to train the RL agent. Furthermore, the paper should clarify how the pre-trained language-grounded RL agent is trained and validated. The authors should provide details on the training data, including the states and sub-goals used for training, and the validation process. This would help to understand the generalization capability of the agent and its ability to perform well on unseen states and sub-goals. The paper should also discuss the potential limitations of the approach, such as the dependence on the quality of the pre-trained language model and the potential for the self-reflection mechanism to get stuck in local optima.\n\nFinally, the paper should provide more details on the evolution of task planning during the self-reflection phase. The authors should explain how the task planning is modified based on the feedback from the environment and how this process leads to improved performance. It would be helpful to provide specific examples of how the task planning evolves over time and how this evolution affects the agent's behavior. The authors should also discuss the potential limitations of the self-reflection mechanism and how these limitations can be addressed. A more thorough analysis of the self-reflection mechanism, including its strengths and weaknesses, would significantly improve the paper's overall quality and impact."
+      }
+    },
+    {
+      "id": "J0aYl8WDgP",
+      "rating": 6,
+      "content": {
+        "summary": "Based on automatic subgoal generation, the authors design a sophisticated framework to perform goal generation, sub-goal assignment, and language-grounded goal-based MARL, along with effective techniques like in-context learning and self-reflection in the prompting engineering domain. The authors evaluate performance of derived policies on two benchmarks, Overcooked and MiniRTS.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "3 good",
+        "strengths": "1. The authors compose several techniques of prompting engineering to realize subgoal generation and train goal-conditioned agents, which seems significantly improve sample efficiency. The authors well introduce multiple advancements from current LLM-agent research and provide thorough discussions about related methods.\n2. The framework the authors propose is comprehensive, though maybe too complicated, it provide a guidance of design an LLM-assisted agent.\n3. The framework, SAMA, realizes semantically useful task decomposition by generating and assign explainable subgoals, which is advantageous compared to previous goal-based methods.",
+        "weaknesses": "1. The major concern is that the sophisticated design of SAMA may hinder its general use on other benchmarks. It seems that the authors create exhaustive prompts for running SAMA on these two benchmarks (Page 23-36). \n2. The accompanied concern is that the deployment of SAMA may induce high costs of calling LLMs (like OpenAI API) and training language-grounded agents. \n3. In the experiments part, the authors do not make some illustrative examples of goal generation but only provide performance curves. \n\nSome minor mistakes:\n1. In the caption of Figure 2, \"subgaol\" -> \"subgoal\". The authors should also consider unifying the term to \"subgoal\" or \"sub-goal\" as they both appear in this paper.\n2. Figure 4 (right) is too small to be read.",
+        "questions": "1. Can you make a list of how many tasks are accomplished with the help of PLMs? Among them, how many can be done in offline setting and how many cannot? I think it will be better to evaluate the contributions. \n2. To hack SAMA for another environment, can you summarize how many prompts/components the practitioner should modify?\n3. How much percentage of goals and subgoals is generated in the offline manner? How many queries are needed during online training? \n4. Can you provide the financial costs and time costs of training SAMA agents?\n5. As the evaluation of Overcooked is based on self-play performance, what is the difference among those ad hoc teamwork methods (SP, FCP, and COLE)? In my opinion, the SP may be reduced to a general MAPPO algorithm. Why do ASG methods perform much worse than SP?\n6. Why do you select the MiniRTS benchmark with splitting units rather than directly evaluating on other MARL benchmarks? It seems a little wired. Meanwhile, why cannot SAMA surpass RED?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. The major concern is that the sophisticated design of SAMA may hinder its general use on other benchmarks. It seems that the authors create exhaustive prompts for running SAMA on these two benchmarks (Page 23-36). \n2. The accompanied concern is that the deployment of SAMA may induce high costs of calling LLMs (like OpenAI API) and training language-grounded agents. \n3. In the experiments part, the authors do not make some illustrative examples of goal generation but only provide performance curves. \n\nSome minor mistakes:\n1. In the caption of Figure 2, \"subgaol\" -> \"subgoal\". The authors should also consider unifying the term to \"subgoal\" or \"sub-goal\" as they both appear in this paper.\n2. Figure 4 (right) is too small to be read.",
+        "suggestions": "The authors should provide a more detailed breakdown of the SAMA framework's components and their individual contributions. While the paper introduces a comprehensive system, it lacks clarity on the necessity and impact of each stage, particularly the prompt engineering aspects. For instance, the paper should specify the exact number of prompts required for each task, the average token length of these prompts, and the specific functions each prompt serves. This would help assess the practical applicability of SAMA to new environments. A table summarizing the different types of prompts, their purposes, and the expected effort for adapting them to new tasks would be beneficial. Furthermore, the authors should elaborate on the specific techniques used to generate diverse states from code, as this is a key step in the offline generation process. It is unclear how the code understanding module of LangChain is used to generate varied and valid states, and more details on this process are needed.\n\nTo address the concerns about the high cost of using LLMs, the authors should provide a more detailed analysis of the financial and time costs associated with each stage of the SAMA framework. This analysis should include the number of API calls to the LLM, the average time for each call, and the total cost for training the agents on both benchmarks. This would help readers understand the practical limitations of the method and assess its feasibility for real-world applications. The authors should also explore and discuss potential strategies for reducing these costs, such as using smaller or open-source LLMs, or optimizing the prompt engineering process to reduce the number of queries. A comparison of the costs associated with SAMA and other MARL methods would also be helpful.\n\nFinally, the authors should include illustrative examples of the goals and subgoals generated by the PLMs. This would provide a more intuitive understanding of the task decomposition process and help readers assess the quality of the generated subgoals. The paper should also clarify the differences between the various ad hoc teamwork methods used in the Overcooked-AI experiments. Specifically, the authors should explain why ASG methods perform worse than SP, and whether this is due to the specific implementation of ASG or inherent limitations of the approach. A more detailed discussion of the differences between SP and MAPPO would also be beneficial, as well as why PBT methods are more efficient for Overcooked-AI. These clarifications would help readers better understand the experimental results and the limitations of the proposed method."
+      }
+    }
+  ]
+}

papers/1P1nxem1jU/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "1P1nxem1jU",
+  "title": "Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-15",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=1P1nxem1jU"
+}

papers/1P1nxem1jU/paper.md

@@ -0,0 +1,477 @@
+# THROUGH THE DUAL-PRISM: A SPECTRAL PERSPEC-TIVE ON GRAPH DATA AUGMENTATION FOR GRAPH CLASSIFICATION
+
+Anonymous authors
+
+Paper under double-blind review
+
+# ABSTRACT
+
+Graph Neural Networks (GNNs) have become the preferred tool to process graph data, with their efficacy being boosted through graph data augmentation techniques. Despite the evolution of augmentation methods, issues like graph property distortions and restricted structural changes persist. This leads to the question: *Is it possible to develop more property-conserving and structure-sensitive augmentation methods?* Through a spectral lens, we investigate the interplay between graph properties, their augmentation, and their spectral behavior, and found that keeping the low-frequency eigenvalues unchanged can preserve the critical properties at a large scale when generating augmented graphs. These observations inform our introduction of the Dual-Prism (DP) augmentation method, comprising DP-Noise and DP-Mask, which adeptly retains essential graph properties while diversifying augmented graphs. Extensive experiments validate the efficiency of our approach, providing a new and promising direction for graph data augmentation.
+
+# 1 INTRODUCTION
+
+Graph structures, modeling complex systems through nodes and edges, are ubiquitous across various domains, including social networks [\(Newman et al., 2002\)](#page-11-0), bioinformatics [\(Yi et al., 2022\)](#page-12-0), and transportation systems [\(Jin et al., 2023a\)](#page-10-0). Graph Neural Networks (GNNs) [\(Kipf & Welling, 2016a\)](#page-10-1) elegantly handle this relational information, paving the way for tasks such as accurate predictions. Their capabilities are further enhanced by graph data augmentation techniques. These methods artificially diversify the dataset through strategic manipulations, thereby bolstering the performance and generalization of GNNs [\(Rong et al., 2019;](#page-11-1) [Feng et al., 2020;](#page-9-0) [You et al., 2020\)](#page-12-1). Graph data augmentation has progressed from early random topological modifications, exemplified by DropEdge [\(Rong et al., 2019\)](#page-11-1) and DropNode [\(Feng et al., 2020\)](#page-9-0), to sophisticated learning-centric approaches like InfoMin [\(Suresh et al., 2021\)](#page-11-2). Furthermore, techniques inspired by image augmentation's mixup principle [\(Zhang et al., 2017\)](#page-12-2) have emerged as prominent contenders in this domain [\(Verma et al.,](#page-11-3) [2019;](#page-11-3) [Wang et al., 2021;](#page-11-4) [Guo & Mao, 2021\)](#page-9-1).
+
+Though promising, these augmentation methods are challenged by three key issues as follows. (1) *Graph Property Distortion.* Before the era of deep learning, graph properties, e.g., graph connectivity and diameter, served as vital features for classification for decades [\(Childs et al., 2009\)](#page-9-2). While now they seem to be ignored, many aforementioned contemporary augmentation methods appear to sidestep this tradition and overlook the graph properties. For instance, an example graph from the IMDB-BINARY dataset [\(Morris et al., 2020\)](#page-10-2) and its augmented graph via DropEdge are illustrated in Figures [1a](#page-1-0) and [1b](#page-1-0), respectively. The polar plot in Figure [1e](#page-1-0) shows the properties of these graphs, where each axis represents a distinct property. It is evident that DropEdge significantly alters the original graph's properties, as indicated by the stark difference between the shapes of the orange (original) and blue (augmented) pentagons. (2) *Limited Structural Impact*. The majority of existing methods' localized alterations do not capture the broader relationships and structures within the graph, limiting their utility. Consider a social network graph, where removing an edge affects just the immediate node and does little to alter the overall community structure. We thus ask: Can we design more *property-retentive* and *structure-aware* data augmentation techniques for GNNs?
+
+<span id="page-1-0"></span>Figure 1: Visualization of (a) a graph from the IMDB-BINARY dataset and its augmented graphs via (b) DropEdge [\(Rong et al., 2019\)](#page-11-1), (c) DP-Noise (ours), and (d) DP-Mask (ours). Dashed line: Dropped edge. Red line: Added edge. (e) Five properties of these graphs. r: radius. d: diameter. conn.: connectivity. ASPL: average shortest path length. #peri: number of periphery. Ori.: Original. D.E.: DropEdge. DP-N: DP-Noise. DP-M: DP-Mask. (f) The eigenvalues of these four graphs.
+
+Through the Dual-Prism: A Spectral Lens. Graph data augmentation involves altering components of an original graph. These modifications, in turn, lead to changes in the graph's spectral frequencies [\(Ortega et al., 2018\)](#page-11-5). Recent research highlighted the importance of the graph spectrum: it can reveal critical graph properties, e.g., connectivity and radius [\(Chung, 1997;](#page-9-3) [Lee et al.,](#page-10-3) [2014\)](#page-10-3). Additionally, it also provides a holistic summary of a graph's intrinsic structure [\(Chang](#page-9-4) [et al., 2021\)](#page-9-4), providing a global view for graph topology alterations. Building on this foundation, a pivotal question arises: *Could the spectral domain be the stage for structure-aware and propertyretentive augmentation efforts?* Drawing inspiration from *dual prisms*—which filter and reconstruct light based on spectral elements—can we design a *polarizer* to shed new light on this challenge? With this in mind, we use spectral graph theory, aiming to answer the following questions: 1) Can a spectral approach to graph data augmentation preserve essential graph properties effectively? 2) How does spectral-based augmentation impact broader graph structures? 3) How does spectralbased augmentation compare to existing methods in enhancing the efficiency of GNNs for graph classification?
+
+We begin with an empirical exploration in Section [3,](#page-2-0) where we aim to understand the interplay between topological modifications and their spectral responses. Our insights reveal that changes in graph properties mainly manifest in *low-frequency components*. Armed with this, in Section [4,](#page-4-0) we unveil our Dual-Prism (DP) augmentation strategies, DP-Noise and DP-Mask, by only changing the high-frequency part of the spectrum of graphs. Figures [1c](#page-1-0) and [1d](#page-1-0) provide a visualization of the augmented graphs via our proposed methods, i.e., DP-Noise and DP-Mask. As shown in Figure [1e](#page-1-0), compared with DropEdge, our approaches skillfully maintain the inherent properties of the original graph, differing only slightly in the ASPL. Note that although we solely present one example underscoring our method's capability, its robustness is consistently evident across all scenarios.
+
+In addition to the properties, we further explore the spectrum comparison, shown in Figure [1f](#page-1-0). Compared with DropEdge, the spectrum shifts caused by our methods are noticeably smaller. Interestingly, despite our approaches' relative stability in the spectral domain, they induce substantial changes in the spatial realm (i.e., notable edge modifications). This spectral stability helps retain the core properties, while the spatial variations ensure a rich diversity in augmented graphs. Conversely, DropEdge, despite only causing certain edge changes, disrupts the spectrum and essential graph properties significantly. Simply put, our methods skillfully maintain graph properties while also diversifying augmented graphs. In Section [5,](#page-6-0) we evaluate the efficacy of our methods on graph classification, across diverse settings: supervised, semi-supervised, unsupervised, and transfer learning on various real-world datasets. Our concluding thoughts are presented in Section [6.](#page-8-0)
+
+Contributions. Our main contributions are outlined as follows. *(1) Prism – Bridging Spatial and Spectral Domains:* We introduce a spectral lens to shed light on spatial graph data augmentation, aiming to better understand the spectral behavior of graph modifications and their interplay with inherent graph properties. *(2) Polarizer – Innovative Augmentation Method:* We propose the globally-aware and property-retentive augmentation methods, Dual-Prism (DP), including DP-Noise and DP-Mask. Our methods are able to preserve inherent graph properties while simultaneously enhancing the diversity of augmented graphs. *(3) New Light – Extensive Evaluations:* We conduct comprehensive experiments spanning supervised, semi-supervised, unsupervised, and transfer learning paradigms on 21 real-world datasets. The experimental results demonstrate that our proposed methods can achieve state-of-art performance on the majority of datasets.
+
+#### 2 RELATED WORK
+
+**Spectrum and GNNs.** Spectral graph theory (Chung, 1997) has found an appealing intersection with GNNs (Ortega et al., 2018; Wu et al., 2019; Dong et al., 2020; Bo et al., 2021; Chang et al., 2021; Yang et al., 2022). Early GNN approaches employed the spectrum of the Laplacian matrix to define convolution operations on graphs in the spectral domain (Hammond et al., 2011; Defferrard et al., 2016). As it evolved, there was a strategic shift towards spectral methods to enhance scalability (Nt & Maehara, 2019). This spectral perspective continues to be influential across various graph learning domains, notably in graph contrastive learning (GCL) (Liu et al., 2022; Lin et al., 2022), adversarial attacks (Entezari et al., 2020; Chang et al., 2021), and multivariate time series learning (Cao et al., 2020; Jin et al., 2023b). Zooming into the GCL domain, where data augmentation plays a pivotal role, Liu et al. (2022) introduced the general rule of effective augmented graphs in GCL via a spectral perspective. Lin et al. (2022) presented a novel augmentation method for GCL, focusing on the invariance of graph representation in the spectral domain. Notably, while these studies offer valuable insights, they mainly concentrate on the GCL paradigm, often neglecting broader discussions about preserving the core properties of graphs and supervised tasks.
+
+Data Augmentations for GNNs. Graph data augmentation refers to the process of modifying a graph to enhance or diversify the information contained within, which can be used to bolster the training dataset for better generalization or model variations in real-world networks Ding et al. (2022); Zhao et al. (2022). Early methods are grounded in random modification to the graph topology. Techniques like DropEdge (Rong et al., 2019), DropNode (Feng et al., 2020), and random subgraph sampling (You et al., 2020) introduce stochastic perturbations in the graph structure. In addition to random modification, there is a wave of methods utilizing more sophisticated, learning-based strategies to generate augmented graphs (Suresh et al., 2021). Another research line is inspired by the efficiency of mixup (Zhang et al., 2017) in image augmentation, blending node features or entire subgraphs to create hybrid graph structures (Verma et al., 2019; Wang et al., 2021; Guo & Mao, 2021; Han et al., 2022; Park et al., 2022; Ling et al., 2023). However, while the above techniques, either spatial or spectral, have advanced the field of graph data augmentation, challenges remain, especially in preserving broader structural changes and graph semantics. Our work presents a new spectral augmentation approach, providing a principled way to modulate a graph's spectrum while preserving the core, low-frequency patterns.
+
+### <span id="page-2-0"></span>3 A SPECTRAL LENS ON GRAPH DATA AUGMENTATIONS
+
+#### 3.1 Preliminaries
+
+An undirected graph  $\mathcal G$  is represented as  $\mathcal G=(V,E)$  where V is the set of nodes with |V|=N and  $E\subseteq V\times V$  is the set of edges. Let  $A\in\mathbb R^{N\times N}$  be the adjacency matrix of  $\mathcal G$ , with elements  $a_{ij}=1$  if there is an edge between nodes i and j, and  $a_{ij}=0$  otherwise. Let  $D\in\mathbb R^{N\times N}$  be the degree matrix, which is a diagonal matrix with elements  $d_{ii}=\sum_j a_{ij}$ , representing the degree of node i. The Laplacian matrix of  $\mathcal G$  is denoted as  $L=D-A\in\mathbb R^{N\times N}$ . The eigen-decomposition of L is denoted as  $U\Lambda U^{\top}$ , where  $\Lambda=diag(\lambda_1,\ldots,\lambda_N)$  and  $U=[u_1^{\top},\ldots,u_N^{\top}]\in\mathbb R^{N\times N}$ . For graph  $\mathcal G$ , L has n non-negative real eigenvalues  $0\leq \lambda_1\leq \lambda_2\leq \ldots \leq \lambda_N$ . Specifically, the low-frequency components refer to the eigenvalues closer to 0, and the high-frequency components refer to the relatively larger eigenvalues.
+
+#### 3.2 Spectral Analysis Insights
+
+Adopting a spectral viewpoint, we conduct a thorough empirical study to understand the interplay between graph properties, graph topology alterations in the spatial domain, and their corresponding impacts in the spectral realm. The findings from our analysis include three crucial aspects as detailed below. Details of experimental settings and more results can be found in Appendices C & D.
+
+#### Obs 1. The position of the edge flip influences the magnitude of spectral changes.
+
+In Figures 2a and 2b, we explore how adding different edges to a toy graph affects its eigenvalues. For instance, the addition of the edge  $1\leftrightarrow 3$  (shown as the red line), which connects two proximate nodes, primarily impacts the high-frequency component  $\lambda_6$  (highlighted by the red rectangle). In contrast, when adding edge  $2\leftrightarrow 6$  (the blue line) between two distant nodes, the low-frequency component  $\lambda_1$  exhibits the most noticeable change (indicated by the blue rectangle). These variations in the spectrum underscore the significance of the edge-flipping position within the graph's overall
+
+![](figures/_page_3_Figure_1.jpeg)
+
+Figure 2: (a) A toy graph  $\mathcal{G}$  consisting of eight nodes. (b) Absolute variation in eigenvalues of  $\mathcal{G}$  when adding an edge at diverse positions. The red and blue rectangles represent when adding the corresponding edges in  $\mathcal{G}$  and the change of the eigenvalues. (c) A real-world case in the REDDIT-BINARY dataset where, when dropping 20% and 50%, the high frequency is more vulnerable.
+
+topology, whose insight is consistent with findings by (Entezari et al., 2020; Chang et al., 2021). Such spectral changes not only affect the graph's inherent structural features but also potentially affect the outcomes of tasks relying on spectral properties, such as graph-based learning.
+
+#### Obs 2. Low-frequency components display greater resilience to edge alterations.
+
+Building on Obs 1, we further investigate the phenomenon of different responses of high- and low-frequency components to topology alterations using a real-world graph from the REDDIT-BINARY dataset. We apply DropEdge (Rong et al., 2019) for data augmentation by first randomly dropping 20% and 50% of edges and then computing the corresponding eigenvalues, as depicted in Figure 2c. Our findings indicate that, under random edge removal, low-frequency components exhibit greater robustness compared to their high-frequency counterparts.
+
+# Obs 3. Graph properties are crucial for graph classification.
+
+Certain fundamental properties of graphs, e.g., diameter and radius, are critical for a variety of downstream tasks, including graph classification (Feragen et al., 2013). In Figures 3a and 3b, we present the distributions of two key graph properties – diameter d and radius r – across the two classes in the REDD-M12 dataset. The different variations in these distributions emphasize their critical role in graph classification. Nevertheless, arbitrary modifications to the graph's topology, e.g., random-manner-based augmentation techniques, could potentially distort these vital properties, illustrated in Figures 1b and 1e.
+
+# Obs 4. Specific low-frequency eigenvalues are closely tied to crucial graph properties. From Obs 3, a question is raised: Can we retain the integrity of these essential graph properties during augmen-
+
+<span id="page-3-0"></span>![](figures/_page_3_Figure_9.jpeg)
+
+<span id="page-3-1"></span>Figure 3: (a) Diameter and (b) radius distributions of different classes in REDD-M12. When (c) adding or (d) removing an edge, variation of the spectral domain  $\Delta L_2$ ,  $1/\lambda_1$  of  $\mathcal{G}'$ , ASPL and diameter d of  $\mathcal{G}'$ .
+
+tation? To explore this, we turn our attention back to the toy graph in Figure 2a and examine the evolution of its properties and eigenvalues in response to single-edge flips. In Figures 3c and 3d, we chart the graph's average shortest path length (denoted by blue dots), diameter d (denoted by green dots) against the reciprocal of its second smallest eigenvalue  $1/\lambda_1$  (denoted by red dots)<sup>1</sup>. Our observations reveal a notable correlation between the alterations in d and  $1/\lambda_1$ .
+
+Further, we investigate correlations among overall spectral shifts, graph properties, and specific eigenvalues. Consistent with established methodologies (Lin et al., 2022; Wang et al., 2022; Wills & Meyer, 2020), we adopt the Frobenius distance to quantify the overall spectral variations by computing the  $L_2$  distance between the spectrum of  $\mathcal{G}$  and augmented graph  $\mathcal{G}'$ . Notably, this spectral shift does not directly correspond with the changes in properties or eigenvalues. This suggests that by maintaining critical eigenvalues, primarily the low-frequency components, we can inject relatively large spectral changes without affecting essential graph properties. This observation thus leads to our proposition: preserving key eigenvalues while modifying others enables the generation of augmented graphs that uphold foundational properties, instead of only focusing on the overall spectral shifts.
+
+<span id="page-3-2"></span><sup>&</sup>lt;sup>1</sup>For visual clarity, we scaled d and  $1/\lambda_1$  by dividing it by 3 and 5, respectively.
+
+#### <span id="page-4-0"></span>4 METHODOLOGY
+
+Drawing inspiration from how prisms decompose and reconstruct light and how a polarizer selectively filters light (see Figure 4a), we design our own "polarizer", i.e., the **Dual-Prism** (DP) method for graph data augmentation, as depicted in Figure 4b. The details are illustrated below, followed by both empirical evidence and theoretical rationale to substantiate our approach.
+
+![](figures/_page_4_Figure_3.jpeg)
+
+<span id="page-4-1"></span>Figure 4: The framework of our Dual-Prism (DP) for graph data augmentation.
+
+#### 4.1 Proposed Augmentation Methods
+
+The proposed Dual-Prism (DP) methods, including DP-Noise and DP-Mask, obtain the augmented graphs by directly changing the spectrum of graphs. A step-by-step breakdown is delineated in Algorithm 1. The DP method starts by extracting the Laplacian Matrix L of a graph  $\mathcal G$  by L=D-A and then computes its eigen-decomposition  $L=U\Lambda U^{\top}$ . Based on the frequency ratio  $r_f$ ,  $N_a$  eigenvalues are selected for augmentation, where  $N_a=N\times r_f$ . Note that since we only target high-frequency eigenvalues, we arrange eigenvalues in increasing order and only focus on the last  $N_a$  eigenvalues. Then, a binary mask M is formed based on the augmentation ratio  $r_a$  to sample the eigenvalues to make a change. Depending on the chosen augmentation type T, either noise is infused to the sampled eigenvalues, modulated by  $\sigma$  and M (from Line 6 to 8), or the eigenvalues are adjusted using the mask M directly (from Line 9 to 10). Finally, we reconstruct the new Laplacian  $\hat{L}$  based on the updated eigenvalues  $\hat{\Lambda}$ . Given the Laplacian matrix is L=D-A, where D is a diagonal matrix, an updated adjacency matrix  $\hat{A}$  can be derived by eliminating self-loops. Lastly, we obtain the augmented graph  $\hat{\mathcal{G}}$  with its original labels and features retained.
+
+**Selection of** L. Note that we adopt the Laplacian matrix L instead of the normalized Laplacian matrix  $L_{\rm norm} = I - D^{-1/2}AD^{-1/2}$ . The rationale behind this choice is that reconstructing the adjacency matrix using  $L_{\rm norm}$  necessitates solving a system quadratic equation, where the number of unknown parameters equals the number of nodes in the graph. The computational complexity of this solution is more than  $O(N^3)$ . Even if we approximate it as a quadratic optimization problem, making it solvable with a gradient-based optimizer, the computational overhead introduced by solving such an optimization problem for each graph to be augmented is prohibitively high.
+
+#### **Algorithm 1** Dual-Prism Augmentation
+
+```
+Input: Graph \mathcal{G}, Frequency Ratio r_f, Augmentation Ratio r_a, Standard Deviation \sigma, Augmentation Type T.
+ 1: N \leftarrow the number of nodes in \mathcal{G}
+ 2: L \leftarrow \text{Laplacian Matrix of } \mathcal{G}
+ 3: U and \Lambda \leftarrow eigenvalue decomposition of L
+                                                                                                        \triangleright \Lambda is arranged in increasing order.
+ 4: N_a \leftarrow int(N \times r_f)
+                                                                                   ▶ Get the number of eigenvalues to be augmented.
+ 5: M \leftarrow \{m_i \sim Bern(r_a)\}_{i=1}^{N_a}
+ 6: if T = \text{noise then}
+          \epsilon \leftarrow \{\epsilon_i \sim \mathcal{N}(0,1)\}_{i=1}^{N_a}
+          for i \in \{1, \dots, N_a\} do \{\lambda_{N-i} \leftarrow \max(0, \lambda_{N-i} + \sigma M_i \epsilon_i)\} \triangleright Add noise to the high-frequency part.
+9: else if T = \max k then
+          for i \in \{1, \dots, N_a\} do \{\lambda_{N-i} \leftarrow (1 - M_i)\lambda_i\}
+
+    ► Mask the high-frequency part.
+
+11: \hat{L} \leftarrow U^{\top} \hat{\Lambda} U, \hat{A} \leftarrow -\hat{L}
+                                                                           ▷ Calculate the new Laplacian and new adjacent matrix.
+12: for i \in \{1, \dots, N\} do \{\hat{A}_{ii} \leftarrow 0\}
+Output: Augmented \hat{\mathcal{G}} with edge_index derived from \hat{A}, and the label and features unchanged
+```
+
+![](figures/_page_5_Figure_1.jpeg)
+
+<span id="page-5-0"></span>Figure 5: (a) Training loss of GIN model on REDDIT-BINARY when graphs are augmented by masking different eigenvalues. (b) Graph classification performance on IMDB-BINARY under various hyperparameters. The lines represent the average accuracy, while the shaded areas indicates the error margins.
+
+#### 4.2 EMPIRICAL EVIDENCE
+
+Next, we aim to verify the correctness of our methods on the improvement of the performance for graph classification via experimental analysis.
+
+Diverse roles of eigenvalues. We begin by masking selected eigenvalues to generate graphs for 20% of REDDIT-BINARY. The training loss when masking the eigenvalues  $\lambda_1$ ,  $\lambda_2$  and  $\lambda_5$  is shown in Figure 5a. These curves suggest that individual eigenvalues contribute differently to the training process. Specifically, masking  $\lambda_1$  results in a notably unstable training loss for the initial 500 epochs, evidenced by the expansive blue-shaded region. For  $\lambda_2$ , while the shaded region's extent is smaller, the curve exhibits noticeable fluctuations, particularly around epoch 200. Conversely, when masking  $\lambda_5$ , the training appears more stable, with the green curve showing relative steadiness and a reduced shaded area. These demonstrate the various significance of eigenvalues:  $\lambda_1$  and  $\lambda_2$  include more crucial structural and property details of the graph compared to  $\lambda_5$ . As a result, they deserve to be prioritized for preservation during augmentation.
+
+Different importance of high- and low-frequency parts. We then conduct experiments on group-level eigenvalues, i.e., the high- and low-frequency eigenvalues, to gain a broader view of the influence exerted by varying frequency eigenvalues. We introduce noise to eigenvalues across various hyperparameter combinations. Concretely, we use the standard deviation  $\sigma$  to determine the magnitude of the noise. The frequency ratio  $r_f$  dictates the number of eigenvalues  $N_a$  we might change, while the augmentation probability  $r_a$  specifies the final eigenvalues sampled for modification. The eigenvalues are arranged in ascending order. The setting of 'Low' means that we select candidates from the first  $N_a$  eigenvalues, while 'High' denotes selection from the last  $N_a$  eigenvalues. As shown in Figure 5b, the orange lines consistently outperform the green lines across all three plots, indicating that the performance associated with perturbing high-frequency eigenvalues consistently exceeds that of their low-frequency counterparts. Moreover, as the frequency ratio  $r_f$  increases, the accuracy of the 'Low' scenario remains relatively stable and low. Contrastingly, for the 'High' scenario, a notable decline in accuracy begins once the ratio exceeds around 30%. This suggests that the eigenvalues outside the top 30% of the high-frequency range may start to include more critical information beneficial for graph classification tasks that should not be distorted.
+
+#### 4.3 THEORETICAL BACKING AND INSIGHTS
+
+The eigenvalues of the Laplacian matrix provide significant insights into various graph properties, as established in prior research (Chung, 1997). Such insights have driven and backed our proposal to modify the high-frequency eigenvalues while preserving their low-frequency counterparts. For example, the second-smallest eigenvalue  $\lambda_1$ , often termed the *Fiedler value*, quantifies the graph's *algebraic connectivity*. A greater Fiedler value indicates a better-connected graph and it is greater than 0 if and only if the graph is a connected graph. The number of times 0 appears as an eigenvalue is the number of connected components in the graph. In addition to the connectivity, the diameter of a graph is also highly related to the eigenvalues – it can be upper and lower bounded from its spectrum (Chung, 1997):  $4/n\lambda_1 \leq d \leq 2[\sqrt{2m/\lambda_1}\log_2 n]$ , where n and m denotes the number of nodes and the maximum degree of the graph, respectively. In addition to these widely-used properties, other properties are also highly related to spectrum, including graph diffusion distance (Hammond et al., 2013). In essence, eigenvalues serve as powerful spectral signatures comprising a myriad of structural and functional aspects of graphs.
+
+# <span id="page-6-0"></span>5 EXPERIMENTS
+
+Experimental Setup. We evaluate our augmentation method for graph classification tasks under four different settings, including supervised learning, semi-supervised learning, unsupervised learning, and transfer learning. We conduct our experiments on 21 real-world datasets across three different domains, including bio-informatics, molecule, and social network, from the TUDatasets benchmark [\(Morris et al., 2020\)](#page-10-2), OGB benchmark [\(Hu et al., 2020a\)](#page-10-10) and ZINC chemical molecule dataset [\(Hu et al., 2020b\)](#page-10-11). The details of the datasets, baselines, and experimental settings can be found in Appendices [A,](#page-13-0) [B,](#page-13-1) and [C,](#page-15-0) respectively. More empirical results, including the evaluations on hyperparameter sensitivity analysis, can be found in Appendix [D.](#page-16-0)
+
+#### 5.1 SUPERVISED LEARNING
+
+Performance. We first evaluate our proposed methods in the supervised learning setting. Following the prior works [\(Han et al., 2022;](#page-10-7) [Ling et al., 2023\)](#page-10-8), we use GIN and GCN as backbones for graph classification on eight different datasets. Table [1](#page-6-1) shows the performance of our proposed methods compared with seven state-of-art (SOTA) baselines, including DropEdge[\(Rong et al., 2019\)](#page-11-1), DropNode[\(Feng et al., 2020\)](#page-9-0), Subgraph[\(You et al., 2020\)](#page-12-1), M-Mixup [\(Verma et al., 2019\)](#page-11-3), Sub-Mix[\(Yoo et al., 2022\)](#page-12-4), G-Mixup[\(Han et al., 2022\)](#page-10-7) and S-Mixup [\(Ling et al., 2023\)](#page-10-8). According to the results, our DP-Noise method consistently outperforms other existing methods across the majority of datasets, establishing its dominance in effectiveness. DP-Mask also shines, often securing a noteworthy second-place standing. GIN tends to obtain superior outcomes, especially when combined with DP-Noise, which is exemplified by its 61.67% classification accuracy on IMDB-M. Note that on REDD-B, GIN achieves more satisfactory performance than GCN, which is a consistent pattern across baselines but becomes particularly pronounced with our methods. This phenomenon may be attributed to the intrinsic characteristics of GIN and GCN. GIN is known for its precision in delineating complex structural intricacies of graphs [\(Xu et al., 2018\)](#page-11-12), while GCN is characterized by its smoothing effect [\(Defferrard et al., 2016\)](#page-9-8). Our methods' superiority in diversifying the graphs' structures naturally amplifies GIN's strengths. In contrast, GCN may not be as adept at leveraging the enhancements offered by our augmentation techniques.
+
+Generalization. Figures [6a](#page-7-0) and [6b](#page-7-0) display the test loss and accuracy curves for the IMDB-B dataset, comparing four distinct augmentation strategies: G-mixup, DP-Noise, DP-Mask, and a scenario without any augmentation (i.e., Vanilla). A notable trend is the consistently lower and more stable test loss curves for DP-Noise and DP-Mask in comparison to Vanilla and G-mixup. Concurrently, the accuracy achieved with DP-Noise and DP-Mask is higher. This indicates our proposed methods' superior generalization and the capacity for enhancing model stability.
+
+#### 5.2 SEMI-SUPERVISED LEARNING
+
+Performance. We then evaluate our methods in a semi-supervised setting comparing with five baselines, including training from scratch without and with augmentations (denoted as Vanilla and Aug., respectively), GAE [\(Kipf & Welling, 2016b\)](#page-10-12), Informax [\(Velickovi](#page-11-13) ˇ c et al., [2018\)](#page-11-13) and GraphCL[\(You](#page-12-1) ´
+
+<span id="page-6-1"></span>Table 1: Performance comparisons with GCN and GIN in the *supervised* learning setting. The best and second best results are highlighted with bold and underline, respectively. \* and \*\* denote the improvement over the second best baseline is statistically significant at level 0.1 and 0.05, respectively[\(Newey & West, 1987\)](#page-10-13). Baseline results are taken from [Ling et al.](#page-10-8) [\(2023\)](#page-10-8); [Han et al.](#page-10-7) [\(2022\)](#page-10-7).
+
+|     | Dataset  | IMDB-B       | IMDB-M       | REDD-B       | REDD-M5      | REDD-M12     | PROTEINS     | NCI1         | ogbg-molhiv  |
+|-----|----------|--------------|--------------|--------------|--------------|--------------|--------------|--------------|--------------|
+|     | Vanilla  | 72.80±4.08   | 49.47±2.60   | 84.85±2.42   | 49.99±1.37   | 46.90±0.73   | 71.43±2.60   | 72.38±1.45   | -            |
+|     | DropEdge | 73.20±5.62   | 49.00±2.94   | 85.15±2.81   | 51.19±1.74   | 47.08±0.55   | 71.61±4.28   | 68.32±1.60   | -            |
+|     | DropNode | 73.80±5.71   | 50.00±4.85   | 83.65±3.63   | 47.71±1.75   | 47.93±0.64   | 72.69±3.55   | 70.73±2.02   | -            |
+|     | Subgraph | 70.90±5.07   | 49.80±3.43   | 68.41±2.57   | 47.31±5.23   | 47.49±0.93   | 67.93±3.24   | 65.05±4.36   | -            |
+| GCN | M-Mixup  | 72.00±5.66   | 49.73±2.67   | 87.05±2.47   | 51.49±2.00   | 46.92±1.05   | 71.16±2.87   | 71.58±1.79   | -            |
+|     | SubMix   | 72.30±4.75   | 49.73±2.88   | 85.15±2.37   | 52.87±2.19   | -            | 72.42±2.43   | 71.65±1.58   | -            |
+|     | G-Mixup  | 73.20±5.60   | 50.33±3.67   | 86.85±2.30   | 51.77±1.42   | 48.06±0.53   | 70.18±2.44   | 70.75±1.72   | -            |
+|     | S-Mixup  | 74.40±5.44   | 50.73±3.66   | 89.30±2.69   | 53.29±1.97   | -            | 73.05±2.81   | 75.47±1.49   | 96.70±0.20   |
+|     | DP-Noise | 77.90±2.30 * | 53.60±1.59** | 84.60±7.61   | 53.42±1.36   | 48.47±0.57   | 75.03±2.66   | 69.20±2.57   | 97.02±0.19** |
+|     | DP-Mask  | 76.00±3.62   | 51.20±1.73   | 76.70±1.34   | 52.42±2.78   | 47.25±1.12   | 73.60±3.10   | 62.45±3.80   | 96.90±0.24*  |
+|     | Vanilla  | 71.30±4.36   | 48.80±2.54   | 89.15±2.47   | 53.17±2.26   | 50.23±0.83   | 68.28±2.47   | 79.08±2.12   | -            |
+|     | DropEdge | 70.50±3.80   | 48.73±4.08   | 87.45±3.91   | 54.11±1.94   | 49.77±0.76   | 68.01±3.22   | 76.47±2.34   | -            |
+|     | DropNode | 72.00±6.97   | 45.67±2.59   | 88.60±2.52   | 53.97±2.11   | 49.95±1.70   | 69.64±2.98   | 74.60±2.12   | -            |
+|     | Subgraph | 70.40±4.98   | 43.74±5.74   | 76.80±3.87   | 50.09±4.94   | 49.67±0.90   | 66.67±3.10   | 60.17±2.33   | -            |
+| GIN | M-Mixup  | 72.00±5.14   | 48.67±5.32   | 87.70±2.50   | 52.85±1.03   | 49.81±0.80   | 68.65±3.76   | 79.85±1.88   | -            |
+|     | SubMix   | 71.70±6.20   | 49.80±4.01   | 90.45±1.93   | 54.27±2.92   | -            | 69.54±3.15   | 79.78±1.09   | -            |
+|     | G-Mixup  | 72.40±5.64   | 49.93±2.82   | 90.20±2.84   | 54.33±1.99   | 50.50±0.41   | 64.69±3.60   | 78.20±1.58   | -            |
+|     | S-Mixup  | 73.40±6.26   | 50.13±4.34   | 90.55±2.11   | 55.19±1.99   | -            | 69.37±2.86   | 80.02±2.45   | 96.84±0.40   |
+|     | DP-Noise | 78.40±1.82** | 61.67±0.71** | 93.42±1.41** | 57.72±1.87** | 53.70±1.16** | 73.51±4.54** | 90.56±5.78** | 97.43±0.48** |
+|     | DP-Mask  | 76.30±2.56   | 51.60±1.32   | 93.25±1.19** | 56.50±0.80*  | 49.11±1.30   | 72.79±1.95** | 80.30±2.01   | 96.98±0.29   |
+
+<span id="page-7-0"></span>Figure 6: (a) The loss and (b) accuracy curves for supervised learning on test data of IMDB-BINARY using GIN, with four augmentation methods. Curves represent mean values from 5 runs, and shaded areas indicate standard deviation. The accuracy gain (%) in semi-supervised learning when contrasting 5 different augmentation methods with (c) DP-Noise and (b) DP-Mask across 7 datasets. Warmer color means better performance gains.
+
+et al., 2020). Table 2 provides the performance comparison when utilizing 1% and 10% label ratios. At the more challenging 1% label ratio, our DP-Noise achieves SOTA results across all three datasets, and DP-Mask secures the second-best performance on two out of the three datasets. As the label ratio increases to 10%, DP-Noise maintains its efficacy, showcasing excellent performance on six out of seven datasets.
+
+**Augmentation Pairing Efficiency.** To investigate optimal combinations that could potentially enhance performance, we evaluate the synergistic effects on accuracy gain (%) when pairing DP-Noise and DP-Mask with different augmentation methods using the same setting in You et al. (2020). From Figures 6c and 6d, overall, the diverse accuracy gains across datasets indicate that there is no one-size-fits-all "partner" for DP-Noise and DP-Mask; the efficacy of each combination varies depending on the dataset. However, generally, both DP-Noise and DP-Mask exhibit enhanced performance when paired with dropN at a large degree.
+
+#### <span id="page-7-2"></span>5.3 Unsupervised representation learning
+
+We next evaluate our strategies in the unsupervised learning setting and compare them with 12 baselines, including three graph kernel methods (GL (Pržulj, 2007), WL(Shervashidze et al., 2011) and DGK(Yanardag & Vishwanathan, 2015)), four representation learning methods (node2vec (Grover & Leskovec, 2016), sub2vec(Adhikari et al., 2018), graph2vec(Narayanan et al., 2017) and InfoGraph(Sun et al., 2019)) and five GCL-based methods (GraphCL(You et al., 2020), MV-GRL(Hassani & Khasahmadi, 2020), AD-GCL(Suresh et al., 2021), JOAO(You et al., 2021) and GCL-SPAN(Lin et al., 2022)). Table 3 shows the performance of our methods in an unsupervised setting. From the results, DP-Noise and DP-Mask surpass other baselines on five out of seven datasets. Notably, compared with another spectral-based method GCL-SPAN (Lin et al., 2022), our methods outperform it on most datasets, especially on the molecules dataset NCI1 (increase of around 11.5% accuracy). This can be explained by that despite GCL-SPAN is also spectral-based, it in fact modifies the spatial graph while optimizing in the spectral realm. In contrast, our methods directly make alterations in the spectral domain to preserve the structural information. Given the
+
+<span id="page-7-1"></span>Table 2: Performance comparisons in the *semi-supervised* learning setting. The best and second best results are highlighted with **bold** and <u>underline</u>, respectively. 1% or 10% is the label ratio. The metric is accuracy (%). \* and \*\* denote the improvement over the second best baseline is statistically significant at level 0.1 and 0.05, respectively. Baseline results are taken from You et al. (2020).
+
+| Dataset      | NCI1             | PROTEINS         | DD               | COLLAB           | REDD-B           | REDD-M5                     | GITHUB                    |
+|--------------|------------------|------------------|------------------|------------------|------------------|-----------------------------|---------------------------|
+| 1% Vallina   | $60.72 \pm 0.45$ | -                | -                | 57.46±0.25       | -                | -                           | 54.25±0.22                |
+| 1% Aug.      | $60.49 \pm 0.46$ | -                | -                | $58.40 \pm 0.97$ | -                | -                           | $56.36 \pm 0.42$          |
+| 1% GAE       | $61.63 \pm 0.84$ | -                | -                | $63.20 \pm 0.67$ | -                | -                           | $59.44 \pm 0.44$          |
+| 1% Infomax   | $62.72 \pm 0.65$ | -                | -                | $61.70 \pm 0.77$ | -                | -                           | $58.99 \pm 0.50$          |
+| 1% GraphCL   | $62.55 \pm 0.86$ | -                | -                | $64.57 \pm 1.15$ | -                | -                           | $58.56 \pm 0.59$          |
+| 1% DP-Noise  | $63.43 \pm 1.39$ | -                | -                | $65.94 \pm 3.13$ | -                | -                           | $60.06 \pm 2.72$          |
+| 1% DP-Mask   | $62.43 \pm 1.08$ | -                | -                | $65.68\pm1.66$ * | -                | -                           | $59.70 \pm 0.53$          |
+| 10% Vallina  | $73.72 \pm 0.24$ | $70.40 \pm 1.54$ | $73.56 \pm 0.41$ | $73.71 \pm 0.27$ | 86.63±0.27       | 51.33±0.44                  | 60.87±0.17                |
+| 10% Aug.     | $73.59 \pm 0.32$ | $70.29 \pm 0.64$ | $74.30 \pm 0.81$ | $74.19 \pm 0.13$ | $87.74 \pm 0.39$ | $52.01 \pm 0.20$            | $60.91 \pm 0.32$          |
+| 10% GAE      | $74.36 \pm 0.24$ | $70.51 \pm 0.17$ | $74.54 \pm 0.68$ | $75.09\pm0.19$   | $87.69 \pm 0.40$ | $53.58 \pm 0.13$            | $63.89 \pm 0.52$          |
+| 10% Infomax  | $74.86 \pm 0.26$ | $72.27 \pm 0.40$ | $75.78 \pm 0.34$ | $73.76 \pm 0.29$ | $88.66 \pm 0.95$ | $\overline{53.61 \pm 0.31}$ | $65.21 \pm 0.88$          |
+| 10% GraphCL  | $74.63 \pm 0.25$ | $74.17 \pm 0.34$ | $76.17 \pm 1.37$ | $74.23 \pm 0.21$ | $89.11 \pm 0.19$ | $52.55 \pm 0.45$            | $65.81 \pm 0.79$          |
+| 10% DP-Noise | 75.30±0.58**     | $74.73 \pm 1.01$ | $76.91 \pm 0.81$ | 77.05±0.82**     | 89.38±0.95       | 54.45±0.64**                | $65.59 \pm 0.88$          |
+| 10% DP-Mask  | $74.88 \pm 1.84$ | $71.37 \pm 4.18$ | $75.64 \pm 0.81$ | 76.90±0.62**     | $88.62 \pm 0.63$ | $52.80 \pm 0.59$            | $\overline{64.95\pm1.03}$ |
+
+critical role that structural patterns in molecular data play on classification tasks, the enhanced performance underscores the efficiency of our direct spectral modifications in creating more effective and insightful augmented graphs for graph classification.
+
+<span id="page-8-1"></span>Table 3: Performance comparisons in the *unsupervised* learning results. The best and second best results are highlighted with bold and underline, respectively. The metric is accuracy (%). \* and \*\* denote the improvement over the second best baseline is statistically significant at level 0.1 and 0.05, respectively. Baseline results are taken from [You et al.](#page-12-1) [\(2020\)](#page-12-1); [Lin et al.](#page-10-5) [\(2022\)](#page-10-5).
+
+| Dataset   | NCI1       | PROTEINS   | DD           | MUTAG       | REDD-B       | REDD-M5    | IMDB-B     |
+|-----------|------------|------------|--------------|-------------|--------------|------------|------------|
+| GL        | -          | -          | -            | 81.66±2.11  | 77.34±0.18   | 41.01±0.17 | 65.87±0.98 |
+| WL        | 80.01±0.50 | 72.92±0.56 | -            | 80.72±3.00  | 68.82±0.41   | 46.06±0.21 | 72.30±3.44 |
+| DGK       | 80.31±0.46 | 73.30±0.82 | -            | 87.44±2.72  | 78.04±0.39   | 41.27±0.18 | 66.96±0.56 |
+| node2vec  | 54.89±1.61 | 57.49±3.57 | -            | 72.63±10.20 | -            | -          | -          |
+| sub2vec   | 52.84±1.47 | 53.03±5.55 | -            | 61.05±15.80 | 71.48±0.41   | 36.68±0.42 | 55.26±1.54 |
+| graph2vec | 73.22±1.81 | 73.30±2.05 | -            | 83.15±9.25  | 75.78±1.03   | 47.86±0.26 | 71.10±0.54 |
+| InfoGraph | 76.20±1.06 | 74.44±0.31 | 75.23±0.39   | 89.01±1.13  | 82.50±1.42   | 53.46±1.03 | 73.03±0.87 |
+| GraphCL   | 77.87±0.41 | 74.39±0.45 | 78.62±0.40   | 86.80±1.34  | 89.53±0.84   | 55.99±0.28 | 71.14±0.44 |
+| MVGRL     | 68.68±0.42 | 74.02±0.32 | 75.20±0.55   | 89.24±1.31  | 81.20±0.69   | 51.87±0.65 | 71.84±0.78 |
+| AD-GCL    | 69.67±0.51 | 73.59±0.65 | 74.49±0.52   | 89.25±1.45  | 85.52±0.79   | 53.00±0.82 | 71.57±1.01 |
+| JOAO      | 72.99±0.75 | 71.25±0.85 | 66.91±1.75   | 85.20±1.64  | 78.35±1.38   | 45.57±2.86 | 71.60±0.86 |
+| GCL-SPAN  | 71.43±0.49 | 75.78±0.41 | 75.78±0.52   | 89.12±0.76  | 83.62±0.64   | 54.10±0.49 | 73.65±0.69 |
+| DP-Noise  | 79.69±0.70 | 74.60±0.43 | 78.59±0.23   | 87.63±1.98  | 90.90±0.32** | 55.54±0.15 | 71.42±0.41 |
+| DP-Mask   | 79.47±0.22 | 74.70±0.29 | 79.97±1.09** | 89.98±1.36  | 91.21±0.24** | 55.92±0.49 | 71.78±0.37 |
+
+#### 5.4 TRANSFER LEARNING
+
+We lastly conduct transfer learning experiments on molecular property prediction in the manner of [Hu et al.](#page-10-11) [\(2020b\)](#page-10-11) to evaluate the capability of our methods for learning generalizable encoders. Specifically, we initially pre-train models on the extensive chemical molecule dataset ZINC [\(Ster](#page-11-18)[ling & Irwin, 2015\)](#page-11-18), then fine-tune the models on eight distinct datasets within a similar domain. We draw comparisons between our methods and six baselines, including a reference model without pre-training (referred to *No-Pre-Train*), Informax [\(Velickovi](#page-11-13) ˇ c et al., [2018\)](#page-11-13), EdgePred [\(Hamilton](#page-9-15) ´ [et al., 2017\)](#page-9-15), AttrMasking [\(Hu et al., 2020b\)](#page-10-11), ContextPred [\(Hu et al., 2020b\)](#page-10-11) and GraphCL [You](#page-12-1) [et al.](#page-12-1) [\(2020\)](#page-12-1). The comparative results are shown in Table [4.](#page-8-2) Our methods demonstrated SOTA performance, outperforming competitors on half of the datasets. Especially, our methods consistently outperform the conventional GraphCL method, which indicates our data augmentation methods as better choices for graph contrastive learning. Notably, DP-Mask achieves an 83.52% ROC-AUC score on ClinTox, exceeding the performance of GraphCL by a substantial margin (nearly 10%). These findings demonstrate the enhanced efficacy of our techniques in the transfer learning setting for graph classification tasks.
+
+<span id="page-8-2"></span>Table 4: Performance comparisons in the *transfer* learning setting. The best and second best results are highlighted with bold and underline, respectively. The metric is ROC-AUC scores (%). \* and \*\* denote the improvement over the second best baseline is statistically significant at level 0.1 and 0.05, respectively. Baseline results are taken from [Hu et al.](#page-10-11) [\(2020b\)](#page-10-11); [You et al.](#page-12-1) [\(2020\)](#page-12-1).
+
+| Dataset      | BBBP          | Tox21       | ToxCast     | SIDER       | ClinTox       | MUV         | HIV         | BACE        |
+|--------------|---------------|-------------|-------------|-------------|---------------|-------------|-------------|-------------|
+| No-Pre-Train | 65.80± 4.50   | 74.00± 0.80 | 63.40± 0.60 | 57.30± 1.60 | 58.00± 4.40   | 71.80± 2.50 | 75.30± 1.90 | 70.10± 5.40 |
+| Infomax      | 68.80± 0.80   | 75.30± 0.50 | 62.70± 0.40 | 58.40± 0.80 | 69.90± 3.00   | 75.30± 2.50 | 76.00± 0.70 | 75.90± 1.60 |
+| EdgePred     | 67.30± 2.40   | 76.00± 0.60 | 64.10± 0.60 | 60.40± 0.70 | 64.10± 3.70   | 74.10± 2.10 | 76.30± 1.00 | 79.90± 0.90 |
+| AttrMasking  | 64.30± 2.80   | 76.70± 0.40 | 64.20± 0.50 | 61.00± 0.70 | 71.80± 4.10   | 74.70± 1.40 | 77.20± 1.10 | 79.30± 1.60 |
+| ContextPred  | 68.00± 2.00   | 75.70± 0.70 | 63.90± 0.60 | 60.90± 0.60 | 65.90± 3.80   | 75.80± 1.70 | 77.30± 1.00 | 79.60± 1.20 |
+| GraphCL      | 69.68± 0.67   | 73.87± 0.66 | 62.40± 0.57 | 60.53± 0.88 | 75.99± 2.65   | 69.80± 2.66 | 78.47± 1.22 | 75.38± 1.44 |
+| DP-Noise     | 70.38± 0.91*  | 74.33± 0.42 | 64.08± 0.25 | 61.52± 0.79 | 76.26± 1.68   | 73.39± 2.08 | 78.63± 0.37 | 76.23± 0.86 |
+| DP-Mask      | 71.63± 1.86** | 74.91± 0.49 | 63.43± 0.28 | 61.33± 0.17 | 83.52± 1.07** | 73.77± 1.40 | 77.80± 1.31 | 78.73± 1.13 |
+
+# <span id="page-8-0"></span>6 CONCLUSION
+
+In this study, we adopt a spectral perspective, bridging graph properties and spectral insights for property-retentive and globally-aware graph data augmentation. Stemming from this point, we propose a novel augmentation method called Dual-Prism (DP), including DP-Noise and DP-Mask. By focusing on different frequency components in the spectrum, our method skillfully preserves graph properties while ensuring diversity in augmented graphs. Our extensive evaluations validate the efficacy of our methods across various learning paradigms on the graph classification task. In summary, our contributions highlight the potential of leveraging spectral insights in graph data augmentation.
+
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+
+#### <span id="page-13-0"></span>A DETAILS OF DATASETS
+
+We conduct our experiments on 21 different graph real-world datasets for graph classification tasks. In this section, we provide detailed descriptions of the datasets used in this paper. Specifically, for the *supervised* learning setting, we include a total of eight datasets from the TUDatasets benchmark (Morris et al., 2020) (i.e., PROTEINS, NCI1, IMDB-BINARY, IMDB-MULTI, REDDIT-BINARY, REDDIT-MULTI-5K, and REDDIT-MULTI-12K) and the OGB benchmark (Hu et al., 2020a) (i.e., ogbg-molhiv). For the *semi-supervised* learning setting, we include seven different datasets from the TUDatasets benchmark (Morris et al., 2020) (i.e., PROTEINS, NCI1, DD, COLLAB, GITHUB, REDDIT-BINARY, and REDDIT-MULTI-5K). For the *unsupervised* learning setting, we include seven different datasets from the TUDatasets benchmark (Morris et al., 2020) (i.e., PROTEINS, NCI1, DD, MUTAG, IMDB-BINARY, REDDIT-BINARY, and REDDIT-MULTI-5K). The detailed of these datasets can be found in Table 5.
+
+<span id="page-13-2"></span>Table 5: Statistical characteristics of the datasets in three learning settings. Supe.: Supervised learning. Semi.: Semi-supervised learning. Unsu.: Unsupervised learning.
+
+| _                | 1                     |          |             | _         |              |              |               |
+|------------------|-----------------------|----------|-------------|-----------|--------------|--------------|---------------|
+| Dataset          | Category              | # Graphs | # Avg edges | # Classes | Task         |              |               |
+| Dataset          | Category              | " Graphs | " Twg cages | " Classes | Supe.        | Semi.        | Unsu.         |
+| IMDB-BINARY      | Social Networks       | 1,000    | 96.53       | 2         | <b>√</b>     |              | $\overline{}$ |
+| IMDB-MULTI       | Social Networks       | 1,500    | 65.94       | 3         | $\checkmark$ |              |               |
+| REDDIT-BINARY    | Social Networks       | 2,000    | 497.75      | 2         | $\checkmark$ | $\checkmark$ | $\checkmark$  |
+| REDDIT-MULTI-5K  | Social Networks       | 4,999    | 594.87      | 5         | $\checkmark$ | $\checkmark$ | $\checkmark$  |
+| REDDIT-MULTI-12K | Social Networks       | 11,929   | 456.89      | 11        | $\checkmark$ |              |               |
+| COLLAB           | Social Networks       | 5,000    | 2457.78     | 3         |              | ✓            |               |
+| GITHUB           | Social Networks       | 12,725   | 234.64      | 2         |              | ✓            |               |
+| DD               | Biochemical Molecules | 1,178    | 715.66      | 2         |              | ✓            | $\checkmark$  |
+| MUTAG            | Biochemical Molecules | 188      | 19.79       | 2         |              |              | $\checkmark$  |
+| PROTEINS         | Biochemical Molecules | 1,113    | 72.82       | 2         | ✓            | ✓            | $\checkmark$  |
+| NCI1             | Biochemical Molecules | 4,110    | 32.30       | 2         | ✓            | ✓            | $\checkmark$  |
+| ogbg-molhiv      | Biochemical Molecules | 41,127   | 27.50       | 2         | $\checkmark$ |              |               |
+
+For the *transfer* learning setting, we pre-train on ZINC-2M chemical molecule dataset (Sterling & Irwin, 2015; Gómez-Bombarelli et al., 2018), and fine-tune on eight different datasets, namely BBBP, Tox21, ToxCast, SIDER, ClinTox, MUV, HIV, and BACE. The detailed of these datasets can be found in Table 6.
+
+<span id="page-13-3"></span>Table 6: Statistical characteristics of the datasets used in the transfer learning setting.
+
+| Dataset | Strategy     | # Molecules | # Binary tasks |
+|---------|--------------|-------------|----------------|
+| ZINC-2M | Pre-training | 2,000,000   | -              |
+| BBBP    | Fine-tuning  | 2,039       | 1              |
+| Tox21   | Fine-tuning  | 7,831       | 12             |
+| ToxCast | Fine-tuning  | 8,576       | 617            |
+| SIDER   | Fine-tuning  | 1,427       | 27             |
+| ClinTox | Fine-tuning  | 1,477       | 2              |
+| MUV     | Fine-tuning  | 93,087      | 17             |
+| HIV     | Fine-tuning  | 41,127      | 1              |
+| BACE    | Fine-tuning  | 1,513       | 1              |
+
+#### <span id="page-13-1"></span>B DETAILS OF BASELINES
+
+**Supervised learning.** For experiments in the supervised setting, we select the following baseline:
+
+- DropEdge (Rong et al., 2019) selectively drops a portion of edges from the input graphs.
+- DropNode (Feng et al., 2020) omits a specific ratio of nodes from the provided graphs.
+- Subgraph (You et al., 2020) procures subgraphs from the main graphs using a random walk sampling technique.
+- M-Mixup (Verma et al., 2019) blends graph-level representations through linear interpolation.
+- SubMix (Yoo et al., 2022) combines random subgraphs from paired input graphs.
+
+- G-Mixup [\(Han et al., 2022\)](#page-10-7) employs a class-focused graph mixup strategy by amalgamating graphons across various classes.
+- S-Mixup [\(Ling et al., 2023\)](#page-10-8) adopts a mixup approach for graph classification, emphasizing soft alignments.
+
+Semi-supervised learning. For experiments in the semi-supervised setting, we select the following baseline methods:
+
+- GAE [\(Kipf & Welling, 2016b\)](#page-10-12) is a non-probabilistic graph auto-encoder model, which is a variant of the VGAE (variational graph autoencoder).
+- Informax [\(Velickovi](#page-11-13) ˇ c et al., [2018\)](#page-11-13) trains a node encoder to optimize the mutual information be- ´ tween individual node representations and a comprehensive global graph representation.
+- GraphCL [\(You et al., 2020\)](#page-12-1) conducts an in-depth exploration of graph structure augmentations, including random edge removal, node dropping, and subgraph sampling.
+
+Unsupervised learning. For experiments in the unsupervised setting, we select the following baseline methods:
+
+- GL (graphlet kernel) [\(Przulj, 2007\)](#page-11-14) measures the similarity between graphs by counting the occur- ˇ rences of small subgraphs, known as graphlets, within them. It captures local topological patterns, thus providing a comprehensive view of the graph structure.
+- WL (Weisfeiler-Lehman sub-tree kernel) [\(Shervashidze et al., 2011\)](#page-11-15) captures the similarity between graphs by comparing subtrees of increasing heights. It effectively distinguishes nonisomorphic graphs and is often employed for graph classification tasks.
+- DGK (deep graph kernel) [\(Yanardag & Vishwanathan, 2015\)](#page-11-16) combines the strengths of both graph kernels and deep learning. It leverages convolutional neural networks to learn hierarchical representations of graphs, enabling the kernel to capture complex patterns and structures within the data for a more refined similarity measure.
+- node2vec [\(Grover & Leskovec, 2016\)](#page-9-13) captures low-dimensional embeddings of graph nodes by leveraging random walks originating from target nodes.
+- sub2vec [\(Adhikari et al., 2018\)](#page-9-14) seeks to capture feature representations of arbitrary subgraphs, addressing the limitations of node-centric embeddings.
+- graph2vec [\(Narayanan et al., 2017\)](#page-10-14) is a neural embedding framework designed to learn data-driven distributed representations of entire graphs.
+- InfoGraph [\(Sun et al., 2019\)](#page-11-17) is designed to maximize the mutual information between complete graph representations and various substructures, such as nodes, edges, and triangles.
+- GraphCL (see above section).
+- MVGRL [\(Hassani & Khasahmadi, 2020\)](#page-10-15) establishes a link between the local Laplacian matrix and a broader diffusion matrix by leveraging mutual information. This approach yields representations at both the node and graph levels, catering to distinct prediction tasks.
+- AD-GCL [\(Suresh et al., 2021\)](#page-11-2) emphasize preventing the capture of redundant information during training. They achieve this by optimizing adversarial graph augmentation strategies in GCL and introducing a trainable non-i.i.d. edge-dropping graph augmentation.
+- JOAO [\(You et al., 2021\)](#page-12-5) utilize a bi-level optimization framework to sift through optimal strategies, exploring multiple augmentation types like uniform edge or node dropping and subgraph sampling.
+- GCL-SPAN [\(Lin et al., 2022\)](#page-10-5) introduces a spectral augmentation approach, which directs topology augmentations to maximize spectral shifts.
+
+Transfer learning. For experiments in the transfer setting, we select the following baseline methods:
+
+• Informax (see above section).
+
+- EdgePred [\(Hamilton et al., 2017\)](#page-9-15) employs an inductive approach that utilizes node features, such as text attributes, to produce node embeddings by aggregating features from a node's local neighborhood, rather than training distinct embeddings for each node.
+- AttrMasking (Attribute Masking) [\(Hu et al., 2020b\)](#page-10-11) is a pre-training method for GNNs that harnesses domain knowledge by discerning patterns in node or edge attributes across graph structures.
+- ContextPred (Context Prediction) [\(Hu et al., 2020b\)](#page-10-11) is designed for pre-training GNNs that simultaneously learn local node-level and global graph-level representations via subgraphs to predict their surrounding graph structures.
+- GraphCL (see above section).
+
+# <span id="page-15-0"></span>C DETAILS OF EXPERIMENTS SETTINGS
+
+We conduct our experiments with PyTorch 1.13.1 on a server with NVIDIA RTX A5000 and CUDA 12.2. For each experiment, we run 10 times. We detail the settings of our experiments in this paper as follows.
+
+Speed up implementation. Our augmentation method involves matrix eigenvalue decomposition, which is highly CPU-intensive. During implementation, we observed that when there is insufficient CPU, parallelly executing numerous matrix eigenvalue decomposition can lead to CPU resource deadlock. To address this issue, we established an additional set of CPU locks to manage CPU scheduling. Let Ncpu represent the number of CPUs available for each matrix eigenvalue decomposition task, and Nparallel denote the number of decomposition tasks that can be executed simultaneously. We set Ncpu × Nparallel to be less than the total CPU number of the server. During task execution, we created a list of CPU locks, with each lock corresponding to Ncpu available CPUs. There is no overlap between the CPUs corresponding to each lock. Before a matrix decomposition task is executed, it must first request a CPU lock. Once the lock is acquired, the task can only be executed on the designated CPUs. After completion, the task releases the CPU lock. If there are no free locks in the current CPU lock list, the matrix decomposition task must wait. By employing this approach, we effectively isolated parallel matrix decomposition tasks.
+
+Empirical studies. We first detail the processes and settings of the empirical studies below.
+
+- Experiment of Figure [1.](#page-1-0) For DropEdge, 20% edges are randomly dropped. For DP-Noise, we use a standard deviation of 7, an augmentation probability of 0.5, and an augmentation frequency ratio of 0.5. For DP-Mask, the augmentation probability is set to 0.3, with an augmentation frequency ratio of 0.4. Detailed variations in edge numbers and properties between the original and augmented graphs can be found in Table [7.](#page-16-1)
+- Experiment of Figure [3.](#page-3-1) In Figures [3a](#page-3-1) and [3b](#page-3-1), labels in REDDIT-MULTI-12K for Class A and Class B are 1 and 10, respectively. The added edges in [3c](#page-3-1) are 3↔5, 3↔7, 1↔6, 2↔6, 0↔2, 1↔3, 1↔4, 2↔4, 4↔6, and 5↔7, respectively. The dropped edges in [3d](#page-3-1) are 0↔4, 3↔4, 4↔5, 4↔7, 0↔1, 2↔3, 0↔3, 5↔6, 6↔7, and 1↔2, respectively. The change of spectrum ∆L<sup>2</sup> is the L<sup>2</sup> distance between the spectrum of G and augmented graph G ′ q , denoted as ∆L<sup>2</sup> = P i (λi(G) − λi(Gˆ))<sup>2</sup>, where λ(G) represent the spectrum of G and λ(Gˆ) is the spectrum of Gˆ.
+- Experiment of Figure [5.](#page-5-0) For both Figure [5a](#page-5-0) and [5b](#page-5-0), we employ GIN as the backbone model and conduct experiments over five runs. In Figure [5b](#page-5-0), while testing one parameter, we draw the other parameters from their respective search spaces: σ ∈ [0.1, 0.5, 1.0, 2.0], r<sup>f</sup> ∈ [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8], and r<sup>a</sup> ∈ [0, 0.2, 0.4, 0.6, 0.8, 1]. In addition, to control the noise adding to low- and high-frequency eigenvalues are in the same scale, the augmented i-th eigenvalue is calculated as λ<sup>i</sup> = max(0, 1 + ϵ) × λ<sup>i</sup> , where ϵ ∼ N (0, σ).
+
+Supervised learning. Following prior works [\(Han et al., 2022;](#page-10-7) [Ling et al., 2023\)](#page-10-8), we utilize two GNN models, namely GCN [\(Kipf & Welling, 2017\)](#page-10-16) and GIN [\(Xu et al., 2018\)](#page-11-12). Details of these GNNs are provided below.
+
+• GCN. For the TUDatasets benchmark, the backbone model has four GCN layers, utilizes a global mean pooling readout function, has a hidden size of 32, and uses the ReLU activation function. For the ogbg-molhiv dataset, the model consists of five GCN layers, a hidden size of 300, the ReLU activation function, and a global mean pooling readout function.
+
+<span id="page-16-1"></span>Table 7: Details of alterations of the number of edges and properties of graphs in Figure [1.](#page-1-0)
+
+|          | Edge Alterations |         | Properties   |          |        |             |      |  |
+|----------|------------------|---------|--------------|----------|--------|-------------|------|--|
+| Graph    | # Dropped        | # Added | Connectivity | Diameter | Radius | # Periphery | ASPL |  |
+| Original | -                | -       | TRUE         | 2        | 1      | 11          | 1.42 |  |
+| DropEdge | 7                | 0       | TRUE         | 3        | 2      | 8           | 1.64 |  |
+| DP-Noise | 6                | 0       | TRUE         | 2        | 1      | 11          | 1.52 |  |
+| DP-Mask  | 14               | 4       | TRUE         | 2        | 1      | 11          | 1.58 |  |
+
+• GIN. For the TUDatasets benchmark, the backbone model comprises four GIN layers, each with a two-layer MLP. It utilizes a global mean pooling readout function, has a hidden size of 32, and adopts the ReLU activation function. Conversely, for the ogbg-molhiv dataset, the model consists of five GIN layers, a hidden size of 300, the ReLU activation function, and employs a global mean pooling for the readout function.
+
+For all other hyper-parameter search space and training configurations of the experiments on the IMDB-B, IMDB-M, REDD-B, REDD-M5, and REDD-M12, we keep consistent with [Han et al.](#page-10-7) [\(2022\)](#page-10-7). For all other hyper-parameter search space and training configurations of the experiments on the PROTEIN, NCI1, and ogbg-hiv, we keep consistent with [Ling et al.](#page-10-8) [\(2023\)](#page-10-8). Note that instead of adopting the results of baseline methods on the ogbg-hiv dataset from the reference directly, we reported the results of rerunning the baseline experiments on the ogbg-hiv dataset, which is higher than the results in the reference.
+
+Semi-supervised learning. We maintain consistency with [You et al.](#page-12-1) [\(2020\)](#page-12-1) for all hyper-parameter search spaces and training configurations. For all datasets, we conduct experiments at label rates of 1% (provided there are more than 10 samples for each class) and 10%. These experiments are performed five times, with each instance corresponding to a 10-fold evaluation. We report both the mean and standard deviation of the accuracies in percentages. During pre-training, we perform a grid search, tuning the learning rate among 0.01, 0.001, 0.0001 and the epoch number within 20, 40, 60, 80, 100.
+
+Unsupervised representation learning. Following [You et al.](#page-12-1) [\(2020\)](#page-12-1); [Lin et al.](#page-10-5) [\(2022\)](#page-10-5), we use a 5 layer GIN as encoders. For all hyper-parameter search spaces and training settings in unsupervised learning, we also align with the configurations presented in [You et al.](#page-12-1) [\(2020\)](#page-12-1). We conduct experiments five times, with each iteration corresponding to a 10-fold evaluation. The reported results in Table [3](#page-8-1) include both the mean and standard deviation of the accuracy percentages.
+
+Transfer learning. Following the transfer learning setting in [Hu et al.](#page-10-11) [\(2020b\)](#page-10-11); [You et al.](#page-12-1) [\(2020\)](#page-12-1); [Lin et al.](#page-10-5) [\(2022\)](#page-10-5), we conduct graph classification experiments on a set of biological and chemical datasets via GIN models. Specifically, an encoder was first pre-trained on the large ZINC-2M chemical molecule dataset [\(Sterling & Irwin, 2015;](#page-11-18) [Gomez-Bombarelli et al., 2018\)](#page-9-16) and then was ´ evaluated on small datasets from the same domains (i.e., BBBP, Tox21, ToxCast, SIDER, ClinTox, MUV, HIV, and BACE).
+
+# <span id="page-16-0"></span>D MORE EXPERIMENTS RESULTS
+
+Empirical studies. In Section [3,](#page-2-0) we investigate spectral alterations due to adding an edge in a toy graph (depicted in Figure [2a](#page-3-0)). The spectral changes are presented in Figure [2b](#page-3-0). Further, in Figure [7,](#page-18-0) we analyze the consequences on the spectrum when edges from the same toy graph are removed. Notably, the removal of edges 0-4 and 3-4 results in minimal spectral variations. However, the removal of edges 5-6 and 6-7 leads to pronounced changes in both high and low frequencies, evident from the pronounced shifts in values λ<sup>2</sup> and λ5. To further illustrate our observation, we present an additional example featuring a nine-node toy graph that also exhibits similar results, as shown in Figure [8.](#page-17-0)
+
+Hyperparameter sensitivities. We conducted experiments on the IMDB-BINARY dataset, leveraging various combinations of standard deviation σ and frequency ratio r<sup>f</sup> for both low and high-frequency components to assess the impacts of DP-Noise parameters. For these experiments, we employed the GIN as our backbone model let σ and r<sup>f</sup> from two search spaces, where σ ∈ [0.1, 0.5, 1.0, 2.0] and r<sup>f</sup> ∈ [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8]. We run 5 experiments and
+
+<span id="page-17-0"></span>![](figures/_page_17_Figure_1.jpeg)
+
+Figure 8: (a) Another toy graph  $\mathcal{G}'$  consisting of nine nodes. (b) Absolute variation in eigenvalues of  $\mathcal{G}'$  when adding an edge at diverse positions. The red and blue rectangles represent when adding the corresponding edges in  $\mathcal{G}'$  and the change of the eigenvalues.
+
+![](figures/_page_17_Figure_3.jpeg)
+
+<span id="page-17-1"></span>Figure 9: Effects of different hyperparameter combinations on the IMDB-BINARY dataset in the supervised learning setting for graph classification via adding noise to (a) low-frequency and (b) high-frequency eigenvalues, respectively. The evaluation metric is accuracy.
+
+report the average values in Figure 9. Our observations indicate that introducing noise in the high-frequency components tends to enhance the test accuracy more markedly than when infused in the low-frequency regions, as illustrated by the prevailing lighter color in Figure 9a. This observation resonates with the insights gleaned from Section 3. Building upon these general observations, we further elucidate the effects of each specific parameter below.
+
+- Effects of Standard Deviation  $\sigma$ . For low-frequency components, the introduction of noise seems to not exhibit a consistent influence on accuracy. In contrast, when noise is applied to high-frequency components, we observe a discernible trend: accuracy tends to increase with increasing standard deviations. This suggests that the diversity introduced by elevating the standard deviation of noise can potentially bolster the classification performance of generated graphs.
+- Effects of Frequency Ratio  $r_f$ . Similar to  $\sigma$ , for low-frequency components, increasing  $r_f$  does not consistently enhance or degrade accuracy across different standard deviations. On the other hand, in the high-frequency regime, a subtle trend emerges. As  $r_f$  increases, there is a nuanced shift in accuracy, suggesting that the spectrum of frequencies impacted by the noise has a nuanced interplay with the graph's inherent structures and the subsequent classification performance.
+
+We also conduct hyperparameter analysis in different learning settings. Figure 10 shows performances across multiple datasets, which reveals distinct trends in performance related to augmentation probability  $(aug_prob)$  and frequency ratio  $(aug_freq_ratio)$ . Specifically, for the DD dataset, performance peaks with a high  $aug_freq_ratio$  and  $aug_prob$ , suggesting a preference for more frequent augmentations. In contrast, the MUTAG dataset shows optimal results at a lower frequency but higher probability, indicating a different augmentation response. The NCI1 dataset's best performance occurs at higher values of both parameters, while REDDIT-BINARY favors moderate to high frequency combined with a high probability, achieving its peak performance under these conditions.
+
+These patterns highlight the necessity of customizing hyperparameters to each dataset for optimal augmentation effectiveness.
+
+![](figures/_page_18_Figure_2.jpeg)
+
+Figure 10: Effects of different hyperparameter combinations on different datasets in the unsupervised learning setting for graph classification via masking. The evaluation metric is accuracy.
+
+Complexity and Time Analysis. Theoritically, the computational bottleneck of our data augmentation method primarily stems from the eigen-decomposition and reconstruction of the Laplacian matrix. For a graph with n nodes, the computational complexity of both operations is  $O(n^3)$ . In terms of implementation, we have measured the time cost required by our method. For each n, we randomly generated 100 graphs and recorded the average time and standard deviation required for our data augmentation method. The results, presented in Table 8, are measured in milliseconds. The average number of nodes in commonly used graph classification datasets is approximately between 10 and 500. Therefore, in the majority of practical training scenarios, the average time consumption of our algorithm for augmenting a single graph is roughly between 1 millisecond and 40 milliseconds. The experiments con-
+
+<span id="page-18-1"></span>![](figures/_page_18_Figure_5.jpeg)
+
+<span id="page-18-0"></span>Figure 7: Absolute variation of eigenvalues when dropping different edges of the toy graph.
+
+ducted here did not employ any parallel computing or acceleration methods. However, in actual training processes, it is common to parallelize data preprocessing using multiple workers or to precompute and store the eigen-decomposition results of training data. Therefore, the actual time consumption required for our method in implementations will be even lower.
+
+Table 8: Time cost required by our method. n: Number of nodes.
+
+<span id="page-18-2"></span>
+
+|          | n = 10          | n = 20          | n = 100         | n = 200         | n = 500          | n = 1000          |
+|----------|-----------------|-----------------|-----------------|-----------------|------------------|-------------------|
+| Time(ms) | $0.76 \pm 0.55$ | $0.89 \pm 0.43$ | $2.50 \pm 0.50$ | $6.45 \pm 0.58$ | $41.35 \pm 2.39$ | $230.75 \pm 8.76$ |
+
+#### E MORE DISCUSSIONS
+
+Intuitions & Advantages of proposed methods. (1) Properties Preservation. Data augmentation should not only increase the quantity of training data but also enrich the quality of the learning experience for the model. Here, quality refers to the diversity, relevance, and realism of the augmented data. Therefore, property-retentive augmentations provide a more genuine learning context for the model, thus directly improving performance. (2) Global Perspective. Looking at the graph globally allows us to understand the larger structures and patterns within the graph. By making broader changes to the graph's structure, global augmentations can create more diverse training instances, compared to local augmentations which might only create minor variations of the existing instances, therefore enhancing understanding of complex graph relationships and contributing to improved performance.
+
+**Broader Impact.** Through a spectral lens, our Dual-Prism (DP) augmentation method presents both significant advancements and implications in the realm of graph-based learning. This can lead to improved performance, robustness, and generalizability of graph neural networks (GNNs) across a myriad of applications, from social network analysis to molecular biology. In addition, by utilizing spectral properties, our method provides a more transparent approach to augmentation. This can help
+
+researchers and practitioners better understand how alterations to graph structures impact learning outcomes, thereby aiding in the interpretability of graph data augmentation.
+
+Limitations & Future Directions. A potential limitation of this study is its primary emphasis on homophily graphs. In contrast, heterophily graphs, where high-frequency information plays a more crucial role, are not extensively addressed [\(Bo et al., 2021\)](#page-9-6). Looking ahead, it would be worth investigating learning strategies tailored to selectively alter eigenvalues, ensuring adaptability across diverse datasets. This includes developing methods to safely create realistic augmented graphs and experimenting with mix-up techniques involving eigenvalues from different graphs.
+
+Comparison with Existing Works. There are two related works about the spectral view on graph data augmentation, i.e., [\(Liu et al., 2022;](#page-10-4) [Lin et al., 2022\)](#page-10-5), while both are grounded in the GCL framework. Specifically, [Liu et al.](#page-10-4) [\(2022\)](#page-10-4) proposes a rule to find the optimal contrastive pair under the GCL framework instead of a general augmentation method. GCL-SPAN [Lin et al.](#page-10-5) [\(2022\)](#page-10-5) centers on maximizing variance in the spectral domain, our observations indicate that overall spectral changes don't always align with graph properties, as detailed in Section [3.](#page-2-0) Thus, constraining specific eigenvalues to remain invariant might be a more effective strategy for generating valid augmented graphs. Despite GCL-SPAN [\(Lin et al., 2022\)](#page-10-5) also utilizing a spectral perspective, it in fact still modifies the spatial domain while optimizing in the spectral realm. In contrast, our techniques directly make alterations in the spectral domain, leading to more meaningful and effective alterations. This is evident by our methods' superior performance in graph classification (see in Section [5.3\)](#page-7-2) and underscores the efficiency of straightforward spectral modifications in creating more effective and discerning augmented graphs for graph classification. In addition, the DP method is specifically designed for graph classification tasks. Unlike node classification tasks [Yoo et al.](#page-12-4) [\(2022\)](#page-12-4) that emphasize node features and local structures, our approach is rooted in the analysis of global graph structures.
+
+Rationale for Choosing Graph Laplacian Decomposition. In our methodology, we chose to decompose the graph Laplacian L (where L = D − A) to do the perturbation and then reconstruct the graph. In terms of implementation, an alternative method can be directly decomposing A and perturbing its smaller eigenvalues. However, our motivation for this work is more on the inherent properties of graphs, and L offers a more nuanced reflection of these properties compared to A [Lutzeyer & Walden](#page-10-17) [\(2017\)](#page-10-17). For future scenarios involving more complex disturbances to eigenvalues, leveraging the eigenvalues of L would be a more appropriate approach. In addition, our decision to decompose L also follows general spectral graph convolution methodologies [Kipf &](#page-10-1) [Welling](#page-10-1) [\(2016a\)](#page-10-1).

papers/1P1nxem1jU/review.json

@@ -0,0 +1,91 @@
+{
+  "id": "1P1nxem1jU",
+  "title": "Through the Dual-Prism: A Spectral Perspective on Graph Data Augmentation for Graph Classification",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "yzjFg4IrXh",
+      "rating": 8,
+      "content": {
+        "summary": "This paper introduces a novel graph data augmentation method called Dual-Prism (DP), which aims to retain essential graph properties while diversifying augmented graphs. The authors draw inspiration from the way prisms decompose and reconstruct light and how polarizers selectively filter light to design their own \"polarizer\". They conduct extensive experiments on diverse real-world datasets and demonstrate that their proposed methods can achieve state-of-the-art performance on most of the datasets. This work provides a promising new direction for graph data augmentation.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "4 excellent",
+        "strengths": "The Dual-Prism (DP) augmentation method proposed in this paper is a novel approach to graph data augmentation. The authors draw inspiration from optics to design their own \"polarizer\" that retains essential graph properties while diversifying augmented graphs. This innovative approach provides a new direction for graph data augmentation.\n\nThe authors conduct extensive experiments on 21 real-world datasets spanning various learning paradigms. The experimental results demonstrate that their proposed methods can achieve state-of-the-art performance on most of the datasets. This extensive evaluation provides strong evidence for the efficacy of the DP augmentation method. \n\nThe authors provide empirical evidence to substantiate their approach. They explain the rationale behind their DP method and how it skillfully preserves graph properties while ensuring diversity in augmented graphs. This work also proposes the globally-aware and property-retentive augmentation methods, DP-Noise and DP-Mask, which are able to preserve inherent graph properties while simultaneously enhancing the diversity of augmented graphs.",
+        "weaknesses": "The authors could delve deeper into the influence of various hyperparameters on the performance of the Dynamic Programming (DP) method. Although they provide some details on the hyperparameters used in their experiments, a more detailed exploration could potentially identify optimal hyperparameters for different types of graphs and learning tasks.\n\nMoreover, it would be compelling to examine the effectiveness of the proposed DP method on larger and more complex graphs. Despite conducting experiments on 21 real-world datasets, extending this to larger, more complex graphs could further validate the efficiency of their proposed method and offer valuable insights into its scalability.",
+        "questions": "The authors could enhance their study by further investigating the effect of various hyperparameters on the Dynamic Programming (DP) method's performance. While details of the used hyperparameters are given, a more comprehensive exploration could help identify optimal hyperparameters for diverse graph types and learning tasks. Additionally, testing the proposed DP method on larger and more complex graphs, beyond their 21 real-world datasets, could further validate the method's efficiency and provide insights into its scalability.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "The authors could delve deeper into the influence of various hyperparameters on the performance of the Dynamic Programming (DP) method. Although they provide some details on the hyperparameters used in their experiments, a more detailed exploration could potentially identify optimal hyperparameters for different types of graphs and learning tasks.\n\nMoreover, it would be compelling to examine the effectiveness of the proposed DP method on larger and more complex graphs. Despite conducting experiments on 21 real-world datasets, extending this to larger, more complex graphs could further validate the efficiency of their proposed method and offer valuable insights into its scalability.",
+        "suggestions": "To enhance the study, the authors should conduct a more thorough investigation into the hyperparameter space of the Dynamic Programming (DP) method. While the paper mentions the hyperparameters used, a systematic analysis is needed to understand how parameters such as the augmentation frequency ratio and augmentation probability interact and affect performance across different graph structures and learning tasks. For instance, a grid search or Bayesian optimization approach could be employed to map the performance landscape for each dataset, revealing optimal parameter combinations. This analysis should not only identify the best performing parameters but also provide insights into why certain parameter settings are more effective for specific types of graphs, such as sparse versus dense graphs or graphs with varying node degree distributions. Furthermore, the authors should explore the sensitivity of the DP method to these hyperparameters, determining how much performance degrades when parameters deviate from their optimal values. This would provide a more complete picture of the robustness and generalizability of the proposed method.\n\nIn addition to hyperparameter analysis, the authors should rigorously evaluate the scalability of the DP method by testing it on significantly larger and more complex graphs. While the 21 real-world datasets provide a good starting point, they may not fully capture the challenges associated with very large graphs, such as those encountered in social networks or biological systems. The authors should consider datasets with orders of magnitude more nodes and edges to assess how the computational cost and performance of the DP method scale with graph size. This evaluation should include both the runtime of the augmentation process and the impact of augmented graphs on downstream learning tasks. Furthermore, the authors should investigate whether the DP method maintains its effectiveness on graphs with different structural properties, such as those with community structures or power-law degree distributions. This would provide a more comprehensive understanding of the method's limitations and potential areas for improvement.\n\nFinally, the authors should consider exploring the impact of the DP method on different graph neural network (GNN) architectures. While the paper demonstrates the method's effectiveness with specific GNN models, it's important to understand how well it generalizes to other architectures. This could involve testing the DP method with a range of GNNs, including those that utilize attention mechanisms or graph pooling layers. Such an analysis would reveal whether the DP method is universally beneficial or if its effectiveness depends on the specific GNN architecture used. Furthermore, the authors could investigate whether the DP method can be combined with other data augmentation techniques to achieve even better performance. This would not only demonstrate the versatility of the proposed method but also provide valuable insights into how different augmentation strategies can be integrated to maximize their benefits."
+      }
+    },
+    {
+      "id": "Wgw0EW9Bxv",
+      "rating": 6,
+      "content": {
+        "summary": "Graph neural networks (GNNs) have become the preferred tool to process graph data. This paper aims to develop property-conserving and structure-sensitive augmentation methods. Through a spectral lens, the authors investigate the interplay between graph properties, their augmentation, and their spectral behavior, and found that keeping the low-frequency eigenvalues unchanged can preserve the critical properties at a large scale when generating augmented graphs.",
+        "soundness": "4 excellent",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1. The writing is clear, and the paper is easy to follow.\n2. Instead of proposing another random approach, the authors provide their rationale clearly and comprehensively based on empirical evidence.\n3. The experiments are done extensively for 4 different tasks, on 21 datasets, and against numerous competitors.",
+        "weaknesses": "1. Since the accuracy improvement over competitors is not dramatic, statistical tests such as the Wilcoxon signed-rank test would be beneficial.\n2. Changing high-frequency eigenvalues is similar to making small, marginal changes to the graph structure while preserving the core properties, such as connectivity. In that sense, NodeSam [1] and MotifSwap [2] are better competitors than mixup-based approaches, which induce more changes to the structure.\n3. Although this paper discusses extensively the reasons why we should focus on high-frequency eigenvalues, there is little discussion on how to actually modify them. Simply using random masking or adding random noise appears too naive. Additional discussion on this part, e.g., how to safely alter these eigenvalues to create plausible augmented graphs, or how we might mix-up the eigenvalues between different graphs, would be valuable.\n\n[1] J. Yoo et al. “Model-Agnostic Augmentation for Accurate Graph Classification.” WWW 2022\n\n[2] J. Zhou et al. \"Data Augmentation for Graph Classification.” CIKM 2020",
+        "questions": "1. How long does it take to eigendecompose the matrix L? Is the complexity linear with the size of a graph?\n2. Apart from Figure 2b, could you provide more examples of augmented graphs resulting from changes to the eigenvalues?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. Since the accuracy improvement over competitors is not dramatic, statistical tests such as the Wilcoxon signed-rank test would be beneficial.\n2. Changing high-frequency eigenvalues is similar to making small, marginal changes to the graph structure while preserving the core properties, such as connectivity. In that sense, NodeSam [1] and MotifSwap [2] are better competitors than mixup-based approaches, which induce more changes to the structure.\n3. Although this paper discusses extensively the reasons why we should focus on high-frequency eigenvalues, there is little discussion on how to actually modify them. Simply using random masking or adding random noise appears too naive. Additional discussion on this part, e.g., how to safely alter these eigenvalues to create plausible augmented graphs, or how we might mix-up the eigenvalues between different graphs, would be valuable.",
+        "suggestions": "The paper would benefit significantly from a more rigorous statistical analysis of the experimental results. While the authors present performance metrics, the lack of statistical significance testing makes it difficult to ascertain whether the observed improvements are truly meaningful or simply due to random variation. Specifically, applying a Wilcoxon signed-rank test, or similar non-parametric tests, would provide a more solid foundation for the claims of the proposed method. This would involve comparing the performance of the proposed augmentation technique against each baseline across all datasets, and reporting the p-values to assess the statistical significance of any observed differences. Furthermore, providing effect sizes would be valuable to understand the magnitude of the improvements, beyond just statistical significance. This additional analysis is crucial to justify the contribution of the proposed method and to ensure the robustness of the findings.\n\nIn addition to statistical validation, the choice of baseline methods could be more carefully considered. While mixup-based approaches are included, they are not the most relevant for comparison given the paper's focus on preserving graph structure. The authors should consider including methods that make minimal structural changes, such as NodeSam [1] and MotifSwap [2], as these are more aligned with the stated goals of the paper. These methods are designed to alter the graph by swapping nodes or motifs, which are more subtle changes than those induced by mixup-based approaches. By comparing against these methods, the authors could better demonstrate the effectiveness of their approach in preserving graph properties while still achieving performance gains. This would also provide a clearer picture of the specific advantages of the proposed method over existing techniques that aim for similar goals.\n\nFinally, the paper needs a more thorough discussion on the practical implementation of high-frequency eigenvalue modification. The current approach of using random masking or adding random noise is not well-justified and lacks a theoretical basis. The authors should explore more principled ways of modifying these eigenvalues to ensure that the resulting augmented graphs are plausible. For instance, they could investigate methods that perturb the eigenvalues within a certain range or explore mixing eigenvalues from different graphs in a way that respects the underlying graph structure. Additionally, they could consider using techniques like spectral graph wavelets to guide the modification process. A more detailed discussion, along with empirical validation of different modification strategies, would significantly enhance the paper's practical value and provide a more complete understanding of the proposed technique."
+      }
+    },
+    {
+      "id": "NhcFllQBxl",
+      "rating": 5,
+      "content": {
+        "summary": "This paper studies the graph-level tasks with graph augmentation techniques. To be specific, they propose to perturb the high-frequency part of the given graphs to generate augmented graph samples, so as to boost the performance of graph-level tasks.",
+        "soundness": "3 good",
+        "presentation": "4 excellent",
+        "contribution": "2 fair",
+        "strengths": "S1. The presentation of this paper is excellent, and the paper is well-organized.\n\nS2. This paper includes comprehensive experiments, including supervised, unsupervised, and transfer learning settings.\n\nS3. The proposed method is concise but its performance on the supervised learning tasks is good.",
+        "weaknesses": "W1. The main concern of this paper is its novelty, which is low and being studied in many existing works.\n\nW2. A minor drawback of this paper is its performance. It shows strong performance in the supervised settings but gets average performance in other settings. In addition, some experimental results are missing, which is not expected.\n\nI will elaborate more in detail in the Questions setting.",
+        "questions": "Q1. My main concern with this paper is its novelty. Which shares great overlap with this paper [1], as multiply mentioned by the authors. Though they are not invented for the same purpose, it is not hard to transfer the idea from [1] into the context of this paper.\n\nQ2. In section 3.2, many observations have been mentioned by existing works. For example, **Obs 2. Low-frequency components display greater resilience to edge alterations** has been mentioned in existing work [2]. **Obs 4. Specific low-frequency eigenvalues are\nclosely tied to crucial graph properties.**, as this paper mentioned in Section 4.3, has been studied thoroughly by Chung in the spectral graph theory [3].\n\nQ3. The proposed Algorithm 1 first decomposes the graph Laplacian L,  perturbs the high-frequency part (larger eigenvalues of L), and finally reconstructs the perturbed adjacency matrix. I think a simpler version is directly decomposing the adjacency matrix A and perturbing its (A's) small eigenvalues. From this perspective, it is similar to many classic low-rank approximation-based works on graphs.\n\nQ4. The performance in the supervised setting is good, which is shown in Table 1. However, its performance in unsupervised learning (Table 3) and transfer learning settings (Table 4) is average.\n\nQ5. A suggestion for this paper is to finish experiments in Tables 1,2, and 3, where now they are shown '-'. Ideally, if the experiments are not conducted in existing papers, authors should implement the baseline methods and report the results in those missing setting by themselves.\n\n[1] Lin, Lu, Jinghui Chen, and Hongning Wang. \"Spectral Augmentation for Self-Supervised Learning on Graphs.\" In The Eleventh International Conference on Learning Representations. 2023.\n\n[2] Wang, Haonan, Jieyu Zhang, Qi Zhu, and Wei Huang. \"Augmentation-free graph contrastive learning with performance guarantee.\" arXiv preprint arXiv:2204.04874 (2022).\n\n[3] https://mathweb.ucsd.edu/~fan/mypaps/fanpap/111diameters.pdf",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "W1. The main concern of this paper is its novelty, which is low and being studied in many existing works.\n\nW2. A minor drawback of this paper is its performance. It shows strong performance in the supervised settings but gets average performance in other settings. In addition, some experimental results are missing, which is not expected.",
+        "suggestions": "The core idea of perturbing the high-frequency components of a graph's Laplacian for augmentation, while showing some promise in supervised tasks, lacks significant novelty. The connection to spectral graph theory and the manipulation of eigenvalues is well-trodden ground. The paper should more clearly articulate the specific novel contribution beyond simply applying these techniques to graph augmentation. A more detailed analysis of the types of perturbations applied, and how they relate to the graph's structural properties, would be beneficial. For instance, the paper could explore how different perturbation magnitudes or patterns affect the resulting augmented graphs and their downstream task performance. Furthermore, a more detailed discussion on the limitations of the proposed method in unsupervised and transfer learning settings is necessary. The average performance in these settings suggests that the method may be overly tailored to supervised learning, and the paper should discuss potential reasons for this limitation and propose possible avenues for improvement.\n\nTo address the performance issues, the authors should conduct a more thorough investigation into the parameters of their augmentation method. The current approach seems to apply a fixed level of perturbation to the high-frequency components. A more adaptive approach, where the level of perturbation is determined based on the characteristics of the input graph, could potentially lead to better results. This could involve analyzing the eigenvalue distribution of the Laplacian matrix and adjusting the perturbation accordingly. Specifically, the paper could explore the use of more sophisticated techniques for selecting which eigenvalues to perturb and by how much. Additionally, the missing experiments in Tables 1, 2, and 3 are a significant issue. The absence of these results makes it difficult to assess the true effectiveness of the proposed method compared to existing baselines. The authors should prioritize completing these experiments to provide a more comprehensive evaluation.\n\nFinally, the paper should delve deeper into the theoretical underpinnings of the proposed method. A more rigorous analysis of how perturbing the high-frequency components of the Laplacian affects the graph's properties would strengthen the paper's claims. This could involve examining the impact of the perturbation on various graph metrics such as node degree distribution, clustering coefficient, and path lengths. Furthermore, the paper could benefit from a more detailed comparison with other spectral-based graph augmentation techniques, highlighting the specific advantages and disadvantages of the proposed method. This would help to better position the work within the existing literature and clarify its unique contribution. The authors should also explore if the proposed method can be extended to other graph-based tasks such as node classification or link prediction."
+      }
+    },
+    {
+      "id": "VuFAlQesFw",
+      "rating": 5,
+      "content": {
+        "summary": "This paper focuses on developing a more property-conserving and structure-sensitive augmentation method. To achieve this, authors first investigate the interplay between graph properties, their augmentation, and their spectral behavior to derive that keeping the low-frequency eigenvalues unchanged can preserve the critical properties at a large scale. They then propose Dual-Prism (DP), an augmentation method that adeptly retains essential graph properties while diversifying augmented graphs.",
+        "soundness": "2 fair",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "1. This paper is well-motivated. Developing a more property-conserving augmentation method has long been focused on.\n2. Comprehensive experiments prove the performance of the proposed method.",
+        "weaknesses": "1. It has long been proven that low-frequency information is valuable for graphs and the idea to augment more high-frequency components can be easily derived from previous works[1], which makes the proposal less innovative. What is the advantage of the proposed method in maintaining low-frequency information? The authors should also compare DP with SpCo[1] in the experiments.\n2. The proposed method looks not efficient enough. It seems that Algorithm 1 involves eigenvalue decomposition and Laplacian Matrix reconstruction, which are both expensive. A time analysis would make the proposal more convincing.\n3. The experiment currently lacks graphs with large node numbers such as ogbn-arxiv and ogbn-proteins[2]. \n4. Why is the improvement of the DP method over previous ones marginal in some cases in Tables 1 to 4?\n5. In Obs 4, proof to the proposition \"preserving key eigenvalues while modifying others enables the generation of augmented graphs that\nuphold foundational properties\"  is relatively insufficient, especially when the authors use the spectral variation defined only by a single previous work.\n6. The font size in some figures is too small.\n\n[1] Revisiting graph contrastive learning from the perspective of graph spectrum. Advances in Neural Information Processing Systems, 2022.\\\n[2] Open graph benchmark: Datasets for machine learning on graphs. Advances in Neural Information Processing Systems, 2020.",
+        "questions": "See weaknesses.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. It has long been proven that low-frequency information is valuable for graphs and the idea to augment more high-frequency components can be easily derived from previous works[1], which makes the proposal less innovative. What is the advantage of the proposed method in maintaining low-frequency information? The authors should also compare DP with SpCo[1] in the experiments.\n2. The proposed method looks not efficient enough. It seems that Algorithm 1 involves eigenvalue decomposition and Laplacian Matrix reconstruction, which are both expensive. A time analysis would make the proposal more convincing.\n3. The experiment currently lacks graphs with large node numbers such as ogbn-arxiv and ogbn-proteins[2].\n4. Why is the improvement of the DP method over previous ones marginal in some cases in Tables 1 to 4?\n5. In Obs 4, proof to the proposition \"preserving key eigenvalues while modifying others enables the generation of augmented graphs that\nuphold foundational properties\"  is relatively insufficient, especially when the authors use the spectral variation defined only by a single previous work.\n6. The font size in some figures is too small.",
+        "suggestions": "The paper's core idea of manipulating the graph spectrum for augmentation is promising, but several aspects need further clarification and improvement. Specifically, the connection between the proposed Dual-Prism (DP) method and existing spectral graph augmentation techniques needs to be more thoroughly addressed. While the paper claims to preserve low-frequency information, it lacks a detailed explanation of how this is achieved in practice and why it is superior to other methods that also manipulate the graph spectrum. A more rigorous theoretical analysis of how DP's specific manipulations of the spectrum translate to the preservation of graph properties would strengthen the paper. Furthermore, the empirical evaluation should include a more direct comparison with methods like SpCo, which also operate in the spectral domain, to better contextualize the novelty and effectiveness of DP. The current experimental setup leaves open the question of whether the observed performance gains are truly due to the unique aspects of DP or simply a result of generic spectral perturbations.\n\nRegarding the computational efficiency, the paper needs a more thorough analysis of the time complexity and practical runtime of the proposed method. The algorithm involves eigenvalue decomposition and Laplacian matrix reconstruction, which are known to be computationally expensive operations, especially for large graphs. While the authors mention these steps, they do not provide a detailed analysis of how these operations scale with the size of the graph, nor do they provide any empirical runtime measurements. This lack of analysis makes it difficult to assess the practical applicability of the method, especially when compared to other augmentation techniques that may have lower computational overhead. The authors should provide a detailed breakdown of the time complexity, and ideally, include empirical runtime measurements on graphs of varying sizes to demonstrate the practical efficiency of their approach. This should include a comparison with the runtime of other augmentation techniques.\n\nFinally, the experimental evaluation needs to be broadened to include a wider range of datasets, particularly those with larger graphs. The current experiments are limited to relatively small graphs, which may not fully capture the behavior of the proposed method in more realistic scenarios. Including datasets like ogbn-arxiv and ogbn-proteins would provide a more comprehensive evaluation of the method's scalability and effectiveness. Furthermore, the paper needs to provide a more in-depth analysis of why the improvements of DP are marginal in some cases. The authors should explore the potential reasons for these marginal improvements, such as the inherent limitations of the datasets or the specific characteristics of the graph neural networks used in the experiments. A more detailed analysis of these factors would provide a more nuanced understanding of the strengths and limitations of the proposed method."
+      }
+    }
+  ]
+}

papers/1hhja8ZxcP/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "1hhja8ZxcP",
+  "title": "Turbulent Flow Simulation using Autoregressive Conditional Diffusion Models",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-15",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=1hhja8ZxcP"
+}

papers/1hhja8ZxcP/review.json

@@ -0,0 +1,92 @@
+{
+  "id": "1hhja8ZxcP",
+  "title": "Turbulent Flow Simulation using Autoregressive Conditional Diffusion Models",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "mZVXucqilj",
+      "rating": 5,
+      "content": {
+        "summary": "This paper proposes autoregressive conditional diffusion models (ACDMs) to simulate turbulent flow systems in an autoregressive rollout fashion. The model shows stability on long rollout horizon simulation. The proposed ACDM is further demonstrated to generate posterior samples that align closely with genuine physical dynamics in different fluid dynamics datasets.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "1 poor",
+        "strengths": "The paper is well-written, and the presentation is clear. The related works are well examined, encompassing the key areas of interest regarding the use of conditional diffusion models for turbulent flow simulation, and the paper is correctly placed in the current literature. The proposed approach is straightforward and the authors provide several experiments (alongside well-appreciated source code) that make evaluation robust.",
+        "weaknesses": "- The novelty is not much - the idea is almost a direct application of conditional diffusion models in autoregressive settings.\n- The inherent resolution at which a diffusion model generalizes is predefined during its training. This set resolution potentially restricts the model's flexibility, thereby impacting its practical utility and adaptability in diverse applications.\n- As depicted in Table 2, the enhancement in accuracy across the five datasets is marginal, with ACDM outperforming other models only on two datasets in terms of LSiM error. Moreover, it is unclear what is generally the best model from this result, given that except FNO, all models seem to obtain at least one best result across datasets.\n- Despite its acknowledgment of the limitations, the substantial computational cost of ACDM considerably undermines its practical utility. As state, the model can generate a solution in ~0.2 seconds; with 1000 time steps, this sums up to more than 3 minutes for a single trajectory against ~11 seconds for UNet. Therefore, it is hard to assess the Pareto-efficiency of the proposed method.\n- The organization of the paper would benefit from distinguishing between the preliminary and methodology sections; Section 3 is a mix of both and as such it is hard to distinguish the real contribution.\n- It would be useful to assess the performance on different datasets, such as from PDEBench [1], particularly in the 3D cases.\n- Stronger baselines could be chosen. For instance, graph neural networks have shown good performance in fluid dynamics such as [2]. Moreover, FNO variants such as AFNO have been shown to be powerful in large-scale real datasets [3].\n- [Minor] The explanation for Figure 4 is unclear. It appears that each subfigure lacks a title indicating the respective dataset name.\n\n---\n\n\n[1 ]Takamoto, Makoto, et al. \"PDEBench: An extensive benchmark for scientific machine learning.\" NeurIPS (2022).\n[2] Li, Zongyi, et al. \"Fourier neural operator with learned deformations for pdes on general geometries.\" arXiv preprint arXiv:2207.05209 (2022).\n[3]  Pathak, Jaideep, et al. \"Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators.\" arXiv preprint arXiv:2202.11214 (2022).",
+        "questions": "1. When the time step between two rollout steps is set to a fixed interval, how can we accurately capture the dynamics between these designated rollout steps?\n2. How would the model perform with real, possibly noisy data, such as the Black Sea and ScalarFlow datasets as in [1]?\n3. This is an additional question that does not influence the score (since the paper should be considered as \"concurrent work\"). How do you think your proposed model would fare against [2]?\n\n---\n\n[1 ] Lienen, Marten, and Stephan Günnemann. \"Learning the dynamics of physical systems from sparse observations with finite element networks.\" ICLR 2022.\n[2] Lippe, Phillip, et al. \"Pde-refiner: Achieving accurate long rollouts with neural pde solvers.\" NeurIPS (2023).",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "- The novelty is not much - the idea is almost a direct application of conditional diffusion models in autoregressive settings.\n- The inherent resolution at which a diffusion model generalizes is predefined during its training. This set resolution potentially restricts the model's flexibility, thereby impacting its practical utility and adaptability in diverse applications.\n- As depicted in Table 2, the enhancement in accuracy across the five datasets is marginal, with ACDM outperforming other models only on two datasets in terms of LSiM error. Moreover, it is unclear what is generally the best model from this result, given that except FNO, all models seem to obtain at least one best result across datasets.\n- Despite its acknowledgment of the limitations, the substantial computational cost of ACDM considerably undermines its practical utility. As state, the model can generate a solution in ~0.2 seconds; with 1000 time steps, this sums up to more than 3 minutes for a single trajectory against ~11 seconds for UNet. Therefore, it is hard to assess the Pareto-efficiency of the proposed method.\n- The organization of the paper would benefit from distinguishing between the preliminary and methodology sections; Section 3 is a mix of both and as such it is hard to distinguish the real contribution.\n- It would be useful to assess the performance on different datasets, such as from PDEBench [1], particularly in the 3D cases.\n- Stronger baselines could be chosen. For instance, graph neural networks have shown good performance in fluid dynamics such as [2]. Moreover, FNO variants such as AFNO have been shown to be powerful in large-scale real datasets [3].\n- [Minor] The explanation for Figure 4 is unclear. It appears that each subfigure lacks a title indicating the respective dataset name.",
+        "suggestions": "The paper would benefit from a more thorough exploration of the limitations of the proposed approach, particularly concerning its computational cost and generalization capabilities. While the authors acknowledge the high computational demands, a more detailed analysis of the trade-offs between accuracy and computational efficiency is needed. For example, the paper could explore techniques such as reduced-order modeling or model compression to mitigate the computational burden of the diffusion model. Furthermore, the paper should investigate the model's performance when extrapolating to resolutions outside the training domain, as this is a crucial aspect for practical applications. This could involve training the model on a range of resolutions or using techniques like super-resolution to enhance the model's adaptability. The current evaluation, while comprehensive, does not fully address the practical limitations of the proposed method in real-world scenarios where computational resources are often constrained and resolution requirements may vary.\n\nIn addition to the computational aspects, the paper should also delve deeper into the model's performance across different datasets and baselines. The current results in Table 2 show that the proposed ACDM does not consistently outperform other models across all datasets, raising questions about its generalizability and robustness. It would be beneficial to include a more diverse set of datasets, such as those available in PDEBench [1], particularly focusing on 3D cases, to provide a more comprehensive evaluation. Moreover, the choice of baselines could be strengthened by including more recent and powerful models, such as graph neural networks [2] and advanced FNO variants [3], which have demonstrated strong performance in fluid dynamics simulations. A more rigorous comparison against these state-of-the-art models would provide a clearer understanding of the relative strengths and weaknesses of the proposed approach.\n\nFinally, the paper's organization could be improved to better distinguish between preliminary concepts and the core methodology. Section 3, which currently mixes both, should be restructured to clearly separate the background information from the specific details of the proposed ACDM. This would enhance the clarity of the paper and make it easier for readers to understand the authors' contribution. Additionally, the explanation for Figure 4 should be clarified by adding titles to each subfigure, indicating the respective dataset name. These changes would improve the overall presentation and accessibility of the paper, making it easier for readers to grasp the key ideas and contributions."
+      }
+    },
+    {
+      "id": "PZ125dvbc6",
+      "rating": 5,
+      "content": {
+        "summary": "This paper proposes to apply conditional diffusion models to turbulence flow simulations. It demonstrates that diffusing the conditional inputs (i.e. the initial conditions of the simulation) aids performance as opposed to using the \"clean\" conditions for all diffusion steps.\nThe authors show that the resulting diffusion model attains good sample diversity and physical consistency, albeit at the expense of slower inference speed. It can also serve as an effective method for stabilizing long inference rollouts.",
+        "soundness": "2 fair",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "Overall, I enjoyed reading this paper but think that switching the focus away from the conditional diffusion model (given the limited novelty and its limitations, see Weaknesses section) to a more general focus on comparing various approaches for data-driven physics simulations could be helpful to the reader so that the authors can focus on candidly analyzing and comparing the different methods, for which the current paper already provides a lot of interesting and valuable content. This is especially so given that the authors have had to come up with their own adaptations to use some interesting baselines such as the TF_VAE. Even if they don't perform well, it is very valuable to discuss them, as is done in this paper.\n\nList of strengths:\n- Diffusing/noising the conditional inputs is shown to be an effective way of improving the performance of the diffusion model. Albeit this is a small and simple design choice, it is not obvious, and it is good to have it documented for interested practitioners.\n- Several interesting observations and analyses are given in this paper, both regarding the proposed diffusion model and some of the baselines. For example, I enjoyed reading about the ablation of the number of diffusion steps and the training rollout and noise, as well as the shortcomings of the transformer-VAE.\n- Data-driven models for probabilistic physics simulation is an important and somewhat underexplored field, albeit see the weaknesses below for relevant related work that goes a bit beyond this work.",
+        "weaknesses": "- The proposed autoregressive conditional diffusion model (ACDM) is a direct application of common diffusion models to turbulence simulation data. That is, except for proposing to diffuse the conditional inputs there are no methodological contributions.\n- Alternative methods to ACDM achieve comparable or even better benefits in terms of accuracy and rollout stability. In the paper, this is notably shown through the U-Net trained on multiple steps (i.e. m>2) or the U-Net where noise is injected into the training batches. This makes me uneasy when reading the abstract that claims *\"We show that this approach offers clear advantages in terms of rollout\nstability compared to other learned baselines\"*.\n- ACDM is extremely slow at inference time compared to the baselines (20x-100x slower almost). This is to be expected given that the baselines are single-forward pass models, but it should be made more clear by the authors when discussing the (dis-)advantages of the different baselines. E.g. in the last paragraph of the discussion and the summaries in the appendix, it is not fair to mention the disadvantages of the multi-step or training-noise U-Net baselines without noting the inference speed issue of ACDM. Especially for the training-noise baseline, I don't see any disadvantages compared to ACDM (except for potentially lower posterior sample quality. But this has not been shown here).\n- A recent work [1] already goes beyond this paper by adapting diffusion models to the same problem setting, lessening the inference speed issue of this paper, and addressing multiple of the outlooks/future work points given in the last paragraph of this paper. While it can be deemed as contemporaneous work, at least, it should be discussed in this paper. Of course, a direct comparison would be optimal, especially since the multi-step U-Net which performs similarly to ACDM in this paper is a baseline that is beaten by the method from [1].\n- It seems to me that some key hyperparameters unnecessarily deviate between ACMD and some baselines. This makes the significance of the results less clear. Notably, 1) ACDM uses two past timesteps as input (k=2), but many baselines only use one (k=1); 2) ACDM is trained with the Huber loss (which is a non-standard choice for diffusion models!) but all baselines use the MSE loss; 3) Number of training epochs varies wildly between models (e.g. 3100 for ACDM vs 1000 U-Net on Inc and Tra datasets). To me, these points seem very important to fix or require some explanation at least.\n- It is possible to sample multiple predictions from (most of) the baselines by perturbing the inputs. This is an important baseline to have for ACDM, and much more straightforward than the transformer-VAE idea. This should be tried at least for the training-noise U-Net (just keep the same variance for noising inference inputs).\n- It would be good to use benchmark datasets rather than creating new ones for the paper. E.g. see [2] which is used by [1] too, or [3]. This would make comparisons so much easier! Given the effort already spent on the current datasets of the paper (e.g. >5 days for some), will you open-source them?\n- ACDM introduces multiple new hyperparameters (e.g. R, diffusion schedule, etc.), so I would advise to not claim that introducing new hyperparameters is a problem of the baselines (e.g. last paragraph of the discussion), especially when said baselines are only introducing a single new HP.\n- I would advise toning down *\"Unlike the original DDPM, we achieve high-quality samples with as little as R = 20 diffusion\nsteps. We believe this stems from our strongly conditioned setting\"* a bit, given that you show that for some problems you need much more diffusion steps (e.g larger R seem to aid performance on the Iso dataset and it may not saturate at the largest R=500 that you tried, which also has the best LSiM).\n- The titles of the subplots in Fig. 4 are missing, so it is hard/impossible to tell what results correspond to which dataset.\n- Discussion of Fig. 6 in the main text should mention that some baselines perform very similarly, I think, on the frequency analysis (shown in Fig. 13 in the appendix)\n\n[1] Cachay, S.R., Zhao, B., James, H. and Yu, R., 2023. \"DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting\", NeurIPS\n\n[2] Otness, K., Gjoka, A., Bruna, J., Panozzo, D., Peherstorfer, B., Schneider, T. and Zorin, D., 2021. \"An extensible benchmark suite for learning to simulate physical systems\", NeurIPS Track on Datasets\n\n[3] Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pflüger, D. and Niepert, M., 2022. \"PDEBench: An extensive benchmark for scientific machine learning\", NeurIPS",
+        "questions": "- Why not use CRPS as a metric for your probabilistic methods?\n- Do you use k=2 for all U-Net models?\n- In your figures showing multiple samples (e.g. Fig 5): Why is the third row separate from the first two? Why is the timestep not ordered by rows?\n- The hidden spaces of 56 (but even 112) for the FNO, and L=32 for the transformer models, seem pretty low to me?\n- How many diffusion steps do you train with?\n- Do you always use 5 samples from the probabilistic methods? \n- Why do you change your transformer adaptations TF_enc and TF_VAE in terms of encoder/decoder and residual prediction or not compared to TF_MGN?\n- Table 3 in the appendix: Can you please run the dashed variants? If not, why? ACDM_R10 on Iso seems like an especially interesting run to try to me.\n- What do you mean by *\"However, this is achieved by significantly reducing the complexity of the learning task, instead of fundamentally increasing the models generalization ability.\"*\n- Table 5 in the appendix: Any intuition on why perturbing the inputs with 1e-3 performs so badly? I would have expected a more or less smooth transition from 1e-2 -> 1e-3 -> 1e-4. Is there a bug maybe?\n- Can you provide visualizations of the multi-step and training-noise baselines?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.",
+        "code_of_conduct": "Yes",
+        "weakness": " - The proposed autoregressive conditional diffusion model (ACDM) is a direct application of common diffusion models to turbulence simulation data. That is, except for proposing to diffuse the conditional inputs there are no methodological contributions.\n- Alternative methods to ACDM achieve comparable or even better benefits in terms of accuracy and rollout stability. In the paper, this is notably shown through the U-Net trained on multiple steps (i.e. m>2) or the U-Net where noise is injected into the training batches. This makes me uneasy when reading the abstract that claims *\"We show that this approach offers clear advantages in terms of rollout\nstability compared to other learned baselines\"*.\n- ACDM is extremely slow at inference time compared to the baselines (20x-100x slower almost). This is to be expected given that the baselines are single-forward pass models, but it should be made more clear by the authors when discussing the (dis-)advantages of the different baselines. E.g. in the last paragraph of the discussion and the summaries in the appendix, it is not fair to mention the disadvantages of the multi-step or training-noise U-Net baselines without noting the inference speed issue of ACDM. Especially for the training-noise baseline, I don't see any disadvantages compared to ACDM (except for potentially lower posterior sample quality. But this has not been shown here).\n- A recent work [1] already goes beyond this paper by adapting diffusion models to the same problem setting, lessening the inference speed issue of this paper, and addressing multiple of the outlooks/future work points given in the last paragraph of this paper. While it can be deemed as contemporaneous work, at least, it should be discussed in this paper. Of course, a direct comparison would be optimal, especially since the multi-step U-Net which performs similarly to ACDM in this paper is a baseline that is beaten by the method from [1].\n- It seems to me that some key hyperparameters unnecessarily deviate between ACMD and some baselines. This makes the significance of the results less clear. Notably, 1) ACDM uses two past timesteps as input (k=2), but many baselines only use one (k=1); 2) ACDM is trained with the Huber loss (which is a non-standard choice for diffusion models!) but all baselines use the MSE loss; 3) Number of training epochs varies wildly between models (e.g. 3100 for ACDM vs 1000 U-Net on Inc and Tra datasets). To me, these points seem very important to fix or require some explanation at least.\n- It is possible to sample multiple predictions from (most of) the baselines by perturbing the inputs. This is an important baseline to have for ACDM, and much more straightforward than the transformer-VAE idea. This should be tried at least for the training-noise U-Net (just keep the same variance for noising inference inputs).\n- It would be good to use benchmark datasets rather than creating new ones for the paper. E.g. see [2] which is used by [1] too, or [3]. This would make comparisons so much easier! Given the effort already spent on the current datasets of the paper (e.g. >5 days for some), will you open-source them?\n- ACDM introduces multiple new hyperparameters (e.g. R, diffusion schedule, etc.), so I would advise to not claim that introducing new hyperparameters is a problem of the baselines (e.g. last paragraph of the discussion), especially when said baselines are only introducing a single new HP.\n- I would advise toning down *\"Unlike the original DDPM, we achieve high-quality samples with as little as R = 20 diffusion\nsteps. We believe this stems from our strongly conditioned setting\"* a bit, given that you show that for some problems you need much more diffusion steps (e.g larger R seem to aid performance on the Iso dataset and it may not saturate at the largest R=500 that you tried, which also has the best LSiM).\n- The titles of the subplots in Fig. 4 are missing, so it is hard/impossible to tell what results correspond to which dataset.\n- Discussion of Fig. 6 in the main text should mention that some baselines perform very similarly, I think, on the frequency analysis (shown in Fig. 13 in the appendix)",
+        "suggestions": "The paper would benefit from a more thorough investigation into the hyperparameter choices for both the proposed ACDM and the baseline models. Specifically, the use of k=2 for ACDM while using k=1 for the baselines introduces a potential confound. While the authors mention that k=1 works better for direct prediction models, it is not clear why this is the case, and a more detailed analysis of the impact of k on both ACDM and the baselines is needed. Similarly, the use of Huber loss for ACDM and MSE for the baselines makes it difficult to isolate the impact of the diffusion process from the choice of loss function. It would be valuable to see results for ACDM trained with MSE and the baselines trained with Huber loss to ensure a fair comparison. The large variation in training epochs also needs to be addressed. It is not sufficient to simply train until convergence; the authors should provide a more rigorous justification for the number of epochs used for each model, perhaps by showing learning curves and demonstrating that all models have reached a similar level of convergence. These inconsistencies in hyperparameter settings make it difficult to draw definitive conclusions about the relative performance of ACDM compared to the baselines.\n\nFurthermore, the claim that ACDM offers clear advantages in terms of rollout stability needs to be more carefully substantiated. The results presented in the paper show that the U-Net models with multi-step training or training noise achieve comparable or even better performance in terms of accuracy and stability. The authors should provide a more detailed analysis of the specific scenarios where ACDM outperforms the baselines, and they should also acknowledge the significant disadvantage of ACDM in terms of inference speed. The discussion of the advantages and disadvantages of each method should be more balanced, and the authors should avoid making overly strong claims about the superiority of ACDM. The fact that the training-noise U-Net baseline does not have any clear disadvantages compared to ACDM (except for potentially lower posterior sample quality, which is not demonstrated) should be explicitly acknowledged and discussed. Moreover, the possibility of generating multiple samples from the baselines by perturbing the inputs should be explored, as this would provide a more direct comparison to the probabilistic nature of ACDM. The current approach of using a transformer-VAE for this purpose is not ideal, and a simpler method of input perturbation should be considered.\n\nFinally, the paper should address the issue of benchmark datasets. While the authors have created their own datasets, this makes it difficult to compare their results to other work in the field. Using established benchmark datasets such as those from [2,3] would greatly improve the reproducibility and comparability of the results. The authors should also clarify whether they intend to make their datasets publicly available, as this would be a valuable contribution to the community. The discussion of the hyperparameters of ACDM should also be toned down. The authors claim that introducing new hyperparameters is a problem of the baselines, but ACDM also introduces multiple new hyperparameters, such as R and the diffusion schedule. The authors should acknowledge that all methods have hyperparameters that need to be tuned, and they should avoid making claims that are not supported by the evidence. The discussion of the number of diffusion steps should also be more nuanced, as the results show that a larger R is needed for some problems, and the claim that high-quality samples can be achieved with as little as R=20 is not universally true."
+      }
+    },
+    {
+      "id": "3O4syfBeFe",
+      "rating": 5,
+      "content": {
+        "summary": "The authors introduced a method that trains diffusion models to capture the joint distribution of turbulent flow states over a few time steps, and apply conditioning at inference time to perform autoregressive rollouts. The authors compare the proposed method against models which are trained autoregressively using multiple flow examples and observed competitive accuracy and temporal stability characteristics.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "* Paper is generally well written and not difficult to follow\n* Evaluation is done with meaningful benchmark methods; ablation studies are comprehensive\n* Proposed model is capable of generating probabilistic predictions, whereas most competitors are deterministic in nature\n* The proposed method does seem to result in good stability characteristics when rolled out for an extended period of time - an important challenge for many existing methods dealing with dynamical systems",
+        "weaknesses": "* The approach is not novel - it simply applies an existing way of conditioning diffusion model to do autoregressive rollouts of turbulent flow trajectories.\n* The presented benchmark is not fair in two ways\n    * Autoregressive diffusion sampling is very expensive, basically taking <the total number of denoising steps> times more (~20 in this case) compute than the U-Net model. A fair comparison would involve a U-Net either with larger capacity or integrated forward at finer time steps such that the compute cost is comparable.\n    * The authors do not show the results for \"rolling out in training\" as the primary baseline in the main text (it is instead presented as ablation studies in section C.5). However, it is well established (authors even include references supporting this) that this is the correct way of training autoregressive models. Indeed, the proposed ACDM does not have better performance compared to the models trained with such multi-step loss. Considering the significantly higher inference cost, it is hard to justify the value of the proposed method. The authors mentioned \"more hyperparameters\" and \"higher training cost\" as counter-arguments, but I do not think the former is a valid reason at all, and the latter is both weak and not supported by numbers comparison.\n* In the attached videos for the isotropic turbulence \"posterior_iso_samples_vort.mp4\", the samples showed visible flickering, i.e. some small-scaled features present in one frame noticeably go missing in the next. This seems to suggest that the conditioning scheme adopted may not lead to sufficient coherence between conditioned and sampled parts ($d$ and $c$). This is not reflected in any of the metrics presented.\n\nThese weaknesses are fundamental enough for me to not recommend a passing score.",
+        "questions": "* It would be helpful to define LSiM somewhere besides including the reference.\n* Figure 4 is missing labels - which plots correspond to which test example?\n* I wasn't able to find spatial frequency analysis for the isotropic turbulence example? The rollouts look a bit smoother compared to the ground truth visually.\n* Appendix C.5 summary - what do you mean by \"significantly reducing the complexity of the learning task, instead of fundamentally increasing the models generalization ability\"? I cannot connect this statement with what is entailed by training rollouts beyond single step\n* Appendix C.6 Table 5 - the \"n1e-x\" subscripts looked really cryptic to me initially. Maybe just create a separate column to indicate the noise level?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": " * The approach is not novel - it simply applies an existing way of conditioning diffusion model to do autoregressive rollouts of turbulent flow trajectories.\n* The presented benchmark is not fair in two ways\n    * Autoregressive diffusion sampling is very expensive, basically taking <the total number of denoising steps> times more (~20 in this case) compute than the U-Net model. A fair comparison would involve a U-Net either with larger capacity or integrated forward at finer time steps such that the compute cost is comparable. The authors should have explored U-Net architectures with increased channel counts or depth to match the computational cost of the diffusion model's iterative denoising process. Furthermore, the comparison should have included a U-Net that is unrolled at finer temporal resolutions, even if it leads to error accumulation, to properly assess the trade-offs between computational cost and accuracy.\n    * The authors do not show the results for \"rolling out in training\" as the primary baseline in the main text (it is instead presented as ablation studies in section C.5). However, it is well established (authors even include references supporting this) that this is the correct way of training autoregressive models. Indeed, the proposed ACDM does not have better performance compared to the models trained with such multi-step loss. Considering the significantly higher inference cost, it is hard to justify the value of the proposed method. The authors mentioned \"more hyperparameters\" and \"higher training cost\" as counter-arguments, but I do not think the former is a valid reason at all, and the latter is both weak and not supported by numbers comparison. The core issue is that the proposed method does not demonstrate a clear advantage over a properly trained autoregressive U-Net, especially when considering the computational overhead during inference. The authors need to provide a more compelling justification for the added complexity of the diffusion approach.\n* In the attached videos for the isotropic turbulence \"posterior_iso_samples_vort.mp4\", the samples showed visible flickering, i.e. some small-scaled features present in one frame noticeably go missing in the next. This seems to suggest that the conditioning scheme adopted may not lead to sufficient coherence between conditioned and sampled parts ($d$ and $c$). This is not reflected in any of the metrics presented. The flickering suggests a lack of temporal consistency in the generated samples, which is a critical issue for time-series prediction. The authors should have included metrics that specifically quantify temporal coherence, such as frame-to-frame difference analysis or spectral analysis of temporal variations. The absence of such metrics makes it difficult to assess the severity of this issue, and the fact that it is not reflected in the presented metrics raises concerns about the completeness of the evaluation.",
+        "suggestions": "The authors should provide a more thorough comparison with autoregressive U-Net models, ensuring that the computational cost is comparable. This would involve either increasing the capacity of the U-Net or integrating it forward at finer time steps. Specifically, they should explore U-Net architectures with a larger number of channels or deeper layers to match the computational cost of the diffusion model's iterative denoising process. Furthermore, the comparison should include a U-Net that is unrolled at finer temporal resolutions during both training and inference, even if it leads to error accumulation, to properly assess the trade-offs between computational cost and accuracy. This would provide a more comprehensive understanding of the performance differences between the proposed diffusion model and a properly trained autoregressive U-Net. The authors should also investigate techniques to mitigate the flickering artifacts observed in the isotropic turbulence samples. This could involve exploring different conditioning strategies or increasing the number of diffusion steps during sampling. They should also include metrics that specifically quantify temporal coherence, such as frame-to-frame difference analysis or spectral analysis of temporal variations, to properly assess the severity of this issue. The current evaluation metrics do not capture the temporal inconsistencies, and a more detailed analysis is needed to demonstrate the model's ability to generate temporally coherent predictions.\n\nFurthermore, the authors should provide a more compelling justification for the added complexity of the diffusion approach, given the significantly higher inference cost. The current arguments based on \"more hyperparameters\" and \"higher training cost\" are not convincing. The authors need to demonstrate a clear advantage of the proposed method over a properly trained autoregressive U-Net, especially when considering the computational overhead during inference. This could involve showing that the diffusion model is able to capture more complex dynamics or generate more diverse samples than a U-Net. The authors should also explore techniques to reduce the inference cost of the diffusion model, such as distillation or improved sampling methods, to make it more practical for real-world applications. Without a clear advantage in performance or a reduction in inference cost, the proposed method is difficult to justify.\n\nFinally, the authors should address the issue of the flickering artifacts observed in the isotropic turbulence samples. This suggests a lack of temporal consistency in the generated samples, which is a critical issue for time-series prediction. The authors should investigate the cause of these artifacts and explore techniques to mitigate them. This could involve exploring different conditioning strategies or increasing the number of diffusion steps during sampling. They should also include metrics that specifically quantify temporal coherence, such as frame-to-frame difference analysis or spectral analysis of temporal variations, to properly assess the severity of this issue. The current evaluation metrics do not capture the temporal inconsistencies, and a more detailed analysis is needed to demonstrate the model's ability to generate temporally coherent predictions. The authors should also consider comparing the spectral properties of the generated samples with the ground truth to ensure that the model is capturing the correct frequency content."
+      }
+    },
+    {
+      "id": "3PbMl6CZwT",
+      "rating": 5,
+      "content": {
+        "summary": "The manuscript describes an application of the conditional diffusion model for the simulation of complex physical system, turbulent flows. The authors performed an extensive numerical studies using a range of solvers and a few different flow geometries. It is shown that overall the diffusion model outperforms supervised approaches.",
+        "soundness": "2 fair",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "The authors performed large-scale simulations and extensive numerical experiments to investigate the conditional diffusion model for the physics problems. The result seems to suggest an advantage of the diffusion model in physics simulations.",
+        "weaknesses": "While it is interesting to see the capability of the diffusion model in learning physics problems, the study does not go beyond a relatively straightforward application of the conditional diffusion model, which does not align well with the scope of ICLR. The authors used simple evaluation metrics, which may miss important characteristics of physics problems.",
+        "questions": "1. One of the most important characteristics of the physics problem is the conservation law. If not the mass conservation constraint, the computation becomes just a very simple matrix vector multiplications. What's the divergence-free error of the diffusion model and how it compares with the computational physics model?\n\n2. MSE error may not be the best metric to investigate the physics problem. For example, it will be helpful to compare the power spectrum to see if the nonlinear energy transfer is correctly represented in the diffusion model. For the turbulent problems considered, there are well defined metrics that give better representation of the physics. The authors need to compare those metrics, instead of simple MSE.\n\n3. What does it mean to have a posterior sampling? While the diffusion model can sample from the probability distribution, the problem itself is deterministic. It does not make a sense, simply because the diffusion model can generate a sample from a distribution, suddenly the authors arguing that they can sample from a posterior distribution when the problem setup is deterministic. If the authors consider the primitive variables as random variables, the problem formulation has also be properly stated and changed.\n\n4. Again from the comment 3, the paper lacks a proper problem formulation.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "details_of_ethics_concerns": "NA",
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.",
+        "code_of_conduct": "Yes",
+        "weakness": "While it is interesting to see the capability of the diffusion model in learning physics problems, the study does not go beyond a relatively straightforward application of the conditional diffusion model, which does not align well with the scope of ICLR. The authors used simple evaluation metrics, which may miss important characteristics of physics problems.\n\nOne of the most important characteristics of the physics problem is the conservation law. If not the mass conservation constraint, the computation becomes just a very simple matrix vector multiplications. What's the divergence-free error of the diffusion model and how it compares with the computational physics model?\n\nMSE error may not be the best metric to investigate the physics problem. For example, it will be helpful to compare the power spectrum to see if the nonlinear energy transfer is correctly represented in the diffusion model. For the turbulent problems considered, there are well defined metrics that give better representation of the physics. The authors need to compare those metrics, instead of simple MSE.\n\nWhat does it mean to have a posterior sampling? While the diffusion model can sample from the probability distribution, the problem itself is deterministic. It does not make a sense, simply because the diffusion model can generate a sample from a distribution, suddenly the authors arguing that they can sample from a posterior distribution when the problem setup is deterministic. If the authors consider the primitive variables as random variables, the problem formulation has also be properly stated and changed.\n\nAgain from the comment 3, the paper lacks a proper problem formulation.",
+        "suggestions": "The paper would significantly benefit from a more rigorous exploration of the physical implications of using a diffusion model for fluid flow simulation. While the authors demonstrate the model's ability to generate plausible flow fields, they do not adequately address whether the generated flows adhere to fundamental physical principles beyond simple error metrics. A key concern is the lack of explicit enforcement of conservation laws within the diffusion model itself. The authors should investigate methods to incorporate such constraints, either through modifications to the model architecture or through post-processing steps. For example, a penalty term could be added to the loss function to encourage divergence-free velocity fields for incompressible flows, or the authors could explore the use of Lagrangian multipliers to enforce these constraints. Furthermore, the analysis should include a detailed comparison of the energy spectra of the generated flows with those of the ground truth simulations, paying particular attention to the inertial range and the dissipation range to ensure that the model captures the correct nonlinear energy transfer. This would require a deeper analysis than just comparing simple MSE values and would provide a more robust understanding of the model's ability to represent turbulent flows.\n\nThe use of posterior sampling needs to be clarified within the context of deterministic flow simulations. The authors claim that the diffusion model can sample from a posterior distribution, but this is only valid if the problem is inherently stochastic, or if the model is explicitly trained to capture the uncertainty in the simulation. For deterministic problems, the concept of a posterior distribution is not well-defined, and the sampling process would merely generate different but equally plausible flow fields. The authors should clearly define the source of uncertainty in their problem setup. If the uncertainty arises from numerical errors or sub-grid scale modeling, this should be explicitly stated and justified. If the problem is indeed deterministic, the authors should focus on the model's ability to generate accurate predictions rather than on sampling from a posterior. The authors could explore techniques such as ensemble averaging to improve the robustness of their predictions. Alternatively, they could consider a Bayesian approach, where the model parameters are treated as random variables, and the posterior distribution represents the uncertainty in the model parameters.\n\nTo enhance the paper's contribution, the authors should present a more thorough analysis of the model's limitations and potential failure modes. This would involve a systematic investigation of the model's performance under various conditions, such as different Reynolds numbers, grid resolutions, and initial conditions. The authors should also discuss the computational cost of the diffusion model compared to traditional simulation methods, and the potential for accelerating the sampling process. Furthermore, the authors should compare the performance of their diffusion model with other state-of-the-art machine learning techniques for fluid flow simulation, such as convolutional neural networks or graph neural networks, using a consistent set of metrics. This would provide a more comprehensive understanding of the strengths and weaknesses of the diffusion model and would help to identify the areas where it can be most effectively applied."
+      }
+    }
+  ]
+}

papers/1qDRwhe379/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "1qDRwhe379",
+  "title": "Refining Corpora from a Model Calibration Perspective for Chinese Spelling Correction",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-22",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=1qDRwhe379"
+}

papers/1qDRwhe379/paper.md

@@ -0,0 +1,462 @@
+# REFINING CORPORA FROM A MODEL CALIBRATION PERSPECTIVE FOR CHINESE SPELLING CORRECTION
+
+Anonymous authors Paper under double-blind review
+
+### ABSTRACT
+
+Chinese Spelling Correction (CSC) commonly lacks large-scale high-quality corpora, due to the labor-intensive labeling of spelling errors in real-life human writing or typing scenarios. Two data augmentation methods are widely adopted: (1) *Random Replacement* with the guidance of confusion sets and (2) *OCR/ASRbased Generation* that simulates character misusing. However, both methods inevitably introduce noisy data (e.g., false spelling errors), potentially leading to over-correction. By carefully analyzing the two types of corpora, we find that though the latter achieves more robust generalization performance, the former yields better-calibrated CSC models. We then provide a theoretical analysis of this empirical observation, based on which a corpus refining strategy is proposed. Specifically, OCR/ASR-based data samples are fed into a well-calibrated CSC model trained on random replacement-based corpora and then filtered based on prediction confidence. By learning a simple BERT-based model on the refined OCR/ASR-based corpus, we set up impressive state-of-the-art performance on three widely-used benchmarks, while significantly alleviating over-correction (e.g., lowering false positive predictions).
+
+# <span id="page-0-1"></span>1 INTRODUCTION
+
+Chinese Spelling Correction (CSC) aims to detect and correct misspellings in the text while maintaining the sentence length [Yu & Li](#page-10-0) [\(2014\)](#page-10-0). It can not only directly facilitate human writing and typing but also serve as a critical pre-processing step for many downstream Chinese NLP tasks such as search engine [Martins & Silva](#page-10-1) [\(2004\)](#page-10-1) and optical character recognition [Afli et al.](#page-9-0) [\(2016\)](#page-9-0). One common challenge of applying CSC is the lack of large-scale high-quality corpora in practice since labeling spelling errors in real-life writing or typing scenarios is labor-extensive [Wang et al.](#page-10-2) [\(2018\)](#page-10-2). Therefore, two data augmentation methods are widely adopted for this task. The first one is *random replacement* with the guidance of confusion sets [Liu et al.](#page-9-1) [\(2013\)](#page-9-1) containing typical human misused cases based on statistics. The second one is leveraging cross-modal models [Wang et al.](#page-10-2) [\(2018\)](#page-10-2), such as optical character recognition (OCR) and automatic speech recognition (ASR), to simulate spelling errors in the shape-close or tone-close patterns.
+
+Compared to random replacement, OCR/ASR-based generation better mimics human misspelling scenarios, becoming the mainstream strategy used by many recent CSC efforts [Cheng et al.](#page-9-2) [\(2020\)](#page-9-2); [Wang et al.](#page-10-3) [\(2021\)](#page-10-3). Unfortunately, both data augmentation methods inevitably introduce noises. For example, we randomly sample 300 sentences in the OCR/ASR-based corpus [Wang et al.](#page-10-2) [\(2018\)](#page-10-2) and check the annotated misused characters manually, finding that 11.3% of them are false spelling errors. Training on these noisy samples can produce unintended over-correction (e.g., a high false positive rate). Previous works mainly alleviate the problem through sophisticated model designs, e.g., integrating phonological and morphological information using multi-modal approaches [Xu et al.](#page-10-4) [\(2021\)](#page-10-4); [Huang et al.](#page-9-3) [\(2021\)](#page-9-3). Unlike these efforts, in this paper, we propose to improve CSC by directly purifying noisy samples in CSC corpora.
+
+Considering model confidence is commonly exploited to denoise data [Northcutt et al.](#page-10-5) [\(2021\)](#page-10-5), we first analyze the two types of CSC corpora by checking the calibration characteristics and performance of models trained on them (see Section [2](#page-1-0) for experiment details). The experimental results on the SIGHAN 13 [Wu et al.](#page-10-6) [\(2013\)](#page-10-6) benchmark are shown in Figure [1](#page-1-1) [1](#page-0-0) . Comparing subplots (a) and (b),
+
+<span id="page-0-0"></span><sup>1</sup>Appendix [B](#page-11-0) shows the results on SIGHAN 14/15
+
+<span id="page-1-1"></span>![](figures/_page_1_Figure_1.jpeg)
+
+Figure 1: Calibration curves and performance of BERT-based CSC models trained on random replacement and OCR/ASR-based data. ECE refers to the Expected Calibration Error metric [Guo et al.](#page-9-4) [\(2017\)](#page-9-4), and FPR represents the sentence-level false positive rate, which measures over-corrections. Combining subplots (a), (b), and (c), OCR/ASR-based data demonstrate superior performance on standard metrics such as precision (P), recall (R), and F1 score. However, random replacement data exhibit better calibration and lower FPR.
+
+we find that although the CSC model trained on OCR/ASR-based data performs better (e.g., with a better F1 score), it is worse calibrated than its counterpart of random replacement. Its calibration curve continuously lies below the dotted line (representing perfectly calibrated), indicating that the model tends to make over-confident predictions. This observation is consistent with its higher false positive rate (despite overall better performance) in subplot (c). To explain the empirical observation, we then perform a theoretical analysis of model confidence based on bayesian inference (Section [3\)](#page-2-0). We reveal why the calibration curve differs between the two categories of training data and identify which data samples negatively affect model confidence.
+
+Guided by the empirical observations and theoretical findings, we propose to refine the OCR/ASRbased corpus with a CSC model trained on random replacement data. Thanks to this CSC model's more trustful confidence, we can use it to filter noisy OCR/ASR-based samples according to their prediction scores. We achieve competitive performance on three open CSC benchmarks by training a simple BERT-based model on the refined corpus. Notably, the model also produces a much lower false positive rate and demonstrates better calibration, which is essential in real-world CSC applications.
+
+In summary, our contributions are as follows:
+
+- We empirically reveal that OSC/ASR-based CSC datasets deliver more robust generalization performance, while random replacement datasets lead to better-calibrated models.
+- We theoretically analyze models' calibration characteristics from a bayesian inference view, explaining how and which data samples bring the unintended over-confidence of predictions.
+- We design a corpus refining strategy that integrates the generalization performance from OSC/ASR-based data and the trustful model confidence from random replacement data.
+
+### <span id="page-1-0"></span>2 A PILOT STUDY OF DATA CHARACTERISTICS
+
+Figure [1](#page-1-1) illustrates the properties of OCR/ASR-based and random replacement data through the calibration curves and performance of their respective models. The Expected Calibration Error (ECE) metric is explained in detail in Appendix [A.](#page-11-1) In this section, we provide a comprehensive description of the experimental methodology and procedures.
+
+#### 2.1 THE BASE CSC MODEL
+
+Given data pair (X, Y ), where X is the original sentence and Y is the generated sample containing spelling errors, Chinese spelling correction aims to restore Y to X. Since X and Y share the same sentence length, this task is usually implemented by a non-autoregressive model. In this work, Y is input into a BERT model, and the output hidden state of each character is fed into a classifier to get the predicted correct character. The training target can be written as the following cross-entropy loss:
+
+$$L_{CE} = -\sum_{i=1}^{L} log[P_{\theta}(x_i|Y)]$$
+
+$$\tag{1}$$
+
+where L is the shared length and  $\theta$  represents model parameters.
+
+#### 2.2 Analysis of Two Datasets
+
+**Dataset Preparation**. We use the OCR/ASR-based dataset containing 271k sentences provided by Wang et al. (2018). We can build a confusion set based on its annotated spell errors. To obtain a random-replacement dataset of similar volume, we collect the same number of sentences and then uniformly substitute correct characters with a probability of 10% with characters in the constructed confusion set. In this way, we can compare two types of datasets fairly.
+
+Metrics Settings. Regarding model performance, in addition to standard metrics (e.g., precision (P), recall (R), and F1), we also examine sentence-level false positive rate (FPR) Li et al. (2022c). A sentence is regarded as a false positive if any initially correct character is wrongly modified to another one. Regarding model confidence, since most of the characters in the dataset are correct, numerous easy positive samples will blur the noteworthy trends in calibration curves. Therefore, we eliminate those characters—in whose prediction distribution the possibility of being corrected to other characters is below 0.1—to draw the calibration curve and calculate ECE.
+
+**Main findings**. The main results of SIGHAN 13 have been shown in Figure 1, and more experimental results of SIGHAN 14 and 15 are placed in Appendix B due to space limitation. In all three datasets, we can observe in the calibration line chart that the CSC model trained on OCR/ASR-based data is flawed regarding the alignment between prediction confidence and accuracy, despite the better overall performance. ECE scores achieved by random replacement and OCR/ASR-based generation are 0.104 and 0.163, respectively, suggesting that the former is closer to the ideal calibration and also explaining why it achieves a lower FPR (e.g., with fewer over-corrections).
+
+#### <span id="page-2-0"></span>3 THEORETICAL ANALYSIS OF MODEL CONFIDENCE
+
+#### 3.1 PROBLEM STATEMENT
+
+In this section, we present a theoretical analysis of the above empirical findings. To begin, we define a set  $\mathcal{X}$  that each element, denoted as  $X=(x_1,x_2,...,x_L)$ , represents a sentence in the real-world corpus comprised of individual characters. The prior probability of the sentence can be determined using the probability function  $P_{\mathcal{X}}$ . By some methods of data augmentation, a mapping function  $\mathcal{F}:\mathcal{X}\to\mathcal{Y}$  is applied to imitate human's writing error set  $\mathcal{Y}$ , which consists of sentences containing a small number of incorrect characters. The probability of sentences in  $\mathcal{Y}$  is obtained from  $P_{\mathcal{Y}}$ .
+
+For any sentence  $X \in \mathcal{X}$ , we assume the mapping function  $\mathcal{F}$  replaces only one character at a time.  $Y = \mathcal{F}(X), y_i = \mathcal{F}(X)_i \neq x_i$ . We denote the context of  $x_i$  as  $X_{\setminus i} = (x_1, ..., x_{i-1}, x_{i+1}, ..., x_L)$ . Based on these assumptions, we can draw the following simple inferences:
+
+- $X_{\setminus i} = Y_{\setminus i}$ : This equality implies that the context surrounding the replaced character remains unchanged when transforming X to Y.
+- $P_{\mathcal{X}}(X_{\setminus i}) = P_{\mathcal{Y}}(Y_{\setminus i})$ . Since the data augmentation methods do not alter the size of the dataset, we can assert that  $|\mathcal{X}| = |\mathcal{Y}|$ . There is a one-to-one correspondence between the contexts in  $\mathcal{X}$  and  $\mathcal{Y}$ . Consequently, we can establish an equation relating the probabilities of  $X_{\setminus i}$  and  $Y_{\setminus i}$ .
+
+#### 3.2 BAYESIAN INFERENCE OF MODEL CONFIDENCE
+
+Combining the inferences, we can derive the theoretical correction model confidence P(X|Y) from a Bayesian inference perspective, as the probability P(Y|X) in the augmentation process is known.
+
+<span id="page-2-1"></span>
+$$P(X|Y) = \frac{P(y_i|X) \cdot P_{\mathcal{X}}(x_i|X_{\setminus i})}{\sum_{v \in \mathcal{V}} P(y_i|X_{\setminus i}, v) P_{\mathcal{X}}(v|X_{\setminus i})}$$
+(2)
+
+In the formulation, the vocabulary  $\mathcal V$  encompasses all possible characters. The detailed calculation procedure is presented in Appendix D.To further decompose Eq. 2, we define a subset  $\hat{\mathcal V}\subset \mathcal V$ , which consists of the characters v that make both  $P(y_i|X_{\setminus i},v)$  and  $P_{\mathcal X}(v|X_{\setminus i})$  non-zero.
+
+ $\hat{\mathcal{V}}$  satisfying the condition is usually categorized into the following three orthogonal cases. The next section will provide more intuitive explanations of the three cases.
+
+Case 1:  $|\hat{\mathcal{V}}| = 1$ , in other word,  $\hat{\mathcal{V}} = \{x_i\}$ .
+
+$$P^{T}(X|Y) = \frac{P(y_i|X) \cdot P_{\mathcal{X}}(x_i|X_{\setminus i})}{P(y_i|X_{\setminus i}, x_i)P_{\mathcal{X}}(x_i|X_{\setminus i})} = 1$$
+(3)
+
+Case 2:  $y_i \in \hat{\mathcal{V}}$ , for simplicity, let  $\hat{\mathcal{V}} = \{x_i, y_i\}$ .
+
+<span id="page-3-1"></span>
+$$P^{N}(X|Y) = \frac{1}{1 + \frac{P_{\mathcal{X}}(y_{i}|X_{\setminus i})}{P_{\mathcal{X}}(x_{i}|X_{\setminus i})} \cdot \frac{P(y_{i}|X_{\setminus i},y_{i})}{P(y_{i}|X_{\setminus i},x_{i})}}$$
+(4)
+
+**Case 3:**  $y_i \notin \hat{\mathcal{V}}$  and  $|\hat{\mathcal{V}}| > 1$ . To simplify the notation, let  $\hat{\mathcal{V}} = \{x_i, a\}, a \neq y_i$ .
+
+<span id="page-3-4"></span>
+$$P^{M}(X|Y) = \frac{1}{1 + \frac{P_{\mathcal{X}}(a|X_{\backslash i})}{P_{\mathcal{X}}(x_{i}|X_{\backslash i})} \cdot \frac{P(y_{i}|X_{\backslash i},a)}{P(y_{i}|X_{\backslash i},x_{i})}}$$
+(5)
+
+#### <span id="page-3-3"></span>3.3 DATA SAMPLE CATEGORIZATION
+
+The three cases discussed in the previous subsection are naturally related to the three sample types in the CSC dataset. Symbolic examples are presented in Table 1. We analyze the impact of different data augmentation methods on these sample types.
+
+**True Sample** corresponds to Case 1, where the context  $X_{\setminus i}$  can determine the unique character  $x_i$ , or there are multiple suitable characters, but  $y_i$  only appears in the confusion set of  $x_i$ .
+
+**Noisy Sample** corresponds to Case 2. In this case, a correct sentence can unexpectedly be transformed into another correct one during data augmentation, generating false spelling errors.
+
+<span id="page-3-0"></span>
+
+| Ca | se | original                     | replaced         | truth set of A?C |
+|----|----|------------------------------|------------------|------------------|
+| 1  |    | A <u>B</u> C                 | ADC              | {B}              |
+| 2  | ,  | A <u>B</u> C                 | ADC              | {B,D}            |
+| 3  |    | $A\overline{\underline{B}}C$ | $A\overline{D}C$ | {B,E}            |
+|    |    |                              |                  |                  |
+
+Table 1: Symbolic illustration of different cases. The characters identified by underscores in the second and third columns correspond to  $x_i$  and  $y_i$  respectively.
+
+When considering the four terms in the denominator of Equation 4, regardless of the data augmentation method,  $P_{\mathcal{X}}(y_i|X_{\backslash i})$  and  $P_{\mathcal{X}}(x_i|X_{\backslash i})$  remain the same. Additionally,  $P(y_i|X_{\backslash i},y_i)$  will be close to 1, as misspellings generally constitute only a small percentage of all characters. Therefore,  $P(y_i|X_{\backslash i},x_i)$  is the primary factor influencing  $P^N(X|Y)$ .
+
+Specifically, random replacement data provide a uniform distribution for  $P(y_i|X_{\setminus i},x_i)$ , which can stabilize  $P^N(X|Y)$ . On the other hand, OCR/ASR-based data may result in large values of  $P(y_i|X_{\setminus i},x_i)$  due to its inherent long-tail distribution  $P(y_i|X_{\setminus i},x_i)$ , which could result in overconfident predictions. In other words, Equation 4 provides an upper bound for  $P^N(X|Y)$  in the case of random replacement data, facilitating the filtering of noisy samples by setting a confidence threshold.
+
+**Multi-answer Sample** corresponds to Case 3, where a spelling error can have multiple correct character alternatives. In this case, it is considered a true spelling error  $(P_{\mathcal{X}}(y_i|X_{\setminus i})=0)$ , but there exist multiple corrections other than  $x_i$  that are equally valid.
+
+<span id="page-3-2"></span><sup>&</sup>lt;sup>2</sup>The most frequent spelling errors in each character's confusion set in the OCR/ASR-based data constitute 58.7% of the whole misspellings. The percentage is 13.8% for random replacement data
+
+Similar to the analysis of noisy samples, the difference between the two data augmentation methods also relies on  $P(y_i|X_{\setminus i},x_i)$ . Further detailed analysis on this matter can be found in Appendix F.
+
+#### 3.4 Lessons from the Theoretical Analysis
+
+The theoretical analyses presented above provide a clear explanation for the empirical findings observed in our pilot study. Moreover, they serve as inspiration to utilize the upper-bounded confidence for denoising purposes.
+
+Considering cases 2 and 3, it is important to note that less than 10% of the characters are replaced in the context of data augmentation,  $P(y_i|X_{\backslash i},y_i)\geq 0.9>>0.1\geq P(y_i|X_{\backslash i},a).$  As long as  $P_{\mathcal{X}}(y_i|X_{\backslash i})$  and  $P_{\mathcal{X}}(a|X_{\backslash i})$  are of the same order of magnitude, it can be derived that
+
+$$0 < P^{N}(X|Y) < P^{M}(X|Y) < P^{T}(X|Y) = 1$$
+(6)
+
+Since the model trained on random replacement data tends to exhibit lower confidence for noisy and multi-answer samples, we can leverage this characteristic to filter out such samples.
+
+The high-level filtering process, guided by the theoretical framework, is illustrated in Figure 2. By using the model's confidence as a threshold, we can effectively identify and remove noisy samples from the dataset, improving the overall quality of the data used for training and evaluation.
+
+<span id="page-4-0"></span>![](figures/_page_4_Figure_8.jpeg)
+
+(d) Flat representation of sentence space
+
+Figure 2: Conceptual illustration of sample confidence and the filtering process for noisy samples. The upper part demonstrates the variability of model confidence across different samples. The bottom part illustrates the utilization of confidence to identify and filter out noisy samples. The dotted line represents a scalar, while the plane serves as a visual aid for better comprehension.
+
+It is worth noting that multi-answer samples can
+
+be real spelling errors (and thus can not be simply treated as noise), but they are rare in the datasets (see Section 6.2). Therefore, removing them from large-scale datasets has a minor impact on the overall performance. Although our primary focus is on eliminating noisy samples, these analyses provide valuable insights into the comprehensive effects of data filtering and its implications for the CSC task itself.
+
+#### 4 APPROACH
+
+#### 4.1 THE FILTERING STRATEGY
+
+Riding on the analysis above, this paper proposes a filtering model to reduce false spelling errors. We fine-tune BERT on a large-scale news corpus to approach  $P(\cdot|X_{\setminus i})$ . As for the mapping  $\mathcal{F}$ , we randomly select 10% of the characters for replacement, and the modified characters are drawn evenly from the confusion set, indicating P(Y|X) = P(Y'|X) for any  $y_i, y_i'$  in the confusion set of  $x_i$ .
+
+The random replacement dataset is used to train our filtering model, which is the Bert-based one introduced in Section 2. Once we obtain a filtering model, we can feed it with data samples of the OCR/ASR-based corpus to be refined. We filter out spelling errors whose recovering confidence of the filtering model is below a certain threshold.
+
+<span id="page-4-1"></span>
+$$y_i' = \begin{cases} y_i & P(X|Y) \ge p \\ x_i & P(X|Y)$$
+
+As threshold p increases, more samples will be removed from the training set. In Section 6.5, we will demonstrate the impact of threshold.
+
+#### 4.2 THE METHOD PIPELINE
+
+After being processed by the filtering model, the dataset is used to train another Bert-based model with the same architecture as the filtering model, obtaining our final correction model. Algorithm 1 demonstrates the entire process of our approach.
+
+#### <span id="page-5-0"></span>Algorithm 1
+
+- 1: Train a filtering model F on a large-scale random replacement dataset  $D_r$
+- 2: Apply the filtering model F to the OCR/ASR-based dataset  $D_o$  and calculate the confidence of spelling errors.
+- 3: Refine  $D_o$  according to Equation 7 and get the denoised dataset D'
+- 4: Fine-tune a model M for the CSC task with the processed data D'
+
+#### 5 EXPERIMENT SETUP
+
+#### 5.1 Dataset
+
+**Auxiliary Training Set.** 9 million sentence pairs are generated with the Chinese News Corpus Xu (2019) by random replacing strategy. The Auxiliary training set is employed to train the filtering model and explore the impact of data volume on the model.
+
+**Training Set.** We use the same training data as previous CSC works Li et al. (2022c); Zhang et al. (2020); Liu et al. (2021); Xu et al. (2021), including the training set from SIGHAN13/14/15 Wu et al. (2013); Yu et al. (2014); Tseng et al. (2015) and the automatic generated data (271k pairs) based on OCR and ASR methods Wang et al. (2018).
+
+**Validation Set.** 1500 pairs from the training set are randomly picked for supervising the training process.
+
+**Test Set.** The test sets from SIGHAN 13/14/15 are employed, and we use the same procedure as previous worksWang et al. (2019); Zhang et al. (2020); Cheng et al. (2020) to transform the text from traditional Chinese to simplified Chinese.
+
+#### 5.2 Baselines
+
+The following baselines are selected: (1) BERT Fine-tuning, BERT model trained on the standard OCR/ASR-based training set; (2) SpellGCN Cheng et al. (2020) employs BERT to extract character representations and constructs two similarity graphs for phonetics and character shapes; (3) PHMO-Spell Huang et al. (2021) extracts phonetic features, character shape features, and context-related semantic features for each character. These features are integrated using an adaptive gate learned through training; (4) DCN Wang et al. (2021) employs an attention-like method to incorporate additional dependency scores for adjacent characters; (5) ECOPO Li et al. (2022c) incorporates an additional contrastive loss to avoid predicting common characters; (6) SCOPE Li et al. (2022a) introduces an auxiliary task of Chinese pronunciation prediction (CPP) to improve CSC; (7) LEAD Li et al. (2022b) also utilizes contrastive learning methods, with negative samples derived from dictionary knowledge and designed based on phonetics, vision, and meaning; (8) Zero-shot ChatGPT (GPT-3.5); (9) Zero-shot ChatGLMDu et al. (2022), a strong Chinese LLM; (10) Finetuned-ChatGLM.
+
+#### 6 EXPERIMENT RESULTS
+
+#### 6.1 MAIN RESULTS
+
+The results of our method and baselines are shown in Table 2. Our results are obtained by taking the average of five different random seeds. Our approach achieves the highest F1 scores on SIGHAN 13 and SIGHAN 14, significantly surpassing the suboptimal model by margins of 4.1 and 2.4, respectively. We also rank second on SIGHAN 15, 0.3 lower than the best model. We believe achieving the performance by an extremely simple BERT-based CSC model is impressive, highlighting the effectiveness of the data filtering mechanism.
+
+<span id="page-6-1"></span>
+
+|                  | SIGHAN13 |      |      | SI   | GHAN | 14   | SIGHAN15 |      |      |
+|------------------|----------|------|------|------|------|------|----------|------|------|
+|                  | P        | R    | F1   | P    | R    | F1   | P        | R    | F1   |
+| SpellGCN         | 78.3     | 72.7 | 75.4 | 63.1 | 67.2 | 65.3 | 72.1     | 77.7 | 75.9 |
+| PHMOSpell        | 99.5     | 74.7 | 85.4 | 81.8 | 63.6 | 71.6 | 88.2     | 68.4 | 77.1 |
+| DCN              | 84.7     | 77.7 | 81.0 | 65.8 | 68.7 | 67.2 | 74.5     | 78.2 | 76.3 |
+| ECOPO            | 88.5     | 82.0 | 85.1 | 67.5 | 71.0 | 69.2 | 76.1     | 81.2 | 78.5 |
+| SCOPE            | 86.3     | 82.4 | 84.3 | 68.6 | 71.5 | 70.1 | 79.2     | 82.3 | 80.7 |
+| LEAD             | 87.2     | 82.4 | 84.7 | 69.3 | 69.6 | 69.5 | 77.6     | 81.2 | 79.3 |
+| ChatGPT          | 60.7     | 70.8 | 65.4 | 48.0 | 75.1 | 58.4 | 70.0     | 87.5 | 77.8 |
+| ChatGLM          | 13.3     | 16.7 | 14.8 | 7.14 | 33.3 | 11.8 | 16.3     | 68.2 | 26.3 |
+| ChatGLM-Finetune | 60.0     | 64.2 | 62.0 | 45.2 | 63.8 | 52.9 | 60.0     | 70.6 | 64.9 |
+| Ours             | 99.7     | 81.2 | 89.5 | 81.7 | 67.7 | 74.0 | 90.1     | 72.5 | 80.4 |
+
+Table 2: The sentence level correction performance on SIGHAN 13/14/15. We use the optimal threshold that achieves the best performance on each dataset. The detailed analysis of confidence thresholding will be presented in Section 6.5. In SIGHAN13, the annotations on "的", "地", "得" are relatively poor, so following the practice of Li et al. (2022c); Xu et al. (2021) we ignore all "约", "地", "得" cases in the evaluation.
+
+Since the CSC task does not involve adding and deleting characters, most previous methods adopt non-autoregressive methods. However, we are interested in how large language models (LLMs) perform in the CSC task due to their powerful learning and generalization abilities. So we further conduct experiments on a proprietary LLM (GPT-3.5) and an open-source LLM (ChatGLM). The reason for unsatisfactory CSC performance for LLMs can be two-fold. On the one hand, they will likely give outputs of different lengths. On the other hand, they may replace some correct words according to their understanding, leading to higher recall and lower precision.
+
+Our data filtering strategy is incorporated into a BERT-based model, so we check its effects by comparing the base model. Table 3 illustrates that our filtering method achieves an all-around improvement on BERT, including higher F1, lower FPR, and lower ECE. We can conclude that training on the refined corpus delivers a performant and well-calibrated CSC model, successfully mitigating over-correction. Therefore, we empirically verify the overall effectiveness of our data filtering strategy.
+
+<span id="page-6-2"></span>
+
+| Dataset  | Model      | F1   | FPR  | ECE   |
+|----------|------------|------|------|-------|
+| SIGHAN13 | BERT       | 80.0 | 37.9 | 0.163 |
+| SIGHANIS | +Filtering | 89.5 | 6.9  | 0.149 |
+| SIGHAN14 | BERT       | 72.9 | 17.0 | 0.169 |
+| SIGNAN14 | +Filtering | 74.0 | 14.6 | 0.134 |
+| SIGHAN15 | BERT       | 78.6 | 15.1 | 0.130 |
+| SIGHANIS | +Filtering | 80.4 | 7.7  | 0.091 |
+
+![](figures/_page_6_Figure_6.jpeg)
+
+![](figures/_page_6_Figure_7.jpeg)
+
+answer samples.
+
+#### <span id="page-6-0"></span>6.2 IDENTIFYING SPECIFIC DATA SAMPLES
+
+Based on the theoretical analysis in Section 3.3, we know that random replacement data can stabilize the model confidence of noisy and multi-answer samples. Here we are keen to see the impacts of our filtering strategy on these samples, but finding that it is non-trivial to accurately identify these samples. Therefore, in this section, we use a heuristic method to roughly find these samples to 1) verify theoretical sample categorization, 2) provide a concrete case study, and 3) support the following experiments about the impacts on noisy and multi-answer samples.
+
+Noisy Sample Identification. We replace the modified characters with [MASK] and apply BERT to get the output logits of the mask token. If the ratio of logits corresponding to the characters before and after replacement does not exceed a certain percentage λ<sup>N</sup> , we presume that they are both reasonable in the context, thus we get the dataset D<sup>N</sup>
+
+Multi-answer Sample Identification. Still, we replace the modified characters with [MASK], and we extract the BERT hidden states of the mask token as the representation of the context. If two different characters produce the same misspelling and the cosine similarity of their context representation is over a certain threshold λM, we consider these samples to be multi-answer samples DM. When a context has more than two suitable characters, there is an intersection between D<sup>N</sup> and DM. Therefore, we need to remove samples in the intersection to produce the final DM.
+
+We randomly select 3000 samples from the training sets. And we set λ<sup>N</sup> = 0.9 and λ<sup>M</sup> = 0.8 to approximate the sample identification process. 160 noisy samples and 34 multi-answer samples are selected out of 3000. Figure [3](#page-6-2) presents two concrete cases, illustrating that the heuristic method can indeed extract noisy and multi-answer samples from the training set. These samples verify our theoretical data categorization and will be further applied to measure the effect of the filtering model in the following experiments.
+
+### 6.3 OTHER METHODS OF CORPUS UTILIZATION
+
+In this section, we briefly analyze alternative approaches for data utilization. The first approach involves directly combining the two types of datasets (Mixing). The second approach employs the heuristic methods described in noisy sample identification (+H-Filtering). The third approach utilizes the OCR/ASRbased corpus to train a filtering CSC model (S-Filtering). The fourth approach utilizes adaptive training to reduce the weight of negative samples [Huang et al.](#page-9-10) [\(2020\)](#page-9-10). Note that the heuristic filtering in this experiment primarily focuses on noisy samples for computational efficiency reasons.
+
+<span id="page-7-0"></span>
+
+| Dataset  | Model          | P    | R    | F1   | FPR  |
+|----------|----------------|------|------|------|------|
+|          | BERT           | 98.3 | 67.4 | 80.0 | 37.9 |
+|          | Mixing         | 99.0 | 74.3 | 84.9 | 22.3 |
+| SIGHAN13 | +H-Filtering   | 99.2 | 79.5 | 88.3 | 20.7 |
+|          | +S-Filtering   | 98.4 | 63.9 | 77.5 | 34.5 |
+|          | +Self-adaptive | 98.7 | 67.8 | 80.4 | 32.1 |
+|          | BERT           | 79.2 | 67.5 | 72.9 | 17.0 |
+|          | Mixing         | 80.5 | 67.6 | 73.5 | 15.5 |
+| SIGHAN14 | +H-Filtering   | 84.1 | 60.9 | 70.7 | 11.1 |
+|          | +S-Filtering   | 75.7 | 62.9 | 68.7 | 19.4 |
+|          | +Self-adaptive | 79.6 | 67.4 | 73.0 | 16.3 |
+|          | BERT           | 82.8 | 74.7 | 78.6 | 15.1 |
+|          | Mixing         | 86.4 | 73.6 | 79.5 | 11.1 |
+| SIGHAN15 | +H-Filtering   | 87.9 | 73.8 | 80.2 | 9.9  |
+|          | +S-Filtering   | 82.5 | 72.3 | 77.1 | 14.9 |
+|          | +Self-adaptive | 84.6 | 73.8 | 78.8 | 12.1 |
+
+Table 4: Performance of BERT and heuristic/self-filtering method (λ<sup>N</sup> = 0.9) on different datasets.
+
+The results in Table [4](#page-7-0) show that the heuristic filtering approach
+
+(+H-Filtering) improves F1 and leads to better FPR. This verifies our research motivation to denoise corpora. Meantime, +H-Filtering lags behind our learnable filtering model in all metrics (refer to Table [3\)](#page-6-2), demonstrating that we purify data more systematically and effectively
+
+The second self-filtering approach is slightly inferior to the baseline model, verifying previous empirical findings and theoretical analysis on the over-confidence of OCR/ASR-based CSC models.
+
+#### 6.4 FILTERING EFFECTS ON DIFFERENT DATA SAMPLES
+
+The heuristic method produces a dataset including both noisy and multi-answer samples, which allows us to measure the effects on these two categories of samples. To corroborate the theoretical analysis, we examine the filtering ratio of these samples by comparing our filter method and self-filtering.
+
+As shown in Figure [4,](#page-8-1) in line with our expectation, our approach is able to effectively eliminate noisy samples and multi-answer samples. Compared with our method, self-filtering is underperforming in terms of the filtering effect, which explains why the model based on self-filtering gains minor or even negative effects on all the metrics in Table [4.](#page-7-0)
+
+<span id="page-8-1"></span>![](figures/_page_8_Figure_1.jpeg)
+
+![](figures/_page_8_Figure_2.jpeg)
+
+Figure 4: The filtering ratio of noisy samples and multi-answer samples with our method and self-filtering method.
+
+Figure 5: F1 and FPR of the method on three datasets with different filtering thresholds p.
+
+#### <span id="page-8-0"></span>6.5 EFFECTS OF CONFIDENCE THRESHOLD
+
+Notably, spelling errors in SIGHAN 13/14/15 come in different styles: texts in SIGHAN 13 are mostly in a formal writing style, but texts in SIGHAN 14/15 are in an informal writing style. The effects of our filtering method on these datasets can be different. To observe the influences of the filtering threshold, we experiment with hyper-parameters p of {1e-1,1e-2,1e-3,1e-4} respectively.
+
+According to Figure [5,](#page-8-1) F1 reduces with decreasing threshold on SIGHAN13 and vice versa on the other two datasets. The reason might be the differences between formal and informal writing styles. Ignoring the outlier, FPR rises as the threshold decreases, which is easy to understand because without filtering the model has a high FPR. The result of ECE is demonstrated in Appendix [B.](#page-11-0) It is optimal at p = 1e − 2 on all three datasets. Specifically, if we uniformly use 1e − 2 as the threshold, our model still outperforms the baselines.
+
+For more auxiliary experiments, refer to Appendix [C.](#page-11-2)
+
+### 7 RELATED WORK
+
+Chinese spelling correction (CSC) has made remarkable progress with the help of pre-trained language models (PLMs) such as BERT [\(Devlin et al., 2018\)](#page-9-11). Fine-tuning over PLMs became mainstream solutions [Zhang et al.](#page-10-8) [\(2020\)](#page-10-8); [Nguyen et al.](#page-10-12) [\(2021\)](#page-10-12); [Bao et al.](#page-9-12) [\(2020\)](#page-9-12). Furthermore, more improvements to CSC are achieved by incorporating phonological and visual information into PLMs [Jin et al.](#page-9-13) [\(2014\)](#page-9-13); [Cheng et al.](#page-9-2) [\(2020\)](#page-9-2); [Xu et al.](#page-10-4) [\(2021\)](#page-10-4); [Zhang et al.](#page-10-13) [\(2021b\)](#page-10-13); [Huang et al.](#page-9-3) [\(2021\)](#page-9-3).
+
+Data denoising is a general concern as noisy labels severely degrade the generalization of a deep learning model [Zhang et al.](#page-10-14) [\(2021a\)](#page-10-14). In addition to regularization and loss design, some works directly conduct sample selection. Assigning weights to potentially incorrect samples is a kind of approach [Jiang et al.](#page-9-14) [\(2018\)](#page-9-14); [Ren et al.](#page-10-15) [\(2018\)](#page-10-15). Usually, the weights are extremely low compared to those of normal samples. Another way is to filter out potentially wrong samples directly [Tam Nguyen](#page-10-16) [et al.](#page-10-16) [\(2019\)](#page-10-16), which means their weights are either zero or one. In this paper, we also drop the false spelling errors, considering that we have an almost infinite training set.
+
+# 8 CONCLUSION
+
+We propose a simple, efficient, and interpretable data filtering method to purify Chinese Spelling Correction (CSC) corpora. We empirically reveal and theoretically prove the promising calibration characteristic of CSC models trained on random replacement datasets. Using a well-calibrated CSC model to filter the OCR/ASR-based corpora, we learn a final CSC model that integrates the strong generalization performance from OSC/ASR-based data and the trustful model confidence from random replacement data. Our method impressively achieves state-of-the-art performance on SIGHAN 13/14/15 and significantly alleviates over-corrections.
+
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+- <span id="page-10-9"></span>Liang-Chih Yu, Lung-Hao Lee, Yuen-Hsien Tseng, and Hsin-Hsi Chen. Overview of sighan 2014 bake-off for chinese spelling check. In *Proceedings of The Third CIPS-SIGHAN Joint Conference on Chinese Language Processing*, pp. 126–132, 2014.
+- <span id="page-10-14"></span>Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning (still) requires rethinking generalization. *Communications of the ACM*, 64(3):107–115, 2021a.
+- <span id="page-10-13"></span>Ruiqing Zhang, Chao Pang, Chuanqiang Zhang, Shuohuan Wang, Zhongjun He, Yu Sun, Hua Wu, and Haifeng Wang. Correcting chinese spelling errors with phonetic pre-training. In *Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021*, pp. 2250–2261, 2021b.
+- <span id="page-10-8"></span>Shaohua Zhang, Haoran Huang, Jicong Liu, and Hang Li. Spelling error correction with soft-masked bert. *arXiv preprint arXiv:2005.07421*, 2020.
+
+<span id="page-11-3"></span>
+
+|              | SIGHAN13 |      |      |      | SIGHAN14 |      |      |      | SIGHAN15 |      |      |      |
+|--------------|----------|------|------|------|----------|------|------|------|----------|------|------|------|
+| Augmentation | P        | R    | F1↑  | FPR↓ | P        | R    | F1↑  | FPR↓ | P        | R    | F1↑  | FPR↓ |
+| Random       | 99.1     | 54.7 | 70.5 | 17.2 | 77.2     | 39.0 | 51.9 | 11.1 | 87.3     | 50.7 | 64.2 | 7.2  |
+| OCR/ASR      | 98.4     | 71.3 | 82.7 | 37.9 | 79.7     | 72.7 | 76.1 | 17.7 | 83.5     | 77.3 | 80.3 | 14.9 |
+
+Table 5: Performance of BERT models trained on differently augmented data. The metrics are Precision(P), Recall(R), F1-score(F), and sentence-level False Positive Rate(FPR). The model trained with OCR/ASR-based data has a higher F1-score at the cost of more erroneous judgement.
+
+### <span id="page-11-1"></span>A PRELIMINARIES: CALIBRATED CONFIDENCE ESTIMATION
+
+Calibration plays a crucial role in enhancing the interpretability of models, primarily because humans have a tendency to associate confidence with probability. To establish a formal understanding, it is essential to define the concept of perfect calibration. We expect the perfect calibration to adhere to the following criterion:
+
+$$P(\hat{Y} = Y | \hat{P} = p) = p, \forall p \in [0, 1]$$
+ (8)
+
+Here, Yˆ and Pˆ represent the predicted labels and corresponding probabilities, while Y denotes the ground truth. This formulation ensures that the predicted probabilities closely match the actual probabilities assigned to the outcomes.
+
+To quantitatively evaluate the calibration performance, we can employ a scalar summary statistic known as the Expected Calibration Error (ECE) [Guo et al.](#page-9-4) [\(2017\)](#page-9-4). The ECE can be defined as follows:
+
+$$ECE = \mathbb{E}_{\hat{P}}[|P(\hat{Y} = Y|\hat{P} = p) - p|]$$
+ (9)
+
+In practical calculations, the accuracy of samples falling within a specific prediction probability interval is often used to approximate the value of p. This approach allows for a practical assessment of calibration performance.
+
+# <span id="page-11-0"></span>B SUPPLEMENTARY EXPERIMENTAL RESULTS FOR DIFFERENT METRICS ON MULTIPLE DATASETS
+
+The figure presented in Section [1](#page-0-1) is derived from the SIGHAN13 dataset, providing a visual representation of the observed results. However, it is important to note that conducting experiments on other widely recognized datasets can further validate and strengthen the findings. In Table [5,](#page-11-3) we showcase the outcomes of experiments performed on these additional datasets, demonstrating the differences between the two types of augmentation methods.
+
+The results of the Expected Calibration Error (ECE) with varying filtering thresholds are visually represented in Figure [6,](#page-12-1) which serves as a valuable supplement to the discussions in Section [6.5.](#page-8-0)
+
+# <span id="page-11-2"></span>C EFFECTS OF DATA VOLUME
+
+Our auxiliary experiments have been centered around P<sup>F</sup> (ˆy<sup>i</sup> |x\<sup>i</sup> , xi) in Equation [4.](#page-3-1) We take P(v|x\i) as a default constant. However, a small
+
+<span id="page-11-4"></span>
+
+|             |      | SIGHAN13 |      | SIGHAN14 | SIGHAN15 |     |  |
+|-------------|------|----------|------|----------|----------|-----|--|
+| Corpus Size | F1   | FPR      | F1   | FPR      | F1       | FPR |  |
+| 5k          | 84.5 | 6.9      | 59.6 | 8.9      | 70.7     | 6.1 |  |
+| 10k         | 82.9 | 6.9      | 59.6 | 8.5      | 70.2     | 5.9 |  |
+| 100k        | 83.7 | 10.3     | 60.0 | 9.2      | 69.6     | 7.5 |  |
+| 200k        | 83.5 | 10.3     | 60.6 | 10.1     | 71.2     | 7.9 |  |
+| 400k        | 84.1 | 10.3     | 62.8 | 9.6      | 71.5     | 7.5 |  |
+| 2m          | 86.7 | 13.8     | 65.7 | 10.0     | 75.1     | 8.1 |  |
+| 9m          | 89.2 | 10.3     | 70.2 | 9.0      | 80.4     | 7.7 |  |
+
+Table 6: Experimental results on the effects of pre-training corpus size.
+
+<span id="page-12-1"></span>![](figures/_page_12_Figure_1.jpeg)
+
+Figure 6: ECE of the method on three datasets with different filtering thresholds p.
+
+corpus size is likely to lead to estimation bias on P(v|x\i) when calculating the confidence, we explore how large a pre-training sample size would be more appropriate.
+
+We set the filtering thresholds p = 1e − 2 and experiment on diverse sizes of the dataset for the pre-trained filtering model. Table [6](#page-11-4) shows that the F1-score of the model gradually increases as the corpus grows, and the FPR remains in a stable interval. In order to achieve better model performance and maintain the stability of P(v|x\i), a million-data volume is necessary.
+
+# <span id="page-12-0"></span>D BAYESIAN INFERENCE OF MODEL CONFIDENCE
+
+This section presents the derivation of Equation [2,](#page-2-1) which builds upon the assumptions outlined in Section [3.](#page-2-0) By applying the Bayesian formula, we can express the equation as follows:
+
+$$P(X|Y) = P(Y|X) \cdot \frac{P_{\mathcal{X}}(X)}{P_{\mathcal{Y}}(Y)}$$
+
+$$= P(y_i|X) \cdot \frac{P_{\mathcal{X}}(x_i|X_{\setminus i})P_{\mathcal{X}}(X_{\setminus i})}{P_{\mathcal{Y}}(y_i|Y_{\setminus i})P_{\mathcal{Y}}(Y_{\setminus i})}$$
+
+$$= P(y_i|X) \cdot \frac{P_{\mathcal{X}}(x_i|X_{\setminus i})}{P_{\mathcal{Y}}(y_i|X_{\setminus i})}$$
+(10)
+
+<span id="page-12-2"></span>In the formulation, P(·|X\i) represents the conditional probability of a character given the context X\<sup>i</sup> . Since P<sup>Y</sup> is influenced by the augmentation method F, we expand P<sup>Y</sup> (y<sup>i</sup> |X\i) as follows:
+
+$$P_{\mathcal{Y}}(y_i|X_{\setminus i}) = \sum_{v \in \mathcal{V}} P(y_i|X_{\setminus i}, v) P_{\mathcal{X}}(v|X_{\setminus i})$$
+(11)
+
+And the Eq. [10](#page-12-2) can be expressed as Eq. [2](#page-2-1)
+
+# E NOISY SAMPLE CONFIDENCE SUPPLEMENT
+
+In Section [3,](#page-2-0) we focus on providing confidence estimates specifically in the case of two correct characters for the same context. The complete formula for this scenario is as follows:
+
+$$P^{N}(X|Y) = \frac{1}{1 + \frac{P_{\mathcal{X}}(y_{i}|X_{\backslash i})}{P_{\mathcal{X}}(x_{i}|X_{\backslash i})} \frac{P(y_{i}|X_{\backslash i},y_{i})}{P(y_{i}|X_{\backslash i},x_{i})} + \sigma(X,Y)}$$
+
+$$\sigma(X,Y) = \sum_{v \in \mathcal{V}\backslash\{x_{i},y_{i}\}} \frac{P_{\mathcal{X}}(v|X_{\backslash i})}{P_{\mathcal{X}}(x_{i}|X_{\backslash i})} \cdot \frac{P(v|X_{\backslash i},v)}{P(v|X_{\backslash i},x_{i})}$$
+(12)
+
+<span id="page-13-1"></span>Here,  $\sigma(X,Y)$  represents a non-negative value that depends on the vocabulary  $\mathcal{V}$ . It is worth noting that if  $x_i$  and  $y_i$  are the only two suitable characters given the context  $X_{\setminus i}$ , then  $\sigma(X,Y)=0$ . Consequently, Equation 4 already provides an upper bound in this case.
+
+### <span id="page-13-0"></span>F QUANTITATIVE ANALYSIS OF MODEL CONFIDENCE
+
+Previous studies have commonly utilized a random selection of 10% of the characters to simulate the distribution of human misspellings  $\mathcal{Y}$ . In line with this established approach, we follow the same methodology in this paper. Accordingly, we assign the following probabilities:  $P(x_i|X_{\setminus i},x_i)=0.9$  and  $P(y_i|X_{\setminus i},x_i)\leq 0.1$ , where  $y_i\neq x_i$ .
+
+Additionally, we make the assumption that for any two characters u and v suitable for a given context, the ratio  $\frac{P_{\mathcal{X}}(u|X_{\backslash i})}{P_{\mathcal{X}}(v|X_{\backslash i})} \geq a$ . With these assumptions in place, we can establish a numerical upper bound for Equation 12:
+
+$$P^{N}(X|Y) = \frac{1}{1 + \frac{P_{\mathcal{X}}(y_{i}|X_{\setminus i})}{P_{\mathcal{X}}(x_{i}|X_{\setminus i})} \frac{P(y_{i}|X_{\setminus i},y_{i})}{P(y_{i}|X_{\setminus i},x_{i})} + \sigma(X,Y)}$$
+
+$$\leq \frac{1}{1 + \frac{P_{\mathcal{X}}(y_{i}|X_{\setminus i})}{P_{\mathcal{X}}(x_{i}|X_{\setminus i})} \cdot \frac{P(y_{i}|X_{\setminus i},y_{i})}{P(y_{i}|X_{\setminus i},x_{i})}}$$
+
+$$\leq \frac{1}{1 + 9a}$$
+(13)
+
+This implies a low model confidence when taking a reasonable a=0.1 and  $P^N(X|Y)\leq 0.53$ , indicating that noisy samples can be easily filtered out by a pre-trained model regardless of the choice of  $\mathcal{F}$ . As mentioned in Section 3, due to the existence of a long-tailed distribution for the OCR method, there exists a  $y_i$  that gives  $P^N$  a larger upper bound compared to random replacement.
+
+Handling multi-answer samples presents a more complex challenge. When  $\mathcal{F}$  represents a mapping of uniformly sampling misspellings from a confusion set, we can derive that  $\forall u,v\in\mathcal{V}x, \frac{P(y_i|X\setminus i,u)}{P(y_i|X\setminus i,v)}=\frac{|C_u|}{|C_v|}$ , where  $C_v$  denotes the confusion set of character v. In this case, we assume that  $\frac{|C_u|}{|C_v|}\geq b$ . Consequently, we can establish a numerical upper bound for Equation 5:
+
+$$P^{M}(X|Y) = \frac{1}{1 + \sum_{v \in \mathcal{V}} \frac{P_{\mathcal{X}}(v|X_{\setminus i})}{P_{\mathcal{X}}(x_{i}|X_{\setminus i})} \frac{P(y_{i}|X_{\setminus i},v)}{P(y_{i}|X_{\setminus i},x_{i})}}$$
+
+$$\leq \frac{1}{1 + \sum_{v \in \mathcal{V}} ab}$$
+
+$$\leq \frac{1}{1 + ab}$$
+(14)
+
+Here, a and b represent lower bounds for the ratio, and in practice, they are typically small values. Let's assume a=0.1 and b=0.5, we find that  $P^N(X|Y) \leq 0.96$ . Consequently, selecting multianswer samples is considerably more challenging than dealing with noisy samples, especially when the pre-trained model fails to achieve the theoretical upper bound of confidence. Furthermore, the long-tailed distribution observed in the OCR method results in a larger potential value for b, thereby further intensifying the challenge of differentiation.
+
+# G LIMITATIONS
+
+The main limitation of our approach is that we need to search for the best threshold for different datasets, even though a rough threshold (e.g., 1e − 2) can also bring significant performance improvement across all datasets. On the one hand, this phenomenon is natural since different datasets commonly have their unique distribution. On the other hand, it will not affect the application of our method in practice too much, since the effort of threshold searching is tolerable, and we typically face similar data distribution (e.g., in a specific domain) in real-world scenarios.
+
+# H IMPLEMENTATION DETAILS
+
+Most hyperparameters are shared across all experiments to avoid dataset-specific tuning. Based on the repository of Transformers, We train our model using AdamW optimizer for 10 epochs with a learning rate decay of 5e-5, and batch size is set to 50 for each experiment. All experiments were performed using 4 Nvidia A100 GPUs.

papers/1qDRwhe379/review.json

@@ -0,0 +1,71 @@
+{
+  "id": "1qDRwhe379",
+  "title": "Refining Corpora from a Model Calibration Perspective for Chinese Spelling Correction",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "dvDeJ0PXgU",
+      "rating": 6,
+      "content": {
+        "summary": "The paper gives a clear picture of 2 mainstream techniques to create mis-spelling dataset for chinese characters, Random Replacement and OCR/ASR. However, each approach of corruption brings its own inherent bias that may lead to problems in training. For example, OCR/ASR way of corrupting characters gives very calibrated scores, as shown as Figure-1, while the Models trained on Random Replacement data has less calibration issues. The authors propose a recipe to train on both Random Replacement and OCR/ASR data, but with some scheduling and post-process steps, which include prioritize Random Replacement training to learn calibration, and then do OCR/ASR training to improve over-all performance. \n\nThere is a typo in the Table-2 SIGHAN15, but overall, the proposed method achieves SOTA performance on benchmark datasets.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "The strength of the paper lies in its clear presentation of the problem, robust experiment designs, and strong performance on benchmark datasets. The problem of calibration vs overall performance is laid out as the bottleneck, and the authors offer a recipe to combine the two methods. \n\nFirst, the paper is well-written.\n\nThe illustration of the problem is made clear by Figure-1, where Calibration on both models are weak, but the OCR/ASR is much worse. However, the overall performance shows OCR methods is better across-the-board. \n\nThe final results is validated on 3 benchmark Chinese spelling datasets, with 6 existing spelling model benchmarks, and 3 Generative AI benchmarks. The performance gain is significant. \n\nLastly, the issue of mis-spelling in Chinese is a practical and important problem. It will be a waste of resources to rely on a 10 billion parameter ChatGPT to do it on everyday use cases, though the paper shows not so great Zero-Shot performance by ChatGPT.",
+        "weaknesses": "The authors made direct reference of \"Random Replacement\" and \"OCR/ASR\" methods as the two mainstream way to construct mis-spelling datasets. The fact that we can train on data created by both methods isn't a source of novelty. \n\nThe paper uses a model trained on Random Replacement to filter/\"refine\" OCR/ASR corpus is kind of interesting, but may be a step that introduces another layer of inductive bias. \n\nThe author mentions that \"We use the optimal threshold that achieves the best performance on each dataset.\" This is not a good idea, because it runs the risk of leaking test data to model developers. The final performance gain should be reported on 1 uniform threshold(might be proportion if different datasets have different absolute values) determined by running ablation on a separated dev-set . In that case, we can be sure that whatever gain that we see in Table-2 is from the novel method.",
+        "questions": "1. Are there other works that combine Random Replacement and OCR methods in training? \n\n2. Is there a leak of test-set when determining the threshold for filtering? \n\n3. Is there a reason to choose different threshold for each dataset? Can you report Table-2 using one uniform cut-off, and report the dev-set/test-set performance separately?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " The authors made direct reference of \"Random Replacement\" and \"OCR/ASR\" methods as the two mainstream way to construct mis-spelling datasets. The fact that we can train on data created by both methods isn't a source of novelty. \n\nThe paper uses a model trained on Random Replacement to filter/\"refine\" OCR/ASR corpus is kind of interesting, but may be a step that introduces another layer of inductive bias. \n\nThe author mentions that \"We use the optimal threshold that achieves the best performance on each dataset.\" This is not a good idea, because it runs the risk of leaking test data to model developers. The final performance gain should be reported on 1 uniform threshold(might be proportion if different datasets have different absolute values) determined by running ablation on a separated dev-set . In that case, we can be sure that whatever gain that we see in Table-2 is from the novel method.",
+        "suggestions": "The paper's core idea of combining Random Replacement and OCR/ASR data is not inherently novel, as these are established methods for generating noisy data. However, the authors' observation regarding the calibration differences between models trained on these two types of data is a valuable insight. To strengthen the contribution, the authors should more clearly articulate the specific challenges posed by OCR/ASR-generated errors, beyond the general notion of overconfidence. For instance, a deeper analysis of the types of errors produced by OCR/ASR systems, and how these errors differ from random replacements in terms of character similarity or phonetic confusability, would be beneficial. This would provide a more compelling justification for their proposed approach, which leverages the calibration properties of random replacement data to filter OCR/ASR data. Furthermore, they should provide a more detailed explanation of the filtering process itself, including the specific criteria used to determine which OCR/ASR errors are considered \"false\" and how this relates to the model's confidence scores.\n\nThe use of a separate threshold for each dataset is a significant concern, as it introduces a potential for test set leakage and makes the results less generalizable. The authors should instead select a single threshold based on performance on a held-out development set, and then report results on the test set using this fixed threshold. This would provide a more rigorous evaluation of their method and ensure that the reported gains are not due to overfitting to the test data. The authors should also consider exploring the sensitivity of their method to different threshold values, as this would provide a better understanding of the robustness of their approach. It would be beneficial to include an ablation study that examines the impact of different threshold values on the performance of the model, which would help to determine the optimal threshold for each dataset and provide a more comprehensive evaluation of the proposed method. This would also allow for a more fair comparison with other methods.\n\nFinally, while the paper demonstrates strong performance on benchmark datasets, it would be valuable to see an analysis of the types of errors that the proposed method still makes. This could provide insights into the limitations of the approach and suggest directions for future research. For example, are there specific types of misspellings that are particularly challenging for the model to correct, even after the filtering process? Are there any systematic biases in the errors that the model makes? A qualitative error analysis, in addition to the quantitative results, would provide a more complete picture of the performance of the proposed method and its potential for real-world applications."
+      }
+    },
+    {
+      "id": "0jdERFxyBS",
+      "rating": 6,
+      "content": {
+        "summary": "This paper centers its attention on addressing the calibration problem within the realm of Chinese Spelling Check (CSC). Due to the lack of large corpus in the field of CSC, two data augmentation methods of random replacement and OCR/ASR-based generation is proposed to generate large-scale corpora. These methods introduce noise into the data, which subsequently causes over-correction. The authors analyze the calibration of the CSC models trained in the two corpora, and observe that random replacement results in better-calibrated CSC models. The authors then propose a corpus refining strategy to filter OCR/ASR-based data. Utilizing a BERT-based model trained on this refined corpus, the authors achieve commendable performance on CSC benchmarks, affirming the efficacy of the proposed method in mitigating over-correction.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1.\tThe paper makes a valuable contribution by highlighting the differences in generalization performance between OCR/ASR-based and random replacement data augmentation techniques. This insight has the potential to inspire further research in the CSC domain.\n2.\tThe paper proposes a novel data filtering method after carefully observation of the two data augmentations in CSC. The method effectively filters the noisy examples, and the model trained on the refined corpus can achieve impressive performance.\n3.\tThe motivation behind the research is clearly justified and based on empirical observations. The proposed methodology is presented in a comprehensible manner, making it suitable for adaptation to other models in the field.",
+        "weaknesses": "1.\tThe statistical data presented in Table 2 appears to contain an error, as the reported F1 score for the SIGHAN 15 dataset does not align with the provided precision and recall values. This discrepancy requires clarification.\n2.\tMissing citations of ChatGLM. It remains unknown that which version of ChatGLM (ChatGLM or ChatGLM2?) is used in this paper. A more comprehensive citation and elaboration on the fine-tuning procedure are needed.\n3.\tExcessive white space around tables, maybe the layout can be adjusted.",
+        "questions": "1.\tHow do you design the prompt of the LLMs to generate the corrected results? Have you tried other templates to generate?\n2.\tThe issue of varying output lengths generated by LLMs is mentioned. Could you provide additional information on the strategies employed to mitigate this problem and ensure consistent results?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1.\tThe statistical data presented in Table 2 appears to contain an error, as the reported F1 score for the SIGHAN 15 dataset does not align with the provided precision and recall values. This discrepancy requires clarification.\n2.\tMissing citations of ChatGLM. It remains unknown that which version of ChatGLM (ChatGLM or ChatGLM2?) is used in this paper. A more comprehensive citation and elaboration on the fine-tuning procedure are needed.\n3.\tExcessive white space around tables, maybe the layout can be adjusted.",
+        "suggestions": "The paper would benefit from a more detailed analysis of the error patterns introduced by the OCR/ASR-based data augmentation. While the authors note that this method leads to over-correction, a deeper dive into the specific types of errors (e.g., phonetic confusions, visual similarities) would be valuable. For instance, providing a breakdown of the most frequent error types and comparing them with the errors generated by random replacement could offer a more nuanced understanding of the problem. Furthermore, the paper could explore whether certain types of errors are more prone to over-correction than others. This analysis could potentially lead to more targeted filtering strategies beyond simply removing samples that are not length-consistent. Additionally, the authors could investigate whether the performance of the filtering strategy is consistent across different error types. Such an analysis would strengthen the paper's findings and provide more actionable insights for future research in this area.\n\nThe paper mentions the use of a BERT-based model, but it lacks details on the specific architecture, pre-training data, and fine-tuning procedure. Providing more information on these aspects would enhance the reproducibility of the results. For example, the authors should specify the exact BERT variant used (e.g., BERT-base, BERT-large, or a Chinese-specific variant), the pre-training dataset, and the fine-tuning hyperparameters. Furthermore, it would be helpful to include a discussion of the training loss function and optimization algorithm used. This level of detail is crucial for other researchers to replicate the experiments and build upon the proposed method. The authors could also consider including an ablation study to assess the impact of different fine-tuning choices on the final performance. This would provide a better understanding of the model's sensitivity to these parameters and help in optimizing the model for other datasets.\n\nThe paper could also benefit from a more thorough comparison with existing state-of-the-art methods in Chinese Spelling Check. While the authors demonstrate the effectiveness of their approach on benchmark datasets, a more comprehensive comparison with other data augmentation techniques and model architectures would be beneficial. For example, the paper could compare the performance of the proposed method with other data filtering strategies or other models trained on similar datasets. This comparison should not only focus on overall performance metrics but also consider other factors such as computational cost and model complexity. Furthermore, the authors could investigate whether their approach could be combined with other existing methods to achieve even better performance. This would provide a more comprehensive view of the contributions of this work and its position within the broader field of Chinese Spelling Check."
+      }
+    },
+    {
+      "id": "a284uelwMp",
+      "rating": 5,
+      "content": {
+        "summary": "The paper proposes an amazingly simple formula (eq 7) for combining observations with pseudo-labels.  The proposed method is shown to be effective for Chinese spelling correction.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "The method is amazingly simple, and appears to be effective.",
+        "weaknesses": "The approach seems too good to be true.  \n\nThere is a huge literature on pseudo-labels, self-training, co-training, EM, etc.  These methods have many applications that go way beyond Chinese spelling correction.\n\nHere are a few highly cited examples:\n\nhttps://arxiv.org/pdf/1905.02249.pdf \nhttps://arxiv.org/pdf/1908.02983.pdf\nhttps://www.cs.cmu.edu/~avrim/Papers/cotrain.pdf\n\nThere are a number of baselines in table 4, but I found it difficult to understand what each of them do.  I wonder if the description of the method could be shortened in order to make more space available for related work and baselines.\n\nMany readers may not appreciate the challenges in spelling correction for Chinese.  I might start with a discussion like Jurafsky's book (https://web.stanford.edu/~jurafsky/slp3/B.pdf), where they have a language model and a channel model.  You assume errors are just one character for one.  Chinese may be simpler than English in that respect.\n\nAs for the channel model, I'm surprised that you have just two models in mind: (1) random and (2) similar in OCR space.  I might have thought of some others like (3) similar in pinyin space, (4) dependencies involving dialects, (5) dependencies involving input methods (6) similar in distribution.  \n\nIt is well known that spelling correction depends a lot on the context.  We should expect to see very different errors depending on the keyboard.  Typos are different when the user is on a laptop or a phone.  Within phones, there are different keyboards.\n\nThe method of estimating the channel model is somewhat similar to the proposed method here.  They used a boot strapping method where they started with a very simple method to find typos that had just one reasonable correction.  They found  enough of those that they could then estimate confusion matrices.  That probably wouldn't work for Chinese, but it isn't that different from your proposal of training on cases where the probability of the correction is reasonably high.",
+        "questions": "Can you generalize your work so the paper could be of interest to a larger community of people interested in pseudo-labels, self-training, co-training, etc.?\n\nCan you say more about the baselines?\n\nCan you say more about how spelling correction is different in Chinese from spelling correction is other languages?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "details_of_ethics_concerns": "N/A",
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "The approach seems too good to be true.  \n\nThere is a huge literature on pseudo-labels, self-training, co-training, EM, etc.  These methods have many applications that go way beyond Chinese spelling correction.\n\nHere are a few highly cited examples:\n\nhttps://arxiv.org/pdf/1905.02249.pdf \nhttps://arxiv.org/pdf/1908.02983.pdf\nhttps://www.cs.cmu.edu/~avrim/Papers/cotrain.pdf\n\nThere are a number of baselines in table 4, but I found it difficult to understand what each of them do.  I wonder if the description of the method could be shortened in order to make more space available for related work and baselines.\n\nMany readers may not appreciate the challenges in spelling correction for Chinese.  I might start with a discussion like Jurafsky's book (https://web.stanford.edu/~jurafsky/slp3/B.pdf), where they have a language model and a channel model.  You assume errors are just one character for one.  Chinese may be simpler than English in that respect.\n\nAs for the channel model, I'm surprised that you have just two models in mind: (1) random and (2) similar in OCR space.  I might have thought of some others like (3) similar in pinyin space, (4) dependencies involving dialects, (5) dependencies involving input methods (6) similar in distribution.  \n\nIt is well known that spelling correction depends a lot on the context.  We should expect to see very different errors depending on the keyboard.  Typos are different when the user is on a laptop or a phone.  Within phones, there are different keyboards.\n\nThe method of estimating the channel model is somewhat similar to the proposed method here.  They used a boot strapping method where they started with a very simple method to find typos that had just one reasonable correction.  They found  enough of those that they could then estimate confusion matrices.  That probably wouldn't work for Chinese, but it isn't that different from your proposal of training on cases where the probability of the correction is reasonably high.",
+        "suggestions": "The paper's core contribution, a simple formula for combining observations with pseudo-labels, is intriguing, but its novelty and generalizability are not fully established given the extensive existing literature on self-training and related methods. While the simplicity of the approach is a strength, the paper would benefit from a more detailed analysis of how it compares to established techniques like Expectation-Maximization (EM) or co-training algorithms. Specifically, the paper should discuss why a simple linear combination of probabilities is sufficient when more sophisticated methods exist, and under what conditions this approach might fail. A more thorough exploration of the method's limitations and boundary conditions would be valuable. The current analysis focuses narrowly on Chinese spelling correction, and it would be helpful to see discussion of how this approach could be applied to other domains or tasks where pseudo-labeling is used. For example, how might this method perform in noisy image classification or speech recognition? This would broaden the paper's appeal and demonstrate the generalizability of the proposed method.\n\nExpanding on the discussion of the channel model is crucial. The current focus on random and OCR-based errors is too narrow. The paper should explore other error sources such as phonetic confusions (pinyin-based errors), dialect-specific errors, and errors arising from different input methods. For instance, a user might misspell a character due to a similar-sounding pinyin input, or a dialect might influence the pronunciation and therefore the written form. Furthermore, errors are not uniformly distributed; they often depend on the context and the input device. Errors on a phone keyboard are likely different from those on a laptop keyboard. A more comprehensive channel model that considers these factors would make the paper more robust and realistic. The paper could also benefit from a discussion of how the proposed method relates to existing techniques for estimating confusion matrices, especially in the context of Chinese character errors. The current bootstrapping approach is similar to some existing methods, but this relationship is not clearly articulated.\n\nFinally, the paper needs to provide a more detailed explanation of the baseline models used in the experiments. The current descriptions are too brief, making it difficult to understand their strengths and weaknesses. For example, SpellGCN, PHMOSpell, DCN, ECOPO, SCOPE, and LEAD are mentioned, but the specific mechanisms of each model are not explained sufficiently. The reader is left wondering what aspects of these models are relevant for comparison and how they differ from the proposed method. A more thorough description of these baselines, including their underlying assumptions and limitations, would strengthen the paper's analysis. It would also be helpful to include a discussion of why these particular baselines were chosen and what they represent in the broader landscape of Chinese spelling correction. This would provide a more solid foundation for the paper's empirical findings."
+      }
+    }
+  ]
+}

papers/2DldCIjAdX/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "2DldCIjAdX",
+  "title": "LayerNAS: Neural Architecture Search in Polynomial Complexity",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-22",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=2DldCIjAdX"
+}

papers/2DldCIjAdX/paper.md

@@ -0,0 +1,864 @@
+# LAYERNAS: NEURAL ARCHITECTURE SEARCH IN POLYNOMIAL COMPLEXITY
+
+**Anonymous authors**Paper under double-blind review
+
+#### **ABSTRACT**
+
+Neural Architecture Search (NAS) has become a popular method for discovering effective model architectures, especially for target hardware. As such, NAS methods that find optimal architectures under constraints are essential. In our paper, we propose LayerNAS to address the challenge of multi-objective NAS by transforming it into a combinatorial optimization problem, which effectively constrains the search complexity to be polynomial. LayerNAS rigorously derives its method from the fundamental assumption that modifications to previous layers have no impact on the subsequent layers. When dealing with search spaces containing L layers that meet this requirement, the method performs layerwise-search for each layer, selecting from a set of search options S. LayerNAS groups model candidates based on one objective, such as model size or latency, and searches for the optimal model based on another objective, thereby splitting the cost and reward elements of the search. This approach limits the search complexity to  $O(H \cdot |\mathbb{S}| \cdot L)$ , where H is a constant set in LayerNAS. Our experiments show that LayerNAS is able to consistently discover superior models across a variety of search spaces in comparison to strong baselines, including search spaces derived from NATS-Bench, MobileNetV2 and MobileNetV3.
+
+### 1 Introduction
+
+With the surge of ever-growing neural models used across all ML-based disciplines, the efficiency of neural networks is becoming a fundamental factor in their success and applicability. A carefully crafted architecture can achieve good quality while maintaining efficiency during inference. However, designing optimized architectures is a complex and time-consuming process – this is especially true when multiple objectives are involved, including the model's performance and one or more cost factors reflecting the model's size, Multiply-Adds (MAdds) and inference latency. Neural Architecture Search (NAS), is a highly effective paradigm for dealing with such complexities. NAS automates the task and discovers more intricate and complex architectures than those that can be found by humans. Additionally, recent literature shows that NAS allows to search for optimal models under specific constraints (e.g., latency), with remarkable applications on architectures such as MobileNetV3 (Howard et al., 2019), EfficientNet (Tan & Le, 2019) and FBNet (Wu et al., 2019).
+
+Most NAS algorithms encode model architectures using a list of integers, where each integer represents a selected search option for the corresponding layer. In particular, notice that for a given model with L layers, where each layer is selected from a set of search options  $\mathbb S$ , the search space contains  $O(|\mathbb S|^L)$  candidates with different architectures. This exponential complexity presents a significant efficiency challenge for NAS algorithms.
+
+In this paper, we present LayerNAS, an algorithm that addresses the problem of Neural Architecture Search (NAS) through the framework of combinatorial optimization. The proposed approach decouples the constraints of the model and the evaluation of its quality, and explores the factorized search space more effectively in a layerwise manner, reducing the search complexity from exponential to polynomial.
+
+LayerNAS rigorously derives the method from the fundamental assumption: high-performing models when searching for layer $_i$  can be constructed from one of the models in layer $_{i-1}$ . For search spaces that satisfy this assumption, LayerNAS enforces a directional search process from the first layer to
+
+![](figures/_page_1_Figure_1.jpeg)
+
+Figure 1: Comparison with baseline models and NAS methods.
+
+the last layer. The directional layerwise search makes the search complexity  $O(C \cdot |\mathbb{S}| \cdot L)$ , where C is the number of candidates to search per layer.
+
+For multi-objective NAS problems, LayerNAS treats model constraints and model quality as separate metrics. Rather than utilizing a single objective function that combines multi-objectives, LayerNAS stores model candidates by their constraint metric value. Let  $\mathcal{M}_{i,h}$  be the best model candidate for layer, with cost = h. LayerNAS searches for high-performing models under different constraints in the next layer by adding the cost of the selected search option for next layer to the current layer, i.e.,  $\mathcal{M}_{i,h}$ . This transforms the problem into the following combinatorial optimization problem: for a model with L layers, what is the optimal combination of options for all layers needed to achieve the best quality under the cost constraint? If we bucketize the potential model candidates by their cost, the search space is limited to  $O(H \cdot |\mathbb{S}| \cdot L)$ , where H is number of buckets per layer. In practice, capping the search at 100 buckets achieves reasonable performance. Since this holds H constant, it makes the search complexity polynomial.
+
+![](figures/_page_1_Figure_5.jpeg)
+
+Figure 2: Illustration of the LayerNAS Algorithm described in Algorithm 1. For each layer: (1) select a model candidate from current layer and generate children candidates; (2) store the candidate in corresponding bucket, and filter out candidates not in the target objective range; (3) update the model in the bucket if there's a candidate with better quality; and finally, move to the next layer.
+
+Our contributions can be summarized as follows:
+
+- We propose LayerNAS, an algorithm that transforms the multi-objective NAS problem to a combinatorial optimization problem. This is a novel formulation of NAS.
+- LayerNAS is directly designed to tackle the search complexity of NAS, and reduce the search complexity from  $O(|\mathbb{S}|^L)$  to  $O(H \cdot |\mathbb{S}| \cdot L)$ , where H is a constant defined in the algorithm.
+
+• We demonstrate the effectiveness of LayerNAS by identifying high-performing model architectures under various Multiply-Adds (MAdds) constraints, by searching through search spaces derived from MobileNetV2 [\(Sandler et al., 2018\)](#page-10-2) and MobileNetV3 [\(Howard](#page-9-0) [et al., 2019\)](#page-9-0).
+
+# 2 RELATED WORK
+
+The survey by [Elsken et al.](#page-9-1) [\(2019\)](#page-9-1) categorizes methods for Neural Architecture Search into three dimensions: search space, search strategy, and performance estimation strategy. The formulation of NAS as different problems has led to the development of a diverse array of search algorithms. Bayesian Optimization is first adopted for hyper-parameter tuning [\(Bergstra et al., 2013;](#page-8-0) [Domhan](#page-9-2) [et al., 2015;](#page-9-2) [Falkner et al., 2018;](#page-9-3) [Kandasamy et al., 2018\)](#page-9-4). Reinforcement Learning is utilized for training an agent to interact with a search space [\(Zoph & Le, 2017;](#page-11-0) [Pham et al., 2018;](#page-10-3) [Zoph et al., 2018;](#page-11-1) [Jaafra et al., 2019\)](#page-9-5). Evolutionary algorithms [\(Liu et al., 2021;](#page-10-4) [Real et al., 2019\)](#page-10-5) have been employed by encoding model architectures to DNA and evolving the candidate pool. ProgressiveNAS [\(Liu](#page-10-6) [et al., 2018a\)](#page-10-6) uses heuristic search to gradually build models by starting from simple and shallow model architectures and incrementally adding more operations to arrive at deep and complex final architectures. This is in contrast to LayerNAS, which iterates over changes in the layers of a full complex model.
+
+Recent advancements in mobile image models, such as MobileNetV3 [\(Howard et al., 2019\)](#page-9-0), EfficientNet [\(Tan & Le, 2019\)](#page-10-0), FBNet [\(Wu et al., 2019\)](#page-10-1), are optimized by NAS. The search for these models is often constrained by metrics such as FLOPs, model size, latency, and others. To solve this multi-objective problem, most NAS algorithms [\(Tan et al., 2019;](#page-10-7) [Cai et al., 2018\)](#page-9-6) design an objective function that combines these metrics into a single objective. LEMONADE [\(Elsken et al.,](#page-9-7) [2018\)](#page-9-7) proposes a method to split two metrics, and searches for a Pareto front of a family of models. Once-for-All [\(Cai et al., 2020\)](#page-9-8) proposes progressive shrinking algorithm to efficiently find optimal model architectures under different constraints.
+
+Larger models tend to have better performance compared to smaller models. However, the increased size of models also means increased computational resource requirement. As a result, the optimization of neural architectures within constrained resources is an important and meaningful aspect of NAS problems, which can be solved as multi-objective optimization [\(Hsu et al., 2018\)](#page-9-9). There is increasing interest in treating NAS as a compression problem [\(Zhou et al., 2019;](#page-11-2) [Yu & Huang, 2019\)](#page-11-3) from an over-sized model. These works indicate that compressing with different configurations on each layer leads to a model better than uniform compression. Here, NAS can be used to search for optimal configurations [\(He et al., 2018;](#page-9-10) [Liu et al., 2019;](#page-10-8) [Wang et al., 2019\)](#page-10-9).
+
+The applicability of NAS is significantly influenced by the efficiency of its search process. One-shot algorithms [\(Liu et al., 2018b;](#page-10-10) [Cai et al., 2018;](#page-9-6) [Bender et al., 2018;](#page-8-1) [2020\)](#page-8-2) provide a novel approach by constructing a supernet from the search space to perform more efficient NAS. However, this approach has limit on number of branches in supernet due to the constraints of supernet size. The search cost is not only bounded by the complexity of search space, but also the cost of training under "train-and-eval" paradigm. Training-free NAS [\(Mellor et al., 2021;](#page-10-11) [Chen et al., 2021;](#page-9-11) [Zhu et al.,](#page-11-4) [2022;](#page-11-4) [Shu et al., 2021\)](#page-10-12) breaks this paradigm by estimating the model quality with other metrics that are fast to compute. However, the search quality heavily relies on the effectiveness of the metrics.
+
+Several prior works, such as [Liu et al.](#page-10-6) [\(2018a\)](#page-10-6), [Li et al.](#page-10-13) [\(2020\)](#page-10-13), [Qian et al.](#page-10-14) [\(2022\)](#page-10-14), have introduced progressive search mechanisms on layerwise search spaces. LayerNAS stands apart by explicitly articulating the underlying assumptions of the layerwise search space, rigorously deriving the method from these assumptions, and effectively constraining the polynomial search space complexity.
+
+# <span id="page-2-0"></span>3 PROBLEM DEFINITION
+
+Most NAS algorithms do not differentiate the various types of NAS problems. Rather, they employ a single encoding of the search space with a general solution for the search process. However, the unique characteristics of NAS problems can be leveraged to design a tailored approach. We categorize NAS problems into three major types:
+
+- Topology search: the search space defines a graph with multiple nodes. The objective is to identify an optimal topology for connecting nodes with different operations. This task allows for the exploration of novel architectures.
+- Size search or compression search: the search occurs on a predefined model architecture with multiple layers. Each layer can be selected from as a set of search options. Empirically, the best-performing model is normally the one with the most parameters per layer. Therefore, in practice, we aim to search for the optimal model under certain constraints. NATSBench size search (Dong et al., 2021) provides a public dataset for this type of task. MobilNetV3 (Howard et al., 2019), EfficientNet (Tan & Le, 2019), FBNet (Wu et al., 2019) also establish the search space in this manner. This problem can also be viewed as a compression problem He et al. (2018), as reducing the layer size serves as a means of compression by decreasing the model size, FLOPs and latency.
+- Scale search: model architectures are uniformly configured by hyper-parameters, such as number of layers or size of fully-connected layers. This task views the model as a holistic entity and uniformly scales it up or down, rather than adjusting individual layers or components.
+
+This taxonomy illustrates the significant variation among NAS problems. Rather than proposing a general solution to address all of them, we propose to tackle with search spaces in a layerwise manner. Specifically, we aim to find a model with L layers. For each layer, we select from a set of search options  $\mathbb{S}_i$ . A model candidate  $\mathcal{M}$  can be represented as a tuple with size L:  $(s_1, s_2, ..., s_L)$ .  $s_i \in \mathbb{S}_i$  is a selected search option on layer, The objective is to find an optimal model architecture  $\mathcal{M} = (s_1, s_2, ..., s_L)$  with the highest accuracy:
+
+$$\underset{(s_1, s_2, \dots, s_L)}{\operatorname{argmax}} Accuracy(\mathcal{M}) \tag{1}$$
+
+# 4 METHOD
+
+We propose LayerNAS as an algorithm that leverages layerwise attributes. When searching models  $\mathcal{M}_i$  on layer<sub>i</sub>, we are searching for architectures in the form of  $(s_{1..i-1}, x_i, o_{i+1..L})$ .  $s_{1..i-1}$  are the selected options for layer<sub>1...i-1</sub>, and  $o_{i+1..L}$  are the default, predefined options.  $x_i$  is the search option selected for layer<sub>i</sub>, which is the current layer in the search. In this formulation, only layer<sub>i</sub> can be changed, all preceding layers are fixed, and all succeeding layers are using the default option. In topology search, the default option is usually no-op; in size search, the default option can be the option with most computation.
+
+LayerNAS operates on a search space that meets the following assumption, which has been implicitly utilized by past chain-structured NAS techniques (Liu et al., 2018a; Tan et al., 2019; Howard et al., 2019).
+
+<span id="page-3-0"></span>**Assumption 4.1.** The optimal model  $\mathcal{M}_i$  on layer<sub>i</sub> can be constructed from a model  $m \in \mathbb{M}_{i-1}$ , where  $\mathbb{M}_{i-1}$  is a set of model candidates on layer<sub>i-1</sub>.
+
+This assumption implies:
+
+- Enforcing a sequential search process is possible when exploring layer<sub>i</sub> because improvements to the model cannot be achieved by modifying layer<sub>i-1</sub>.
+- The information for finding an optimal model architecture on layer $_i$  was collected when searching for model architectures on layer $_{i-1}$ .
+- Search spaces that are constructed in a layerwise manner, such as those in size search
+  problems discussed in Section 3, can usually meet this assumption. Each search option can
+  completely define how to construct a succeeding layer, and does not depend on the search
+  options in previous layers.
+- It's worth noting that not all search spaces can meet the assumption. Succeeding layers may be coupled with or affect preceding layers in some cases. In practice, we transform the search space in Section 5 to ensure that it meets the assumption.
+
+# Algorithm 1 LayerNAS algorithm
+
+```
+Inputs: L (num layers), R (num searches per layer), T (num models to generate in next layer)
+l = 1
+\mathbb{M}_1 = \{ \forall \mathcal{M}_1 \}
+repeat
+   for i = 1 to R do
+      \mathcal{M}_l = \operatorname{select}(\mathbb{M}_l)
+      for j = 1 to T do
+          \mathcal{M}_{l+1} = \text{apply\_search\_option}(\mathcal{M}_l, \mathbb{S}_{l+1})
+          h = \varphi(\mathcal{M}_{l+1})
+          accuracy = train\_and\_eval(\mathcal{M}_{l+1})
+          if accuracy > Accuracy(M_{l+1,h}) then
+             \mathbb{M}_{l+1,h} = \mathcal{M}_{l+1}
+          end if
+       end for
+   end for
+   l = l + 1
+   if l == L then
+      l = 1
+   end if
+until no available candidates
+```
+
+### 4.1 LAYERNAS FOR TOPOLOGY SEARCH
+
+The LayerNAS algorithm is described by the pseudo code in Algorithm 1.  $\mathbb{M}_l$  is a set of model candidates on layer<sub>l</sub>.  $\mathbb{M}_{l,h}$  is the model on layer<sub>l</sub> mapped to  $h \in \mathbb{H}$ , a lower dimensional representation.  $\mathbb{H}$  is usually a finite integer set, so that we can index and store models.
+
+ $\varphi: \mathbb{M} \to \mathbb{H}$  maps model architecture in  $\mathbb{M}$  to a lower dimensional representation  $\mathbb{H}$ .  $\varphi$  could be an encoded index of model architecture, or other identifiers that group similar model architectures. We discuss this further in 4.2. When there is a unique id for each model, LayerNAS will store all model candidates in  $\mathbb{M}$ .
+
+In this algorithm, the total number of model candidates we need to search is  $\sum_{i=1}^L |\mathbb{M}_i| \cdot |\mathbb{S}_i|$ . It has a polynomial form, but  $|\mathbb{M}_L| = O(|\mathbb{S}|^L)$  if we set  $\varphi(\mathcal{M})$  as unique id of models. This does not limit the order of  $|\mathbb{M}_L|$  to search. For topology search, we can design a sophisticated  $\varphi$  to group similar model candidates. In the following discussion, we will demonstrate how to lower the order of  $|\mathbb{M}_L|$  in multi-objective NAS.
+
+# <span id="page-4-1"></span>4.2 LayerNAS for Multi-objective NAS
+
+LayerNAS is aimed at designing an efficient algorithm for size search or compression search problems. As discussed in Section 3, such problems satisfy Assumption 4.1 by nature. Multi-objective NAS usually searches for an optimal model under some constraints, such as model size, inference latency, hardware-specific FLOPs or energy consumption. We use "cost" as a general term to refer to these constraints. These "cost" metrics are easy to calculate and can be determined when the model architecture is fixed. This is in contrast to calculating accuracy, which requires completing the model training. Because the model is constructed in a layer-wise manner, the cost of the model can be estimated by summing the costs of all layers.
+
+Hence, we can express the multi-objective NAS problem as,
+
+<span id="page-4-2"></span>
+$$\underset{(s_1, s_2, \dots, s_L)}{\operatorname{argmax}} \quad \underset{(s_1, s_2, \dots, s_L)}{Accuracy}(\mathcal{M}_L)$$
+s.t. 
+$$\sum_{i=1}^{L} Cost(s_i) \leq \text{target}$$
+(2)
+
+where  $Cost(s_i)$  is the cost of applying option  $s_i$  on layer,
+
+We introduce an additional assumption by considering the cost in Assumption 4.1:
+
+<span id="page-5-1"></span>**Assumption 4.2.** The optimal model  $\mathcal{M}_i$  with cost = C when searching for layer<sub>i</sub> can be constructed from the optimal model  $\mathcal{M}_{i-1}$  with cost  $= C - Cost(s_i)$  from  $\mathbb{M}_{i-1}$ .
+
+In this assumption, we only keep one optimal model out of a set of models with similar costs. Suppose we have two models with the same cost, but  $\mathcal{M}_i$  has better quality than  $\mathcal{M}'_i$ . The assumption will be satisfied if any changes on following layers to  $\mathcal{M}_i$  will generate a better model than making the same change to  $\mathcal{M}'_i$ .
+
+By applying Assumption 4.2 to Equation (2), we can formulate the problem as combinatorial optimization:
+
+$$\underset{x_{i}}{\operatorname{argmax}} \quad Accuracy(\mathcal{M}_{i})$$
+s.t. 
+$$\sum_{j=1}^{i-1} Cost(s_{1..i-1}, x_{i}, o_{i+1,L}) \leq \operatorname{target}$$
+where 
+$$\mathcal{M}_{i} = (s_{1..i-1}, x_{i}, o_{i+1..L}), \mathcal{M}_{i-1} = (s_{1..i-1}, o_{i..L}) \in \mathbb{M}_{i-1,h'}$$
+(3)
+
+This formulation decouples cost from reward, so there is no need to manually design an objective function to combine these metrics into a single value, and we can avoid tuning hyper-parameters of such an objective. Formulating the problem as combinatorial optimization allows solving it efficiently using dynamic programming.  $\mathbb{M}_{l,h}$  can be considered as a memorial table to record best models on layer<sub>l</sub> at cost h. For layer<sub>l</sub>,  $\mathcal{M}_l$  generates the  $\mathcal{M}_{l+1}$  by applying different options selected from  $\mathbb{S}_{l+1}$  on layer<sub>l+1</sub>. The search complexity is  $O(H \cdot |\mathbb{S}| \cdot L)$ .
+
+We do not need to store all  $\mathbb{M}_{l,h}$  candidates, but rather group them with the following transformation:
+
+<span id="page-5-2"></span>
+$$\varphi(\mathcal{M}_i) = \left\lfloor \frac{Cost(\mathcal{M}_i) - \min Cost(\mathbb{M}_i)}{\max Cost(\mathbb{M}_i) - \min Cost(\mathbb{M}_i)} \times H \right\rfloor$$
+(4)
+
+where H is the desired number of buckets to keep. Each bucket contains model candidates with costs in a specific range. In practice, we can set H=100, meaning we store optimal model candidates within 1% of the cost range.
+
+Equation (4) limits  $|\mathbb{M}_i|$  to be a constant value since H is a constant.  $\min Cost(\mathbb{M}_i)$  and  $\max Cost(\mathbb{M}_i)$  can be easily calculated when we know how to select the search option from  $\mathbb{S}_{i+1}..\mathbb{S}_L$  in order to maximize or minimize the model cost. This can be achieved by defining the order within  $\mathbb{S}_i$ . Let  $s_i=1$  represent the option with the maximal cost on layer, and  $s_i=|\mathbb{S}|$  represent the option with the minimal cost on layer. This approach for constructing the search space facilitates an efficient calculation of maximal and minimal costs.
+
+The optimization applied above leads to achieving polynomial search complexity  $O(H \cdot |\mathbb{S}| \cdot L)$ .  $O(|\mathbb{M}|) = H$  is upper bound of the number of model candidates in each layer, and becomes a constant after applying Equation (4).  $|\mathbb{S}|$  is the number of search options on each layer.
+
+LayerNAS for Multi-objective NAS does not change the implementation of Algorithm 1. With the same framework, we just need to set  $\varphi$  to group  $\mathbb{M}_i$  by their costs with Equation (4). In practice, Assumption 4.2 is not always true because accuracy may vary in each training trial. The algorithm may store a lucky model candidate that happens to get a better accuracy due to variation. We store multiple candidates for each h to reduce the problem from training accuracy variation.
+
+# <span id="page-5-0"></span>5 EXPERIMENTS
+
+#### 5.1 SEARCH ON IMAGENET
+
+**Search Space:** we construct several search spaces based on MobileNetV2, MobileNetV2 (width multiplier=1.4), MobileNetV3-Small and MobileNetV3-Large. For each search space, we set similar backbone of the base model. For each layer, we consider kernel sizes from {3, 5, 7}, base filters and expanded filters from a set of integers, and a fixed strides. The objective is to find better models with similar MAdds of the base model.
+
+To avoid coupling between preceding and succeeding layers, we first search the shared base filters in each block to create residual shortcuts, and search for kernel sizes and expanded filters subsequently. This ensures the search space satisfy Assumption [4.1.](#page-3-0)
+
+We estimate and compare the number of unique model candidates defined by the search space and the maximal number of searches in Table [1.](#page-6-0) In the experiments, we set H = 100, and store 3 best models with same h-value. Note that the maximal number of searches does not mean actual searches conducted in the experiments, but rather an upper bound defined by the algorithm.
+
+<span id="page-6-0"></span>A comprehensive description of the search spaces and discovered model architectures in this experiment can be found in the Appendix for further reference.
+
+| # Max    |
+|----------|
+| Trials   |
+| 1.2e + 5 |
+| 1.5e + 5 |
+| 1.4e + 5 |
+| 2.0e + 6 |
+|          |
+
+Table 1: Comparison of model candidates in the search spaces
+
+# Search, train and evaluation:
+
+During the search process, we train the model candidates for 5 epochs, and use the top-1 accuracy on ImageNet as a proxy metrics. Following the search process, we select several model architectures with best accuracy on 5 epochs, train and evaluate them on 4x4 TPU with 4096 batch size (128 images per core). We use RMSPropOptimizer with 0.9 momentum, train for 500 epochs. Initial learning rate is 2.64, with 12.5 warmup epochs, then decay with cosine schedule.
+
+# Results
+
+We list the best models discovered by LayerNAS, and compare them with baseline models and results from recent NAS works in Table [6.](#page-16-0) For all targeted MAdds, the models discovered by LayerNAS achieve better performance: 69.0% top-1 accuracy on ImageNet for 61M MAdds, a 1.6% improvement over MobileNetV3-Small; 75.6% for 229M MAdds, a 0.4% improvement over MobileNetV3-Large; 77.1% accuracy for 322M MAdds, a 5.1% improvement over MobileNetV2; and finally, 78.6% accuracy for 627M MAdds, a 3.9% improvement over MobileNetV2 1.4x.
+
+Note that for all of these models, we include squeeze-and-excitation blocks [\(Hu et al., 2018\)](#page-9-13) and use Swish activation [\(Ramachandran et al., 2017\)](#page-10-15), in order to to achieve the best performance. Some recent works on NAS algorithms, as well as the original MobileNetV2, do not use these techniques. For a fair comparison, we also list the model performance after removing squeeze-and-excitation and replacing Swish activation with ReLU. The results show that the relative improvement from LayerNAS is present even after removing these components.
+
+# 5.2 NATS-BENCH
+
+The following experiments compare LayerNAS with other NAS algorithms on NATS-Bench [\(Dong](#page-9-12) [et al., 2021\)](#page-9-12). We evaluate NAS algorithms from three perspectives:
+
+- Candidate quality: the quality of the best candidate model found by the algorithm, i.e. the peak evaluation accuracy during search.
+- Stability: the ability to find the best candidate, after running multiple searches and analyzing the average value and range of variation.
+- Efficiency: The training time required to find the best candidate. The sooner the peak accuracy candidate is reached, the more efficient the algorithm.
+
+# NATS-Bench topology search
+
+NATS-Bench topology search defines a search space on 6 ops that connect 4 tensors, each op has 5 options (conv1x1, conv3x3, maxpool3x3, no-op, skip). It contains 15625 candidates with
+
+| 1                                                    | •         | _      |       |
+|------------------------------------------------------|-----------|--------|-------|
+| Model                                                | Top1 Acc. | Params | MAdds |
+| MobileNetV3-Small (Howard et al., 2019) <sup>†</sup> | 67.4      | 2.5M   | 56M   |
+| MNasSmall (Tan et al., 2019)                         | 64.9      | 1.9M   | 65M   |
+| LayerNAS (Ours) <sup>†</sup>                         | 69.0      | 3.7M   | 61M   |
+| MobileNetV3-Large (Howard et al., 2019) <sup>†</sup> | 75.2      | 5.4M   | 219M  |
+| LayerNAS (Ours) †                                    | 75.6      | 5.1M   | 229M  |
+| MobileNetV2 (Sandler et al., 2018)*                  | 72.0      | 3.5M   | 300M  |
+| ProxylessNas-mobile (Cai et al., 2018)*              | 74.6      | 4.1M   | 320M  |
+| MNasNet-A1 (Tan et al., 2019)                        | 75.2      | 3.9M   | 315M  |
+| FairNAS-C (Chu et al., 2021)*                        | 74.7      | 5.6M   | 325M  |
+| LayerNAS-no-SE(Ours)*                                | 75.5      | 3.5M   | 319M  |
+| EfficientNet-B0 (Tan & Le, 2019)                     | 77.1      | 5.3M   | 390M  |
+| SGNAS-B (Huang & Chu, 2021)                          | 76.8      | -      | 326M  |
+| FairNAS-C (Chu et al., 2021) <sup>†</sup>            | 76.7      | 5.6M   | 325M  |
+| GreedyNAS-B (You et al., 2020) <sup>†</sup>          | 76.8      | 5.2M   | 324M  |
+| LayerNAS (Ours) <sup>†</sup>                         | 77.1      | 5.2M   | 322M  |
+| MobileNetV2 1.4x (Sandler et al., 2018)*             | 74.7      | 6.9M   | 585M  |
+| ProgressiveNAS (Liu et al., 2018a)*                  | 74.2      | 5.1M   | 588M  |
+| Shapley-NAS (Xiao et al., 2022)*                     | 76.1      | 5.4M   | 582M  |
+| MAGIC-AT (Xu et al., 2022)*                          | 76.8      | 6M     | 598M  |
+|                                                      |           |        |       |
+
+Table 2: Comparison of models on ImageNet
+
+LayerNAS-no-SE (Ours)\*
+
+their number of parameters, FLOPs, accuracy on Cifar-10, Cifar-100 (Krizhevsky et al., 2009), ImageNet16-120 (Chrabaszcz et al., 2017). In Table 3, we compare with recent state-of-the-art methods. Although training-free NAS has advantage of lower search cost, LayerNAS can achieve much better results.
+
+77.1
+
+**78.6** 
+
+7.6M
+
+9.7M
+
+598M
+
+627M
+
+<span id="page-7-0"></span>
+
+| Table 3: Comparisor | on NATS-Bench topology | search. Average test | accuracy on 5 runs. |
+|---------------------|------------------------|----------------------|---------------------|
+|---------------------|------------------------|----------------------|---------------------|
+
+|                             | Cifar10          | Cifar100         | ImageNet16-120   | Cost (sec) |
+|-----------------------------|------------------|------------------|------------------|------------|
+| RS                          | 92.39±0.06       | 63.54±0.24       | 42.71±0.34       | 1e+5       |
+| RE (Real et al., 2019)      | $94.13\pm0.18$   | $71.40\pm0.50$   | $44.76\pm0.64$   | 1e+5       |
+| PPO (Schulman et al., 2017) | $94.02\pm0.13$   | $71.68 \pm 0.65$ | $44.95{\pm}0.52$ | 1e+5       |
+| KNAS (Xu et al., 2021)      | 93.05            | 68.91            | 34.11            | 4200       |
+| TE-NAS (Chen et al., 2021)  | $93.90\pm0.47$   | $71.24\pm0.56$   | $42.38\pm0.46$   | 1558       |
+| EigenNas (Zhu et al., 2022) | $93.46 \pm 0.02$ | $71.42\pm0.63$   | $45.54\pm0.04$   | -          |
+| NASI (Shu et al., 2021)     | $93.55\pm0.10$   | $71.20\pm0.14$   | $44.84{\pm}1.41$ | 120        |
+| FairNAS (Chu et al., 2021)  | $93.23 \pm 0.18$ | $71.00\pm1.46$   | $42.19\pm0.31$   | 1e+5       |
+| SGNAS (Huang & Chu, 2021)   | $93.53\pm0.12$   | $70.31\pm1.09$   | $44.98\pm2.10$   | 9e+4       |
+| LayerNAS                    | $94.34 \pm 0.12$ | $73.01 \pm 0.63$ | $46.58 \pm 0.59$ | 1e+5       |
+| Optimal test accuracy       | 94.37            | 73.51            | 47.31            |            |
+
+# **NATS-Bench size search**
+
+NATS-Bench size search defines a search space on a 5-layer CNN model, each layer has 8 options on different number of channels, from 8 to 64. The search space contains 32768 model candidates. The one with the highest accuracy has 64 channels for all layers, we can refer this candidate as "the largest model". Instead of searching for the best model, we set the goal to search for the optimal model with 50% FLOPs of the largest model.
+
+Under this constraints for size search, we implement popular NAS algorithms for comparison, which are also used in the original benchmark papers (Ying et al., 2019; Dong et al., 2021): random search, proximal policy optimization (PPO) (Schulman et al., 2017) and regularized evolution (RE) (Real
+
+<sup>\*</sup> Without squeeze-and-excitation blocks.
+
+<sup>†</sup> With squeeze-and-excitation blocks.
+
+et al., 2019). We conduct 5 runs for each algorithm, and record the best accuracy at different training costs.
+
+LayerNAS treats this as a compression problem. The base model, which is the largest model, has 64 channels on all layers. By applying search options with fewer channels, the model becomes smaller, faster and less accurate. The search process is to find the optimal model with expected FLOPs. By filtering out candidates that do not produce architectures falling within the expected FLOPs range, we can significantly reduce the number of candidates that need to be searched.
+
+|                             | Cifar10 | Cifar100 | ImageNet16-120 |
+|-----------------------------|---------|----------|----------------|
+| Training time (sec)         | 2e+5    | 4e+5     | 6e+5           |
+| Target mFLOPs               | 140     | 140      | 35             |
+| RS                          | 0.9265  | 0.6935   | 0.4381         |
+| RE (Real et al., 2019)      | 0.9282  | 0.6962   | 0.4476         |
+| PPO (Schulman et al., 2017) | 0.9283  | 0.6957   | 0.4438         |
+| LayerNAS                    | 0.9320  | 0.7064   | 0.4537         |
+| Optimal validation          | 0.9264  | 0.6922   | 0.4500         |
+| Optimal test                | 0.9334  | 0.7086   | 0.4553         |
+
+Table 4: Comparison on NATS-Bench size search. Average test accuracy on 5 runs.
+
+# 6 CONCLUSION AND FUTURE WORK
+
+In this research, we propose LayerNAS that formulates Multi-objective Neural Architecture Search to Combinatorial Optimization. By decoupling multi-objectives into cost and accuracy, and leverages layerwise attributes, we are able to reduce the search complexity from  $O(|S|^L)$  to  $O(H \cdot |S| \cdot L)$ .
+
+Our experiment results demonstrate the effectiveness of LayerNAS in discovering models that achieve superior performance compared to both baseline models and models discovered by other NAS algorithms under various constraints of MAdds. Specifically, models discovered through LayerNAS achieve top-1 accuracy on ImageNet of 69% for 61M MAdds, 75.6% for 229M MAdds, 77.1% for 322M MAdds, 78.6% for 627M MAdds. Furthermore, our analysis reveals that LayerNAS outperforms other NAS algorithms on NATS-Bench in all aspects including best model quality, stability and efficiency.
+
+While the current implementation of LayerNAS has shown promising results, several current limitations that can be addressed by future work:
+
+- LayerNAS is not designed to solve scale search problems mentioned in Section 3, because many hyper-parameters of model architecture are interdependent in scale search problem, which contradicts the statement in Assumption 4.1.
+- One-shot NAS algorithms have been shown to be more efficient. We aim to investigate the potential of applying LayerNAS to One-shot NAS algorithms.
+
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+
+# A NOTATION
+
+ $\mathbb{S}_i$ : Search options for layer<sub>i</sub>.
+
+ $|S_i|$ : Num of search options on layer,
+
+ $s_i$ : selected search option on layer, from the set  $\mathbb{S}_i$ 
+
+ $o_i$ : default search option applied on layer,  $o_{1..L}$  is the architecture of the baseline model.
+
+ $(s_1, s_2, ..., s_L)$ : A model architecture that applies  $s_1$  on layer,  $s_2$  on layer, ...,  $s_L$  on layer
+
+ $(s_{1..i-1}, x_i, o_{i+1..L})$ : A model architecture that applies  $s_1$  on layer<sub>1</sub>,  $s_2$  on layer<sub>2</sub>, ..., default search option  $o_{i+1}$  on layer<sub>i+1</sub>, ...  $o_L$  on layer<sub>L</sub>, and search  $x_i$  on layer<sub>i</sub>.
+
+ $\mathcal{M}_i$ : A model candidate that is searched on layer, it's in the form of  $(s_{1..i-1}, x_i, o_{i+1..L})$ .
+
+ $M_i$ : All model candidates searching on layer<sub>i</sub>.
+
+ $\mathbb{M}_{i,h}$ : Model candidates searching on layer, and are mapped to  $h \in \mathbb{H}$ .
+
+ $\varphi: \mathbb{M} \to \mathbb{H}$ : transforms a model architecture  $\mathcal{M} \in \mathbb{M}$  to a finite integer set  $\mathbb{H}$ 
+
+# B NASBENCH-101 SEARCH DETAILS
+
+NASBench-101 defines a search space on 5 ops, each op has 3 options (conv1x1, conv3x3, maxpool 3x3), and 21 potential edges to connect these ops and input, output ops. It contains 509M candidates with their number of parameters, accuracy on Cifar-10, and other information.
+
+We construct the LayerNAS search space by adding a new edge for each layer. Search options in each layer are used to determine either to include a new op or connect two existing ops. By doing so, all constructed candidates can be legit, because all candidates are connected graphs. And this approach of search space construction can satisfy the assumption of LayerNAS: the best model candidate in layer $_i$  can be constructed from candidates in layer $_{i-1}$  by adding an new edge.
+
+In the experiments, Regularized Evolution (RE) sets population\_size=50, tournament\_size=10; Proximal Policy Optimization (PPO) sets train\_batch\_size=16, update\_batch\_size=8, num\_updates\_per\_feedback=10. Both RE and PPO are using MNAS as objective function:  $Accuracy \times (Cost/Target)^{-0.07}$ 
+
+In Figure 3, we observe that in earlier searching iterations LayerNAS performs slightly worse than other algorithms. This is because LayerNAS initially searches model candidates with fewer ops and edges, which intuitively perform poorly. However, after collecting enough information from early layers, LayerNAS consistently performs better. This is because LayerNAS does not rely on randomness, rather, it adds ops and edges from successful candidates in each layers, leading to continuous improvement.
+
+<span id="page-12-0"></span>![](figures/_page_12_Figure_17.jpeg)
+
+Figure 3: NASBench-101 test accuracy on Cifar-10, average on 100 runs
+
+Table 5: Comparison on NASBench-101
+
+| Algorithm | Validation accuracy | Test accuracy |
+|-----------|---------------------|---------------|
+| RS        | 0.9480              | 0.9401        |
+| RE        | 0.9497              | 0.9416        |
+| PPO       | 0.9476              | 0.9396        |
+| LayerNAS  | 0.9505              | 0.9426        |
+| Optimal   | 0.9432              | 0.9445        |
+
+# C NATS-BENCH SEARCH DETAILS
+
+In the experiments, Regularized Evolution (RE) sets population\_size=50, tournament\_size=10; Proximal Policy Optimization (PPO) sets train\_batch\_size=16, update\_batch\_size=8, num\_updates\_per\_feedback=10. Both RE and PPO are using MNAS as objective function: Accuracy × (Cost/T arget) −0.07
+
+# C.1 NATS-BENCH TOPOLOGY SEARCH
+
+NATS-Bench topology search defines a search space on 6 ops that connect 4 tensors, each op has 5 options (conv1x1, conv3x3, maxpool3x3, no-op, skip).
+
+In our experiments, we construct the LayerNAS search space by adding a new tensor for each layer. Search options in each layer are encoded with all op types that connect this tensor to previous tensors. So it has only 3 layers, each layer has 5, 25, 125 options.
+
+Validation and test accuracy are shown in Figure [4](#page-13-0) and Figure [5.](#page-13-1)
+
+![](figures/_page_13_Figure_9.jpeg)
+
+![](figures/_page_13_Figure_10.jpeg)
+
+<span id="page-13-0"></span>![](figures/_page_13_Figure_11.jpeg)
+
+Figure 4: NATS-Bench topology search valid accuracy on (a) Cifar10 (b) Cifar100 (c) Imagenet16- 120
+
+![](figures/_page_13_Figure_13.jpeg)
+
+![](figures/_page_13_Figure_14.jpeg)
+
+<span id="page-13-1"></span>![](figures/_page_13_Figure_15.jpeg)
+
+Figure 5: NATS-Bench topology search test accuracy on (a) Cifar10 (b) Cifar100 (c) Imagenet16-120
+
+# C.2 NATS-BENCH SIZE SEARCH
+
+NATS-Bench size search provides a dataset with information on model architectures with 5 layers. Each layer is a convolutional layer with different num of channels selected from {8, 16, 24, 32, 40, 48, 56, 64}. The model with 64 channels for all layers has the most model parameters, the largest latency and the best accuracy. The objective is to find the optimal model with 50% FLOPs.
+
+LayerNAS constructs the search space by using the largest model as base model, and applies search options that reduce channels per layer. Althoughh LayerNAS steadily improves valid accuracy over time, test accuracy drops. This is due to in-correlation between test accuracy and valid accuracy.
+
+Validation and test accuracy are shown in Figure 6 and Figure 7. We can observe that LayerNAS can outperform other algorithms on both validation and test accuracy. We can also attribute test accuracy drop in LayerNAS to the lack of correlation with validation accuracy.
+
+![](figures/_page_14_Figure_4.jpeg)
+
+<span id="page-14-0"></span>Figure 6: NATS-Bench size search valid accuracy on (a) Cifar10 (b) Cifar100 (c) Imagenet16-120
+
+![](figures/_page_14_Figure_6.jpeg)
+
+<span id="page-14-1"></span>Figure 7: NATS-Bench size search test accuracy on (a) Cifar10 (b) Cifar100 (c) Imagenet16-120
+
+# D DYNAMIC PROGRAMMING IMPLEMENTATION OF LAYERNAS FOR MULTI-OBJECTIVE NAS
+
+Algorithm 2 demonstrates how to implement LayerNAS with Dynamic Programming, which has clear explanation why search complexity is  $O(H \cdot |\mathbb{S}| \cdot L)$ .
+
+The implementation is not used in practice because it spends most of time searching in layer<sub>1..L-1</sub>, we cannot get a model in expected cost range until last layer is searched.
+
+# Algorithm 2 Dynamic Programming for Combinatorial Optimization
+
+```
+\begin{aligned} & \textbf{for } l = 1 \text{ to } L - 1 \textbf{ do} \\ & \textbf{for } \mathcal{M}_l \in \mathbb{M}_l \textbf{ do} \\ & \textbf{for } s \in \mathbb{S}_{l+1} \textbf{ do} \\ & \mathcal{M}_{l+1} = \text{apply\_search\_option}(\mathcal{M}_l, s) \\ & h = \text{cost}(\mathcal{M}_{l+1}) \\ & accuracy = \text{train\_and\_eval}(\mathcal{M}_{l+1}) \\ & \textbf{ if } accuracy > \text{Accuracy}(\mathbb{M}_{l+1,h}) \textbf{ then} \\ & \mathbb{M}_{l+1,h} = \mathcal{M}_{l+1} \\ & \textbf{ end if} \\ & \textbf{ end for} \\ & \textbf{ end for} \end{aligned}
+```
+
+#### E DISCUSSION ON SEARCH SPACE ASSUMPTIONS
+
+Assumption 4.1 sets some characteristics of search spaces that can be leveraged to improve the search efficiency. Instead of expecting all search spaces can satisfy this assumption, in experiments, we construct search spaces based on MobileNet to intentionally make them satisfy Assumption 4.1. While we cannot guarantee that all search spaces can be transformed to satisfy Assumption 4.1, most search spaces used in existing models or studies either implicitly use this assumption or can be transformed to satisfy it. We also demonstrate the effectiveness of this assumption from the experiments on MobileNet.
+
+#### E.1 SEARCH SPACE IS COMPLETE
+
+Assume we are searching for the optimal model  $s_1...s_n$ , and we store all possible model candidates on each layer. During the search process on layer<sub>n</sub>, we generate model architectures by modifying  $o_n$  to other options in  $\mathbb S$ . Since we store all model architectures for layer<sub>n-1</sub>, the search process can create all  $|\mathbb S|^n$  candidates on layer<sub>n</sub> by adding each  $s_n \in \mathbb S$  to the models in  $\mathbb M_{n-1}$ . Therefore,  $\mathbb M_n$  contains all possibilities in the search space. This process can then be applied backward to the first layer.
+
+# E.2 SEQUENTIAL SEARCH ORDER
+
+Assume, after LayerNAS sequential search, we get optimal model defined as  $a_1...a_i...a_n$ . For sake of contradiction, there exists a model  $a_1..b_i...a_n$ , with superior performance, by applying a change in previous layers. Since the search space is complete, model  $a_1..b_io_{i+1}..o_n$  must exist, and has been processed in  $\mathbb{M}_i$ . In the sequential search, model  $a_1..b_ia_{i+1}..o_n$  can be created by using  $a_{i+1}$  on layer<sub>i+1</sub>. Repeating this process for all subsequent layers will eventually lead to  $a_1..b_i..a_n$ , contradicting our assumption that optimal model from sequential search is  $a_1..a_i..a_n$ . Therefore, we can search sequentially.
+
+#### E.3 LIMIT OF THE ASSUMPTION
+
+MobileNet architecture does not satisfy Assumption 4.1 by default. Residual requires layer<sub>i</sub> and layer<sub>j</sub> have the same num of filters. Suppose  $\mathbb{S}_i = \{32, 64, 96\}$ ,  $\mathbb{S}_j = \{64, 96, 128\}$ , the residual shortcut cannot be created if  $s_i = 32, s_j = 96$ . This is the case when preceding layers are coupled with succeeding layers. To overcome this issue, we introduce a virtual layer, with options  $\{64, 96\}$ . We first search this shared filter to create residual shortcuts, and then search specs for each layer. This transformation ensures that the new search space satisfy Assumption 4.1. In the case of MobileNet search space, we first search for the common filters for the block and then for the expanded filters for each layer. This approach allows us to perform LayerNAS on a search space that satisfies Assumption 4.1.
+
+# F DISCUSSION ON NUM OF REPLICAS TO STORE
+
+From experiments on MobileNet, we observed that multiple runs on the same model architecture can yield standard deviations of accuracy ranging from 0.08% to 0.15%. Often times, the difference can be as high as 0.3%. To address this, we propose storing multiple candidates for the same cost to increase the likelihood of keeping the better model architecture for every layer search.
+
+Suppose we have two models with the same cost, x and y, where x is inferior and y is superior, and the training accuracy follows a Gaussian distribution  $N(\mu, \sigma^2)$ . The probability of x obtaining a higher accuracy than y is P(x-y>0), where  $x-y\sim N(\mu_x-\mu_y,\sigma_x^2+\sigma_y^2)$ . In emprical examples,  $\mu_x-\mu_y=-0.002$  and  $\sigma_x=0.001$ , then x has the probability of 9.2% of obtaining a higher accuracy. When we have L=20 layers, the probability of keeping the better model architecture for every layer search is  $(1-p)^{20}=18\%$ .
+
+By storing k candidates with the same cost, we can increase the probability of keeping the better model architecture. When k=3, the probability of storing all inferior models is  $p^k=0.08\%$ . The probability of keeping the better model architecture for all L=20 layer searches is 98.4%, which is practically good enough.
+
+Theoretically, if we store infinite candidates per layer, we are performing a complete grid search, which guarantees a optimal model architecture.
+
+# G TRANSFERABILITY
+
+LayerNAS's explored model architectures exhibit improved performance across various tasks as well.
+
+<span id="page-16-0"></span>
+
+| -                 |                    |          |        |       |
+|-------------------|--------------------|----------|--------|-------|
+| Model             | ImageNet top-1 acc | CoCo mAP | Params | MAdds |
+| MobileNetV2       | 72.0               | 22.1     | 3.5M   | 300M  |
+| LayerNAS w/o SE   | 77.1               | 23.85    | 7.6M   | 598M  |
+| LayerNAS          | 78.6               | 24.84    | 9.7M   | 527M  |
+| MobileNetV3-Small | 67.4               | 16       | 2.5M   | 56M   |
+| LayerNAS          | 69.0               | 17.94    | 3.7M   | 61M   |
+| MobileNetV3-Large | 75.2               | 22.0     | 5.4M   | 219M  |
+| LayerNAS          | 75.6               | 23.75    | 5.1M   | 229M  |
+
+Table 6: Comparison of models on ImageNet
+
+# H MOBILENETV2 AND MOBILENETV3 SEARCH DETAILS
+
+We aim to search models under different MAdds constrants: 60M (similar to MobileNetV3-Small), 220M (similar to MobileNetV3-Large), 300M (similar to MobileNetV2), 600M (similar to MobileNetV2 1.4x).
+
+For each block, we will search the number of output filters of the block first. All layers in the block have the same number of output filters to create residual block correctly. Following the search for the block output filters, we search expanded filter and kernel size of each layers in this block. Strides are fixed for all layers. We use  $|\mathbb{S}|$  to denote the number of search options of this layer, which facilitates the computation on the number of unique model architectures, and max number of required search trials in LayerNAS.
+
+#### H.1 60M MADDS MODEL
+
+The search spaces has L=16 encoded length. Number of unique model architecture is  $\prod |\mathbb{S}| = 5.0e + 20$ . We store up to 300 model candidates per layer, so max number of trials is  $300 \times \sum |\mathbb{S}| = 1.2e + 5$ .
+
+#### H.2 220M MADDS MODEL
+
+The search spaces has L=21 encoded length, the number of unique model architecture is  $\prod |\mathbb{S}|=4.8e+26$  For LayerNAS, we store up to 300 model candidates per layer, so max number of trials is  $300 \times \sum |\mathbb{S}| = 1.5e+5$ 
+
+# H.3 300M MADDS MODEL
+
+The search spaces has L=26 encoded length, the number of unique model architectures is  $\prod |\mathbb{S}|=5.3e+30$ . We store up to 300 model candidates per layer, so max number of trials is  $300\times\sum |\mathbb{S}|=1.4e+5$ .
+
+# H.4 600M MADDS MODEL
+
+The search spaces has L=31 encoded length, the number of unique model architecture is  $\prod |\mathbb{S}|=1.6e+39$  For LayerNAS, we store up to 300 model candidates per layer, so max number of trials is  $300\times \sum |\mathbb{S}|=2.0e+6$ 
+
+Table 7: 60M MAdds Search Space
+
+| Operator              | # Output filter                      | # Expanded Filter                  | strides | S  |
+|-----------------------|--------------------------------------|------------------------------------|---------|----|
+| conv2d{3x3}           | 16                                   |                                    | 2       |    |
+| bneck {3x3}           | {24, 20, 18, 16, 14, 12}             |                                    | 2       | 6  |
+| Block filter          | {36, 32, 28, 24, 20, 18, 16}         |                                    |         | 7  |
+|                       |                                      | {144, 136, 128, 120, 112, 104,     |         |    |
+| bneck {3x3, 5x5}      |                                      | 96, 88, 80, 72, 68, 64, 60, 56}    | 2       | 28 |
+|                       |                                      | {144, 136, 128, 120, 112, 104,     |         |    |
+| bneck {3x3, 5x5}      |                                      | 96, 88, 80, 72 68, 64, 60, 56}     | 1       | 28 |
+| Block filter          | {60, 56, 52, 48, 44, 40, 36, 32, 28} |                                    |         | 9  |
+|                       |                                      | {192, 176, 160, 144, 128,          |         |    |
+| bneck {3x3, 5x5, 7x7} |                                      | 112, 104, 96, 88, 80, 72, 64}      | 2       | 36 |
+|                       |                                      | {480, 440, 400, 360, 320, 300,     |         |    |
+| bneck {3x3, 5x5, 7x7} |                                      | 280, 260, 240, 220, 200, 180, 160} | 1       | 39 |
+|                       |                                      | {480, 440, 400, 360, 320, 300,     |         |    |
+| bneck {3x3, 5x5, 7x7} |                                      | 280, 260, 240, 220, 200, 180, 160} | 1       | 39 |
+|                       | {96, 88, 80, 72, 64, 60, 56,         |                                    |         |    |
+| Block filter          | 52, 48, 44, 40, 36, 32}              | {240, 200, 180, 160, 140,          |         | 13 |
+| bneck {3x3, 5x5, 7x7} |                                      | 120, 100, 90, 80}                  | 1       | 27 |
+|                       |                                      | {288, 256, 224, 208, 192, 176,     |         |    |
+| bneck {3x3, 5x5, 7x7} |                                      | 160, 152, 144, 136, 128, 120}      | 1       | 36 |
+|                       | {192, 176, 160, 144, 128, 120, 112,  |                                    |         |    |
+| Block filter          | 104, 96, 88, 80, 72, 64}             |                                    |         | 13 |
+|                       |                                      | {576, 544, 512, 480, 448, 416,     |         |    |
+| bneck {3x3, 5x5, 7x7} |                                      | 384, 352, 320, 288, 256, 224}      | 2       | 36 |
+|                       |                                      | {1152, 1088, 1024, 960, 896, 832,  |         |    |
+| bneck {3x3, 5x5, 7x7} |                                      | 768, 704, 640, 576, 516, 448}      | 1       | 36 |
+|                       |                                      | {1152, 1088, 1024, 960, 896, 832,  |         |    |
+| bneck {3x3, 5x5, 7x7} |                                      | 768, 704, 640, 576, 516, 448}      | 1       | 36 |
+| conv2d 1x1            | {864, 576},                          |                                    |         | 2  |
+| pool, 7x7             |                                      |                                    |         |    |
+| conv2d 1x1            | {1536, 1024}                         |                                    |         | 2  |
+| conv2d 1x1            | {1001}                               |                                    |         |    |
+
+Table 8: LayerNAS Model under 60M MAdds
+
+| Input          | Operator   | # Output filter | # Expanded Filter | strides |
+|----------------|------------|-----------------|-------------------|---------|
+| 224 × 224 × 3  | conv2d 3x3 | 16              |                   | 2       |
+| 112 × 112 × 16 | bneck 3x3  | 16              |                   | 2       |
+| 56 × 56 × 16   | bneck 3x3  | 28              | 144               | 2       |
+| 28 × 28 × 28   | bneck 3x3  | 28              | 128               | 1       |
+| 28 × 28 × 28   | bneck 5x5  | 44              | 96                | 2       |
+| 14 × 14 × 44   | bneck 3x3  | 44              | 220               | 1       |
+| 14 × 14 × 44   | bneck 3x3  | 44              | 200               | 1       |
+| 14 × 14 × 44   | bneck 7x7  | 40              | 160               | 1       |
+| 14 × 14 × 40   | bneck 3x3  | 40              | 152               | 1       |
+| 14 × 14 × 96   | bneck 5x5  | 96              | 224               | 2       |
+| 7 × 7 × 96     | bneck 3x3  | 96              | 448               | 1       |
+| 7 × 7 × 96     | bneck 3x3  | 96              | 512               | 1       |
+| 7 × 7 × 96     | conv2d 1x1 | 864             |                   | 1       |
+| 7 × 7 × 864    | pool, 7x7  |                 |                   | 1       |
+| 7 × 7 × 864    | conv2d 1x1 | 1536            |                   | 1       |
+| 7 × 7 × 1536   | conv2d 1x1 | 1001            |                   | 1       |
+
+Table 9: 220M MAdds Search Space
+
+| Operator              | # Output filter                     | # Expanded Filter                                                | strides | S  |
+|-----------------------|-------------------------------------|------------------------------------------------------------------|---------|----|
+| Conv2d{3x3}           | 16                                  |                                                                  | 2       |    |
+| bneck {3x3}           | {24, 20, 18, 16, 14, 12}            |                                                                  | 1       | 6  |
+| Block filter          | {36, 32, 28, 24, 20, 16}            |                                                                  |         |    |
+|                       |                                     | {96, 88, 80, 72,                                                 |         |    |
+| bneck {3x3, 5x5}      |                                     | 68, 64, 60, 56, 48}                                              | 2       | 18 |
+|                       |                                     | {124, 116, 108, 100, 92, 84,                                     |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 72, 68, 64, 56, 48}                                              | 1       | 33 |
+|                       | {64, 56, 52, 48,                    |                                                                  |         |    |
+| Block filter          | 44, 40, 36, 32, 24}                 | {128, 120, 112, 104, 96,                                         |         | 9  |
+| bneck {3x3, 5x5, 7x7} |                                     | 88, 80, 76, 72, 64, 56}                                          | 2       | 33 |
+|                       |                                     | {240, 200, 180, 160,                                             |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 140, 120, 110, 100, 80}                                          | 1       | 27 |
+|                       |                                     | {240, 200, 180, 160,                                             |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 140, 120, 110, 100, 80}                                          | 1       | 27 |
+|                       | {160, 140, 130, 120,                |                                                                  |         |    |
+| Block filter          | 110, 100, 80, 70, 60}               |                                                                  |         | 9  |
+|                       |                                     | {360, 320, 300, 280, 260,                                        |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 240, 220, 200, 180, 160}                                         | 2       | 30 |
+|                       |                                     | {400, 360, 340, 320, 300, 280,                                   |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 260, 240, 220, 200, 180, 160, 120}                               | 1       | 36 |
+|                       |                                     | {368, 336, 304, 288, 272, 256,                                   |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 240, 224, 208, 184, 168, 152}                                    | 1       | 36 |
+| bneck {3x3, 5x5, 7x7} |                                     | {368, 336, 304, 288, 272, 256,<br>240, 224, 208, 184, 168, 152}  | 1       | 36 |
+|                       | {224, 208, 192, 176, 160,           |                                                                  |         |    |
+| Block filter          | 144, 128, 112, 96, 80}              |                                                                  |         | 10 |
+|                       |                                     | {960, 880, 800, 720, 640, 560,                                   |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 520, 480, 440, 400, 360}                                         | 1       | 33 |
+|                       |                                     | {1344, 1200, 1056, 960, 888,                                     |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 816, 768, 720, 624, 576, 480}                                    | 1       | 33 |
+|                       | {320, 280, 240, 220,                |                                                                  |         |    |
+| Block filter          | 200, 180, 160, 120, 100 }           |                                                                  |         | 9  |
+|                       |                                     | {1344, 1200, 1056, 960, 888,                                     |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 816, 768, 720, 624, 576, 480}                                    | 2       | 33 |
+|                       |                                     | {1920, 1760, 1600, 1440, 1280,                                   |         |    |
+| bneck {3x3, 5x5, 7x7} |                                     | 1120, 960, 880, 800, 720, 640}<br>{1920, 1760, 1600, 1440, 1280, | 1       | 33 |
+| bneck {3x3, 5x5, 7x7} |                                     | 1120, 960, 880, 800, 720, 640}                                   | 1       | 33 |
+|                       |                                     | {1728, 1664, 1600,                                               |         |    |
+| bneck {3x3, 5x5, 7x7} | {480, 440, 400, 360, 320, 300, 280} | 1536, 1440, 1280, 1216}                                          | 1       | 7  |
+| conv2d 1x1            | {960}                               |                                                                  |         |    |
+| pool, 7x7             |                                     |                                                                  |         |    |
+| conv2d 1x1            | {1440, 1280}                        |                                                                  |         | 2  |
+| conv2d 1x1            | {1001}                              |                                                                  |         |    |
+
+Input Operator # Output filter # Expanded Filter strides 224 × 224 × 3 conv2d 3x3 16 2 112 × 112 × 16 bneck 3x3 18 1 112 × 112 × 16 bneck 3x3 24 64 2 56 × 56 × 28 bneck 3x3 24 48 1 56 × 56 × 28 bneck 5x5 56 80 2 28 × 28 × 44 bneck 5x5 56 200 1 28 × 28 × 44 bneck 5x5 56 100 1 28 × 28 × 44 bneck 5x5 80 400 2 14 × 14 × 40 bneck 3x3 80 200 1 14 × 14 × 96 bneck 3x3 80 272 1 7 × 7 × 96 bneck 3x3 80 168 1 14 × 14 × 44 bneck 5x5 112 440 1 14 × 14 × 40 bneck 5x5 112 576 1 14 × 14 × 96 bneck 7x7 160 624 2 7 × 7 × 96 bneck 5x5 160 640 1 7 × 7 × 96 bneck 3x3 160 640 1 7 × 7 × 96 conv2d 1x1 960 1 7 × 7 × 864 pool, 7x7 1 7 × 7 × 864 conv2d 1x1 1280 1 7 × 7 × 1536 conv2d 1x1 1001 1
+
+Table 10: LayerNAS Model under 220M MAdds
+
+# I EXAMPLE
+
+Consider a model with 3 layers, each with 4 options: A, B, C, D, corresponding to computational costs of 1M, 2M, 3M, and 4M MAdds, respectively. A sample model architecture can be represented as BCA, indicating that the 1st layer uses B, the 2nd layer uses C, and the 3rd layer uses A. The total cost of this model is 2+3+1=6M MAdds. The goal is to search for the optimal model architecture within the cost range of 8-9M MAdds.
+
+# LayerNAS settings:
+
+- For each layer, candidates are grouped into 4 buckets, each bucket stores up to 2 candidates.
+- In each iteration, 2 candidates are randomly selected to generate 2 valid children.
+
+# Cost range:
+
+- 1st layer cost range: 9-12M, buckets: [9M], [10M], [11M], [12M]
+- 2nd layer cost range: 6-12M, buckets: [6-7M], [8M], [9M, 10M], [11M, 12M]
+- 3rd layer: only stores [8M, 9M]
+
+# Marks:
+
+- Candidates that fall outside the designated cost range are marked as "drop"
+- Once all child architectures have been generated, the model is marked with "[x]"
+
+1st layer: train and eval: ADD (9M, 0.3), CDD (11M, 0.45)
+
+2nd layer: Choose ADD and CDD
+
+ADD generates ABD (7M drop), ACD (8M, 0.27), AAD(6M drop), all children searched CDD generates CAD(8M, 0.4), CBD(9M, 0.42)
+
+[6-7M]: []
+
+[8M]: [ACD(8M, 0.27), CAD(8M, 0.4)]
+
+[9-10M]: [ADD(9M, 0.3)]
+
+Table 11: 300M MAdds Search Space
+
+| Operator                              | # Output filter                      | # Expanded Filter                                                        | strides | S  |
+|---------------------------------------|--------------------------------------|--------------------------------------------------------------------------|---------|----|
+| Conv2d{3x3}                           | 32                                   |                                                                          | 2       |    |
+| bneck {3x3}                           | {24, 20, 16, 14}                     |                                                                          | 1       | 4  |
+| Block filter                          | {48, 44, 40, 36, 32, 28, 24}         |                                                                          |         | 7  |
+| bneck {3x3, 5x5}                      |                                      | {72, 64, 56, 52, 48, 44, 40}<br>{144, 128, 120, 112,                     | 2       | 14 |
+| bneck {3x3, 5x5}                      |                                      | 104, 96, 92, 88, 80, 76}<br>{144, 128, 120, 112,                         | 1       | 20 |
+| bneck {3x3, 5x5}                      |                                      | 104, 96, 92, 88, 80, 76}                                                 | 1       | 20 |
+| Block filter                          | {60, 56, 52, 48, 44, 40, 36, 32}     |                                                                          |         | 8  |
+| bneck {3x3, 5x5}                      |                                      | {144, 128, 120, 112,<br>104, 96, 92, 88, 80, 76}<br>{180, 160, 140, 130, | 2       | 20 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 120, 110, 100, 80}<br>{180, 160, 140, 130,                               | 1       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 120, 110, 100, 80}<br>{180, 160, 140, 130,                               | 1       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 120, 110, 100, 80}                                                       | 1       | 24 |
+| Block filter                          | {120, 110, 100, 90, 80, 70, 60}      |                                                                          |         | 7  |
+| bneck {3x3, 5x5, 7x7}                 |                                      | {360, 320, 280, 260,<br>240, 220, 200, 180}<br>{360, 320, 280, 260,      | 2       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 240, 220, 200, 180}<br>{360, 320, 280, 260,                              | 1       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 240, 220, 200, 180}                                                      | 1       | 24 |
+| Block filter                          | {144, 128, 120, 104, 96, 88, 80, 72} |                                                                          |         | 8  |
+|                                       |                                      | {360, 320, 280, 260,                                                     |         |    |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 240, 220, 200, 180}<br>{432, 400, 368, 336,                              | 1       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 304, 288, 272, 256, 240}<br>{432, 400, 368, 336,                         | 1       | 27 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 304, 288, 272, 256, 240}<br>{432, 400, 368, 336,                         | 1       | 27 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 304, 288, 272, 256, 240}                                                 | 1       | 27 |
+| Block filter                          | {288, 256, 224, 192, 160, 144}       |                                                                          |         | 6  |
+|                                       |                                      | {864, 800, 736, 672,                                                     |         |    |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 608, 576, 512, 448}<br>{864, 800, 736, 672,                              | 2       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 608, 576, 512, 448}<br>{864, 800, 736, 672,                              | 1       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 608, 576, 512, 448}<br>{864, 800, 736, 672,                              | 1       | 24 |
+| bneck {3x3, 5x5, 7x7}                 |                                      | 608, 576, 512, 448}                                                      | 1       | 24 |
+| bneck {3x3, 5x5, 7x7}                 | {480, 440, 400, 360, 320, 300, 280}  | {1728, 1664, 1600,<br>1536, 1440, 1280, 1216}                            | 1       | 7  |
+| pool, 7x7<br>conv2d 1x1<br>conv2d 1x1 | {1920, 1600, 1280}<br>{1001}         |                                                                          |         | 3  |
+
+Table 12: LayerNAS Model under 300M MAdds
+
+| Input          | Operator   | # Output filter | # Expanded Filter | strides |
+|----------------|------------|-----------------|-------------------|---------|
+| 224 × 224 × 3  | conv2d 3x3 | 32              |                   | 2       |
+| 112 × 112 × 32 | bneck 3x3  | 24              |                   | 1       |
+| 112 × 112 × 24 | bneck 3x3  | 28              | 40                | 2       |
+| 56 × 56 × 28   | bneck 3x3  | 28              | 144               | 1       |
+| 56 × 56 × 28   | bneck 3x3  | 28              | 88                | 1       |
+| 56 × 56 × 28   | bneck 3x3  | 40              | 104               | 2       |
+| 28 × 28 × 40   | bneck 5x5  | 40              | 110               | 1       |
+| 28 × 28 × 40   | bneck 3x3  | 40              | 180               | 1       |
+| 28 × 28 × 40   | bneck 5x5  | 40              | 130               | 1       |
+| 28 × 28 × 40   | bneck 7x7  | 90              | 260               | 2       |
+| 14 × 14 × 90   | bneck 3x3  | 90              | 220               | 1       |
+| 14 × 14 × 90   | bneck 3x3  | 90              | 200               | 1       |
+| 14 × 14 × 90   | bneck 7x7  | 120             | 320               | 1       |
+| 14 × 14 × 120  | bneck 5x5  | 120             | 288               | 1       |
+| 14 × 14 × 120  | bneck 7x7  | 120             | 256               | 1       |
+| 14 × 14 × 120  | bneck 3x3  | 120             | 368               | 1       |
+| 14 × 14 × 120  | bneck 7x7  | 160             | 608               | 2       |
+| 7 × 7 × 160    | bneck 7x7  | 160             | 576               | 1       |
+| 7 × 7 × 160    | bneck 5x5  | 160             | 608               | 1       |
+| 7 × 7 × 160    | bneck 3x3  | 160             | 448               | 1       |
+| 7 × 7 × 160    | bneck 3x3  | 280             | 1216              | 1       |
+| 7 × 7 × 280    | pool, 7x7  |                 |                   | 1       |
+| 7 × 7 × 280    | conv2d 1x1 | 1920            |                   | 1       |
+| 7 × 7 × 1920   | conv2d 1x1 | 1001            |                   | 1       |
+
+[11-12M]: [CDD(11M, 0.45)]
+
+3rd layer: Choose ACD and CDD
+
+ACD generates ACA (5M drop), ACB(6M drop), ACC(7M drop), all children searched CDD generates CDC(10M drop), CDB(9M, 0.4), CDA(8M, 0.37), all children searched [8-9M]: [CAD(8M, 0.4), ADD(9M, 0.3) CDB(9M, 0.4)]
+
+Start from 1st layer again
+
+1st layer: train and eval BDD (10M, 0.35), DDD(12M, 0.5)
+
+ADD (9M, 0.3)[x], BDD (10M, 0.35), CDD (11M, 0.45), DDD(12M, 0.5)
+
+2nd layer: Choose BDD, CDD
+
+BDD generates BAD (7M drop), BCD (9M, 0.33), BBD (8M, 0.32), all children searched
+
+CDD generates CCD(10M, drop), all children searched
+
+[6-7M]: []
+
+[8M]: [ACD(8M, 0.27) (BBD is better, remove ACD), CAD(8M, 0.4), BBD(8M, 0.32)]
+
+[9-10M]: [ADD(9M, 0.3), BCD(9M, 0.33)]
+
+[11-12M]: [CDD(11M, 0.45)[x]]
+
+3rd layer: Choose BCD, BBD
+
+BCD: BCA(6M, drop), BCB(7M, drop), BCC(8M, 0.32), all children searched BBD: BBA(5M, drop), BBC(7M, drop), BBB(6M, drop), all children searched
+
+[8-9M]: [CAD(8M, 0.4), CDB(9M, 0.4)]
+
+Move to 1st layer
+
+1st layer:
+
+Table 13: 600M MAdds Search Space
+
+| Operator              | # Output filter                               | # Expanded Filter                                               | strides | S  |
+|-----------------------|-----------------------------------------------|-----------------------------------------------------------------|---------|----|
+| Conv2d{3x3}           | 32                                            |                                                                 | 2       |    |
+| bneck {3x3}           | {36, 32, 28, 24, 20, 16}                      |                                                                 | 1       | 6  |
+| Block filter          | {56, 52, 48, 44, 40, 36, 32, 28}              |                                                                 |         | 8  |
+| bneck {3x3, 5x5}      |                                               | {88, 80, 72, 64, 56, 52, 48}                                    | 2       | 14 |
+| bneck {3x3, 5x5}      |                                               | {88, 80, 72, 64, 56, 52, 48}                                    | 1       | 14 |
+| bneck {3x3, 5x5}      |                                               | {88, 80, 72, 64, 56, 52, 48}                                    | 1       | 14 |
+| bneck {3x3, 5x5}      |                                               | {88, 80, 72, 64, 56, 52, 48}                                    | 1       | 14 |
+| Block filter          | {72, 64, 60, 56, 52, 48, 44, 40}              |                                                                 |         | 8  |
+|                       |                                               | {180, 160, 144, 128, 120,                                       |         |    |
+| bneck {3x3, 5x5}      |                                               | 112, 104, 96, 92, 88, 80}<br>{240, 220, 200, 180,               | 2       | 22 |
+| bneck {3x3, 5x5, 7x7} |                                               | 160, 140, 130, 120, 100}<br>{240, 220, 200, 180,                | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | 160, 140, 130, 120, 100}<br>{240, 220, 200, 180,                | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | 160, 140, 130, 120, 100}                                        | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | {240, 220, 200, 180,<br>160, 140, 130, 120, 100}                | 1       | 27 |
+| Block filter          | {200, 180, 160, 140, 120, 100, 90, 80}        |                                                                 |         | 8  |
+|                       |                                               | {440, 400, 360, 320,                                            |         |    |
+| bneck {3x3, 5x5, 7x7} |                                               | 280, 260, 240, 200}<br>{560, 520, 480, 440,                     | 2       | 24 |
+| bneck {3x3, 5x5, 7x7} |                                               | 400, 360, 320, 280, 240}<br>{560, 520, 480, 440,                | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | 400, 360, 320, 280, 240}<br>{560, 520, 480, 440,                | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | 400, 360, 320, 280, 240}                                        | 1       | 27 |
+| Block filter          | {180, 160, 144, 128,<br>120, 104, 96, 88, 80} |                                                                 |         | 9  |
+| bneck {3x3, 5x5, 7x7} |                                               | {560, 520, 480, 440,<br>400, 360, 320, 280, 240}                | 1       | 27 |
+|                       |                                               | {560, 528, 496, 464, 432, 400,                                  |         |    |
+| bneck {3x3, 5x5, 7x7} |                                               | 368, 336, 304, 288, 272, 256}<br>{560, 528, 496, 464, 432, 400, | 1       | 36 |
+| bneck {3x3, 5x5, 7x7} |                                               | 368, 336, 304, 288, 272, 256}<br>{560, 528, 496, 464, 432, 400, | 1       | 36 |
+| bneck {3x3, 5x5, 7x7} |                                               | 368, 336, 304, 288, 272, 256}<br>{560, 528, 496, 464, 432, 400, | 1       | 36 |
+| bneck {3x3, 5x5, 7x7} |                                               | 368, 336, 304, 288, 272, 256}                                   | 1       | 36 |
+| Block filter          | {320, 288, 256, 224, 192, 160}                | {992, 928, 864, 800,                                            |         | 6  |
+| bneck {3x3, 5x5, 7x7} |                                               | 736, 672, 608, 576, 512}<br>{992, 928, 864, 800,                | 2       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | 736, 672, 608, 576, 512}<br>{992, 928, 864, 800,                | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | 736, 672, 608, 576, 512}                                        | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | {992, 928, 864, 800,<br>736, 672, 608, 576, 512}                | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} |                                               | {992, 928, 864, 800,<br>736, 672, 608, 576, 512}                | 1       | 27 |
+| bneck {3x3, 5x5, 7x7} | {600, 560, 520, 480,<br>440, 400, 360, 320}   | {1920, 1856, 1792, 1728,<br>1664, 1600, 1536, 1440}             | 1       | 24 |
+| pool, 7x7             |                                               |                                                                 |         |    |
+| conv2d 1x1            | {2560, 2240, 1920}                            |                                                                 |         | 3  |
+| conv2d 1x1            | {1001}                                        |                                                                 |         |    |
+|                       |                                               |                                                                 |         |    |
+
+Table 14: LayerNAS Model under 600M MAdds
+
+| Input          | Operator   | # Output filter | # Expanded Filter | strides |
+|----------------|------------|-----------------|-------------------|---------|
+| 224 × 224 × 3  | conv2d 3x3 | 32              |                   | 2       |
+| 112 × 112 × 32 | bneck 3x3  | 36              |                   | 1       |
+| 112 × 112 × 36 | bneck 5x5  | 36              | 80                | 2       |
+| 56 × 56 × 36   | bneck 5x5  | 36              | 72                | 1       |
+| 56 × 56 × 36   | bneck 3x3  | 36              | 80                | 1       |
+| 56 × 56 × 36   | bneck 5x5  | 36              | 72                | 1       |
+| 56 × 56 × 36   | bneck 3x3  | 48              | 144               | 2       |
+| 28 × 28 × 48   | bneck 3x3  | 48              | 140               | 1       |
+| 28 × 28 × 48   | bneck 3x3  | 48              | 160               | 1       |
+| 28 × 28 × 48   | bneck 3x3  | 48              | 130               | 1       |
+| 28 × 28 × 48   | bneck 5x5  | 48              | 140               | 1       |
+| 28 × 28 × 48   | bneck 7x7  | 140             | 360               | 2       |
+| 14 × 14 × 140  | bneck 5x5  | 140             | 360               | 1       |
+| 14 × 14 × 140  | bneck 3x3  | 140             | 560               | 1       |
+| 14 × 14 × 140  | bneck 5x5  | 140             | 440               | 1       |
+| 14 × 14 × 140  | bneck 7x7  | 144             | 360               | 1       |
+| 14 × 14 × 144  | bneck 5x5  | 144             | 560               | 1       |
+| 14 × 14 × 144  | bneck 3x3  | 144             | 288               | 1       |
+| 14 × 14 × 144  | bneck 5x5  | 144             | 400               | 1       |
+| 14 × 14 × 144  | bneck 5x5  | 144             | 256               | 1       |
+| 14 × 14 × 144  | bneck 3x3  | 192             | 864               | 2       |
+| 7 × 7 × 192    | bneck 5x5  | 192             | 928               | 1       |
+| 7 × 7 × 192    | bneck 7x7  | 192             | 736               | 1       |
+| 7 × 7 × 192    | bneck 7x7  | 192             | 800               | 1       |
+| 7 × 7 × 192    | bneck 3x3  | 192             | 928               | 1       |
+| 7 × 7 × 192    | bneck 3x3  | 320             | 1440              | 1       |
+| 7 × 7 × 320    | pool, 7x7  |                 |                   | 1       |
+| 7 × 7 × 320    | conv2d 1x1 | 2560            |                   | 1       |
+| 7 × 7 × 2560   | conv2d 1x1 | 1001            |                   | 1       |
+
+ADD (9M, 0.3)[x], BDD (10M, 0.35)[x], CDD (11M, 0.45)[x], DDD(12M, 0.5)
+
+2nd layer: Choose DDD
+
+DDD: DDA(9M, 0.37), DDB(10M, drop), DDC(11M, drop), all children searched
+
+[6-7M]: []
+
+[8M]: [CAD(8M, 0.4), BBD(8M, 0.32)[x]]
+
+[9-10M]: [ADD(9M, 0.3), BCD(9M, 0.33)[x], DDA(9M, 0.37)]
+
+[11-12M]: [CDD(11M, 0.45)[x]]
+
+3rd layer: Choose CAD, DDA
+
+CAD: CAA(5M, drop), CAC(7M, drop), CAB(6M, drop), all children searched
+
+DDA: DDB(10M, drop), DDC(11M, drop), all children searched
+
+No more potential candidates, the best model found is CAD(8M, 0.4). Out of a total of 4 <sup>3</sup> = 64 candidates, LayerNAS train and eval 12 candidates.

papers/2DldCIjAdX/review.json

@@ -0,0 +1,91 @@
+{
+  "id": "2DldCIjAdX",
+  "title": "LayerNAS: Neural Architecture Search in Polynomial Complexity",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "NxabnQa82U",
+      "rating": 5,
+      "content": {
+        "summary": "This paper proposes a novel progressive search method and decouples the search constraints from the optimization objective in order to reduce the search space.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "1. The proposed method provides a new idea for progressive architecture search strategies.\n2. Extensive empirical experiments demonstrate the effectiveness of LayerNAS.",
+        "weaknesses": "1. Figure 2 is somewhat confusing and seems to have little relevance to the description of Algorithm 1. It would help the reader to understand the details of the algorithm if the authors could give a concrete example of a LayerNAS that contains specific hyperparameters\n2. Assumption 4.1 is too strong. This strategy means that a large number of candidate architectures will be ignored. It is promising in terms of experimental performance. However, the authors do not give some theoretical or other analysis to justify their hypothesis.\n3. I'm not sure if most of the search space meets the assumptions of the proposed approach. If not, a specific transformation of the search space is necessary to satisfy the assumptions of the search algorithm, however the transformation may be very complex. This makes me concerned about the ease of use and generalizability of the algorithm.",
+        "questions": "In the experimental part, the analysis for the hyperparameter $H$ is missing. I am curious how the performance changes when $H$ is greater than 100.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. Figure 2 is somewhat confusing and seems to have little relevance to the description of Algorithm 1. It would help the reader to understand the details of the algorithm if the authors could give a concrete example of a LayerNAS that contains specific hyperparameters\n2. Assumption 4.1 is too strong. This strategy means that a large number of candidate architectures will be ignored. It is promising in terms of experimental performance. However, the authors do not give some theoretical or other analysis to justify their hypothesis.\n3. I'm not sure if most of the search space meets the assumptions of the proposed approach. If not, a specific transformation of the search space is necessary to satisfy the assumptions of the search algorithm, however the transformation may be very complex. This makes me concerned about the ease of use and generalizability of the algorithm.",
+        "suggestions": "The paper would benefit from a more detailed explanation of how the LayerNAS algorithm handles the search space, particularly concerning the interaction between the search layers and the architecture layers. The current description lacks clarity on how the algorithm navigates the space of possible architectures, especially when considering that each layer might have multiple options, and these options might have different computational costs. A concrete example, as suggested, would be invaluable, but it should also include a discussion of how the algorithm ensures that the search process remains efficient and effective. This should include a more detailed explanation of how the algorithm handles dependencies between layers and how it avoids getting trapped in local optima. The authors should also clarify the relationship between the hyperparameter H and the search space, specifically how the number of buckets and the number of candidates per bucket influence the search process and the final architecture.\n\nFurthermore, the assumption that the search space can be effectively explored by restricting the number of candidates per layer needs more justification. While this approach might lead to computational efficiency, it also raises concerns about the completeness of the search. The authors should provide a theoretical analysis or empirical evidence to support the claim that this restriction does not significantly limit the algorithm's ability to find optimal or near-optimal architectures. This analysis should include a discussion of the trade-offs between search space coverage and computational cost, and it should clarify under what conditions this assumption is most likely to hold. The authors should also consider exploring alternative strategies for managing the search space, such as using a more adaptive approach that adjusts the number of candidates per layer based on the search progress.\n\nFinally, the paper should address the practical challenges of applying LayerNAS to more complex search spaces. The current discussion focuses on relatively simple scenarios, and it is unclear how the algorithm would perform in situations where the search space is highly non-uniform or contains a large number of interdependent parameters. The authors should provide a more detailed discussion of the limitations of the proposed approach and suggest potential solutions for overcoming these limitations. This should include a discussion of how the algorithm can be adapted to handle different types of search spaces and how it can be integrated with existing NAS frameworks. The authors should also consider providing a more detailed analysis of the computational cost of the algorithm, including the time and memory requirements for different search space sizes."
+      }
+    },
+    {
+      "id": "pydCIGqekA",
+      "rating": 8,
+      "content": {
+        "summary": "This paper propose a simple method to break down the neural architecture search approach into a layer-wise one. Specifically, for a search space of L-layer network, it only searchs for one layer at each training iteration instead of all layers. Experiments are conducted on MobileNetV2, MobileNet-V3, NASBench101 and NATS-Bench spaces.",
+        "soundness": "4 excellent",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "The paper is well-written and easy to follow. The authors provide clear explanations and examples throughout the paper.\n\nBreaking down the search problem into a Combinatorial Optimization problem seems novel and interesting, and reducing the search cost to polynomial time, which is clearly a breakthrough to the research community.\n\nLayerNAS can be applied to operation, topology and multi-objective NAS search\n\nResults on ImageNet seems to surpass state-of-the-art methods by a clear margin, evidencing their effectiveness of LayerNAS.",
+        "weaknesses": "I do not particular have a question, this paper seems to be easy enough to follow.",
+        "questions": "N/A",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "I do not particular have a question, this paper seems to be easy enough to follow.",
+        "suggestions": "While the paper is indeed well-written and easy to follow, a deeper dive into the practical implications and potential limitations of the proposed LayerNAS method would be beneficial. Specifically, the paper could explore the sensitivity of the method to different hyperparameter settings during the layer-wise search. For instance, how does the learning rate, batch size, or the number of search iterations per layer affect the final architecture and its performance? A more detailed analysis of these factors would provide valuable insights for practitioners looking to apply LayerNAS in different contexts. Furthermore, it would be useful to see a comparison of the computational cost of LayerNAS against other NAS methods, not just in terms of theoretical complexity but also in terms of actual wall-clock time on different hardware platforms. This would help to better understand the practical advantages of the method.\n\nAnother area that could be explored further is the generalizability of the LayerNAS method across different types of neural network architectures and datasets. The paper focuses primarily on MobileNet variants and image classification tasks. It would be interesting to see how well LayerNAS performs on other types of architectures, such as transformers or recurrent neural networks, and on different types of data, such as text or audio. This would help to establish the robustness and versatility of the proposed method. Additionally, the paper could provide more details on how the layer-wise search is implemented in practice. For example, how are the search spaces for each layer defined? Are there any constraints or regularizations applied during the search process? A more detailed explanation of these implementation details would make the method more accessible and reproducible.\n\nFinally, while the results on ImageNet are impressive, it would be beneficial to see a more thorough ablation study to understand the contribution of each component of the LayerNAS method. For example, what is the impact of searching for one layer at a time compared to searching multiple layers simultaneously? How does the choice of the search algorithm affect the final performance? A more detailed ablation study would provide a deeper understanding of the method's inner workings and help to identify potential areas for further improvement. It would also be helpful to discuss the potential limitations of the method, such as the possibility of getting stuck in local optima during the layer-wise search. Addressing these limitations would provide a more balanced and complete picture of the proposed approach."
+      }
+    },
+    {
+      "id": "wBUaSZNYHy",
+      "rating": 5,
+      "content": {
+        "summary": "This papers shows layerwise NAS approach to search a neural architecture layer by layer under computational constraints.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "1. They propose a new layerwise NAS approach for search neural architecture under constraints. \n2. LayerNAS can find out some interesting architectures that outperform the previous NAS algorithms.",
+        "weaknesses": "1. What does the improvement of LayerNAS networks over other networks actually come from is uncertain. As mentioned in the end of Sec. 5.1, the architecture mechanisms of the searched networks in this work and other networks are not the same: for example, the authors used SE and Swish while others did not. These details including the undisclosed training strategy (like the learning, weight decay, data augmentation) might largely affect the accuracy, as demonstrated in [1], ConvNeXt [2], and many other followups. This is the key issues to evaluate this paper. Without the claim of using the exact same architecture and training strategy for fair comparison across methods, it is hard to evaluate this paper.\n\n2. Strong assumption based. This paper has to search per-layer. For layer i, it has to assume all the succeeding layers use the default operation (e.g. the most expensive operation) as stated in the first paragraph of Sec. 4. There is no theoretical analysis why this simple and strong assumption leads to better searched architecture than other NAS algorithms. \n\n3. Lack of literature.  Named as LayerNAS, this work lacks comparisons to pioneering work in layerwise NAS: SGAS [3], TNAS [4], and many other followups. Please compare with these works in related work.\n\n[1] Steiner, Andreas, Alexander Kolesnikov, Xiaohua Zhai, Ross Wightman, Jakob Uszkoreit, and Lucas Beyer. \"How to train your vit? data, augmentation, and regularization in vision transformers.\" arXiv preprint arXiv:2106.10270 (2021).\n[2] Liu, Zhuang, Hanzi Mao, Chao-Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie. \"A convnet for the 2020s.\" In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 11976-11986. 2022.\n[3] Li, Guohao, Guocheng Qian, Itzel C. Delgadillo, Matthias Muller, Ali Thabet, and Bernard Ghanem. \"Sgas: Sequential greedy architecture search.\" In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1620-1630. 2020.\n[4] Qian, Guocheng, Xuanyang Zhang, Guohao Li, Chen Zhao, Yukang Chen, Xiangyu Zhang, Bernard Ghanem, and Jian Sun. \"When NAS Meets Trees: An Efficient Algorithm for Neural Architecture Search.\" In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 2782-2787. 2022.",
+        "questions": "A detailed example of LayerNAS could have been provided. For example, you can show the step-by-step details of LayerNAS on ImageNet. What are the 100 candidates in each searching layer and which one is chosen.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. What does the improvement of LayerNAS networks over other networks actually come from is uncertain. As mentioned in the end of Sec. 5.1, the architecture mechanisms of the searched networks in this work and other networks are not the same: for example, the authors used SE and Swish while others did not. These details including the undisclosed training strategy (like the learning, weight decay, data augmentation) might largely affect the accuracy, as demonstrated in [1], ConvNeXt [2], and many other followups. This is the key issues to evaluate this paper. Without the claim of using the exact same architecture and training strategy for fair comparison across methods, it is hard to evaluate this paper. The inclusion of SE and Swish, while potentially beneficial, introduces a confounding variable that makes it difficult to isolate the impact of the LayerNAS search algorithm itself. Furthermore, the lack of transparency regarding specific training hyperparameters makes it challenging to reproduce the results and assess the true contribution of the proposed method.\n\n2. Strong assumption based. This paper has to search per-layer. For layer i, it has to assume all the succeeding layers use the default operation (e.g. the most expensive operation) as stated in the first paragraph of Sec. 4. There is no theoretical analysis why this simple and strong assumption leads to better searched architecture than other NAS algorithms. This assumption of using the most expensive operation for subsequent layers during the search process is a significant limitation. It restricts the search space and may lead to suboptimal architectures. The lack of theoretical justification for this assumption raises concerns about the generality and robustness of the proposed method. It is unclear why this specific assumption is more effective than other possible strategies for layer-wise search.\n\n3. Lack of literature.  Named as LayerNAS, this work lacks comparisons to pioneering work in layerwise NAS: SGAS [3], TNAS [4], and many other followups. Please compare with these works in related work.",
+        "suggestions": "To address the first weakness, the authors should conduct a more rigorous ablation study to isolate the impact of LayerNAS from other architectural choices. Specifically, they should compare the performance of networks found by LayerNAS with and without SE and Swish, using identical training procedures. Furthermore, the authors should provide a detailed description of all training hyperparameters, including learning rate, weight decay, and data augmentation techniques, to ensure reproducibility and fair comparison. It is crucial to establish a baseline where all factors except the NAS algorithm are kept constant to accurately evaluate the effectiveness of LayerNAS. This would involve training both the LayerNAS-discovered architectures and the baseline architectures with the same set of hyperparameters, and ideally, multiple random seeds to account for variance.\n\nRegarding the second weakness, the authors should provide a more thorough justification for their assumption of using the most expensive operation for subsequent layers during the search process. A theoretical analysis or empirical evidence should be provided to support this design choice. It would be beneficial to explore alternative strategies for layer-wise search, such as using a weighted average of operations or a more adaptive approach that considers the cost and performance of different operations. The authors could also consider a multi-objective optimization approach that simultaneously optimizes for both accuracy and computational cost, rather than relying on a fixed assumption. This would allow for a more flexible and potentially more effective search process. Furthermore, the authors should discuss the limitations of their assumption and its potential impact on the quality of the searched architectures.\n\nFinally, to address the lack of literature, the authors should include a more comprehensive comparison with existing layer-wise NAS methods, such as SGAS [3] and TNAS [4]. This comparison should not only include a discussion of the differences in methodology but also a quantitative evaluation of the performance of LayerNAS against these methods. It is important to contextualize the contributions of LayerNAS within the existing body of work and to clearly demonstrate its advantages and limitations. The authors should also discuss the potential reasons for any observed differences in performance, such as differences in search space, optimization strategy, or evaluation metrics. This would provide a more complete and nuanced understanding of the proposed method and its place within the field of NAS."
+      }
+    },
+    {
+      "id": "xZMvH8O8Bx",
+      "rating": 5,
+      "content": {
+        "summary": "The author attempted to solve NAS via dynamic programming. In order to do so, they made an approximation about the search space that the optimal decision for the i-th layer does not depend on the decision for layers afterward, i.e., the searching problem is simplified to satisfy the optimal substructure requirement (e.g., an optimal solution can be obtained from optimal solutions of its subproblems). In order to make the search complexity manageable, the proposed method, LayerNAS, relies on a grouping/bucketing function which splits the search space into groups/buckets, with each group/bucket only keeping a small amounts of model architectures.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "The authors provided a new way of tackling the search problem in NAS: dividing the search space into sub-problems and adding the assumption that satisfy the requirements of dynamic programming. To the best of my knowledge, no one has done similar things before. In the task of size search on ImageNet, and both size search and topology search on NATS-Bench, the authors demonstrated the effectiveness of LayerNAS.\n\nIn general, the idea is clearly described and easy to follow.",
+        "weaknesses": "- The whole idea of LayerNAS is based on the assumption that the optimal decision for the i-th layer does not depend on the decision for the succeeding layers. The paper didn't investigate the soundness of this assumption. For example, in algorithm 1, for a certain layer l and a certain value of h, only a few models with better performance are kept. Is it possible that in the final optimal model, the selected options for some layer i are different from ones that are kept during the search? This situation may become more likely given that each candidate is only trained for a small amount of epochs (e.g., 5 epochs used in the paper), as some architectures are easier to converge (e.g., showing lower loss at the early stage) but cannot keep the momentum till the end (e.g., the loss stop decreasing and the model is eventually surpassed by models with higher loss at the early stage).\n\n- In Table 2, the comparisons stops at FLOPs 627M. How does LayerNAS compare with EfficientNet-B1 and B2? It seems that the comparison with OFA is missing. OFA achieves 76.9% at 230M FLOPs and 80.0% at ~600M FLOPs.\n\n- It is unclear to me how LayerNAS can save some search cost by designing the mapping function $\\varphi$, in the case of topology search. The search space in the experiment \"NATS-Bench topology search\" is too small.",
+        "questions": "I'd like to see the authors' response to my questions in the weakness section, especially the second and the third question. For the first question, it is acceptable that LayerNAS may miss some promising architectures under the assumption as long as the final model has good performance.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.",
+        "code_of_conduct": "Yes",
+        "weakness": " - The whole idea of LayerNAS is based on the assumption that the optimal decision for the i-th layer does not depend on the decision for the succeeding layers. The paper didn't investigate the soundness of this assumption. For example, in algorithm 1, for a certain layer l and a certain value of h, only a few models with better performance are kept. Is it possible that in the final optimal model, the selected options for some layer i are different from ones that are kept during the search? This situation may become more likely given that each candidate is only trained for a small amount of epochs (e.g., 5 epochs used in the paper), as some architectures are easier to converge (e.g., showing lower loss at the early stage) but cannot keep the momentum till the end (e.g., the loss stop decreasing and the model is eventually surpassed by models with higher loss at the early stage). Specifically, the method's reliance on early-stage performance as a proxy for final performance is a significant concern, as it could lead to the selection of suboptimal architectures that exhibit rapid initial convergence but ultimately plateau at a lower accuracy than other architectures that might have a slower initial learning rate but better long-term performance. The paper should include an analysis of the correlation between the performance of models trained for 5 epochs and those trained for the full duration, and how this correlation impacts the final architecture selection.\n\n- In Table 2, the comparisons stops at FLOPs 627M. How does LayerNAS compare with EfficientNet-B1 and B2? It seems that the comparison with OFA is missing. OFA achieves 76.9% at 230M FLOPs and 80.0% at ~600M FLOPs. The lack of comparison with EfficientNet and a more complete comparison with OFA, especially at different FLOP regimes, makes it difficult to fully assess the method's performance relative to state-of-the-art methods. The paper should include a more comprehensive comparison with EfficientNet and OFA, including models with similar computational costs, to better contextualize the performance of LayerNAS.\n\n- It is unclear to me how LayerNAS can save some search cost by designing the mapping function $\\varphi$, in the case of topology search. The search space in the experiment \"NATS-Bench topology search\" is too small. The paper does not adequately explain how the mapping function $\\varphi$ reduces the search space complexity for topology search. The experiments on NATS-Bench topology search are not sufficient to demonstrate the effectiveness of the mapping function, as the search space is too small to show any significant reduction in search cost. The paper should provide a more detailed explanation of how the mapping function reduces search complexity in topology search, and conduct experiments on larger search spaces to demonstrate its effectiveness.",
+        "suggestions": "The authors should address the concern regarding the assumption that the optimal decision for the i-th layer is independent of subsequent layers. While the authors claim that all possible candidates are retained, the selection process based on early-stage performance could still lead to suboptimal choices. A more thorough analysis is needed to justify the use of 5-epoch training as a proxy for full training, including an investigation into the correlation between early-stage and full-training performance. The authors should also consider incorporating techniques that mitigate the risk of selecting architectures that converge quickly but plateau early, such as using a more robust performance metric or employing a multi-stage training approach. Furthermore, the paper should include an ablation study to demonstrate the impact of the number of candidates kept at each layer on the final performance.\n\nThe paper should also include a more comprehensive comparison with state-of-the-art methods, such as EfficientNet and OFA, across a range of FLOPs. The current comparison is limited and does not provide a complete picture of the method's performance relative to existing approaches. Specifically, the authors should include results for EfficientNet-B1 and B2, as well as a more detailed comparison with OFA, including models with similar computational costs. This would help to better contextualize the performance of LayerNAS and demonstrate its competitiveness with other state-of-the-art methods. The authors should also provide a more detailed explanation of the experimental setup, including the specific training parameters used for each model, to ensure reproducibility.\n\nFinally, the authors need to clarify how the mapping function $\\varphi$ reduces search cost in the case of topology search. The current explanation is insufficient, and the experiments on NATS-Bench are not convincing, given the small search space. The authors should provide a more detailed explanation of how the mapping function groups similar architectures and reduces the search space. They should also conduct experiments on larger and more complex search spaces to demonstrate the effectiveness of the mapping function in reducing search cost for topology search. The authors could consider using graph semi-isomorphism techniques to group similar architectures, which could further reduce the search space and improve the efficiency of the method."
+      }
+    }
+  ]
+}

papers/2lDQLiH1W4/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "2lDQLiH1W4",
+  "title": "Instant3D: Fast Text-to-3D with Sparse-view Generation and Large Reconstruction Model",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Accept",
+  "date": "2024-09-27",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=2lDQLiH1W4"
+}

papers/2lDQLiH1W4/paper.md

@@ -0,0 +1,427 @@
+# INSTANT3D: FAST TEXT-TO-3D WITH SPARSE-VIEW GENERATION AND LARGE RECONSTRUCTION MODEL
+
+Jiahao Li1,2<sup>∗</sup> Hao Tan<sup>1</sup> Kai Zhang<sup>1</sup> Zexiang Xu<sup>1</sup> Fujun Luan<sup>1</sup> Yinghao Xu1,<sup>3</sup> Yicong Hong1,<sup>4</sup> Kalyan Sunkavalli<sup>1</sup> Greg Shakhnarovich<sup>2</sup> Sai Bi<sup>1</sup>
+
+<sup>1</sup>Adobe Research <sup>2</sup>TTIC <sup>3</sup>Stanford University <sup>4</sup> Australian National Univeristy
+
+{jiahao,greg}@ttic.edu yhxu@stanford.edu mr.yiconghong@gmail.com {hatan,kaiz,zexu,fluan,sunkaval,sbi}@adobe.com
+
+# ABSTRACT
+
+Text-to-3D with diffusion models has achieved remarkable progress in recent years. However, existing methods either rely on score distillation-based optimization which suffer from slow inference, low diversity and Janus problems, or are feed-forward methods that generate low-quality results due to the scarcity of 3D training data. In this paper, we propose Instant3D, a novel method that generates high-quality and diverse 3D assets from text prompts in a feed-forward manner. We adopt a two-stage paradigm, which first generates a sparse set of four structured and consistent views from text in one shot with a fine-tuned 2D text-to-image diffusion model, and then directly regresses the NeRF from the generated images with a novel transformer-based sparse-view reconstructor. Through extensive experiments, we demonstrate that our method can generate diverse 3D assets of high visual quality within 20 seconds, which is two orders of magnitude faster than previous optimization-based methods that can take 1 to 10 hours. Our project webpage is: <https://jiahao.ai/instant3d/>.
+
+# 1 INTRODUCTION
+
+In recent years, remarkable progress has been achieved in the field of 2D image generation. This success can be attributed to two key factors: the development of novel generative models such as diffusion models [\(Song et al.,](#page-13-0) [2021;](#page-13-0) [Ho et al.,](#page-10-0) [2020;](#page-10-0) [Ramesh et al.,](#page-13-1) [2022;](#page-13-1) [Rombach et al.,](#page-13-2) [2021\)](#page-13-2), and the availability of large-scale datasets like Laion5B [\(Schuhmann et al.,](#page-13-3) [2022\)](#page-13-3). Transferring this success in 2D image generation to 3D presents challenges, mainly due to the scarcity of available 3D training data. While Laion5B has 5 billion text-image pairs, Objaverse-XL [\(Deitke et al.,](#page-10-1) [2023a\)](#page-10-1), the largest public 3D dataset, contains only 10 million 3D assets with less diversity and poorer annotations. As a result, previous attempts to directly train 3D diffusion models on existing 3D datasets [\(Luo & Hu,](#page-11-0) [2021;](#page-11-0) [Nichol et al.,](#page-12-0) [2022;](#page-12-0) [Jun & Nichol,](#page-10-2) [2023;](#page-10-2) [Gupta et al.,](#page-10-3) [2023;](#page-10-3) [Chen](#page-9-0) [et al.,](#page-9-0) [2023b\)](#page-9-0) are limited in the visual (shape and appearance) quality, diversity and compositional complexity of the results they can produce.
+
+To address this, another line of methods [\(Poole et al.,](#page-12-1) [2022;](#page-12-1) [Wang et al.,](#page-14-0) [2023a;](#page-14-0) [Lin et al.,](#page-11-1) [2023;](#page-11-1) [Wang et al.,](#page-14-1) [2023b;](#page-14-1) [Chen et al.,](#page-9-1) [2023c\)](#page-9-1) leverage the semantic understanding and high-quality generation capabilities of pretrained 2D diffusion models. Here, 2D generators are used to calculate gradients on rendered images, which are then used to optimize a 3D representation, usually a NeRF [\(Mildenhall et al.,](#page-11-2) [2020\)](#page-11-2). Although these methods yield better visual quality and text-3D alignment, they can be incredibly time-consuming, taking hours of optimization for each prompt. They also suffer from artifacts such as over-saturated colors and the "multi-face" problem arising from the bias in pretrained 2D diffusion models, and struggle to generate diverse results from the same text prompt, with varying the random seed leading to minor changes in geometry and texture.
+
+In this paper, we propose Instant3D, a novel feed-forward method that generates high-quality and diverse 3D assets conditioned on the text prompt. Instant3D, like the methods noted above, builds on top of pretrained 2D diffusion models. However, it does so by splitting 3D generation into
+
+<sup>∗</sup>This work was done while the author was an intern at Adobe Research.
+
+<span id="page-1-0"></span>![](figures/_page_1_Figure_1.jpeg)
+
+Figure 1: Our method generates high-quality 3D NeRF assets from the given text prompts within 20 seconds. Here we show novel view renderings from our generated NeRFs as well as the renderings of the extracted meshes from their density field.
+
+two stages: 2D generation and 3D reconstruction. In the first stage, instead of generating images sequentially [\(Liu et al.,](#page-11-3) [2023b\)](#page-11-3), we fine-tune an existing text-to-image diffusion model [\(Podell et al.,](#page-12-2) [2023\)](#page-12-2) to generate a sparse set of four-view images in the form of a 2×2 grid in a single denoising process. This design allows the multi-view images to attend to each other during generation, leading to more view-consistent results. In the second stage, instead of relying on a slow optimizationbased reconstruction method, inspired by [Hong et al.](#page-10-4) [\(2024\)](#page-10-4), we introduce a novel sparse-view *large reconstruction model* with a transformer-based architecture that can directly regress a triplanebased [\(Chan et al.,](#page-9-2) [2022\)](#page-9-2) NeRF from a sparse set of multi-view images. Our model projects sparseview images into a set of pose-aware image tokens using pretrained vision transformers [\(Caron et al.,](#page-9-3) [2021\)](#page-9-3), which are then fed to an image-to-triplane decoder that contains a sequence of transformer blocks with cross-attention and self-attention layers. Our proposed model has a large capacity with more than 500 million parameters and can robustly infer correct geometry and appearance of objects from just four images.
+
+Both of these stages are fine-tuned/trained with multi-view rendered images of around 750K 3D objects from Objaverse [\(Deitke et al.,](#page-10-5) [2023b\)](#page-10-5), where the second stage makes use of the full dataset and the first stage can be fine-tuned with as little as 10K data. While we use a relatively smaller dataset compared to the pre-training dataset for other modalities (e.g., C4 [Raffel et al.](#page-13-4) [\(2020\)](#page-13-4) for text and Laion5B for image), by combining it with the power of pretrained 2D diffusion models, Instant3D's two-stage approach is able to generate high-quality and diverse 3D assets even from input prompts that contain complex compositional concepts (see Figure [1\)](#page-1-0) and do not exist in the 3D dataset used for training. Due to its feed-forward architecture, Instant3D is exceptionally fast, requiring only about 20 seconds to generate a 3D asset, which is 200× faster than previous optimization-based methods [\(Poole et al.,](#page-12-1) [2022;](#page-12-1) [Wang et al.,](#page-14-1) [2023b\)](#page-14-1) while achieving comparable or even better quality.
+
+# 2 RELATED WORKS
+
+3D generation. Following the success of generative models on 2D images using VAEs [\(Kingma](#page-11-4) [& Welling,](#page-11-4) [2013;](#page-11-4) [Van Den Oord et al.,](#page-14-2) [2017\)](#page-14-2), GANs [\(Goodfellow et al.,](#page-10-6) [2014;](#page-10-6) [Karras et al.,](#page-11-5) [2019;](#page-11-5) [Gu et al.,](#page-10-7) [2022;](#page-10-7) [Kang et al.,](#page-10-8) [2023\)](#page-10-8), and autoregressive models [\(Oord et al.,](#page-12-3) [2016;](#page-12-3) [Van Den Oord](#page-14-3) [et al.,](#page-14-3) [2016\)](#page-14-3), people have also explored the applications of such models on 3D generation. Previous approaches have explored different methods to generate 3D models in the form of point clouds [\(Wu](#page-14-4) [et al.,](#page-14-4) [2016;](#page-14-4) [Gadelha et al.,](#page-10-9) [2017;](#page-10-9) [Smith & Meger,](#page-13-5) [2017\)](#page-13-5), triangle meshes [\(Gao et al.,](#page-10-10) [2022;](#page-10-10) [Pavllo](#page-12-4) [et al.,](#page-12-4) [2020;](#page-12-4) [Chen et al.,](#page-9-4) [2019;](#page-9-4) [Luo et al.,](#page-11-6) [2021\)](#page-11-6) , volumes [\(Chan et al.,](#page-9-2) [2022;](#page-9-2) [Or-El et al.,](#page-12-5) [2022;](#page-12-5) [Bergman et al.,](#page-9-5) [2022;](#page-9-5) [Skorokhodov et al.,](#page-13-6) [2022;](#page-13-6) [Mittal et al.,](#page-12-6) [2022\)](#page-12-6) and implicit representations [\(Liu](#page-11-7) [et al.,](#page-11-7) [2022;](#page-11-7) [Fu et al.,](#page-10-11) [2022;](#page-10-11) [Sanghi et al.,](#page-13-7) [2022\)](#page-13-7) in an unconditional or text/image-conditioned manner. Such methods are usually trained on limited categories of 3D objects and do not generalize well to a wide range of novel classes.
+
+Diffusion models [\(Rombach et al.,](#page-13-2) [2021;](#page-13-2) [Podell et al.,](#page-12-2) [2023;](#page-12-2) [Ho et al.,](#page-10-0) [2020;](#page-10-0) [Song et al.,](#page-13-0) [2021;](#page-13-0) [Saharia et al.,](#page-13-8) [2022\)](#page-13-8) open new possibilities for 3D generation. A class of methods directly train 3D diffusion models on the 3D representations [\(Nichol et al.,](#page-12-0) [2022;](#page-12-0) [Liu et al.,](#page-11-8) [2023c;](#page-11-8) [Zhou et al.,](#page-14-5) [2021;](#page-14-5) [Sanghi et al.,](#page-13-9) [2023\)](#page-13-9) or project the 3D models or multi-view rendered images into latent representations [\(Ntavelis et al.,](#page-12-7) [2023;](#page-12-7) [Zeng et al.,](#page-14-6) [2022;](#page-14-6) [Gupta et al.,](#page-10-3) [2023;](#page-10-3) [Jun & Nichol,](#page-10-2) [2023;](#page-10-2) [Chen et al.,](#page-9-0) [2023b\)](#page-9-0) and perform the diffusion process in the latent space. For example, Shap-E [\(Jun & Nichol,](#page-10-2) [2023\)](#page-10-2) encodes each 3D shape into a set of parameters of an implicit function, and then trains a conditional diffusion model on the parameters. These approaches face challenges due to the restricted availability and diversity of existing 3D data, consequently resulting in generated content with poor visual quality and inadequate alignment with the input prompt. Therefore, although trained on millions of 3D assets, Shap-E still fails to generate 3D shapes with complex compositional concepts and high-fidelity textures.
+
+To resolve this, another line of works try to make use of 2D diffusion models to facilitate 3D generation. Some works [\(Jain et al.,](#page-10-12) [2022;](#page-10-12) [Mohammad Khalid et al.,](#page-12-8) [2022\)](#page-12-8) optimize meshes or NeRFs to maximize the CLIP [Radford et al.](#page-13-10) [\(2021\)](#page-13-10) score between the rendered images and input prompt utilizing pretrained CLIP models. While such methods can generate diverse 3D content, they exhibit a deficiency in visual realism. More recently, some works [\(Poole et al.,](#page-12-1) [2022;](#page-12-1) [Wang et al.,](#page-14-1) [2023b;](#page-14-1) [Lin et al.,](#page-11-1) [2023;](#page-11-1) [Chen et al.,](#page-9-1) [2023c\)](#page-9-1) optimize 3D representations using score distillation loss (SDS) based on pretrained 2D diffusion models. Such methods can generate high-quality results, but suffer from slow optimization, over-saturated colors and the Janus problem. For example, it takes 1.5 hours for DreamFusion [\(Poole et al.,](#page-12-1) [2022\)](#page-12-1) and 10 hours for ProlificDreamer [Wang et al.](#page-14-1) [\(2023b\)](#page-14-1) to generate a single 3D asset, which greatly limits their practicality. In contrast, our method enjoys the benefits of both worlds: it's able to borrow information from pretrained 2D diffusion models to generate diverse multi-view consistent images that are subsequently lifted to faithful 3D models, while still being fast and efficient due to its feed-forward nature.
+
+Sparse-view reconstruction. Traditional 3D reconstruction with multi-view stereo [\(Agarwal](#page-9-6) [et al.,](#page-9-6) [2011;](#page-9-6) [Schonberger et al.](#page-13-11) ¨ , [2016;](#page-13-11) [Furukawa et al.,](#page-10-13) [2015\)](#page-10-13) typically requires a dense set of input images that have significant overlaps to find correspondence across views and infer the geometry correctly. While NeRF [\(Mildenhall et al.,](#page-11-2) [2020\)](#page-11-2) and its variants [\(Muller et al.](#page-12-9) ¨ , [2022;](#page-12-9) [Chen et al.,](#page-9-7) [2022;](#page-9-7) [2023a\)](#page-9-8) have further alleviated the prerequisites for 3D reconstruction, they perform per-scene optimization that still necessitates a lot of input images. Previous methods [\(Wang et al.,](#page-14-7) [2021;](#page-14-7) [Chen](#page-9-9) [et al.,](#page-9-9) [2021;](#page-9-9) [Long et al.,](#page-11-9) [2022;](#page-11-9) [Reizenstein et al.,](#page-13-12) [2021;](#page-13-12) [Trevithick & Yang,](#page-14-8) [2021;](#page-14-8) [Shen et al.,](#page-13-13) [2023\)](#page-13-13) have tried to learn data priors so as to infer NeRF from a sparse set of images. Typically they extract per-view features from each input image, and then for each point on the camera ray, aggregate multiview features and decode them to the density (or SDF) and colors. Such methods are either trained in a category-specific manner, or only trained on small datasets such as ShapeNet; they have not been demonstrated to generalize beyond these datasets especially to the complex text-to-2D outputs.
+
+More recently, some methods utilize data priors from pretrained 2D diffusion models to lift a single 2D image to 3D by providing supervision at novel views using SDS loss [\(Liu et al.,](#page-11-3) [2023b;](#page-11-3) [Qian](#page-12-10) [et al.,](#page-12-10) [2023;](#page-12-10) [Melas-Kyriazi et al.,](#page-11-10) [2023\)](#page-11-10) or generating multi-view images [\(Liu et al.,](#page-11-11) [2023a\)](#page-11-11). For instance, One-2-3-45 [\(Liu et al.,](#page-11-11) [2023a\)](#page-11-11) generates 32 images at novel views from a single input image using a fine-tuned 2D diffusion model, and reconstructs a 3D model from them, which suffers from inconsistency between the many generated views. In comparison, our sparse-view reconstructor adopts a highly scalable transformer-based architecture and is trained on large-scale 3D data. This gives it the ability to accurately reconstruct 3D models of novel unseen objects from a sparse set of 4 images without per-scene optimization.
+
+# <span id="page-2-0"></span>3 METHOD
+
+Our method Instant3D is composed of two stages: sparse-view generation and feed-forward NeRF reconstruction. In Section [3.1,](#page-3-0) we present our approach for generating sparse multi-view images conditioned on the text input. In Section [3.2,](#page-4-0) we describe our transformer-based sparse-view large reconstruction model.
+
+<span id="page-3-1"></span>![](figures/_page_3_Figure_1.jpeg)
+
+Figure 2: Overview of our method. Given a text prompt ('a car made out of sushi'), we perform multi-view generation with Gaussian blobs as initialization using fine-tuned 2D diffusion model, producing a 4-view image in the form of a 2 × 2 grid. Then we apply a transformer-based sparseview 3D reconstructor on the 4-view image to generate the final NeRF.
+
+### <span id="page-3-0"></span>3.1 TEXT-CONDITIONED SPARSE VIEW GENERATION
+
+Given a text prompt, our goal is to generate a set of multi-view images that are aligned with the prompt and consistent with each other. We achieve this by fine-tuning a pretrained text-to-image diffusion model to generate a 2 × 2 image grid as shown in Figure [2.](#page-3-1)
+
+In the following paragraphs, we first illustrate that large text-to-image diffusion models (i.e., SDXL [\(Podell et al.,](#page-12-2) [2023\)](#page-12-2)) have the capacity to generate view-consistent images thus a lightweight fine-tuning is possible. We then introduce three essential techniques to achieve it: the image grid, the curation of the dataset, and also the Gaussian Blob noise initialization in inference. As a result of these observations and technical improvements, we can fine-tune the 2D diffusion model for only 10K steps (on 10K data) to generate consistent sparse views.
+
+Multi-view generation with image grid. Previous methods [\(Liu et al.,](#page-11-3) [2023b](#page-11-3)[;a\)](#page-11-11) on novel-view synthesis show that image diffusion models are capable of understanding the multi-view consistency. In light of this, we compile the images at different views into a single image in the form of an image grid, as depicted in Figure [2.](#page-3-1) This image-grid design can better match the original data format of the 2D diffusion model, and is suitable for simple direct fine-tuning protocol of 2D models. We also observe that this simple protocol only works when the base 2D diffusion has enough capacity, as shown in the comparisons of Stable Diffusion v1.5 [\(Rombach et al.,](#page-13-2) [2021\)](#page-13-2) and SDXL [\(Podell](#page-12-2) [et al.,](#page-12-2) [2023\)](#page-12-2) in Section [4.3.](#page-7-0) The benefit from simplicity will also be illustrated later in unlocking the lightweight fine-tuning possibility.
+
+Regarding the number of views in the image grid, there is a trade-off between the requirements of multi-view generation and 3D reconstruction. More generated views make the problem of 3D reconstruction easier with more overlaps but increase possibility of view inconsistencies in generation and reduces the resolution of each generated view. On the other hand, too few views may cause insufficient coverage, requiring the reconstructor to hallucinate unseen parts, which is challenging for a deterministic 3D reconstruction model. Our transformer-based reconstructor learns generic 3D priors from large-scale data, and greatly reduces the requirement for the number of views. We empirically found that using 4 views achieves a good balance in satisfying the two requirements above, and they can be naturally arranged in a 2 × 2 grid as shown in Figure [2.](#page-3-1) Next, we detail how the image grid data is created and curated.
+
+Multi-view data creation and curation. To fine-tune the text-to-image diffusion model, we create paired multi-view renderings and text prompts. We adopt a large-scale synthetic 3D dataset Objaverse [\(Deitke et al.,](#page-10-5) [2023b\)](#page-10-5) and render four 512 × 512 views of about 750K objects with Blender. We distribute the four views at a fixed elevation (20 degrees) and four equidistant azimuths (0, 90, 180, 270 degrees) to achieve a better coverage of the object. We use Cap3D [\(Luo et al.,](#page-11-12) [2023\)](#page-11-12) to generate captions for each 3D object, which consolidates captions from multi-view renderings generated with pretrained image captioning model BLIP-2 [\(Li et al.,](#page-11-13) [2023\)](#page-11-13) using a large language model (LLM). Finally, the four views are assembled into a grid image in a fixed order and resized to the input resolution compatible with the 2D diffusion model.
+
+We find that naively using all the data for fine-tuning reduces the photo-realism of the generated images and thus the quality of the 3D assets. Therefore, we train a simple scorer on a small amount
+
+![](figures/_page_4_Figure_1.jpeg)
+
+Figure 3: Architecture of our sparse-view reconstructor. The model applies a pretrained ViT to encode multi-view images into pose-aware image tokens, from which we decode a triplane representation of the scene using a transformer-based decoder. Finally we decode per-point triplane features to its density and color and perform volume rendering to render novel views. We illustrate here with 2 views and the actual implementation uses 4 views.
+
+(2000 samples) of manually labeled data to predict the quality of each 3D object. The model is a simple SVM on top of pretrained CLIP features extracted from multi-view renderings of the 3D object (please see Appendix for details). During training, our model only takes the top 10K data ranked by our scorer. We provide a quantitative study in Section 4.3 to validate the impact of different data curation strategies. Although the difference is not very significant from the metric perspective, we found that our curated data is helpful in improving the visual quality.
+
+Inference with Gaussian blob initialization. While our training data is multi-view images with a white background, we observe that during inference starting from standard Gaussian noise still results in images that have cluttered backgrounds (see Figure 5); this introduces extra difficulty for the feed-forward reconstructor in the second stage (Section 3.2). To guide the model toward generating images with a clean white background, inspired by SDEdit (Meng et al., 2022), we first create an image of a  $2 \times 2$  grid with a solid white background that has the same resolution as the output image, and initialize each sub-grid with a 2D *Gaussian blob* that is placed at the center of the image with a standard deviation of 0.1 (please see Appendix for details). The visualization of this Gaussian Blob is shown in Figure 2. The Gaussian blob image grid is fed to the auto-encoder to get its latent. We then add diffusion noise (e.g., use t=980/1000 for 50 DDIM denoising steps), and use it as the starting point for the denoising process. As seen in Figure 5, this technique effectively guides the model toward generating images with a clean background.
+
+**Lightweight fine-tuning.** With all the above observations and techniques, we are able to adapt a text-to-image diffusion model to a text-to-multiview model with lightweight fine-tuning. This lightweight fine-tuning shares a similar spirit to the 'instruction fine-tuning' (Mishra et al., 2022; Wei et al., 2021) for LLM alignment. The assumption is that the base model is already capable of the task, and the fine-tuning is to unlock the base model's ability without introducing additional knowledge.
+
+Since we utilize an image grid, the fine-tuning follows the exactly same protocol as the 2D diffusion model pre-training, except that we decrease the learning rate to  $10^{-5}$ . We train the model with a batch size of 192 for only 10K iterations on the 10K curated multi-view data. The training is done using 32 NVIDIA A100 GPUs for only 3 hours. We study the impact of different training settings in Section 4.3. For more training details, please refer to Appendix.
+
+#### <span id="page-4-0"></span>3.2 FEED-FORWARD SPARSE-VIEW LARGE RECONSTRUCTION MODEL
+
+In this stage, we aim to reconstruct a NeRF from the four-view images  $\mathcal{I} = \{\mathbf{I}_i \mid i = 1,...,4\}$  generated in the first stage. 3D reconstruction from sparse inputs with a large baseline is a challeng-
+
+ing problem, which requires strong model priors to resolve the inherent ambiguity. Inspired by a recent work LRM (Hong et al., 2024) that introduces a transformer-based model for single image 3D reconstruction, we propose a novel approach that enables us to predict a NeRF from a sparse set of input views with known poses. Similar to Hong et al. (2024), our model consists of an image encoder, an image-to-triplane decoder, and a NeRF decoder. The image encoder encodes the multiview images into a set of tokens. We feed the concatenated image tokens to the image-to-triplane decoder to output a triplane representation (Chan et al., 2022) for the 3D object. Finally, the triplane features are decoded into per-point density and colors via the NeRF MLP decoder.
+
+In detail, we apply a pretrained Vision Transformer (ViT) DINO (Caron et al., 2021) as our image encoder. To support multi-view inputs, we inject camera information in the image encoder to make the output image tokens pose-aware. This is different from Hong et al. (2024) that feeds the camera information in the image-to-triplane decoder because they take single image input. The camera information injection is done by the AdaLN (Huang & Belongie, 2017; Peebles & Xie, 2022) camera modulation as described in Hong et al. (2024). The final output of the image encoder is a set of pose-aware image tokens  $f_{I_i}^*$ , and we concatenate the per-view tokens together as the feature descriptors for the multi-view images:  $f_{\mathcal{I}} = \oplus (f_{I_1}^*, ... f_{I_4}^*)$ 
+
+We use triplane as the scene representation. The triplane is flattened to a sequence of learnable tokens, and the image-to-triplane decoder connects these triplane tokens with the pose-aware image tokens  $f_{\mathcal{I}}$  using cross-attention layers, followed by self-attention and MLP layers. The final output tokens are reshaped and upsampled using a de-convolution layer to the final triplane representation. During training, we ray march through the object bounding box and decode the triplane features at each point to its density and color using a shared MLP, and finally get the pixel color via volume rendering. We train the networks in an end-to-end manner with image reconstruction loss at novel views using a combination of MSE loss and LPIPS (Zhang et al., 2018) loss.
+
+**Training details.** We train the model on multi-view renderings of the Objaverse dataset (Deitke et al., 2023b). Different from the first stage that performs data curation, we use all the 3D objects in the dataset and scale them to  $[-1,1]^3$ ; then we generate multi-view renderings using Blender under uniform lighting with a resolution of  $512 \times 512$ . While the output images from the first stage are generated in a structured setup with fixed camera poses, we train the model using random views as a data augmentation mechanism to increase the robustness. Particularly, we randomly sample 32 views around each object. During training, we randomly select a subset of 4 images as input and another random set of 4 images as supervision. For inference, we will reuse the fixed camera poses in the first stage as the camera input to the reconstructor. For more details on the training, please refer to the Appendix.
+
+### 4 EXPERIMENTS
+
+In this section, we first do comparisons against previous methods on text-to-3D (Section 4.1), and then perform ablation studies on different design choices of our method. By default, we report the results generated with fine-tuned SDXL models, unless otherwise noted.
+
+#### <span id="page-5-0"></span>4.1 TEXT-TO-3D
+
+We make comparisons to state-of-the-art methods on text-to-3D, including a feed-forward method Shap-E (Jun & Nichol, 2023), and optimization-based methods including DreamFusion (Poole et al., 2022) and ProlificDreamer (Wang et al., 2023b). We use the official code for Shap-E, and the implementation from three-studio (Guo et al., 2023) for the other two as there is no official code. We use default hyper-parameters (number of optimization iterations, number of denoising steps) of these models. For our own model we use the SDXL base model fine-tuned on 10K data for 10K steps. During inference we take 100 DDIM steps.
+
+**Qualitative comparisons.** As shown in Figure 4, our method generates visually better results than those of Shap-E, producing sharper textures, better geometry and substantially improved text-3D alignment. Shap-E applies a diffusion model that is exclusively trained on million-level 3D data, which might be evidence for the need of 2D data or models with 2D priors. DreamFusion and ProlificDreamer achieve better text-3D alignment utilizing pretrained 2D diffusion models. However,
+
+<span id="page-6-0"></span>![](figures/_page_6_Figure_1.jpeg)
+
+Figure 4: Qualitative comparisons on text-to-3D against previous methods. We include more uncurated comparisons in the supplementary material.
+
+<span id="page-6-1"></span>Table 1: Quantitative comparisons on CLIP scores against baseline methods. Our method outperforms previous feed-forward method Shap-E and optimization-based method DreamFusion, and achieves competitive performance compared to ProlificDreamer while being  $1800 \times$  faster.
+
+|                 | ViT-L/14↑ | ViT-bigG-14↑ | $Time(s) \downarrow$ |
+|-----------------|-----------|--------------|----------------------|
+| Shap-E          | 20.51     | 32.21        | 6                    |
+| DreamFusion     | 23.60     | 37.46        | 5400                 |
+| ProlificDreamer | 27.39     | 42.98        | 36000                |
+| Ours            | 26.87     | 41.77        | 20                   |
+
+Table 2: Quantitative comparisons against previous sparse-view reconstruction methods on GSO dataset.
+
+|            | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
+|------------|--------|--------|---------|
+| SparseNeus | 20.62  | 0.8360 | 0.1989  |
+| Ours       | 26.54  | 0.8934 | 0.0643  |
+
+DreamFusion generates results with over-saturated colors and over-smooth textures. While ProlificDreamer results have better details, it still suffers from low-quality geometry (as in 'A bulldozer clearing ...') and the Janus problem (as in "a squirrel dressed like ...", also more detailed in Appendix Figure 11). In comparison, our results have more photorealistic appearance with better geometric details. Please refer to the Appendix and supplementary materials for video comparisons and more results.
+
+Quantitative comparisons. In Table 4, we quantitatively assess the coherence between the generated models and text prompts using CLIP-based scores. We perform the evaluation on results with 400 text prompts from DreamFusion. For each model, we render 10 random views and calculate the average CLIP score between the rendered images and the input text. We report the metric using multiple variants of CLIP models with different model sizes and training data (i.e., ViT-L/14 from OpenAI and ViT-bigG-14 from OpenCLIP). From the results we can see that our model achieves higher CLIP scores than Shap-E, indicating better text-3D alignment. Our method even achieves consistently higher CLIP scores than optimization-based method DreamFusion and competitive scores to ProlificDreamer, from which we can see that our approach can effectively inherit the great text understanding capability from the pretrained SDXL model and preserve them in the generated 3D assets via consistent sparse-view generation and robust 3D reconstruction.
+
+Inference time comparisons. We present the time to generate a 3D asset in Table [1.](#page-6-1) The timing is measured using the default hyper-parameters of each method on an A100 GPU. Notably, our method is significantly faster than the optimization-based methods: while it takes 1.5 hours for DreamFusion and 10 hours for ProlificDreamer to generate a single asset, our method can finish the generation within 20 seconds, resulting in a 270× and 1800× speed up respectively. In Figure [10,](#page-22-0) we show that our inference time can be further reduced without obviously sacrificing the quality by decreasing the number of DDIM steps.
+
+#### 4.2 COMPARISONS ON SPARSE VIEW RECONSTRUCTION
+
+We make comparisons to previous sparse-view NeRF reconstruction works. Most of previous works [\(Reizenstein et al.,](#page-13-12) [2021;](#page-13-12) [Trevithick & Yang,](#page-14-8) [2021;](#page-14-8) [Yu et al.,](#page-14-11) [2021\)](#page-14-11) are either trained on small-scale datasets such as ShapeNet, or trained in a category-specific manner. Therefore, we make comparisons to a state-of-the-art method SparseNeus [\(Long et al.,](#page-11-9) [2022\)](#page-11-9), which is also applied in One-2-3-45 [\(Liu et al.,](#page-11-11) [2023a\)](#page-11-11) where they train the model on the same Objaverse dataset for sparseview reconstruction. We do the comparisons on the Google Scan Object (GSO) dataset [\(Downs](#page-10-16) [et al.,](#page-10-16) [2022\)](#page-10-16), which consists of 1019 objects. For each object, we render 4-view input following the structured setup and randomly select another 10 views for testing. We adopt the pretrained model from [Liu et al.](#page-11-11) [\(2023a\)](#page-11-11). Particularly, SparseNeus does not work well for 4-view inputs with such a large baseline; therefore we add another set of 4 input views in addition to our four input views (our method still uses 4 views as input), following the setup in [Liu et al.](#page-11-11) [\(2023a\)](#page-11-11). We report the metrics on novel view renderings in Table [2.](#page-6-1) From the table, we can see that our method outperforms the baseline method even with fewer input images, which demonstrates the superiority of our sparse-view reconstructor.
+
+### <span id="page-7-0"></span>4.3 ABLATION STUDY FOR SPARSE VIEW GENERATION
+
+We ablate several key decisions in our method design, including (1) the choice of the larger 2D base model SDXL, (2) the use of Gaussian Blob during inference, (3) the quality and size of the curated dataset, and lastly, (4) the need and requirements of lightweight fine-tuning. We gather the quantitative results in Table [3](#page-8-1) and place all qualitative results in the Appendix. We observe that qualitative results are more evident than quantitative results, thus we recommend a closer examination.
+
+Scalability with 2D text-to-image models. One of the notable advantages of our method is that its efficacy scales positively with the potency of the underlying 2D text-to-image model. In Figure [12,](#page-23-1) we present qualitative comparisons between two distinct backbones (with their own tuned hyperparameters): SD1.5 [\(Rombach et al.,](#page-13-2) [2021\)](#page-13-2) and SDXL [\(Podell et al.,](#page-12-2) [2023\)](#page-12-2). It becomes readily apparent that SDXL, which boasts a model size 3× larger than that of SD1.5, exhibits superior text comprehension and visual quality. We also show a quantitative comparison on CLIP scores in Table [3.](#page-8-1) By comparing Exp(l, m) with Exp(d, g), we can see that the model with SD1.5 achieves consistently lower CLIP scores indicating worse text-3D alignment.
+
+Gaussian blob initialization. In Figure [5,](#page-8-0) we show our results generated with and without Gaussian blob initialization. From the results we can see that while our fine-tuned model can generate multi-view images without Gaussian blob initialization, they tend to have cluttered backgrounds, which challenges the second-stage feed-forward reconstructor. In contrast, our proposed Gaussian blob initialization enables the fine-tuned model to generate images with a clean white background, which better align with the requirements of the second stage.
+
+Quality and size of fine-tuning dataset. We evaluate the impact of the quality and size of the dataset used for fine-tuning 2D text-to-image models. We first make comparisons between curated and uncurated (randomly selected) data. The CLIP score rises slightly as shown in Table [3](#page-8-1) (i.e., comparing Exp(d, i)), while there is a substantial quality improvement as illustrated in Appendix Figure [7.](#page-19-0) This aligns with the observation that the data quality can dramatically impact the results in the instruction fine-tuning stage of LLM [\(Zhou et al.,](#page-14-12) [2023\)](#page-14-12).
+
+When it comes to data size, we observe a double descent from Table [3](#page-8-1) Exp(a, d, g) with 1K, 10K, and 100K data. We pick Exp(a, d, g) here because they are the best results among different training steps for the same training data size. The reason for this double descent can be spotlighted by the
+
+<span id="page-8-0"></span>![](figures/_page_8_Figure_1.jpeg)
+
+Figure 5: Qualitative comparisons on results generated with and without Gaussian blob initialization.
+
+<span id="page-8-1"></span>Table 3: Comparison on CLIP scores of NeRF renderings with different variants of fine-tuning settings.
+
+| Exp ID | Exp Name                  | Base  | # Data | Curated  | # Steps | ViT-L/14 | ViT-bigG-14 |
+|--------|---------------------------|-------|--------|----------|---------|----------|-------------|
+| (a)    | Curated-1K-s1k            | SDXL  | 1K     | /        | 1K      | 26.33    | 41.09       |
+| ` '    |                           |       |        | V .      |         |          |             |
+| (b)    | Curated-1K-s10k           | SDXL  | 1K     | /        | 10k     | 22.55    | 35.59       |
+| (c)    | Curated-10K-s4k           | SDXL  | 10K    | /        | 4k      | 26.55    | 41.08       |
+| (d)    | Curated-10K-s10k          | SDXL  | 10K    | /        | 10k     | 26.87    | 41.77       |
+| (e)    | Curated-10K-s20k          | SDXL  | 10K    | ✓        | 20k     | 25.96    | 40.56       |
+| (f)    | Curated-100K-s10k         | SDXL  | 100K   | <b>√</b> | 10k     | 25.79    | 40.32       |
+| (g)    | Curated-100K-s40k         | SDXL  | 100K   | ✓        | 40k     | 26.59    | 41.29       |
+| (h)    | Curated-300K-s40k         | SDXL  | 300K   | ✓        | 40K     | 26.43    | 40.72       |
+| (i)    | Random-10K-s10k           | SDXL  | 10K    | Х        | 10k     | 26.87    | 41.47       |
+| (j)    | Random-100K-s40k          | SDXL  | 100K   | ×        | 40k     | 26.28    | 40.90       |
+| (k)    | AllData-s40k              | SDXL  | 700K   | X        | 40k     | 26.13    | 40.60       |
+| (1)    | Curated-10K-s10k (SD1.5)  | SD1.5 | 10K    | /        | 10k     | 23.50    | 36.90       |
+| (m)    | Curated-100K-s40k (SD1.5) | SD1.5 | 100K   | ✓        | 40k     | 25.48    | 39.07       |
+
+qualitative comparisons in Appendix Figure 13, where training with 1K data can lead to inconsistent multi-view images, while training with 100K data can hurt the compositionality, photo-realism, and also text alignment.
+
+**Number of fine-tuning steps.** We also quantitatively and qualitatively analyze the impact of fine-tuning steps. For each block in Table 3 we show the CLIP scores of different training steps. Similar to the findings in instruction fine-tuning (Ouyang et al., 2022), the results do not increase monotonically regarding the number of fine-tuning steps but have a peak in the middle. For example, in our final setup with the SDXL base model and 10K curated data (i.e., Exp(c, d, e)), the results are peaked at 10K steps. For other setups, the observations are similar. We also qualitatively compare the results at different training steps for 10K curated data in Appendix Figure 14. There is an obvious degradation in the quality of the results for both 4K and 20K training steps.
+
+Another important observation is that the peak might move earlier when the model size becomes larger. This can be observed by comparing between Exp(l,m) for SD1.5 and Exp(d,g) for SDXL. Note that this comparison is not conclusive yet from the Table given that SD1.5 does not perform reasonably with our direct fine-tuning protocol. More details are in the Appendix.
+
+We also found that Exp(a) with 1K steps on 1K data can achieve the best CLIP scores but the view consistency is actually disrupted. A possible reason is that the CLIP score is insensitive to certain artifacts introduced by reconstruction from inconsistent images, which also calls for a more reliable evaluation metric for 3D generation.
+
+#### 5 CONCLUSIONS
+
+In this paper we presented a novel feed-forward two-stage approach Instant3D that can generate high-quality and diverse 3D assets from text prompts within 20 seconds. Our method finetunes a 2D text-to-image diffusion model to generate consistent 4-view images, and lifts them to 3D with a robust transformer-based large reconstruction model. The experiment results show that our method outperforms previous feed-forward methods in terms of quality while being equally fast, and achieves comparable or better performance to previous optimization-based methods with a speed-up of more than 200 times. Instant3D allows novice users to easily create 3D assets and enables fast prototyping and iteration for various applications such as 3D design and modeling.
+
+Ethics Statement. The generation ability of our model is inherited from the public 2D diffusion model SDXL. We only do lightweight fine-tuning over the SDXL model thus it is hard to introduce extra knowledge to it. Also, our model can share similar ethical and legal considerations to SDXL. The curation of the data for lightweight fine-tuning does not introduce outside annotators. Thus the quality of the data might be biased towards the preference of the authors, which can lead to a potential bias on the generated results as well. The text input to the model is not further checked by the model, which means that the model will try to do the generation for every text prompt it gets without the ability to acknowledge unknown knowledge.
+
+Reproducibility Statement. In the main text, we highlight the essential techniques to build our model for both the first stage (Section [3.1\)](#page-3-0) and the second stage (Section [3.2\)](#page-4-0). We discuss how our data is created and curated in Section [3.](#page-2-0) The full model configurations and training details can be found in Appendix Section [A.3](#page-15-0) and Section [A.6.](#page-17-0) We have detailed all the optimizer hyperparameters and model dimensions. We present more details on our data curation process in Section [A.2.](#page-15-1) We also attach the IDs of our curated data in Supplementary Materials to further facilitate the reproduction.
+
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+
+# A APPENDIX
+
+### A.1 DIVERSITY OF GENERATION
+
+Inheriting the generation capability from the base SDXL model, our method can generate diverse results from the same text prompt by using different random seeds in the feed-forward pass. As shown in Figure [6,](#page-15-2) our approach excels in generating diverse 3D assets featuring strikingly distinct textures and geometries from the same prompt. This is in contrast to previous SDS-optimization based methods, which are prone to generate similar results even with different initializations [\(Poole](#page-12-1) [et al.,](#page-12-1) [2022\)](#page-12-1).
+
+<span id="page-15-2"></span>![](figures/_page_15_Figure_1.jpeg)
+
+Figure 6: Our method can generate diverse results from the same text prompt.
+
+#### <span id="page-15-1"></span>A.2 DATA CURATION DETIALS
+
+We apply a quality scorer to curate high-quality data from the Objaverse dataset. To train the quality scorer, we first randomly sample 2000 3D objects from the dataset and manually label each 3D asset as good or bad. Good assets have realistic textures and complex geometry, while bad ones have simple shapes and flat or cartoon-like textures. This criterion is subjective and imprecise, but we found it good enough for the purpose of data filtering.
+
+Since the amount of annotated data is limited, we use a pretrained CLIP (Radford et al., 2021) model to extract high-level image features of rendered images at 5 randomly sampled camera viewpoints for each object. Then we train a simple binary SVM classifier on top of the averaged CLIP features over different views. We use the NuSVC implementation from the popular scikit-learn framework Pedregosa et al. (2011), which also gives us a probability estimation of the classification. We use the trained SVM model to predict the classification probability for all objects in the dataset by extracting CLIP features in the same way as done for the training data. These probabilities are used as scores to rank the data from high to low quality. Finally, we use the top 10K objects as our fine-tuning data.
+
+To render the 4-view data, we scale the curated objects and center them at a cube  $[-1,1]^3$ . We render the objects with a white background following the structured setup discussed in Section 3.1 using a field of view  $50^{\circ}$  at a distance of 2.7 under uniform lighting. We use the physically-based path tracer Cycles in Blender for rendering.
+
+In Figure 7 we show qualitative comparisons on results from models trained with curated data and random data. Models trained with random data tend to generate cartoon-like 3D assets with simple and flat textures. This is not surprising since a bulk of the Objaverse dataset contains simple shapes with simple textures, and without curation these data will guide the model to over-denoise the results, leading to large areas of flat colors. On the contrary, models trained with curated data tend to generate more photorealistic assets with complex textures and geometries.
+
+#### <span id="page-15-0"></span>A.3 SDXL FINE-TUNING DETAILS
+
+We use SDXL as the base model for our first-stage fine-tuning. We use AdamW optimizer with a fixed learning rate  $10^{-5}$ ,  $\beta_1 = 0.9$ ,  $\beta_2 = 0.999$  and a weight decay of  $10^{-2}$ . We fine-tune the model using fp16 on 32 NVIDIA A100 GPUs with a total batch size of 192. No gradient accumulation is used. We train the model on 10K curated data for 40K steps, which takes around 3 hours.
+
+We train the model with the standard denoising diffusion loss (Ho et al., 2020)
+
+$$L(\boldsymbol{\theta}) = \mathbb{E}_{t,\boldsymbol{x}_0,\boldsymbol{\epsilon}} \left[ \|\boldsymbol{\epsilon} - \boldsymbol{\epsilon}_{\boldsymbol{\theta}} (\sqrt{\overline{\alpha}_t} \boldsymbol{x}_0 + \sqrt{1 - \overline{\alpha}_t} \boldsymbol{\epsilon}, t) \|^2 \right]$$
+ (1)
+
+where  $\epsilon_{\theta}$  is the denoising U-Net and  $\theta$  are the trainable parameters.
+
+SDXL introduces image resolution and aspect ratio conditioning that allow mixing training on images of different resolutions and aspect ratios. As for our training data, we render 4 views each with a resolution of  $512 \times 512$  and assemble them into a  $1024 \times 1024$  image. Therefore we fix the resolution and aspect ratio conditioning to be (1024, 1024) throughout the fine-tuning procedure. We don't do random cropping in our training and fixed the crop conditioning to be (0,0). All the other training setups are identical to the original SDXL.
+
+<span id="page-16-0"></span>
+
+|       | #Layers | Render | Supervision | PSNR ↑  | SSIM ↑ | LPIPS ↓ |
+|-------|---------|--------|-------------|---------|--------|---------|
+| exp01 | 6       | 64     | All         | 23.6551 | 0.8616 | 0.1281  |
+| exp02 | 12      | 64     | All         | 23.8257 | 0.8631 | 0.1266  |
+| exp03 | 24      | 64     | All         | 23.8351 | 0.8635 | 0.1258  |
+| exp04 | 12      | 32     | All         | 23.1704 | 0.8561 | 0.1358  |
+| exp05 | 12      | 64     | w/o novel   | 18.2359 | 0.8103 | 0.2256  |
+| exp06 | 12      | 64     | w/o LPIPS   | 24.1699 | 0.8641 | 0.1934  |
+
+Table 4: Ablation study of the sparse-view reconstruction model.
+
+### A.4 SD1.5 FINE-TUNING DETAILS
+
+We use 8 A100 GPUs for fine-tuning SD1.5 on 100K data with a total batch size of 64. We use the same AdamW optimizer as the one for SDXL with the same hyper-parameters. We also use gradient accumulation of 3 steps, which gives an effective batch size of 192. The training loss is the same as SDXL. We train the model for 120K steps (40K parameter updates due to gradient accumulation), which takes roughly 33 hours.
+
+### A.5 GAUSSIAN BLOBS INITIALIZATION
+
+Since the diffusion model is fine-tuned with only a relatively small number of steps, it still largely possesses the original denoising behavior on images that are not in the form of 2 × 2 grids and do not have a white background. Naively applying the standard backward denoising process starting from random Gaussian noise will likely lead to results far from the distribution of the fine-tuning data (see Figure [5\)](#page-8-0).
+
+The spatial structure of the training images is simple: four views of the same object are placed at the center of each quadrant. Also, the background is always white. Since the model is fine-tuned on such data with a denoising objective, it is natural that, when presented with a noisy input whose underlying clean image has these two characteristics, the model will tend to denoise the image to a clean one where the four-quadrant objects are view consistent. Following this, and inspired by SDEdit [Meng et al.](#page-11-14) [\(2022\)](#page-11-14), we introduce Gaussian blobs initialization to guide the model toward generating samples consistent with the distribution of the fine-tuning data.
+
+The standard latent diffusion inference starts with a Gaussian noise image ϵ with the same size as the image latents. Instead, we modify the initial iteration to be a composition of Gaussian noise and an image with the two aforementioned characteristics: object quadrants and white background. We construct such an image by generating a grayscale image with a clean white background and a black Gaussian blob at the center. Specifically, we construct a H × W grayscale image I, where H and W are the height and width of the input RGB image with a value range [0, 1]. For all our models H = W, and we denote them using S. For a given pixel (x, y), its pixel value is computed as
+
+$$I(x,y) = 1 - \exp\left(-\frac{(x - S/2)^2 + (y - S/2)^2}{2\sigma^2 S^2}\right)$$
+ (2)
+
+where σ is a hyper-parameter controlling the width of the Gaussian blob. Such an image looks like a black disc at the center of a white image slowly fading away toward the edges of the image. We then assemble four such images into a 2 × 2 image grid. Some examples of such images with different σ can be seen at the first row of figure [5.](#page-8-0)
+
+Next we construct the initial noise for the denoising step by blending a complete Gaussian noise latent with the latent of the Gaussian blobs. We denote the latent of the Gaussian blobs image I as ˜I, and the latent of a noise image with i.i.d. Gaussian values as ϵ. For a N step denoising inference process with timesteps {t<sup>N</sup> , tN−1, ..., t0}, we mix the two latents with a weighted sum
+
+$$\epsilon_{t_N} = \sqrt{\overline{\alpha}_{t_N}} \tilde{I} + \sqrt{1 - \overline{\alpha}_{t_N}} \epsilon \tag{3}$$
+
+Then ϵ<sup>t</sup><sup>N</sup> is used as the initial noise of the denoising process, e.g., t<sup>N</sup> is 980 for a denoising step with 50 (and the total number of timesteps is 1000).
+
+## <span id="page-17-0"></span>A.6 SPARSE-VIEW RECONSTRUCTION DETAILS
+
+Model details We use the DINO-ViT-B/16 as our image encoder. This model is transformerbased, which has 12 layers and the hidden dimension of the transformer is 768. The ViT begins with a convolution of kernel size 16, stride 16, and padding 0. It is essentially patchifying the input image with a patch size of 16 × 16. For our final model, the input image resolution is 512, thus it leads to 32 × 32 = 1024 spatial tokens in the vision transformer. In ablation studies, we reduce the input resolution from 512 to 256 to save compute budget. The original DINO is trained with a resolution of 224 × 224, thus the positional embedding has only a size of 14 × 14 = 196. We thus use 2D bilinear extrapolation (with torch.nn.functional.interpolate function) to extrapolate it to the desired token size.
+
+To integrate camera information into the image encoder, we inject modulation layers [\(Peebles &](#page-12-12) [Xie,](#page-12-12) [2022\)](#page-12-12) into each of the transformer layer (for both self-attention layers and MLP layers). The modulation layer is initialized to be an identity mapping and thus it is suitable to be added to a pre-trained vision transformer.
+
+After the image encoder, we have 1025 image feature tokens for each image, since we also include the output of the [CLS] token. We concatenate the tokens from all four images to construct a sequence of condition features of length 4100. This condition feature will be used to create the keys and values in the cross-attention layers of the image-to-triplane transformer decoder.
+
+The image-to-triplane transformer decoder starts with a token sequence of (3 × 32 × 32) × 1024, where (3 × 32 × 32) is the number of tokens and 1024 is the hidden dimension of the transformer. We use 16 layers in our transformer decoder. All attention layers have 16 attention heads and each head has a dimension of 64. We remove the bias term in the attention layer as in [Touvron et al.](#page-13-14) [\(2023\)](#page-13-14). We take the pre-normalization architecture of the transformer where each sub-layer will be in the format of x + f(LayerNorm(x)).
+
+After the transformer, we apply a de-convolution layer to map the transformer output from (3×32× 32)×1024 to 3×(64×64)×80. It means that there are 3 planes (XY, YZ, XZ) [\(Chan et al.,](#page-9-2) [2022\)](#page-9-2) and each plane has a size of 64 × 64. The dimension of each plane is 80. All three planes share the same deconvolution layer. The deconvolution is of kernal size 2, stride 2, and pad 0.
+
+In NeRF volumetric rendering, the features from the three planes are bilinearly interpolated and concatenated to get a 240-dimensional feature for each point. Then, we have a 10-layer MLP with a hidden dimension of 64 to map this 240-dim feature to a 4-dim feature. The first three dimensions will be treated as RGB colors of the point and normalized to [0, 1] with a sigmoid function. The last dimension will be treated as the density value and we use an exponential function to map the MLP's output to be non-negative.
+
+For the exact formulation of the above operators, please refer to LRM [\(Hong et al.,](#page-10-4) [2024\)](#page-10-4) and DiT [\(Peebles & Xie,](#page-12-12) [2022\)](#page-12-12).
+
+Training details. We adopt the AdamW [\(Kingma & Ba,](#page-11-15) [2014;](#page-11-15) [Loshchilov & Hutter,](#page-11-16) [2017\)](#page-11-16) optimizer to train our model. We use a peak learning rate of 4 × 10<sup>−</sup><sup>4</sup> with a linear warm-up (on the first 3K steps) and a cosine decay. We change the β<sup>2</sup> of the AdamW optimizer to 0.95 for better stability. We use a weight-decay of 0.05 for non-bias and non-layernorm parameters. We also apply a gradient clipping of 1.
+
+For the initialization of the image encoder, we use the official DINO pre-trained weight. For the initialization of the triplane decoder, and NeRF MLP, we use the default initializer in the PyTorch implementation. We empirically found that the pre-normalization transformer is robust to different initialization of linear layers. For the positional embedding of the triplane tokens in the transformer decoder, we initialize them with a Gaussian of zero-mean and std of 1/ √ 1024.
+
+For each training step, we randomly sample 4 views as input and another 4 as supervision. The number of sample points per ray in NeRF rendering is 128, which are uniformly distributed along the segment within the [−1, 1]<sup>3</sup> bounding box. The rendering resolution is 128 × 128. To allow higher actual supervising resolution, we first resize the image to a smaller resolution (uniformly sampled from [128, 384]) and then crop a patch of 128 × 128 from it. Thus we can go beyond the rendering resolution of 128.
+
+We utilize flash attention (Dao et al., 2022), mixed-precision training (with bf16 as the half-precision format) (Micikevicius et al., 2018), and gradient checkpointing (Chen et al., 2016) to improve the compute/memory efficiency of the training.
+
+We perform the training for 120 epochs on our rendered Objaverse data with a training batch size of 1024. We use both L2 loss and LPIPS loss to supervise the model and the weights of the two losses are 1 and 2 respectively. The model is trained on 128 NVIDIA A100 GPUs and the whole training can be finished in 7 days.
+
+#### A.7 Sparse View Reconstruction Ablation Study
+
+We conduct an ablation study of our sparse-view reconstruction model to validate different design choices including the number of layers in the image-to-triplane decoder, the rendering resolution and the losses used during training, and the usage of novel view supervision. We train the model on the same dataset as our final model, however, we change the training recipe to reduce the computation cost to 32 A100 GPUs for 1 day. The changes of configuration for ablation include (1) a resolution of  $256 \times 256$  for the input image resolution, (2) 96 points per ray during rendering, (3) 5 layers instead of 10 layers in the NeRF MLP, (4) 30 epochs of training.
+
+To evaluate the performance of different variants, we test them on another 3D dataset Google Scanned Object (GSO) (Downs et al., 2022). For each object in GSO, we render a set of 64-view images rendered with a resolution of  $512 \times 512$  at elevations  $0^{\circ}$ ,  $20^{\circ}$ ,  $40^{\circ}$ ,  $60^{\circ}$ . Each elevation has 16 views with equidistant azimuths starting from 0. We use 4 views with elevation  $20^{\circ}$  and azimuths  $45^{\circ}$ ,  $135^{\circ}$ ,  $225^{\circ}$ ,  $315^{\circ}$  as input, and randomly sample 5 views from the remaining views as our testing set, which stay the same for different variants. We render the 5 testing views and report their difference from the ground truth using 3 metrics including PSNR, SSIM and LPIPS. These metrics are averaged over all 1019 objects in the GSO dataset.
+
+The results of the ablation studies are in Figure 4. From the table we can see that the model is robust to the number of transformer layers in the image-to-triplane decoder as shown in exp01, exp02, and exp03. We also observe that the LPIPS loss can largely affect the results by comparing the exp02 and exp06. Without the LPIPS loss, the model drops a lot on the LPIPS metric while getting a slight improvement on PSNR and SSIM. However, we empirically find that LPIPS is much more aligned with human perception and the rendered images become blurry without it. The rendering resolution is also important (as shown in exp04) since LPIPS can be more robust and accurate at a higher resolution, which also motivates us to use a rendering resolution of 128 by 128 when training our final model.
+
+Also, the inclusion of novel view supervision in the training is critical as shown in exp05. All three metrics got a significant drop when only supervising the four input views. Upon reviewing the results, we find that it's due to the insufficient coverage of the four views, which typically leads to floaters in regions not covered by the input views.
+
+#### A.8 EXTENSION TO IMAGE-CONDITIONED GENERATION
+
+Our method can also be extended to support additional image conditioning to provide more fine-grained control over the 3D model to be generated. In this process, the input to the model includes an input text prompt that describes the object to be generated as well as an image of the object. We use the same training data as our text-conditioned model. During training, for a randomly sampled time step, we keep the latent of the input image (top-left quadrant) untouched and only add noise to the latents of the remaining three views. This allows the diffusion model to generate the other views while accounting for the conditioning image. During inference, similarly, we replace the upper left quadrant of the latent feature with the latent of the clean conditioning image at each iteration. Figure 8 shows some visual results of our image-conditioned model. From the results we can see that our method is able to effectively generate the other views with faithful details that are coherent with the input text prompt and image, thus giving us high-quality 3D models with our sparse view reconstructor.
+
+<span id="page-19-0"></span>![](figures/_page_19_Figure_1.jpeg)
+
+Figure 7: Comparisons on novel view renderings of NeRF assets generated from SDXL models finetuned with 10K curated data and random data. We can see that that curated data enables the model to generate more photorealistic 3D assets with more geometric and texture details. Here curated and random correspond to Exp d (Curated-10K-s10K) and i (Random-10K-s10K) in Table [3.](#page-8-1)
+
+### A.9 LIMITATIONS
+
+While our model can generate high-quality and diverse 3D assets, it still suffers from several limitations. First, while we perform a light-weight fine-tuning that enables the model to mostly preserve the capability of the SDXL model in textual understanding and generation, we do observe that our model fails to handle some over-complicated prompts, for example, those related to complex spatial arrangements of multiple subjects and complex scenes (see Figure [15\)](#page-24-2). In addition, the generated assets are not as photorealistic as the 2D images generated by the original SDXL, which may be attributed to the information loss in the fine-tuning stage. Secondly, there is a lack of 3D inductive bias when generating multi-view images, and therefore it's still possible for our model to generate inconsistent images that result in low-quality 3D assets with corrupted geometries and textures. Finally, our feed-forward reconstructor tends to generate blurry textures compared to the input images due to the usage of a relatively low-resolution triplane.
+
+<span id="page-20-0"></span>![](figures/_page_20_Figure_1.jpeg)
+
+Figure 8: Comparison to previous methods on single image-conditioned 3D generation. We compared to previous methods Zero-1-to-3 [\(Liu et al.,](#page-11-3) [2023b\)](#page-11-3) and One-2-3-45 [\(Liu et al.,](#page-11-11) [2023a\)](#page-11-11). Our method can faithfully generate the details in the invisible regions, thus empowering us to reconstruct 3D assets of higher quality than baseline methods. All input images are generated with a public text-to-image platform Adobe Firefly [\(Adobe,](#page-9-12) [2023\)](#page-9-12).
+
+![](figures/_page_21_Figure_1.jpeg)
+
+Figure 9: 2 × 2 grid images generated with Gaussian blobs of different sigma σ.
+
+<span id="page-22-0"></span>![](figures/_page_22_Figure_1.jpeg)
+
+Figure 10: Comparison on the NeRF assets generated with different numbers of DDIM steps and their inference time. While we use 100 steps in our experiments that take 20 seconds to generate a NeRF asset, we find that using a smaller number of steps can also give us results of similar quality with a much shorter inference time.
+
+<span id="page-23-0"></span>![](figures/_page_23_Figure_1.jpeg)
+
+Figure 11: SDS optimization-based methods such as ProlificDreamer [\(Wang et al.,](#page-14-1) [2023b\)](#page-14-1) can possibly suffer from the Janus problem, which greatly degrades the quality of the 3D assets. In contrast, our method can mostly get rid of this problem.
+
+<span id="page-23-1"></span>![](figures/_page_23_Figure_3.jpeg)
+
+Figure 12: Comparisons on the quality of the NeRF assets generated with fine-tuned SDXL and SD1.5 models. SDXL has a model size that is three times larger than SD1.5 and thus has better text comprehension. As shown in the figure, the 3D assets generated by our fine-tuned SDXL have better photo-realism and text alignment. The used SDXL and SD1.5 models are from Exp d (Curated-10Ks10K) and m (Curated-100K-s40K) in Table [3.](#page-8-1)
+
+<span id="page-24-0"></span>![](figures/_page_24_Figure_1.jpeg)
+
+Figure 13: Comparison on the effect of different fine-tuning data sizes. Training on too little data such as 1K results in inconsistency between the generated 4 views, thus resulting in incorrect geometry. On the other side, training on too much data such as 100K makes the model biased toward the fine-tuning dataset, thus negatively affecting the quality of generated 3D assets. Here 1K, 10K and 100K correspond to Exp a (Curated-1K-s1K), d (Curated-10K-s10K) and g (Curated-100K-s40K) in Table 3 respectively.
+
+<span id="page-24-1"></span>![](figures/_page_24_Figure_3.jpeg)
+
+Figure 14: Comparison on different numbers of fine-tuning steps. 4K training steps lead to inconsistent 4-view generation, while 20K result in biasing towards the fine-tuning data. In contrast, 10K achieve a balance between these two. Here 4K, 10K and 20K correspond to Exp c (Curated-10K-s4K), d(Curated-10K-s10K) and e (Curated-10K-s20K) in Table 3.
+
+<span id="page-24-2"></span>![](figures/_page_24_Figure_5.jpeg)
+
+Figure 15: Some examples of our failure cases. (a) Incorrect understanding of compositional concepts. (b) Inability to generate the exact quantity. (c) Fail to generate objects with complex structures. (d) Missing important concepts in the prompt.

papers/2lDQLiH1W4/review.json

@@ -0,0 +1,70 @@
+{
+  "id": "2lDQLiH1W4",
+  "title": "Instant3D: Fast Text-to-3D with Sparse-view Generation and Large Reconstruction Model",
+  "decision": "Accept",
+  "reviews": [
+    {
+      "id": "wPAKUD6n3F",
+      "rating": 6,
+      "content": {
+        "summary": "The paper proposes a 3D distillation method from fine-tuned text-to-2D diffusion models fintuned. The method tackles the diversity and Janus problem in prior methods and achieves significant speedup compared to prior approaches.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "* There are several technical components proposed in the method to achieve good visual quality. \n* The speedup compared to prior optimization-based methods is significant.",
+        "weaknesses": "* In Figure 11, the paper claims to get rid of the Janus problem, but such a claim should be rigorously verified across a large set of text prompts instead of using the selected examples. \n* The paper proposes to use a feedforward transformer for sparse-view reconstruction, and both this model and the fine-tuned Stable-Diffusion model are trained on the Objaverse dataset, which can potentially introduce a large domain gap when applying the model to arbitrary text prompts. A discussion on failure cases related to the domain gap, if there are prominent ones, may help readers better assess its applicability.",
+        "questions": "* The paper provides qualitative examples suggesting an improved diversity compared to prior methods but lacks a discussion on which technical component in the proposed pipeline contributes to such diversity.\n\n___\nPost-rebuttal response: \nI've read comments from other authors and the rebuttal responses. \n* I am convinced that the output 3D asset quality from this work and the speedup compared to prior works are significant based on the thorough experiments and examples shown in the paper. \n* The performance gain largely rely on the the powerful backbone model, which shares a lot of similar design choices and training strategies compared to LRM which is appended in the supplementary and briefly discussed, but not directly compared to, in the paper. \n\nI'm raising my score to be 6 based on the performance and additional failure cases analysis during the rebuttal. Additional comparisons to a simple baseline adapting LRM could further help clarify the contribution delta of this work.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " * In Figure 11, the paper claims to get rid of the Janus problem, but such a claim should be rigorously verified across a large set of text prompts instead of using the selected examples. \n* The paper proposes to use a feedforward transformer for sparse-view reconstruction, and both this model and the fine-tuned Stable-Diffusion model are trained on the Objaverse dataset, which can potentially introduce a large domain gap when applying the model to arbitrary text prompts. A discussion on failure cases related to the domain gap, if there are prominent ones, may help readers better assess its applicability.\n* The paper provides qualitative examples suggesting an improved diversity compared to prior methods but lacks a discussion on which technical component in the proposed pipeline contributes to such diversity.",
+        "suggestions": "The paper should provide a more thorough analysis of the Janus problem by evaluating the method on a larger and more diverse set of text prompts. The current evaluation relies on a limited set of examples, which might not be representative of the method's performance across a wide range of prompts. A quantitative analysis, perhaps using a metric that measures the degree of symmetry or self-occlusion in the generated 3D models, could also strengthen the claim. Furthermore, the paper should include a more detailed discussion of the limitations of the approach, specifically addressing the domain gap issue arising from training on the Objaverse dataset. It would be beneficial to analyze failure cases where the model struggles with prompts that are significantly different from the training data, such as complex scenes with multiple objects or highly abstract concepts. This analysis should include both qualitative examples and a discussion of the underlying reasons for the failures, which could be related to the limited diversity of the training data or the specific architecture of the models used. \n\nTo address the lack of clarity regarding the source of the improved diversity, the paper should include an ablation study that examines the contribution of each technical component in the proposed pipeline to the diversity of the generated 3D assets. For example, the authors could investigate the impact of different sampling strategies in the fine-tuned diffusion model or the effect of the sparse-view reconstruction model on the final diversity. This analysis should also discuss the inherent properties of the diffusion sampling process that contribute to diversity, and how these properties are leveraged in the proposed method. A comparison with other methods that use different sampling techniques could also be insightful. Furthermore, the paper should also explore the potential limitations of the proposed method in terms of diversity, such as the possibility of generating similar shapes even with different random seeds, and discuss potential solutions to mitigate these limitations.\n\nFinally, the paper could benefit from a more detailed comparison with existing methods, particularly those that also leverage pre-trained models for 3D generation. This comparison should go beyond just qualitative examples and include quantitative metrics that measure the quality and diversity of the generated 3D models. It would be useful to compare the proposed method with a baseline that adapts a similar architecture, such as LRM, to better isolate the contribution of the proposed method. This comparison should also consider the computational cost and efficiency of the different methods, providing a more comprehensive evaluation of the proposed approach."
+      }
+    },
+    {
+      "id": "AAbU2Wru1U",
+      "rating": 8,
+      "content": {
+        "summary": "The authors propose a framework for text-to-3D generation in a feed-forward manner, without requiring an optimization loop during inference. The approach first generates multi view images from a text prompt and gaussian blob initialization. The multiview images are then fed through a transformer based reconstruction network that generates a triplane, which can then be used for volume rendering novel views. State of the art performance is  demonstrated compared to recent text-to-image baselines.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1. **Novelty**: The ideas introduced in this manuscript are reasonably novel. In particular, gaussian blob initialization for multiview generation is a potentially useful trick that can be applied to a variety of text-to-3D or image-to-3D pipelines. \n1. **Paper quality**: The paper is well-written and clearly presented, with attention to detail. The authors have clearly put a lot of effort into making the paper easy to read and understand.\n3. **Related work**: An adequate treatment of related works have been provided to place this work in the context of current literature.\n4. **Reproducibility**: The exact details of the approach, architecture specifics and training details have been provided to aid in the reproducibility of the approach. Furthermore, finetuning datatset information has also been provided in the supplm.\n2. **Comparisons**: The paper provides adequate comparisons to baselines, which is important for demonstrating the effectiveness of the proposed approach. Implementations of Dreamfusion on IF has been used as a strong baseline\n3. **Ablation**: Ablation studies are provided to highlight the need for each of the components introduced. Particularly, the motivation for the gaussian blob initialization and finetuning on different data.\n4. **Approach**: The proposed solution of generating 4 views is interesting and adds to the multiview consistency to some extent. \n5. **Appendix**: The authors provide a clear and detailed appendix section with additional reference to LRM for Image-to-3D reconstruction. A number of uncurated text to image examples are provided.",
+        "weaknesses": "1. **Need for gaussian blob**: How important is it for the initialization to be a gaussian blob? Can’t the same effect be achieved with a square mask since the primary intent is to localize the generated outputs to a region?\n3. **Image features**: How important are the Dino features? In particular, is there a significant drop in performance with features obtained from other pre-trained networks? Ablation with say VGG or other conv features would be insightful to determine the importance of the choice of features. \n5. **Comparison**: Additional comparison to amortized text-to-3D approaches like ATT3D[1] both in terms of quality and in terms of compute and inference costs will help highlight the contributions of this work. Additionally, most of the comparisons are against volume synthesis methods, how does the quality compare to mesh synthesis methods like Magic3D[2] ?\n6. **Novel view consistency**: It is unclear how multi-view consistent the rendered novel views are. Although table 2 provides comparison of pixel aligned metrics against SparseNeus, the work would greatly benefit by presenting video results of turntables of the rendered objects. This will help with the qualitative evaluation of the multiview consistency of the object.\n7. **Tiled generation vs multichannel**: Although contemporary to this work, motivating the need for tiling the views as opposed to generating them as separate channels as in MVDream[3]. Strict qualitative comparisons are not warranted, but highlighting the advantage of the tiled 4 view representation (particularly, since this reduces the resolution) would be insightful. \n8. **Number of view**: Section 3.1 mentions trade-off of number of views vs quality. Providing some qualitative/ quantitative justification for this (either in the appendix or supplm) would be very helpful.\n9. **Data distribution**: Since stage 2 is only trained on Objaverse-XL renders, is there an issue with the kinds of 3D assets that can be generated? In particular, the generated assets look synthetic and from the distribution of Objaverse instances. \n10. **Choice of Diffusion model**: The tiled approach works well for latent space models like SD and SD-XL due to the inherent high resolution input output. Can this framework also be adapted in pixel space diffusion models like DeepFloyd. Providing some insight for this will be helpful in determining the choice of diffusion model.\n10. **SD vs SDXL**: Although quantitative evaluations are presented, providing some qualitative comparison of assets generated from SD finetuning vs SDXL finetuning would be helpful (in appendix or supplm). \n\n[1] Lorraine et al. ATT3D, ICCV23. \n[2] Lin et al. Magic3D, CVPR23. \n[3] Shi et al. MVDream arxiv23",
+        "questions": "1. How important are DINO features?\n2. What is the advantages of tiled generation of 4 views over generating on multiple channels.?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.",
+        "code_of_conduct": "Yes",
+        "weakness": " 1. **Need for gaussian blob**: How important is it for the initialization to be a gaussian blob? Can’t the same effect be achieved with a square mask since the primary intent is to localize the generated outputs to a region? Furthermore, what is the sensitivity of the approach to the variance of the gaussian blob? A more detailed study on the effect of the gaussian initialization parameters would be insightful. \n3. **Image features**: How important are the Dino features? In particular, is there a significant drop in performance with features obtained from other pre-trained networks? Ablation with say VGG or other conv features would be insightful to determine the importance of the choice of features. Additionally, are the features extracted from all layers of the Dino network, and if not, what is the impact of using different layers or combinations of layers?\n5. **Comparison**: Additional comparison to amortized text-to-3D approaches like ATT3D[1] both in terms of quality and in terms of compute and inference costs will help highlight the contributions of this work. Additionally, most of the comparisons are against volume synthesis methods, how does the quality compare to mesh synthesis methods like Magic3D[2] ? The comparison to ProlificDreamer is appreciated, however a more direct comparison to other mesh based approaches would be beneficial.\n6. **Novel view consistency**: It is unclear how multi-view consistent the rendered novel views are. Although table 2 provides comparison of pixel aligned metrics against SparseNeus, the work would greatly benefit by presenting video results of turntables of the rendered objects. This will help with the qualitative evaluation of the multiview consistency of the object. Furthermore, how does the consistency vary with the number of views used for reconstruction?\n7. **Tiled generation vs multichannel**: Although contemporary to this work, motivating the need for tiling the views as opposed to generating them as separate channels as in MVDream[3]. Strict qualitative comparisons are not warranted, but highlighting the advantage of the tiled 4 view representation (particularly, since this reduces the resolution) would be insightful. What is the impact of this reduced resolution on the final 3D reconstruction quality?\n8. **Number of view**: Section 3.1 mentions trade-off of number of views vs quality. Providing some qualitative/ quantitative justification for this (either in the appendix or supplm) would be very helpful. Specifically, what is the performance drop when using 2 views vs 4 views, and what is the computational trade-off?\n9. **Data distribution**: Since stage 2 is only trained on Objaverse-XL renders, is there an issue with the kinds of 3D assets that can be generated? In particular, the generated assets look synthetic and from the distribution of Objaverse instances. Furthermore, is there a bias towards object categories present in the Objaverse-XL dataset?\n10. **Choice of Diffusion model**: The tiled approach works well for latent space models like SD and SD-XL due to the inherent high resolution input output. Can this framework also be adapted in pixel space diffusion models like DeepFloyd. Providing some insight for this will be helpful in determining the choice of diffusion model. What are the challenges in adapting this approach to pixel space diffusion models?\n10. **SD vs SDXL**: Although quantitative evaluations are presented, providing some qualitative comparison of assets generated from SD finetuning vs SDXL finetuning would be helpful (in appendix or supplm). ",
+        "suggestions": "The paper presents a novel approach for text-to-3D generation using a feed-forward network, which is a significant contribution to the field. However, several aspects of the method require further investigation and clarification. Firstly, the initialization using a Gaussian blob is a key component of the approach, but the paper lacks a detailed analysis of its sensitivity to the variance parameter and a comparison to alternative initialization methods such as a square mask. A thorough ablation study on different initialization parameters and shapes would strengthen the claims of the method. Furthermore, the choice of DINO features is not sufficiently justified, and it is unclear whether other pre-trained networks or even features extracted from different layers of DINO could yield similar or better results. A more comprehensive analysis of the feature extraction process is needed to understand the importance of this component. Finally, the paper would benefit from a more in-depth comparison with existing text-to-3D methods, particularly mesh-based approaches, and a more detailed analysis of the multi-view consistency of the generated 3D objects. Specifically, providing video results of the rendered objects would be useful to qualitatively evaluate the consistency of the novel views.\n\nSecondly, the approach of tiling the four views is interesting, but the paper does not adequately motivate this choice over generating the views as separate channels. A clear explanation of the advantages and disadvantages of each approach, along with an analysis of the impact of reduced resolution due to tiling, would be beneficial. The trade-off between the number of views and the quality of the generated 3D objects should also be explored in more detail, with quantitative and qualitative results presented to support the choice of using four views. Additionally, the paper should address the potential bias introduced by training the second stage on the Objaverse-XL dataset. An analysis of the distribution of the generated 3D assets and their similarity to the objects in the training dataset would be helpful. It is also important to consider the applicability of the approach to different types of diffusion models, specifically pixel-space diffusion models, and discuss the challenges and potential solutions for adapting the method to such models. A qualitative comparison of the assets generated from SD and SDXL fine-tuning would further strengthen the results.\n\nFinally, the paper should address the limitations of the approach in terms of the types of 3D assets that can be generated. While the current results are promising, it is important to acknowledge the potential biases and limitations of the method, particularly when generating objects that are not well-represented in the training dataset. Future work should focus on improving the generalization capabilities of the approach and exploring ways to generate a wider variety of 3D assets. The authors should also discuss the computational cost of their approach and compare it to other text-to-3D methods. This would provide a more complete picture of the strengths and weaknesses of the proposed method and help guide future research in this area. Specifically, a discussion of the inference time and memory requirements would be helpful for the reader to understand the practical implications of the approach."
+      }
+    },
+    {
+      "id": "Kkv15tMq86",
+      "rating": 8,
+      "content": {
+        "summary": "The paper presents a method for generating 3D shapes from text. The paper observes problems in the current score distillation-based optimization method, including slow inference, low diversity, and Janus problems, and proposes methods to solve them. As a first step, it proposed a text-conditioned sparse-view generation model, finetuned from a large-scale diffusion model of text-to-image generation. It is capable of generating high-quality sparse-view images without clustering the background. Second, it reconstructs the 3D shape based on the sparse views it generates. To reconstruct the sparse views, view-conditioned image tokens are encoded. Image tokens are concatenated from four views and fed into a triplane decoder. A NeRF decoder takes the decoded triplane features and reconstructs them into a 3D shape. Using the proposed method, high-quality and diverse 3D shapes can be created in 20 seconds. Using the proposed method, the Janus problem is prevented by maintaining shapes across views.",
+        "soundness": "3 good",
+        "presentation": "4 excellent",
+        "contribution": "4 excellent",
+        "strengths": "This paper is well written, clearly motivated, significantly contributed, and extensively experimented. The strengths I found about this paper include but are not limited to: \n+ It proposes an effective method for resolving the Janus problem in text-to-image optimization-based method for text-to-shape generation. The experiment shows that the generated 3D shapes have better 3D structure and texture consistency across views. \n+ It proposes a lightweight fine-tuning method and conducts extensive experiments for text-to-sparse view image generation. The method leverages the capability of a large-scale text-image generated model and proves that it has the ability to generate images across sparse views with light fine-tuning. I believe this model can not only contribute to text-to-shape generation but also to other domains. \n+ It proposes an effective sparse-view reconstruction method that outperforms other sparse-view reconstruction methods in object-only datasets. \n+ As a feedforward method, it generates 3D shapes efficiently within only 20 seconds.",
+        "weaknesses": "The paper still has some limitations which I think are not discussed thoroughly: \n\n+ Over-saturated problem. In Figure 4, the paper provides examples that have more photorealistic colors. However, it still suffers from an over-saturated problem to some extent, especially in the examples provided in Figure 5. I think the increment of texture quality majorly resulted from the curated training dataset, which removes cartoonish and low-quality instances, but not a result of improving the texture generate method itself(i.e. improving the rendering method, adding extra photo-realistic losses). If my interpretation is correct, I think this should be stated in the limitation section. \n+ Resolution. As the author stated in the limitation section, generating four sparse view images leads to a degradation of texture quality. It would be better to provide a qualitative experiment by measuring the PSNR/SSIM/LPIPS of single image and multi-view images.\n+ Diversity. In Figure 6, the paper provides examples showing the method is able to generate diverse results. My question is if the method provides more diverse results compared with other optimization-based methods. Will the feed-forward method be helpful in providing more diverse results than the optimization-based method practically? It would be better to provide some examples here. \n+ In A.3 the paper detailed how to use CLIP features to filter out low-quality shapes. While I'm convinced the CLIP feature can filter out shapes with a cartoonish style, I'm not very convinced that the CLIP feature is able to tell apart shape quality. I hope the authors can provide some positive and negative examples here.\n+ Some missing citations. \n 1. Section 2.1 paragraph 1. Missing methods using implicit representation[1-3]. \n 2. Section 2.1 paragraph 2. Missing some diffusion-based generation methods[4]. \n[1] Towards Implicit Text-Guided 3D Shape Generation\n[2] ShapeCrafter: A Recursive Text-Conditioned 3D Shape Generation Model\n[3] CLIP-Forge: Towards Zero-Shot Text-to-Shape Generation\n[4] CLIP-Sculptor: Zero-Shot Generation of High-Fidelity and Diverse Shapes from Natural Language",
+        "questions": "+ Object-centric COCO. Considering all of the models are finetuned with the Objaverse-XL dataset, I'm wondering if it is still able to generate some shapes whose distribution is outside the Objaverse-XL dataset. I acknowledge it would be hard to prove, but I'm curious to see if the method is able to generate meaningful shapes in the Object-centric COCO dataset[1]. \n+ View condition. When training the view-conditioned image-to-triplane decoder, are the training shapes canonicalized or not? Let's say we input a set of views V = [v1, v2, v3, v4] and generate a shape A.  Then we multiply all the views with a transformation matrix M and generate a shape B. Will shape A and shape B under the same canonicalized coordinate frame? \n+ Minor writing mistakes. \n 1. Section 2.2. \"unseeen\" -> \"unseen\".\n 2. Section A.4. \"The dimension of each plane is 80 All three....\" -> \"The dimension of each plane is 80. All three....\"\n\n[1] DREAMFUSION: TEXT-TO-3D USING 2D DIFFUSION",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.",
+        "code_of_conduct": "Yes",
+        "weakness": "The paper still has some limitations which I think are not discussed thoroughly: \n\n+ Over-saturated problem. In Figure 4, the paper provides examples that have more photorealistic colors. However, it still suffers from an over-saturated problem to some extent, especially in the examples provided in Figure 5. I think the increment of texture quality majorly resulted from the curated training dataset, which removes cartoonish and low-quality instances, but not a result of improving the texture generate method itself(i.e. improving the rendering method, adding extra photo-realistic losses). If my interpretation is correct, I think this should be stated in the limitation section. \n+ Resolution. As the author stated in the limitation section, generating four sparse view images leads to a degradation of texture quality. It would be better to provide a qualitative experiment by measuring the PSNR/SSIM/LPIPS of single image and multi-view images.\n+ Diversity. In Figure 6, the paper provides examples showing the method is able to generate diverse results. My question is if the method provides more diverse results compared with other optimization-based methods. Will the feed-forward method be helpful in providing more diverse results than the optimization-based method practically? It would be better to provide some examples here. \n+ In A.3 the paper detailed how to use CLIP features to filter out low-quality shapes. While I'm convinced the CLIP feature can filter out shapes with a cartoonish style, I'm not very convinced that the CLIP feature is able to tell apart shape quality. I hope the authors can provide some positive and negative examples here.\n+ Some missing citations. \n 1. Section 2.1 paragraph 1. Missing methods using implicit representation[1-3]. \n 2. Section 2.1 paragraph 2. Missing some diffusion-based generation methods[4]. \n[1] Towards Implicit Text-Guided 3D Shape Generation\n[2] ShapeCrafter: A Recursive Text-Conditioned 3D Shape Generation Model\n[3] CLIP-Forge: Towards Zero-Shot Text-to-Shape Generation\n[4] CLIP-Sculptor: Zero-Shot Generation of High-Fidelity and Diverse Shapes from Natural Language",
+        "suggestions": "The paper would benefit from a more detailed analysis of the color saturation issue. While the curated dataset likely contributes to improved texture quality, the method's inherent limitations in handling color saturation should be further investigated. For instance, a comparison of color histograms between the generated images and the training data could reveal if the model is biased towards specific color distributions, potentially explaining the over-saturation. Furthermore, the authors could explore the impact of different rendering techniques or the inclusion of perceptual loss functions during training to mitigate this problem. A more thorough discussion of these aspects would strengthen the paper's analysis and provide a more complete understanding of the method's limitations regarding photorealism.\n\nRegarding diversity, the paper should provide a more rigorous comparison against optimization-based methods. While the paper shows examples of diverse outputs, it lacks a quantitative measure of diversity. It would be beneficial to use metrics such as the Fréchet Inception Distance (FID) or the Kernel Inception Distance (KID) to compare the distribution of generated shapes from the proposed method and other existing methods. These metrics can provide a more objective assessment of the diversity of generated shapes. Furthermore, it would be helpful to analyze the latent space of the model to understand how different textual prompts are mapped and how they affect the generated shapes. This analysis could reveal potential biases or limitations in the model's ability to generate diverse shapes.\n\nThe paper should also address the concerns about the CLIP-based filtering method. While the authors claim that CLIP features can filter out low-quality shapes, the paper does not provide sufficient evidence to support this claim. It would be helpful to show examples of shapes that are filtered out by CLIP and demonstrate why they are considered low quality. Furthermore, it would be beneficial to provide a quantitative analysis of the effectiveness of the CLIP-based filtering method. For example, the authors could measure the correlation between the CLIP scores and the perceived quality of the generated shapes. This analysis would provide a more objective assessment of the method's ability to filter out low-quality shapes. Additionally, the authors should clarify whether the CLIP features are used to filter out shapes based on style, shape, or both, and provide more details on how the CLIP features are used to determine the quality of the generated shapes."
+      }
+    }
+  ]
+}

papers/30N3bNAiw3/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "30N3bNAiw3",
+  "title": "Separating common from salient patterns with Contrastive Representation Learning",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Accept",
+  "date": "2023-09-19",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=30N3bNAiw3"
+}

papers/30N3bNAiw3/review.json

@@ -0,0 +1,112 @@
+{
+  "id": "30N3bNAiw3",
+  "title": "Separating common from salient patterns with Contrastive Representation Learning",
+  "decision": "Accept",
+  "reviews": [
+    {
+      "id": "90CMGlIehS",
+      "rating": 8,
+      "content": {
+        "summary": "The paper provides a novel concept of contrastive learning for separating common and silent patterns. The approach utilizes two encoders, one responsible for learning silent representation and one for common. The authors propose the criterion to train the model that is based on the InfoMax principle. Due to the fact the direct optimization of the criterion for the problem is difficult and general for the problem, they propose a set of assumptions that allow to training of the model directly using a gradient-based approach. The approach is evaluated using big number of use cases.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "- The presentation of the paper is good, and the work is clear and well-written. \n- The proposed method is very interesting and sounds good technically. The flow of the proposed solution seems to be accurate. The authors clearly formulate the problem and general criterion given by eq. 1. Further, they decompose each component and propose a well-justified form of the component for given encoders. \n- The experiments are well-motivated, and the results seem to confirm the hypothesis stated in this work. It is very beneficial that datasets are from a variety of domains, going beyond standard benchmarks.",
+        "weaknesses": "- The model is designed only to model $p(c|\\cdot)$ and $p(s|\\cdot )$. It would be nice to see some approximation of the distribution over data $p(\\cdot|s,c)$. I think that the proposed architecture can be enriched with the decoder that models this probability. \n- I am not quite sure if setting the same architecture for the proposed and reference methods is a good approach. In my opinion, the best architecture for each individual method should be used in experiments. \n- Only VAE-based methods are used as reference approaches. VAEs are doing the additional jobs, they have decoders and serve as generative models, while SEPCLR is only learning the common and silent representation. It would be nice to see the comparison with the models from similar groups, either SEPCLR as VAE, or reference methods that do not preserve autoencoding properties.",
+        "questions": "I would like to ask the authors to respond to the weaknesses section. I will also would like to ask about selecting KDE as a model for this case. Can KDE be replaced with the normalizing flow instead?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " - The model is designed only to model $p(c|\\cdot)$ and $p(s|\\cdot )$. It would be beneficial to see some approximation of the joint distribution over data $p(\\cdot|s,c)$. The proposed architecture could be enriched with a decoder that models this probability, allowing for a more complete generative model. \n- I am not quite sure if setting the same architecture for the proposed and reference methods is a good approach. In my opinion, the best architecture for each individual method should be used in experiments. Specifically, it is unclear if the encoder architecture is optimal for both the proposed method and the reference methods, potentially skewing the comparison.\n- Only VAE-based methods are used as reference approaches. VAEs perform additional tasks, such as having decoders and serving as generative models, while SEPCLR focuses solely on learning common and silent representations. It would be more appropriate to compare with models from similar groups, either by extending SEPCLR to a VAE or by comparing with reference methods that do not preserve autoencoding properties. This would provide a more fair and comprehensive evaluation.",
+        "suggestions": "The paper presents an interesting approach to contrastive learning for separating common and silent patterns, but there are several avenues for improvement that could strengthen the work. First, the model's current focus on learning $p(c|\\cdot)$ and $p(s|\\cdot)$ is somewhat limiting. To fully leverage the learned representations, the authors should explore modeling the joint distribution $p(\\cdot|s,c)$. This could be achieved by incorporating a decoder network that takes the common and silent representations as input and attempts to reconstruct the original data. This would not only allow for a more complete generative model but also enable interesting applications such as attribute swapping or novel sample generation by manipulating the latent representations. The current architecture, while effective for representation learning, lacks this generative aspect, which could be a significant advantage.\n\nSecond, the experimental setup could be improved by ensuring that each method is evaluated using its optimal architecture. While using the same architecture for all methods provides a controlled comparison, it does not guarantee that each method is performing at its best. The authors should consider performing a more thorough architecture search for each method, including the proposed SEPCLR and the reference methods, to determine the optimal configuration. This would provide a more accurate assessment of each method's capabilities. For example, the encoder architecture might be well-suited for the proposed method but suboptimal for the VAE-based reference methods, or vice versa. This could be addressed by performing a hyperparameter search for each method individually, or by using a more flexible architecture that can be adapted to different tasks. This would also help to clarify whether the performance differences are due to the method itself or the specific architecture used.\n\nFinally, the choice of VAE-based methods as the sole reference point is questionable. While VAEs are a common approach for representation learning, they are not directly comparable to SEPCLR, which does not have a generative component. To provide a more comprehensive evaluation, the authors should include reference methods that are more closely aligned with the goals of SEPCLR. This could include other contrastive learning methods or methods that focus on disentangled representation learning. Alternatively, the authors could extend SEPCLR to include a decoder, effectively turning it into a VAE, and then compare it with other VAE-based methods. This would provide a more fair and comprehensive comparison. Additionally, it would be beneficial to include a comparison with methods that do not preserve autoencoding properties, as this would provide a more complete picture of the method's performance in different scenarios."
+      }
+    },
+    {
+      "id": "eFnE8afrSc",
+      "rating": 8,
+      "content": {
+        "summary": "This paper presents a theoretically grounded approach based on contrastive learning, SepCLR, to separate salient features from common features given a weak supervision in the form of a target dataset that contains both salient and common features and a background dataset that contains only common features. A series of mutual information based objective functions and regularization terms are presented along with clear motivation and background behind each of the terms, and the approximate loss functions are derived to achieve these objectives. Experimental results on multiple vision and medical benchmarks demonstrate that a good separation of latents is achieved and the method out-performs prior work. Visualizations of retrievals support their experiments.",
+        "soundness": "4 excellent",
+        "presentation": "3 good",
+        "contribution": "4 excellent",
+        "strengths": "This paper is well-organized and well-written. It covers the necessary background on contrastive analysis, provides the theoretical and intuitive motivations on their various objective functions and puts them in context with prior literature, provide the derivations, and also discuss their limitations well.\n\nThe main novelty lies in their information-theoritic formulation of the various objectives and more importantly, exploiting contrastive learning and other prior literature to make the various objectives tractable. Another novelty is that they proposed joint entropy maximization to prevent information leakage between the common and salient latents as opposed to mutual information minimization, as the latter strategy can lose information.\n\nResults in Table 1 and 2 show good latent separation on synthetic vision tasks, and that the proposed approach outperforms prior approaches. In addition, they also reveal that the proposed joint entropy maximization is better than other strategies to prevent information leakage. Table 3, 4, and 5 show similar results on the medical domain and the retrieval visualizations support their findings.",
+        "weaknesses": "This paper presents several objectives, but it's unclear which objectives are important and how they work together. This makes it unclear for a practitioner to transfer the results to a different problem. So, I encourage the authors to ablate the different objectives. \n\nAnother weakness is that in Table .4, which is perhaps an important real-world application of the proposed approach, the improvements over prior work is not much. This is in contrast with other experiments i.e. Table 1, 2, 3, 5. The reasoning for this is unclear and also not provided.  \n\nNit: MMD abbreviates to maximum mean discrepancy and is referred in the paper as moment matching distance [1]. \n\n[1]: A Kernel Two-Sample Test https://jmlr.csail.mit.edu/papers/v13/gretton12a.html",
+        "questions": "1. Could you provide an ablation study on the various objectives and their impact?\n2. In Table 1, 2, what is the performance on the background dataset? Is the salient latent non-informative as it is supposed to be? Is the common term informative?\n3. Is the task switch from classification to regression affecting the proposed approach's effectiveness in Table 4?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "This paper presents several objectives, but it's unclear which objectives are important and how they work together. This makes it unclear for a practitioner to transfer the results to a different problem. So, I encourage the authors to ablate the different objectives. \n\nAnother weakness is that in Table .4, which is perhaps an important real-world application of the proposed approach, the improvements over prior work is not much. This is in contrast with other experiments i.e. Table 1, 2, 3, 5. The reasoning for this is unclear and also not provided.  \n\nNit: MMD abbreviates to maximum mean discrepancy and is referred in the paper as moment matching distance [1].",
+        "suggestions": "The paper introduces several loss terms, including a joint entropy maximization term, a salient feature learning term, and a common feature learning term, along with an infoless regularization term. While the paper provides a theoretical justification for each term, it does not offer sufficient empirical evidence to understand their individual contributions. An ablation study is crucial to determine the relative importance of each loss term and to understand how they interact. For example, it would be beneficial to see the performance of the model when the joint entropy maximization term is removed, or when the infoless regularization term is removed. This would help to understand if the joint entropy maximization is indeed superior to mutual information minimization, as claimed by the authors. Furthermore, the ablation should also consider the impact of the weighting parameters for each loss term. This would provide a more comprehensive understanding of the model's behavior and allow practitioners to adapt the method to new problems by tuning these parameters effectively. Without this analysis, it is difficult to determine which components of the model are most critical for its performance, and the transferability of the method is limited.\n\nIn Table 4, the performance gains over prior work are marginal compared to other experiments. This discrepancy raises questions about the robustness of the proposed approach in real-world scenarios. The authors should investigate the reasons behind this performance gap. For example, is the complexity of the real-world dataset a limiting factor? Does the proposed method struggle with the increased variability in the data? Are there specific characteristics of the medical imaging data that make it less amenable to the proposed approach? It would be helpful to analyze the performance on a per-class basis to identify specific areas where the model performs poorly. This analysis could reveal potential limitations of the proposed approach and guide future research. Furthermore, it would be beneficial to compare the performance of the proposed method with other state-of-the-art methods specifically designed for medical imaging tasks. This would provide a more comprehensive evaluation of the proposed method's effectiveness in a real-world setting.\n\nFinally, the paper refers to MMD as moment matching distance, while it is more commonly known as maximum mean discrepancy. While this is a minor point, it is important to use the correct terminology to avoid confusion. The authors should correct this in the paper. In addition, the authors should also consider providing more details on the implementation of the proposed method. For example, what is the architecture of the encoder and decoder networks? What are the specific hyperparameter settings used in the experiments? Providing these details would help other researchers to reproduce the results and build upon the proposed method. Furthermore, it would be beneficial to provide a more detailed analysis of the computational complexity of the proposed method. This would help to understand the scalability of the method and its applicability to large-scale datasets."
+      }
+    },
+    {
+      "id": "GEMagnvX1j",
+      "rating": 8,
+      "content": {
+        "summary": "This paper proposes a technique called SepCLR that uses contrastive learning in order to learn representations that separate common elements from salient ones for the downstream task at hand. The authors examine the performance of their method in creating separate representations for these two elements, and demonstrate improvements over previous work on the same subject.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "- The method proposed by the authors is novel, as far as I am aware. Limiting the shared information between the common and the salient space explicitly is an interesting way to ensure that the two encoders model different aspects of the data, leading to less overlap in the information between the two encoders.\n\n- The authors have performed extensive experiments on a variety of datasets, and have also examined several different variations of their proposed method, as can be seen in Table 1. I also appreciate the fact that the datasets used are not only standard ones like MNIST or CIFAR-10, but also come from the medical domain (although I would also appreciate results involving more complicated datasets like CIFAR-100 or ImageNet, which have more object classes available).\n\n- I also appreciate the detailed analysis that the authors provide for the datasets used in the appendix.",
+        "weaknesses": "- As far as I understand, there is an inherent limitation for the method in that knowing the labels for the target dataset is required during training. This limits the applicability of SepCLR in the unsupervised setting, which is also the one most commonly examined by contrastive learning works.\n\n- I believe that there are some issues with the proposed method, that I would be grateful if the authors could elaborate on:\n\n  - The authors make some decisions when designing the loss that go against what is commonly done in related contrastive learning papers. In particular, the loss they propose has the formulation of $L_{unif}$ as found in Wang & Isola [A], but the most commonly used formulation is that of InfoNCE, which differs in that the resulting loss is a sum of Log-Sum-Exp functions, instead of a single Log-Sum-Exp. Similarly, in the alignment term they use a formulation closer to $L_{out}$ from Supervised Contrastive Learning [B], but the same paper notes that another formulation that simply sums the inner products, named $L_{in}$, is better experimentally (the authors examine this in the appendix, but do not explain why they chose $L_{out}$). I would be grateful if the authors could elaborate on these design decisions.\n\n  - Related to the above, it seems that the alignment terms in the common space and in the salient space are different (and similar to $L_{out}$ and $L_{in}$ respectively). I would be glad if the authors could explain why this is the case.\n\n  - In Equation (7), the first term in the sums essentially forces the representations of the salient encoder to be far from the constant vector $s’$. It’s not immediately clear to me why this term is there - it doesn’t seem to arise from optimizing $\\hat{H}(S)$, and the informationless hypothesis only comes into play in Equation (8). I think the authors need to explain this part a bit more.\n\n  - Finally, the zero mutual information constraint is somewhat misleading - I understand the point the authors make that minimizing $I(c;s)$ is not the best thing to do, but at the same time, the proposed method does not directly force $I(c; s) = 0$. There is no guarantee that maximizing $H(c,s)$ does not affect the maximization of $H(c) + H(s)$, nor that the final solution will have $H(c,s) = H(c) + H(s)$. I believe that the authors should be clearer about this point.\n\n- I also believe that some points regarding the presentation of the paper can be improved:\n\n  - Tables 1 and 2 contain several variants of SepCLR, but it is not clear what each of them signify. The authors should better explain the variants of SepCLR in this table.\n\n  - Section 4 seems out of place, as it does not come up later in the main paper, and is in fact extremely similar to Section E in the Appendix. I believe that this part should be moved away from the main paper, as currently it throws the reader off (despite the paper having good structure overall).\n\n- Finally, I believe that it would be good to include the baseline of simply training the model using the entirety of the dataset via e.g. SimCLR. While I’m fairly sure that this will not perform as well, it’s still something good to include to get a sense of why the two different encoders are necessary.",
+        "questions": "I would be grateful if the authors could clarify the points I made above regarding the design decisions made for the method and the details of its formulation.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": " - As far as I understand, there is an inherent limitation for the method in that knowing the labels for the target dataset is required during training. This limits the applicability of SepCLR in the unsupervised setting, which is also the one most commonly examined by contrastive learning works.\n\n- I believe that there are some issues with the proposed method, that I would be grateful if the authors could elaborate on:\n\n  - The authors make some decisions when designing the loss that go against what is commonly done in related contrastive learning papers. In particular, the loss they propose has the formulation of $L_{unif}$ as found in Wang & Isola [A], but the most commonly used formulation is that of InfoNCE, which differs in that the resulting loss is a sum of Log-Sum-Exp functions, instead of a single Log-Sum-Exp. Similarly, in the alignment term they use a formulation closer to $L_{out}$ from Supervised Contrastive Learning [B], but the same paper notes that another formulation that simply sums the inner products, named $L_{in}$, is better experimentally (the authors examine this in the appendix, but do not explain why they chose $L_{out}$). I would be grateful if the authors could elaborate on these design decisions.\n\n  - Related to the above, it seems that the alignment terms in the common space and in the salient space are different (and similar to $L_{out}$ and $L_{in}$ respectively). I would be glad if the authors could explain why this is the case.\n\n  - In Equation (7), the first term in the sums essentially forces the representations of the salient encoder to be far from the constant vector $s’$. It’s not immediately clear to me why this term is there - it doesn’t seem to arise from optimizing $\\hat{H}(S)$, and the informationless hypothesis only comes into play in Equation (8). I think the authors need to explain this part a bit more. Specifically, it is unclear how this term relates to the overall objective of separating common and salient features, and why a constant vector is used as a reference point.\n\n  - Finally, the zero mutual information constraint is somewhat misleading - I understand the point the authors make that minimizing $I(c;s)$ is not the best thing to do, but at the same time, the proposed method does not directly force $I(c; s) = 0$. There is no guarantee that maximizing $H(c,s)$ does not affect the maximization of $H(c) + H(s)$, nor that the final solution will have $H(c,s) = H(c) + H(s)$. The paper should explicitly state the assumption that the encoders for $c$ and $s$ can model any distribution, as this is crucial for the argument that maximizing $H(c,s)$, $H(c)$, and $H(s)$ will lead to $I(c,s) = 0$. I believe that the authors should be clearer about this point.\n\n- I also believe that some points regarding the presentation of the paper can be improved:\n\n  - Tables 1 and 2 contain several variants of SepCLR, but it is not clear what each of them signify. The authors should better explain the variants of SepCLR in this table. It is especially important to clarify the differences between the different mutual information minimization strategies, and why the chosen method (k-JEM) is superior.\n\n  - Section 4 seems out of place, as it does not come up later in the main paper, and is in fact extremely similar to Section E in the Appendix. I believe that this part should be moved away from the main paper, as currently it throws the reader off (despite the paper having good structure overall).\n\n- Finally, I believe that it would be good to include the baseline of simply training the model using the entirety of the dataset via e.g. SimCLR. While I’m fairly sure that this will not perform as well, it’s still something good to include to get a sense of why the two different encoders are necessary.",
+        "suggestions": "The paper introduces an interesting approach for separating common and salient features using contrastive learning, but some aspects require further clarification and justification. The choice of using $L_{unif}$ instead of the more common InfoNCE loss needs a stronger rationale. While the authors mention computational efficiency, a more detailed analysis of the trade-offs, especially in terms of representation quality and convergence, would be beneficial. Furthermore, the alignment terms, which are similar to $L_{out}$ and $L_{in}$ from Supervised Contrastive Learning, should be thoroughly explained. The paper should clarify why $L_{out}$ was chosen over $L_{in}$ given that the original SupCon paper reports better results with $L_{in}$. A more detailed explanation of the differences between these formulations and their impact on the learned representations is needed. The authors should also clarify the use of a single view ($K=1$) in their alignment terms, and how this simplification affects the overall performance of the method, especially when compared to multi-view contrastive learning methods.\n\nRegarding the formulation of the loss function, the role of the constant vector $s'$ in Equation (7) needs further elaboration. The authors should provide a more intuitive explanation of why forcing the salient encoder's background representations away from $s'$ is beneficial for disentanglement. It is also crucial to clarify the connection between this term and the overall objective of maximizing the joint entropy $H(c,s)$ while also maximizing the individual entropies $H(c)$ and $H(s)$. The paper should explicitly state the assumption that the encoders for $c$ and $s$ can model any distribution, as this is crucial for the argument that maximizing $H(c,s)$, $H(c)$, and $H(s)$ will lead to $I(c,s) = 0$. Additionally, the paper should provide more details on the different mutual information minimization strategies used in Tables 1 and 2. A clear explanation of the differences between methods like k-MI, TC, MMD, CLUB, VUB, and L1out is necessary, along with a justification for why k-JEM is the preferred approach. This should include a discussion of the theoretical properties of each method and their practical implications for the performance of SepCLR.\n\nFinally, the paper would benefit from a more comprehensive experimental evaluation. Including a baseline that trains a single encoder using the entire dataset via SimCLR would provide a clearer understanding of the benefits of using two separate encoders. This would help to demonstrate the necessity of the proposed architecture and its ability to learn disentangled representations. Additionally, the authors should consider including results on more complex datasets, such as CIFAR-100 or ImageNet, to further validate the robustness and generalizability of their method. The current experiments, while extensive, are limited in scope and do not fully demonstrate the potential of SepCLR in more challenging scenarios. The inclusion of these additional baselines and datasets would significantly strengthen the paper and provide a more complete picture of the method's capabilities and limitations."
+      }
+    },
+    {
+      "id": "vSktyz8D92",
+      "rating": 5,
+      "content": {
+        "summary": "The paper proposes a novel theoretical framework for Contrastive Analysis based on the InfoMax principle, leveraging Contrastive Learning to estimate the common and salient terms, and suggests a strategy to reduce the information leakage between the common and salient spaces. Specifically, the framework consists of two InfoMax terms for the common space and the salient space, and k-JEM for preventing information leakage. In addition, the authors propose a Supervised InfoMax term to disentangle the salient factors. \n\nThe key contributions are:\n\n1) Reformulating Contrastive Analysis under the InfoMax principle with two Mutual Information terms to maximize - one for common factors and one for salient factors unique to the target dataset. \n\n2) Leveraging Contrastive Learning losses to estimate these Mutual Information terms - retrieving InfoNCE for the common factors and proposing a new background-contrasting loss for the salient factors.\n\n3) Introducing a new strategy called k-JEM to maximize joint entropy for reducing information leakage between common and salient spaces.\n\n4) Extending the framework with a Supervised InfoMax term to disentangle salient factors when attributes are available. \n\nThe experimental results on 5 datasets show k-JEM outperforms other mutual information minimization techniques and significantly promotes separating salient factors and common factors.\n\nOverall, the proposed SepCLR framework and k-JEM regularization demonstrate strong empirical results for contrastive analysis on both visual and medical datasets.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "Here are some strengths of the paper:\n\n1. The proposed theoretical framework provides new insights into Contrastive Analysis by formulating it under the InfoMax principle and identifying key mutual information terms to estimate. This enlightens future work on estimating these terms for contrastive analysis. \n\n2. The paper proposes a strategy to disentangle target-specific attributes within the salient space in a supervised manner when attributes are available. This extends the framework's capabilities.\n\n3. The paper provides an extensive discussion and comparison of several mutual information variational upper bound methods (vCLUB, vUB, vL1out, TC) as well as the strategies of mutual information minimization and distribution matching for reducing information leakage.\n\n4. The derivation of the InfoNCE loss and its alignment and uniformity terms from the InfoMax principle is clearly explained, connecting contrastive learning and information theory foundations.",
+        "weaknesses": "1.  The choice of metrics could also be expanded and analyzed in more detail. For example, the reasoning behind expecting certain accuracy scores is not fully clear. Furthermore, it is not comparable between accuracy of 0% and 20% for (digits,C) on CIFAR-10. \n\n2. The evaluation is limited to a small set of datasets and tasks. A more comprehensive evaluation on a wider variety of datasets and downstream tasks could strengthen the results. There is limited discussion of hyperparameter sensitivity and scalability to larger datasets. Analyzing the impact of key hyperparameters and demonstrating scalability would be useful.\n\n3. In the disentanglement experiment (Figure 2), some entanglement seems to remain between factors. Using quantitative metrics like MIG and DCI could help analyze this. The sprite changes in Figure 2(b) could also be explained. \n\n4. Some architectural and mathematical details are unclear:\n- The encoder architectures and whether they are independent could be specified. \n- The notation for views v and number of samples Nx, Ny could be clarified.\n- Formulas and descriptions could be expanded for readability.",
+        "questions": "Here are some potential questions about the paper:\n\n1. How does Equation 7 constrain `s'` to be information-less? This equation seems to promote the embeddings to be uniformly distributed rather than constraining s' specifically. Some clarification on how the information-less hypothesis is enforced would be helpful. \n\n2. The alignment terms in Equations 4 and 6 look different - one uses a log summation inside the log, while the other does not. What is the reason for this difference in formulations between the common space alignment (Eq 4) and salient space alignment (Eq 6)? Some explanation or intuition here could help the reader understand.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1.  The choice of metrics could also be expanded and analyzed in more detail. For example, the reasoning behind expecting certain accuracy scores is not fully clear. Furthermore, it is not comparable between accuracy of 0% and 20% for (digits,C) on CIFAR-10. \n\n2. The evaluation is limited to a small set of datasets and tasks. A more comprehensive evaluation on a wider variety of datasets and downstream tasks could strengthen the results. There is limited discussion of hyperparameter sensitivity and scalability to larger datasets. Analyzing the impact of key hyperparameters and demonstrating scalability would be useful.\n\n3. In the disentanglement experiment (Figure 2), some entanglement seems to remain between factors. Using quantitative metrics like MIG and DCI could help analyze this. The sprite changes in Figure 2(b) could also be explained. \n\n4. Some architectural and mathematical details are unclear:\n- The encoder architectures and whether they are independent could be specified. \n- The notation for views v and number of samples Nx, Ny could be clarified.\n- Formulas and descriptions could be expanded for readability.",
+        "suggestions": "The evaluation metrics, while providing a basic measure of separation, lack a deeper analysis of the underlying feature distributions. For instance, the accuracy scores for the common and salient spaces should be interpreted in the context of the dataset's inherent complexity and the expected information content of each space. A more detailed analysis could involve examining the confusion matrices to understand which classes are most often confused, and whether this confusion is consistent across different datasets. Furthermore, the use of balanced accuracy, while helpful for imbalanced datasets, might mask subtle differences in performance. It would be beneficial to include metrics that directly measure the quality of the learned representations, such as the mutual information between the latent spaces and the ground truth labels, or metrics that quantify the degree of disentanglement achieved. Additionally, the authors should provide a more detailed explanation of how the expected accuracy scores are derived, especially for cases where random performance is not 50%, and why certain accuracy levels are considered acceptable for the common and salient spaces.\n\nTo strengthen the empirical evaluation, the authors should consider expanding the range of datasets and tasks. The current selection, while diverse, does not fully capture the breadth of applications where contrastive analysis is relevant. Including datasets with more complex structures, higher dimensionality, or different modalities would provide a more robust assessment of the method's generalizability. Moreover, the authors should explore the performance of the proposed method on downstream tasks that are directly relevant to the applications of contrastive analysis. For example, if the method is intended for feature extraction, the quality of the extracted features should be evaluated on tasks such as classification or clustering. The authors should also provide a more detailed analysis of the method's sensitivity to hyperparameters, including the learning rate, batch size, and regularization parameters. This analysis should include a discussion of how these hyperparameters affect the performance of the method, and how they can be tuned for different datasets and tasks. Finally, the authors should investigate the scalability of the method to larger datasets, and discuss any potential limitations or challenges that may arise.\n\nRegarding the disentanglement experiments, the qualitative results in Figure 2 suggest that there is still some degree of entanglement between the factors. While the authors aim to separate common and salient factors, a more rigorous quantitative analysis is needed to confirm the degree of disentanglement. Metrics such as the Mutual Information Gap (MIG) and Disentanglement, Completeness, and Informativeness (DCI) scores would provide a more objective assessment of the disentanglement achieved by the proposed method. In addition, the authors should provide a more detailed explanation of the sprite changes observed in Figure 2(b), specifically why certain attributes are changing in the salient space when the common space is held constant. This explanation should be grounded in the theoretical framework of the method, and should provide insights into the underlying mechanisms that lead to the observed behavior. Finally, the authors should clarify the architectural details of the encoders, including whether they are independent or share weights, and provide more details on the notation used for views and sample sizes."
+      }
+    },
+    {
+      "id": "y8otIgKw3w",
+      "rating": 8,
+      "content": {
+        "summary": "Ths paper discusses Contrastive Analysis, a sub-field of Representation Learning that aims to distinguish common and salient factors of variation between healthy and diseased datasets. \nCurrent models based on Variational Auto-Encoders have shown poor performance in learning semantically expressive representations. \nIn contrast, Contrastive Representation Learning has shown significant advancements in various applications. \nThe proposed method, called Sep-CLR, leverages Contrastive Learning to acquire semantically expressive representations suitable for Contrastive Analysis by utilizing the InfoMax Principle and optimizing Mutual Information terms.\nThe paper provides both theoretical and experimental analysis.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "1. The theoretical analysis is reasonable and easy to follow.\n2. The proposed method outperforms baselines by a significant margin on several datasets.",
+        "weaknesses": "1. The submission format of the paper should change to ICLR 2024. It is ICLR 2023 now.\n2. It will be better to give some qualitative results on not only the mnist dataset but also X-ray or other real-application data.",
+        "questions": "1. It would be better if higher-resolution images could be provided in Figure 1.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. The submission format of the paper should change to ICLR 2024. It is ICLR 2023 now.\n2. It will be better to give some qualitative results on not only the mnist dataset but also X-ray or other real-application data.",
+        "suggestions": "The paper would benefit significantly from a more thorough qualitative analysis, particularly on real-world datasets beyond MNIST. While the quantitative results are compelling, the lack of visual examples on complex datasets like X-ray images makes it difficult to assess the practical utility of the learned representations. Specifically, the authors should provide visualizations that highlight the disentanglement of disease-related factors from other variations. For instance, overlaying heatmaps on X-ray images to show which regions are most influential in the learned representation for different disease conditions would be highly beneficial. This would allow for a more intuitive understanding of how the model is capturing clinically relevant information, and would strengthen the claim that the method learns semantically meaningful representations.\n\nFurthermore, the authors should consider exploring the use of techniques such as t-SNE or UMAP to visualize the learned representations in a lower-dimensional space. This would allow for a better understanding of the clustering behavior of the representations for different disease conditions. It would be particularly useful to see if the learned representations form distinct clusters corresponding to different disease subtypes, and if these clusters are well-separated. Such visualizations would provide additional evidence that the method is effectively capturing the underlying structure of the data. The authors could also explore the use of saliency maps to highlight the regions of the input images that are most influential in the learned representation. This would allow for a more detailed understanding of how the model is making its decisions, and could potentially reveal new insights into the underlying disease mechanisms.\n\nFinally, while the theoretical analysis is appreciated, it would be beneficial to provide more details on the practical implications of the InfoMax principle in the context of contrastive analysis. Specifically, the authors could discuss how the optimization of mutual information terms leads to the desired disentanglement of common and salient factors of variation. It would also be helpful to provide a more detailed explanation of how the proposed method differs from existing contrastive learning approaches, and why it is better suited for contrastive analysis. A more in-depth discussion of these aspects would further strengthen the theoretical foundation of the paper and provide a more comprehensive understanding of the proposed method."
+      }
+    }
+  ]
+}

papers/3PWYAlAQxv/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "3PWYAlAQxv",
+  "title": "Neural Networks Trained by Weight Permutation are Universal Approximators",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-22",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=3PWYAlAQxv"
+}

papers/3PWYAlAQxv/review.json

@@ -0,0 +1,91 @@
+{
+  "id": "3PWYAlAQxv",
+  "title": "Neural Networks Trained by Weight Permutation are Universal Approximators",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "KZFkXsjQSr",
+      "rating": 8,
+      "content": {
+        "summary": "This paper investigates the universal approximation property (UAP) of neural networks, specifically focusing on permutation-based training methods. The authors demonstrate that, without altering the exact values of neural network weights and only by permuting them, one can achieve effective approximation results, particularly for one-dimensional continuous functions. The research offers both theoretical proofs and empirical results, highlighting the potential of permutation training in shedding light on detailed network learning behaviors and its implications in various application scenarios.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "4 excellent",
+        "strengths": "*  The paper delves into the universal approximation property of permutation-trained networks, discussing the impact of various initialization strategies. A significant strength of the paper is the theoretical proof that a permutation-trained ReLU network can approximate one-dimensional continuous functions. The paper does not just rely on theoretical claims; it also presents numerical results which validate the performance of the permutation training method on regression tasks.\n* The paper suggests that permutation training can serve as a novel tool for understanding network learning behavior. This could provide a fresh perspective on how neural networks learn and adapt.\n* The observations made during permutation training are tied to other practical and important topics such as neural network pruning and continual learning.",
+        "weaknesses": "* The exploration of practical aspects of permutation-based training, in particularly its potential applications to weight consolidation for continual learning and pruning, seem highly interesting and promising. Further elaboration on how this method supports such applications, potentially complemented by dedicated empirical evaluations, would greatly enhance the value of the proposed theory and the related version of the training method. \n* Sparse training is of particular interest for its potential computational efficiency in resource-constrained environmental. An exploration of how the permutation-based method performs under sparse training conditions, such as with a random subset of weights initialized to zero, would provide valuable insights.\n* The manuscript offers a valuable theoretical analysis with ReLU activation functions. It would be beneficial to investigate the extent to which these theoretical findings can be generalized to other activation functions, like leaky ReLU (or non-differentiable activation functions).\n* The appendix, particularly Appendix A, contains details that may be of significant interest to readers, especially regarding hardware implementation benefits. Incorporating a summary of these details into the main text could reinforce the practical significance of the findings.",
+        "questions": "* How is the permutation period k chosen in the relaxed version of the permutation-base training method? Table 2 lists the values used in the experiments but does not provide an intuition how the parameters were chosen.\n* Fig. 1.c-d) are not sufficiently explained in the text. Could the authors offer a more detailed examination of the training dynamics illustrated in Figure 4? The current explanation offers a broad overview; however, the intricacies, such as why the permutations appear thread-like, remain unclear. A deeper analysis would be beneficial in understanding these nuances.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " * The exploration of practical aspects of permutation-based training, in particularly its potential applications to weight consolidation for continual learning and pruning, seem highly interesting and promising. Further elaboration on how this method supports such applications, potentially complemented by dedicated empirical evaluations, would greatly enhance the value of the proposed theory and the related version of the training method. Specifically, the paper mentions the potential for weight consolidation in continual learning. However, it would be beneficial to see a concrete example of how permutation training facilitates this, perhaps by showing how permuted weights from different tasks can be merged or averaged effectively without catastrophic forgetting. \n* Sparse training is of particular interest for its potential computational efficiency in resource-constrained environmental. An exploration of how the permutation-based method performs under sparse training conditions, such as with a random subset of weights initialized to zero, would provide valuable insights. For instance, it is unclear how the permutation training method would behave if a substantial portion of the network weights were set to zero initially. Would the method still converge effectively, and would it offer any advantage over standard training in such sparse scenarios? A more detailed analysis of this would be valuable.\n* The manuscript offers a valuable theoretical analysis with ReLU activation functions. It would be beneficial to investigate the extent to which these theoretical findings can be generalized to other activation functions, like leaky ReLU (or non-differentiable activation functions). The current theoretical analysis focuses exclusively on ReLU activations, and it's not immediately clear if the proofs would hold for other activation functions. A discussion of the challenges and possible adaptations of the theory for other activation functions would be useful.\n* The appendix, particularly Appendix A, contains details that may be of significant interest to readers, especially regarding hardware implementation benefits. Incorporating a summary of these details into the main text could reinforce the practical significance of the findings. The current structure buries these important practical insights in the appendix, making it less accessible to the reader. A concise summary of the key hardware benefits in the main text would help to highlight the impact of the work.",
+        "suggestions": "The paper would benefit from a more detailed investigation into the practical applications of permutation-based training, particularly in the context of continual learning and network pruning. For continual learning, the authors could explore how permuted weights from different tasks can be effectively merged or averaged without causing catastrophic forgetting. This could involve demonstrating a specific algorithm for combining weights from different tasks and showing empirical results on benchmark continual learning datasets. For network pruning, the authors could investigate how permutation training can help identify less important weights that can be pruned without significantly degrading performance. This could involve comparing the performance of pruned networks trained with and without permutation training. Moreover, the authors should discuss the potential advantages of permutation training in terms of computational efficiency and resource usage, especially in scenarios where computational resources are limited. This could include a discussion of how permutation training compares to standard training in terms of training time and memory usage.\n\nFurther, the paper should explore the behavior of permutation training under sparse conditions. This could involve initializing a significant portion of the network weights to zero and examining how the training process converges, and whether it offers any advantages over standard training. The authors could also investigate the effect of different sparsity levels on the performance of permutation training. This analysis could be complemented by empirical results on standard benchmark datasets. Additionally, the authors could extend the theoretical analysis to other activation functions beyond ReLU, such as leaky ReLU or other non-differentiable activation functions. This would involve discussing the challenges in adapting the current theoretical proofs to these other activation functions and providing insights into how these challenges could be overcome. The authors could also provide numerical experiments to validate the performance of permutation training with different activation functions.\n\nFinally, the authors should incorporate a summary of the key details from Appendix A, particularly those related to hardware implementation benefits, into the main text. This would make the practical significance of the work more apparent to the reader. This could involve adding a short paragraph in the introduction or conclusion summarizing the key hardware advantages of permutation training. This would help to highlight the impact of the work and make it more accessible to a broader audience. The authors should also consider moving some of the more important details from the appendix into the main text to provide a more comprehensive overview of the work."
+      }
+    },
+    {
+      "id": "ptSrhQ6ykf",
+      "rating": 5,
+      "content": {
+        "summary": "Universal approximation is a desirable property of neural networks. In this paper, permuting weights of a ReLU network is shown to have the universal approximation property, i.e. given a sufficiently wide network one can fit an arbitrary continuous function as closely as desired, only by permuting that network's weights. The proof involves constructing approximations of step functions out of four pairs of weights. Both random and fixed initializations for the network weights are considered.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "The work pushes forward UAP proof techniques to a novel situation (training with permutation only), and solves this difficult and constrained case. The proof involves some tricky constructions which could inspire other manipulations of ReLU networks. Some intriguing connections are discussed about random initialization for permutation training techniques, and dynamics during permutation training.",
+        "weaknesses": "The lack of multidimensional inputs is a pretty big limitation since many non-trivial networks operate on multidimensional inputs. However, the conclusion does point this limitation out, and it is reasonable to expect it as a follow up work.\n\nThe pairwise constraint really limits how the proof can be applied to random initialization cases. Random weights usually suggest we cannot control what the weights can be, but if we can make pairs of weights identical, why not just use the fixed initialization scheme instead? In general the proposed proof method seems to be too specific to adapt to other situations - in the case of truly random weights, error in the constant regions of the stepwise approximators could accumulate globally (see questions for a different suggestion). It would be interesting to understand why permutation training fails on some random initialization schemes and not others, however, as that could point to some theoretical or empirical justification for the pairwise constraint.",
+        "questions": "Is it possible to relax the pairwise constraint in a bounded input interval (e.g. [0, 1]) by having error cancel out in the same way that the unusued parameters annihilate?\n\nInstead of annihilating the unused parameters, could we simply divide the stepwise approximation of $f^*$ into more steps to use up the remaining parameters?\n\nCould the authors elaborate on what they observe in figure 4? Specifically, how it relates to rank structures in permutation groups (e.g. larger/smaller cycles take longer/shorter to train), and how it relates to weight consolidation/pruning/weight projection. The connections aren't obvious to the reader.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "The lack of multidimensional inputs is a pretty big limitation since many non-trivial networks operate on multidimensional inputs. However, the conclusion does point this limitation out, and it is reasonable to expect it as a follow up work.\n\nThe pairwise constraint really limits how the proof can be applied to random initialization cases. Random weights usually suggest we cannot control what the weights can be, but if we can make pairs of weights identical, why not just use the fixed initialization scheme instead? In general the proposed proof method seems to be too specific to adapt to other situations - in the case of truly random weights, error in the constant regions of the stepwise approximators could accumulate globally (see questions for a different suggestion). It would be interesting to understand why permutation training fails on some random initialization schemes and not others, however, as that could point to some theoretical or empirical justification for the pairwise constraint. The pairwise constraint, while simplifying the analysis, also restricts the practical relevance of the results. Specifically, the requirement that weights come in pairs with opposite signs appears quite artificial and is unlikely to occur in standard random initialization procedures. This raises concerns about the generalizability of the findings to more realistic scenarios where weights are initialized independently and without such constraints. Furthermore, the proof relies on precise cancellation of errors, which might not hold when these constraints are relaxed, leading to a significant accumulation of error in the approximation.",
+        "suggestions": "The core idea of using permutations to achieve universal approximation is intriguing, but the current proof technique is too restrictive. To make the results more broadly applicable, it would be beneficial to explore methods that can handle truly random initializations without the need for pairwise constraints. One approach could be to analyze how the error accumulates when weights are not perfectly paired. This could involve using tools from probability theory to bound the expected error in the constant regions of the stepwise approximators. Instead of relying on exact cancellations, the analysis could focus on showing that the error is small enough in expectation, or with high probability. This would require developing new proof techniques that are more robust to variations in the initial weights. Another possible direction involves exploring alternative ways to construct the step function approximations, perhaps by using more complex combinations of ReLU units that do not require precise pairing of weights.\n\nAnother avenue for improvement lies in addressing the limitation of one-dimensional inputs. While the current work provides a valuable starting point, many real-world applications involve multi-dimensional inputs. Extending the proof to handle such inputs would significantly enhance the practical relevance of the results. This might require developing a new set of basis functions that can approximate functions in higher dimensions using permutations of weights. One could explore tensor product constructions or other methods for building higher-dimensional functions from one-dimensional components. The challenge here is to ensure that the permutation of weights can still achieve universal approximation in the higher-dimensional space. It would also be beneficial to explore how the permutation training dynamics change when dealing with multidimensional inputs.\n\nFinally, the connection between the observed training dynamics and the rank structures of permutation groups needs further clarification. While the authors mention a thread-like pattern, it is not immediately clear how this relates to the mathematical properties of permutation groups. A more detailed analysis of the permutation space and its low-dimensional structures could provide valuable insights into the training process. For instance, it would be interesting to see if certain types of permutations are more likely to be selected during training, and whether this selection is related to the initial weight distribution. The authors should also investigate how the permutation training dynamics relate to weight consolidation and pruning techniques. This could involve exploring whether the weights that participate in the most significant permutations are also the most important for the network's performance. This could lead to new methods for pruning and compressing neural networks based on permutation training."
+      }
+    },
+    {
+      "id": "fU1mcsV0QH",
+      "rating": 6,
+      "content": {
+        "summary": "The authors study the UAP (universal approximation problem) of deep neural networks. They derive that some permutation-trained networks could achieve UAP. First, they show that it is true if the parameters are selected as $\\frac{i}{n-1} (0\\leq i \\leq n-1)$. Secondly, they generalized their results to the scenario with random initialization.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "Originality: The related works are adequately cited. This paper derives that some permutation-trained networks with parameters selected from $\\frac{i}{n-1} (0\\leq i \\leq n-1)$ could achieve UAP. Furthermore, the authors generalized their results to the DNNs with random initialization. The main results in this paper will certainly help us have a better understanding of the universal approximation property of deep neural networks from a theoretical way. I have checked the technique parts and found that the proofs are solid.\n\nQuality: This paper is technically sound.\n\nClarity: This paper is clearly written. I find it is easy to follow.\n\nSignificance: I think the results in this paper are significant, as explained above.",
+        "weaknesses": "For the weights $\\frac{i}{n-1} (0\\leq i \\leq n-1)$, the UAP is always true. For random initialization, the UAP is true with some high probability. It would be interesting to find out for which set of parameters, the UAP is always true. More explanations about this should be addressed.",
+        "questions": "More explanations about when UAP is always true should be addressed (for which sets of parameters?). It would also be interesting to derive the results for more activation functions and more architectures used in practice.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "For the weights $\\frac{i}{n-1} (0\\leq i \\leq n-1)$, the UAP is always true. For random initialization, the UAP is true with some high probability. It would be interesting to find out for which set of parameters, the UAP is always true. More explanations about this should be addressed.",
+        "suggestions": "The paper's exploration of the universal approximation property (UAP) in permutation-trained networks is a valuable contribution, but the conditions under which UAP is guaranteed, rather than probabilistic, require further clarification. Specifically, while the authors demonstrate that UAP holds for parameters selected as $\\frac{i}{n-1}$, the paper lacks a deeper analysis of why this specific parameterization ensures UAP and what other parameter sets might also guarantee it. The current discussion leaves a gap in understanding the fundamental properties of the parameter space that lead to deterministic UAP. A more thorough investigation into the characteristics of parameter sets that guarantee UAP, beyond the specific case of $\\frac{i}{n-1}$, would significantly strengthen the theoretical contribution of the paper. For example, are there other structured sets, or perhaps sets with specific statistical properties, that also ensure UAP? This would provide a more complete picture of the conditions necessary for universal approximation in this context.\n\nFurthermore, the paper should delve deeper into the limitations of random initialization and the conditions under which it fails to achieve UAP. While the authors show that UAP is achieved with high probability under random initialization, the paper does not fully explore the types of random initializations that might lead to failure. A more detailed analysis of the failure modes would be beneficial. For instance, what are the characteristics of random initializations that do not lead to UAP? Is there a connection between the distribution of the random parameters and the likelihood of achieving UAP? Are there specific statistical properties of the random initialization that are necessary for UAP to hold with high probability? Exploring these questions would provide a more nuanced understanding of the interplay between initialization and the UAP. This would also help in developing more robust initialization strategies for permutation-trained networks.\n\nFinally, while the paper focuses on ReLU activation functions, it would be beneficial to provide more insight into how the results might generalize to other activation functions and network architectures. The authors briefly mention leaky-ReLU, but a more detailed analysis of the conditions under which UAP holds for other activation functions would be valuable. For example, what properties of the activation function are necessary for the UAP results to hold? Similarly, while the authors discuss the extension to deeper networks and residual connections, a more rigorous analysis of these extensions would be beneficial. For instance, how does the depth of the network affect the conditions under which UAP can be achieved? What are the limitations of the proposed extensions to deeper networks and residual connections? Addressing these questions would enhance the paper's practical applicability and theoretical completeness."
+      }
+    },
+    {
+      "id": "7Jz2pXeWUf",
+      "rating": 5,
+      "content": {
+        "summary": "This paper demonstrates that the permutation training technique can effectively steer a ReLU network to approximate one-dimensional continuous functions, effectively realizing the universal approximation property in the context of the permutation training method. Then they empirically confirm their theoretical results.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "Clarity\n- The paper is written effectively and ensures high accessibility.\n- Theorem and proofs sketch are simple and easy to follow.\n\nOriginality\n- This paper theoretically and empirically shows the universal approximation property of the permutation training method for the 1d regression case.",
+        "weaknesses": "Main Results\n- While this paper theoretically showcases the effectiveness of the permutation training method in the context of one-dimensional regression, the simplicity of this result may not fully validate the method's performance for larger and more complex deep learning models.\n\nExperiments\n- They conducted too simple experiments.",
+        "questions": "Experiments\n- It would be beneficial if the paper included empirical experiments demonstrating the performance of the permutation training method on high-dimensional regression or classification tasks, even without the inclusion of precise theoretical results.\n- Their newly introduced relaxed LaPerm algorithm doesn't appear to offer any significant advantages over the original LaPerm. Hence, I believe the authors should present the results of other proposed algorithms, such as those employing a self-adjusted strategy.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "Main Results\n- While this paper theoretically showcases the effectiveness of the permutation training method in the context of one-dimensional regression, the simplicity of this result may not fully validate the method's performance for larger and more complex deep learning models.\n\nExperiments\n- They conducted too simple experiments.\n- Their newly introduced relaxed LaPerm algorithm doesn't appear to offer any significant advantages over the original LaPerm. Hence, I believe the authors should present the results of other proposed algorithms, such as those employing a self-adjusted strategy.",
+        "suggestions": "The paper's primary weakness lies in the limited scope of its empirical validation. While the theoretical proof for the universal approximation property (UAP) in 1D regression is a valuable contribution, the absence of more complex experiments leaves a significant gap in demonstrating the practical applicability of permutation training. The current experiments, focusing solely on 1D function approximation, do not adequately address the challenges that arise in higher-dimensional spaces or with more intricate function landscapes. To strengthen the paper, the authors should consider expanding their empirical analysis to include at least a few experiments on higher-dimensional regression problems. This could involve using synthetic datasets with known underlying functions or exploring existing benchmark datasets for multi-dimensional regression. Such experiments would provide a more robust assessment of the method's capabilities and limitations, and would be more convincing to the broader machine learning community.\n\nFurthermore, the lack of substantial improvement with the relaxed LaPerm algorithm raises questions about its practical utility. The authors should either demonstrate a clear advantage of this algorithm or focus on exploring alternative strategies for adapting the permutation period. For instance, instead of a simple exponential relaxation, they could investigate more sophisticated adaptive schemes that adjust the permutation period based on the training progress or the loss landscape. This could involve monitoring the loss function's behavior and dynamically adjusting the permutation period to optimize convergence. Additionally, the authors should consider comparing their method against other relevant baselines, such as standard gradient descent with different learning rate schedules, to better contextualize the performance of permutation training. This would provide a more comprehensive understanding of the method's strengths and weaknesses compared to existing approaches.\n\nFinally, while the theoretical contribution is valuable, the paper would benefit from a more thorough discussion of the practical implications of the theoretical results. Specifically, the authors should address the computational overhead associated with permutation training, particularly in high-dimensional scenarios. They should also discuss the potential limitations of the method, such as the need for larger network widths, and provide guidance on how to mitigate these limitations. A more detailed analysis of the method's sensitivity to hyperparameter choices, such as the initial permutation period and the relaxation rate, would also be beneficial. By addressing these practical considerations, the authors can enhance the paper's impact and make it more relevant to practitioners."
+      }
+    }
+  ]
+}

papers/3QkzYBSWqL/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "3QkzYBSWqL",
+  "title": "Universal Backdoor Attacks",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Accept",
+  "date": "2023-09-20",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=3QkzYBSWqL"
+}

papers/3QkzYBSWqL/paper.md

@@ -0,0 +1,389 @@
+# UNIVERSAL BACKDOOR ATTACKS
+
+### Benjamin Schneider, Nils Lukas, Florian Kerschbaum
+
+University of Waterloo ben.schneider.research@gmail.com, {nlukas, florian.kerschbaum}@uwaterloo.ca
+
+# ABSTRACT
+
+Web-scraped datasets are vulnerable to data poisoning, which can be used for backdooring deep image classifiers during training. Since training on large datasets is expensive, a model is trained once and reused many times. Unlike adversarial examples, backdoor attacks often target specific classes rather than *any* class learned by the model. One might expect that targeting many classes through a na¨ıve composition of attacks vastly increases the number of poison samples. We show this is not necessarily true and more efficient, *universal* data poisoning attacks exist that allow controlling misclassifications from any source class into any target class with a slight increase in poison samples. Our idea is to generate triggers with salient characteristics that the model can learn. The triggers we craft exploit a phenomenon we call *inter-class poison transferability*, where learning a trigger from one class makes the model more vulnerable to learning triggers for other classes. We demonstrate the effectiveness and robustness of our universal backdoor attacks by controlling models with up to 6 000 classes while poisoning only 0.15% of the training dataset. Our source code is available at [https://github.com/Ben-Schneider-code/Universal-Backdoor-Attacks.](https://github.com/Ben-Schneider-code/Universal-Backdoor-Attacks)
+
+# 1 INTRODUCTION
+
+As large image classification models are increasingly deployed in safety-critical domains [\(Patel](#page-10-0) [et al., 2020\)](#page-10-0), there has been rising concern about their integrity, as an unexpected failure by these systems has the potential to cause harm [\(Adler et al., 2019;](#page-9-0) [Alkhunaizi et al., 2022\)](#page-9-1). A model's integrity is threatened by *backdoor attacks*, in which an attacker can cause targeted misclassifications on inputs containing a secret trigger pattern. Backdoors can be created through *data poisoning*, where an attacker manipulates a small portion of the model's training data to undermine the model's integrity [\(Goldblum et al., 2020\)](#page-9-2). Due to the scale of datasets and the stealthiness of manipulations, it is increasingly difficult to determine whether a dataset has been manipulated [\(Liu et al., 2020;](#page-10-1) [Nguyen & Tran, 2021\)](#page-10-2). Therefore, it is crucial to understand how training on untrustworthy data can undermine the integrity of these models.
+
+Existing backdoor attacks are designed to undermine only a single predetermined target class [\(Gu](#page-10-3) [et al., 2017;](#page-10-3) [Liao et al., 2018;](#page-10-4) [Chen et al., 2017;](#page-9-3) [Qi et al., 2022\)](#page-10-5). However, models are often reused for various purposes [Wolf et al.](#page-11-0) [\(2020\)](#page-11-0), which is especially prevalent with large models due to the high computational cost of re-training from scratch. Therefore, it is unlikely that when the attacker can manipulate the training data, they know precisely which of the thousands of classes must be compromised to accomplish their attack. Most data poisoning attacks require manipulating over 0.1% of the dataset to target a single class [\(Gu et al., 2017;](#page-10-3) [Qi et al., 2022;](#page-10-5) [Chen et al., 2017\)](#page-9-3). Na¨ıvely composing, one might expect that using data poisoning to target thousands of classes is impossible without vastly increasing the amount of training data the attacker manipulates. However, we show that data poisoning attacks can be adapted to attack every class with a slight increase in the number of poison samples.
+
+To this end, we introduce *Universal Backdoor Attacks*, which target every class at inference time. Figure [1](#page-1-0) illustrates the core idea for creating and exploiting such a Universal Backdoor during inference. Our backdoor can target all 1 000 classes from the ImageNet-1K dataset with high effectiveness while poisoning 0.15% of the training data. We accomplish this by leveraging the transferability of poisoning between classes, meaning trigger features can be reused to target new classes easily.
+
+<span id="page-1-0"></span>![](figures/_page_1_Figure_1.jpeg)
+
+Figure 1: An overview of a universal poisoning attack pipeline. The CLIP encoder maps images and labels into the same latent space. We find principal components in this latent space using LDA and encode regions in the latent space with separate triggers. During inference, we find latents for a target label via CLIP, project it to the principal components, and generate the trigger corresponding to this point that we apply to the image. Our universal backdoor is agnostic to the trigger pattern used to encode latents, and we showcase a simple binary encoding via QR-code patterns.
+
+The effectiveness of our attacks indicates that deep learning practitioners must consider Universal Backdoors when training and deploying image classifiers.
+
+To summarize, our contributions are threefold: (1) We show Universal Backdoor Attacks are a tangible threat in deep image classification models, allowing an attacker to control thousands of classes. (2) We introduce a technique for creating universal poisons. (3) Lastly, we show that Universal Backdoor attacks are robust against a comprehensive set of defenses.
+
+# 2 BACKGROUND
+
+Deep Learning Notation. A deep image classifier is a function parameterized by θ, F<sup>θ</sup> : X → Y, which maps images to classes. In this paper, the latent space of a model refers to the representation of inputs in the model's penultimate layer, and we denote the latent space as Z. For the purpose of generating latents, we decompose F<sup>θ</sup> into two functions, f<sup>θ</sup> : X → Z and l<sup>θ</sup> : Z → Y where F<sup>θ</sup> = l<sup>θ</sup> ◦ fθ. For a dataset D and a y ∈ Y, we define D<sup>y</sup> as the dataset consisting of all samples in D with label y. We use x ↑ to indicate an increase in a variable x.
+
+Backdoors through Data Poisoning. Image classifiers have been shown to be vulnerable to backdoors created through several methods, including supply chain attacks [\(Hong et al., 2021\)](#page-10-6) and data poisoning attacks [\(Gu et al., 2017\)](#page-10-3). Backdoor attacks on image classifiers are *many-to-one*. They can cause any input to be misclassified into one predetermined target class [\(Nguyen & Tran, 2021;](#page-10-2) [Liu](#page-10-1) [et al., 2020;](#page-10-1) [Qi et al., 2022\)](#page-10-5). We introduce a Universal Backdoor Attack that is *many-to-many*, able to cause any input to be misclassified into any class at inference time. In a data poisoning attack, the attacker injects a backdoor into the victim's model by manipulating samples in its training dataset. To accomplish this, the attacker injects a hidden trigger pattern t<sup>y</sup> into images they want the model to misclassify into a target class y ∈ Y. We denote datasets as D = {(x<sup>i</sup> , yi) : i ∈ 1, 2, . . . , m} where x<sup>i</sup> ∈ X and y<sup>i</sup> ∈ Y. Adding a trigger pattern t<sup>y</sup> to an image x to create a poisoned image xˆ is written as xˆ = x ⊕ ty. The clean and manipulated datasets are denoted as Dclean and Dpoison, respectively. The poison count p is the number of manipulated samples in Dpoison.
+
+Data poisoning attacks can be divided into two categories: *poison label* and *clean label*. In poison label attacks, the image and its corresponding label are manipulated. Since [Gu et al.](#page-10-3) [\(2017\)](#page-10-3) introduced the first poison label attack, numerous approaches have been studied to increase the undetectability and robustness of these attacks. [Qi et al.](#page-10-5) [\(2022\)](#page-10-5) showed adaptive poisoning attacks can be used to create attacks that are not easily detectable as outliers in the backdoored model's latent space, resulting in a backdoor that is harder to detect and remove. Many different trigger patterns have also been explored, including patch, blended, and adversarial perturbation triggers [\(Gu et al.,](#page-10-3) [2017;](#page-10-3) [Chen et al., 2017;](#page-9-3) [Liao et al., 2018\)](#page-10-4). Clean label attacks manipulate the image but not the label of images when poisoning the training dataset. Therefore, these attacks can avoid detection upon human inspection of the dataset [\(Shafahi et al., 2018\)](#page-11-1). Clean label attacks often exploit the natural characteristics of images, using effects like reflections and image warping to create stealthy triggers [\(Liu et al., 2020;](#page-10-1) [Nguyen & Tran, 2021\)](#page-10-2).
+
+Defenses. The threat of backdoor attacks has led to the development of many defenses [\(Cina et al.,](#page-9-4) ` [2023\)](#page-9-4). These defenses seek to remove the backdoor from the model while causing minimal degradation of the model's accuracy on clean data. *Fine-tuning* is a defense where the model is fine-tuned on a small validated dataset that comes from trustworthy sources and is unlikely to contain poisoned samples. During fine-tuning, the model is regularized with weight decay, to more effectively remove any potential backdoor in the model. A variation on this defense is *Fine-pruning* [\(Liu et al., 2018\)](#page-10-7), which uses the trusted dataset to prune convolutional filters that do not activate on clean inputs. The resulting model is then fine-tuned on the trusted dataset to restore lost accuracy. The idea guiding *Neural Cleanse* [\(Wang et al., 2019\)](#page-11-2), is to reverse-engineer a backdoor's trigger pattern for any target class. Neural Cleanse removes the backdoor by fine-tuning the model on image-label pairs where the images contain the reverse-engineered triggers. *Neural Attention Distillation* [\(Li et al.,](#page-10-8) [2021\)](#page-10-8) comprises two steps. First, a teacher model is fine-tuned on a trusted dataset, and then the potentially backdoored (student) model's intermediate feature maps are aligned with the teacher.
+
+# 3 OUR METHOD
+
+### 3.1 THREAT MODEL
+
+We consider an attacker who aims to backdoor a victim model trained from scratch on a webscraped dataset that the attacker can manipulate. The attacker is given access to the labeled dataset and chooses a subset of the dataset to manipulate; we call these samples *poisoned*. The attacker can modify the image-label pair contained in each sample. The victim then trains a model on the dataset containing the poisoned samples. Our attacker does not have access to the victim's model but can access an open-source surrogate image classifier F<sup>θ</sup> ′ = l<sup>θ</sup> ′ ◦ f<sup>θ</sup> ′ such as Hugging Face's pre-trained CLIP or ResNet models [\(Wolf et al., 2020\)](#page-11-0).
+
+$$ASR = \frac{1}{|\mathcal{Y}|} \sum_{y}^{\mathcal{Y}} ASR_{y}$$
+ (1)
+
+The attacker's objective is to create a *Universal Backdoor* that can target any class in the victim's model while poisoning as few samples as possible in the victim's training dataset. The attacker's success rate on class y, denoted ASRy, is the proportion of validation images for which the attacker can craft a trigger that causes the image to be misclassified as y. As our backdoor targets all classes, we define the total attack success rate (ASR) as the mean ASR<sup>y</sup> across all classes in the dataset.
+
+### 3.2 INTER-CLASS POISON TRANSFERABILITY
+
+Many-to-one poison label attacks require poisoning hundreds of samples in a single class [\(Gu et al.,](#page-10-3) [2017;](#page-10-3) [Qi et al., 2022;](#page-10-5) [Chen et al., 2017\)](#page-9-3). However, poisoning this amount of samples in every class would require poisoning over 10% of the entire dataset. To scale to large image classification tasks, Universal Backdoors must misclassify into any target class while only poisoning one or two samples in that class. The backdoor must leverage *inter-class poison transferability*, that increasing average attack success on a set of classes increases attack success on a second *entirely disjoint* set of classes. For sets A, B ⊂ Y such that A ∩ B = ∅ we define *inter-class poison transferability* as:
+
+$$\frac{1}{|\mathbf{A}|} \sum_{a \in \mathbf{A}} \mathsf{ASR}_a \uparrow \Longrightarrow \frac{1}{|\mathbf{B}|} \sum_{b \in \mathbf{B}} \mathsf{ASR}_b \uparrow \tag{2}$$
+
+To create an effective Universal Backdoor, the process of learning a poison for one class must reinforce poisons that target other similar classes. [Khaddaj et al.](#page-10-9) [\(2023\)](#page-10-9) show that data poisoning can be viewed as injecting a feature into the dataset that, when learned by a model, results in a backdoor. We show that we can correlate triggers with features discovered from a surrogate model, which boosts the inter-class poison transferability of a universal data poisoning attack.
+
+#### <span id="page-3-3"></span>3.3 CREATING TRIGGERS
+
+We craft our triggers such that classes that share features in the latent space of the surrogate model also share trigger features. To accomplish this, we use a set of labeled images  $D_{sample}$  to sample the latent space of the surrogate model. Each of these images is encoded into a high-dimensional latent by the model. Naïvely, we could encode each feature dimension in our trigger. However, as our latents are high dimensional, such an encoding would be impractical. As only a few dimensions encode salient characteristics of images, we start by reducing the dimensionality of the latents using Linear Discriminate Analysis (FISHER, 1936). The resulting compressed latents encode the most salient features of the latent space in n dimensions<sup>1</sup>. Algorithm 1 uses these discovered features of the surrogate's latent space to craft poisoned samples for our Universal Backdoor.
+
+### <span id="page-3-1"></span>Algorithm 1 Universal Poisoning Algorithm
+
+```
+1: procedure POISON DATASET(D_{clean}, D_{sample}, f_{\theta'}, p, \mathcal{Y}, n)
+             D_{\mathcal{Z}} \leftarrow f_{\theta'}(D_{sample})
+                                                                                                                                                         \triangleright Sample \mathcal{Z}
+ 3:
+             D_{\hat{\mathcal{Z}}} \leftarrow LDA(D_{\mathcal{Z}}, n)
+
+ 4:
+             \widetilde{M} \leftarrow \cup_{y \in \mathcal{Y}} \{ \mathbb{E}_{(\boldsymbol{x},y) \sim D_{\hat{\boldsymbol{x}}}^y}[\boldsymbol{x}] \}
+
+    Class-wise means
+
+             B \leftarrow \text{Encode Latent}(M, \mathcal{Y})
+ 5:
+
+ 6:
+
+             for i \in \{1, 2, \dots, \lfloor \frac{p}{|\mathcal{Y}|} \rfloor\} do
+ 7:
+ 8:
+                    for y_t \in \mathcal{Y} do
+ 9:
+                           (\boldsymbol{x}, y) \leftarrow \text{randomly sample from } D_{clean}
+10:
+                           D_{clean} \leftarrow D_{clean} \setminus \{(\boldsymbol{x}, y)\}
+                           t_{y_t} \leftarrow \text{Encoding Trigger}(\boldsymbol{x}, B_{y_t}) \quad \triangleright \text{Create a trigger that encodes binary string}
+11:
+
+\hat{\mathbf{x}} \leftarrow \mathbf{x} \oplus t_{y_t} 
+
+P \leftarrow P \cup \{(\hat{\mathbf{x}}, y_t)\}
+
+    Add trigger to image
+
+12.
+13:
+             D_{poison} \leftarrow D_{clean} \cup P
+14:
+15:
+             return D_{poison}
+16: procedure ENCODE LATENT(M, \mathcal{Y})
+             c \leftarrow \frac{1}{|M|} \sum_{y \in \mathcal{Y}} M_y
+
+17:
+             for y \in \mathcal{Y} do
+18:
+                   \Delta \leftarrow M_y - c
+b_i = \begin{cases} 1 & \text{if } \Delta_i > 0 \\ 0 & \text{otherwise} \end{cases}
+                                                                                             Difference between class mean and centroid
+19:
+20:
+                    B_u \leftarrow \mathbf{b}
+21:
+             return B
+```
+
+Algorithm 1 begins by sampling the latent space of the surrogate image classifier and compressing the generated latents into an n-dimensional representation using LDA (lines 2 and 3). Then, each class's mean in the compressed latent dataset is computed (line 4). Next, the ENCODE LATENT procedure is used to create a list containing a binary encoding of each class's latent features (line 5). For each class, an n-bit encoding is calculated such that the  $i_{th}$  bit is set to 1 if the class's mean is greater than the centroid of class means in the  $i_{th}$  feature and 0 if it is not. As we construct our encodings from the same latent principal components, each encoding contains relevant information for learning all other encodings. This results in high inter-class poison transferability, which allows our attack to efficiently target all classes in the model's latent space. Lines 7-13 use the calculated binary encodings to construct a set of poisoned samples. For each poison sample, ENCODING TRIGGER embeds the  $y_t$ 's binary encoding as a trigger in x. This can be accomplished using various techniques, as described in Section 3.4.
+
+#### <span id="page-3-2"></span>3.4 ENCODING APPROACH
+
+Many triggers have been proposed for data poisoning attacks, each with trade-offs in effectiveness and robustness (Gu et al., 2017; Liao et al., 2018; Shafahi et al., 2018; Liu et al., 2020; Nguyen &
+
+<span id="page-3-0"></span> $<sup>^{1}</sup>n$  is a chosen hyper-parameter
+
+[Tran, 2021;](#page-10-2) [Doan et al., 2019\)](#page-9-6). Our method can be used with any trigger that can encode the binary string calculated in Section [3.3.](#page-3-3) Our paper evaluates two common trigger crafting methods: patch and blend triggers [\(Gu et al., 2017;](#page-10-3) [Chen et al., 2017\)](#page-9-3).
+
+![](figures/_page_4_Picture_2.jpeg)
+
+<span id="page-4-0"></span>![](figures/_page_4_Picture_3.jpeg)
+
+Figure 2: Two exemplary methods of encoding latent directions. (Left) Universal Backdoor with a patch trigger encoding. (Right) Universal Backdoor with a blended trigger encoding.
+
+Patch Trigger. To create a patch corresponding to the target class, we encode its corresponding binary string as a black-and-white grid and stamp it in the top left of the base image.
+
+Blend Trigger. We partition the base image into n disjoint rectangular masks, each representing a bit in the target class's binary string. We choose two colors and color each mask based on its corresponding bit. Lastly, we blend the masks over the base image to create the poisoned sample.
+
+# 4 EXPERIMENTS
+
+In this section, we empirically evaluate the effectiveness of our backdoor using different encoding methods. We extend this evaluation process to demonstrate the effectiveness of our backdoor when scaling the image classification task in both the number of samples and classes. By choosing which classes are poisoned, we measure the *inter-class poison transferability* of our poison. Lastly, we evaluate our Universal Backdoor Attack against a suite of popular defenses.
+
+Baselines. As we are the first to study many-to-many backdoors, there exists no baseline to compare against to demonstrate the effectiveness of our method. For this purpose, we develop two baseline many-to-many backdoor attacks from well-known attacks: BadNets [\(Gu et al., 2017\)](#page-10-3) and Blended Injection [\(Chen et al., 2017\)](#page-9-3) We compare our Universal Backdoor against the effectiveness of these two baseline many-to-many attacks. For our baseline triggers, we generate a random trigger pattern for each targeted class, as in [Gu et al.](#page-10-3) [\(2017\)](#page-10-3). For our patch trigger baseline, we construct a grid consisting of n randomly colored squares. To embed this baseline trigger, we stamp the patch into an image using the same position and dimensions as our Universal Backdoor patch trigger. For our blend trigger baseline, we blend the randomly sampled grid across the whole image, using the same blend ratio as our Universal Backdoor blend trigger.
+
+### 4.1 EXPERIMENTAL SETUP
+
+Datasets and Models. For our inital effectiveness evaluation, we use ImageNet-1k with random crop and horizontal flipping [\(Russakovsky et al., 2014\)](#page-11-3). We use three datasets, ImageNet-2k, ImageNet-4k, ImageNet-6k, for our scaling experiments. These datasets comprise the largest 2 000, 4 000, and 6 000 classes from the ImageNet-21K dataset [\(Deng et al., 2009\)](#page-9-7). These datasets contain 3 024 392, 5 513 146, and 7 804 447 labeled samples, respectively. We use ResNet-18 for the ImageNet-1K experiments and ResNet-101 for the experiments on ImageNet-2k, ImageNet-4k, and ImageNet-6k in Section [4.3](#page-6-0) [\(He et al., 2015\)](#page-10-10).
+
+Attack Settings. We use a binary encoding with n = 30 features for all experiments. In our patch triggers, we use an 8x8 square of pixels to embed each feature, resulting in a patch that covers 3.8% of the base image. Our blended triggers use a blend ratio of 0.2, as in [Chen et al.](#page-9-3) [\(2017\)](#page-9-3). We use a pre-trained surrogate from Hugging Face for all of our attacks. For attacks on the ImageNet-1K classification task, Hugging Face Transformers pre-trained ResNet-18 model [\(Wolf et al., 2020\)](#page-11-0). As no model pre-trained on the ImageNet-2K, ImageNet-4K, or ImageNet-6K exists, we use Hugging Face Transformer's clip-vit-base-patch32 model as a zero-shot image classifier on these datasets to generate latents (Wolf et al., 2020). We use 25 images from each class to sample the latent space of our surrogate model.
+
+**Model Training.** We train our image classifiers using stochastic gradient descent (SGD) with a momentum of 0.9 and a weight decay of 0.0001. Models trained on ImageNet-1K are trained for 90 epochs, while models trained on ImageNet-2K, ImageNet-4K, and ImageNet-6K are trained for 60 epochs to adjust for the larger dataset size. The initial learning rate is set to 0.1 and is decreased by a factor of 10 every 30 epochs on ImageNet-1K and every 20 epochs on the larger datasets. We use a batch size of 128 images for all training runs. *Early stopping* is applied to all training runs; we stop training when the model's accuracy is no longer improving or the model begins overfitting. All of our models achieve equivalent validation accuracy to pre-trained counterparts in the Hugging Face Transformers library (Wolf et al., 2020). We include an analysis of backdoored models' clean accuracy in Appendix A.1.
+
+#### <span id="page-5-2"></span>4.2 EFFECTIVENESS ON IMAGENET-1K
+
+<span id="page-5-0"></span>Table 1: Attack success rate (%) of our Universal Backdoor compared to baseline approach.
+
+| Poison Samples (p) | Poison % | Patch |          | Blend |          |
+|--------------------|----------|-------|----------|-------|----------|
+|                    |          | Ours  | Baseline | Ours  | Baseline |
+| 2000               | 0.16     | 80.1% | 0.1%     | 0.4%  | 0.1%     |
+| 5000               | 0.39     | 95.5% | 2.1%     | 74.9% | 0.1%     |
+| 8000               | 0.62     | 95.7% | 100%     | 92.9% | 0.1%     |
+
+Table 1 summarizes our results on ImageNet-1K using patch and blend triggers while injecting between 2000 and 8000 poisoned samples. Our patch encoding triggers perform the best, achieving over 80.1% ASR across all classes while only manipulating 0.16% of the dataset. Our method performs significantly better than the baseline at low poisoning rates. The patch baseline is completely learned at high poisoning rates and achieves perfect ASR. Our chosen value of n=30 is too low to distinguish the binary encodings of all classes, resulting in our backdoor achieving less than perfect ASR even with many poison samples. A larger value of n would allow us to encode more principal components of the latent space, allowing our Universal Backdoor to achieve perfect ASR. However, as this would require embedding a longer binary encoding, it would increase the number of sample poisons required for a successful attack. Across all experiments, we find that a patch encoding is more effective than a blend encoding.
+
+<span id="page-5-1"></span>![](figures/_page_5_Figure_7.jpeg)
+
+Figure 3: Our attack versus a baseline using patch encoding triggers. We measure the attack success rate and use early stopping at 70 epochs.
+
+![](figures/_page_5_Figure_9.jpeg)
+
+Figure 4: Attack success rate on a subset of *observed* target classes while increasing poisoning in other classes in the dataset.
+
+Figure 3 shows that the baseline backdoor is learned only after the model overfits the training data (after about 70 epochs). Therefore, the baseline backdoor is very vulnerable to early stopping. The baseline requires significantly more poisons to ensure it is learned earlier in the training process and not removed by early stopping. Because of this behavior, the baseline backdoor is either thoroughly learned or achieves negligible attack success. This results in a sudden increase in the baseline's
+
+attack success when the number of poison samples increases to 8 000 in Table [1.](#page-5-0) Our Universal Backdoor is gradually learned throughout the training process, so any early stopping procedure that would mitigate our backdoor would also significantly reduce the model's clean accuracy.
+
+### <span id="page-6-1"></span><span id="page-6-0"></span>4.3 SCALING
+
+Table 2: Attack success rate of the backdoor on larger datasets (%), using p = 12 000.
+
+| Poison Attack      | ImageNet-2K | ImageNet-4K | ImageNet-6K |
+|--------------------|-------------|-------------|-------------|
+| Universal Backdoor | 99.73       | 91.75       | 47.31       |
+| Baseline           | 99.98       | 0.03        | 0.02        |
+
+In this experiment, we measure our backdoor's ability to scale to larger datasets. We fix the number of poisons the attacker injects into each dataset at p = 12 000 across all runs. As larger image classification datasets naturally contain more classes and samples, so do our datasets [\(Deng et al.,](#page-9-7) [2009;](#page-9-7) [Kuznetsova et al., 2018\)](#page-10-11). Table [2](#page-6-1) summarizes the results on our backdoor compared to a baseline on the ImageNet-2K, ImageNet-4K, and ImageNet-6K image classification tasks. We find that the trigger patterns of the baseline do not effectively scale to larger image classification datasets. Although the baseline backdoor has near-perfect ASR on the ImageNet-2K dataset, it has negligible ASR on both the ImageNet-4K and ImageNet-6K datasets. This is because of the all-or-nothing attack success behavior observed in Section [4.2.](#page-5-2) In contrast, our Universal Backdoor can scale to image classification tasks containing more classes and samples. Our Universal backdoor achieves above 90% ASR on the ImageNet-4K task and 47.31% ASR on the largest dataset, ImageNet-6K.
+
+### 4.4 MEASURING INTER-CLASS POISON TRANSFERABILITY
+
+To measure the inter-class transferability of poisoning, we examine how increasing the number of poisons in one set of classes increases attack success on a disjoint set of classes in the dataset. We divide the classes into the observed set B and the variation set A. B contains 10% of the classes in the dataset (100 classes), while A contains the remaining 90% of classes (900 classes). We use the ImageNet-1K dataset and a patch trigger for our backdoor. We poison exactly one sample in each class in B. In Figure [4,](#page-5-1) we ablate over the total number of poisons in the dataset, distributing all poisons except for the 100 poisons in B evenly in classes in A.
+
+We find that by poisoning a class with a single sample, our Universal Backdoor can achieve a successful attack on a class if sufficient poisoning is achieved elsewhere in the dataset. Increasing the number of poison samples in A improved the backdoor's ASR on classes in B from negligible to over 70%. *Therefore, we find that protecting the integrity of a single class requires protecting the integrity of the entire dataset*. Our Universal Backdoor shows that every sample, even if they are associated with an insensitive class label, can be used by an attacker as part of an extremely poisonefficient backdoor attack on a small subset of high-value classes. We provide further evidence for this in Appendix [A.2,](#page-12-0) where we show that A can contain significantly fewer than 900 classes while preserving the strength of inter-class poison transferability on B. The baseline method does not demonstrate any inter-class transferability, as increasing the poisoning in A does not increase the attack success rate on B.
+
+# <span id="page-6-2"></span>4.5 ROBUSTNESS AGAINST DEFENSES
+
+We evaluate the robustness of our poisoning model against four state-of-the-art defenses: finetuning, fine-pruning [\(Liu et al., 2018\)](#page-10-7), neural attention distillation [\(Li et al., 2021\)](#page-10-8), and neural cleanse [\(Wang et al., 2019\)](#page-11-2). We use a ResNet-18 model trained on the ImageNet-1k dataset for all robustness evaluations. We use patch triggers for both our method and the baseline. For all defenses, we use hyper-parameters optimized for removing a BadNets backdoor [\(Gu et al., 2017\)](#page-10-3) on ImageNet-1K as proposed by [Lukas & Kerschbaum](#page-10-12) [\(2023\)](#page-10-12). Defenses requiring clean data are given 1% of the clean dataset, approximately 12,800 clean samples. We limit the degradation of the model's clean accuracy, halting any defense that degrades the model's clean accuracy by more than 2%. Table [3](#page-7-0) summarizes the changes in ASR after applying each defense. As in [Lukas &](#page-10-12) Kerschbaum (2023), we find that backdoored models trained on ImageNet-1K are robust against defenses. A complete table of defense parameters can be found in Appendix A.
+
+<span id="page-7-0"></span>Table 3: The robustness of our universal backdoor against a naïve baseline, measured by the attack success rate (ASR). ▼ denotes ASR lost after applying defense. Only backdoors above 5% ASR were evaluated. Backdoors that were not evaluated are marked with N/A.
+
+| Defense        | Poison Samples (p)      | Universal               | Backdoor (ASR)           | Baseline            | e (ASR) |
+|----------------|-------------------------|-------------------------|--------------------------|---------------------|---------|
+| Fine-Tuning    | 2 000<br>5 000<br>8 000 | 70.3%<br>94.5%<br>95.5% | ▼ 9.8<br>▼ 1.0<br>▼ 0.2  | N/A<br>N/A<br>99.5% | ▼ 0.5   |
+| Fine-Pruning   | 2 000<br>5 000<br>8 000 | 73.5%<br>95.2%<br>95.6% | ▼ 6.6<br>▼ 0.3<br>▼ 0.1  | N/A<br>N/A<br>99.9% | ▼ 0.1   |
+| Neural Cleanse | 2 000<br>5 000<br>8 000 | 70.1%<br>95.1%<br>95.4% | ▼ 10.0<br>▼ 0.4<br>▼ 0.3 | N/A<br>N/A<br>98.0% | ▼ 2.0   |
+| NAD            | 2 000<br>5 000<br>8 000 | 73.9%<br>94.6%<br>95.3% | ▼ 6.2<br>▼ 0.9<br>▼ 0.4  | N/A<br>N/A<br>99.9% | ▼ 0.1   |
+
+**Fine-tuning.** This defense fine-tunes the dataset on a small validated subset of the training dataset. We fine-tune the model using the SGD with a learning rate of 0.0005 and a momentum of 0.9.
+
+**Fine-pruning.** As in Liu et al. (2018), we prune the last convolutional layer of the model. We find that the pruning rate in Lukas & Kerschbaum (2023) is too high and degrades the clean accuracy of the model more than the 2% cutoff. We set the pruning rate to 0.1%, which is the maximum pruning rate that prevents the defense from degrading the model below the accuracy cutoff.
+
+**Neural Cleanse.** Neural Cleanse (Wang et al., 2019) uses outlier detection to decide which candidate trigger is most likely the result of poisoning. This candidate trigger is then used to remove the backdoor in the model. As our Universal Backdoor targets every class and has a unique trigger for each class, class-wise anomaly detection is poorly suited for removing our backdoor.
+
+**Neural Attention Distillation.** We train a teacher model for 1 000 steps using SGD. We then align the backdoored model with the teacher for 8000 steps, using SGD with a learning rate of 0.0005. We use a power term of 2 for the attention distillation loss, as recommended in Li et al. (2021).
+
+#### 4.6 Measuring the Clean Data Trade-off
+
+There is a known trade-off between the availability of clean data and the effectiveness of defenses (Li et al., 2021). Figure 5 measures the proportion of the clean dataset required to remove the universal backdoor with fine-tuning without degrading the model below the 2% cutoff. For this experiment, we use a ResNet-18 model backdoored using 2 000 poison samples on the ImageNet-1K dataset. Due to the higher availability of clean data, we find that a higher learning rate of 0.001 and a weight decay of 0.001 are appropriate.
+
+Data poisoning defenses for backdoored models trained on web-scale datasets must be effective with a validated dataset that is a small portion of the training dataset due to the cost of manually validating
+
+<span id="page-7-1"></span>![](figures/_page_7_Figure_11.jpeg)
+
+Figure 5: Clean data as a percentage of the training dataset size required to remove our Universal Backdoor.
+
+samples. Validating a 1% portion of our web-scale ImageNet-6k dataset would require manually inspecting over  $78\,000$  samples, a task larger than inspecting the CIFAR-100 or GTSRB datasets in
+
+their entirety [\(Krizhevsky, 2009;](#page-10-13) [Stallkamp et al., 2011\)](#page-11-6). We find that approximately 40% (512 466 samples) of the clean dataset is required to completely remove our Universal Backdoor, which is more data than most victims can manually validate.
+
+# 5 DISCUSSION AND RELATED WORK
+
+Attacking web-scale datasets. [Carlini et al.](#page-9-8) [\(2023\)](#page-9-8) demonstrate two realistic ways an attacker could poison a web-scale dataset: domain hijacking and snapshot poisoning. They show that more than 0.15% of the samples in these online datasets could be poisoned by an attacker. However, existing many-to-one poison label attacks cannot exploit these vulnerabilities, as they require compromising many samples *in a single class* [\(Gu et al., 2017;](#page-10-3) [Qi et al., 2022;](#page-10-5) [Chen et al., 2017\)](#page-9-3). As web-scale datasets contain thousands of classes [\(Deng et al., 2009;](#page-9-7) [Kuznetsova et al., 2018\)](#page-10-11), it is improbable that any one class would have enough compromised samples for a many-to-one poison label attack. By leveraging inter-class poison transferability, our backdoor can utilize compromised samples outside a class the attacker is attempting to misclassify into.
+
+Scaling to larger datasets. The largest dataset we evaluate is our ImageNet-6K dataset, which consists of 6 000 classes and 7 804 447 samples. We created a Universal Backdoor in a model trained on this dataset while poisoning only 0.15%. As our backdoor effectively scales to datasets containing more classes and samples, we expect a smaller proportion of poison samples to be required to backdoor models trained on larger datasets, like LAION-5B [\(Schuhmann et al., 2022\)](#page-11-7).
+
+Alternative methodology for targeting multiple classes at inference time. Although we are the first to study how to target every class in the data poisoning setting, other types of attacks, like *adversarial examples*, can be used to target specific classes at inference time [\(Wu et al., 2023;](#page-11-8) [Goodfellow et al., 2015\)](#page-10-14). Through direct optimization on an input, the attacker finds an adversarial perturbation that acts as a trigger; adding it to the input causes a misclassification. Defenses against adversarial examples seek to make models robust against adversarial perturbations [\(Cohen et al.,](#page-9-9) [2019;](#page-9-9) [Geiping et al., 2021\)](#page-9-10). However, as data poisoning backdoors utilize triggers that are not adversarial perturbations, these defenses are ineffective at mitigating data poisoning backdoors.
+
+Limitations. We focus on patch and blend triggers that are visible modifications to the image and hence could be detected by a data sanitation defense. Our attacks are agnostic to the trigger; even if a specific trigger could be reliably detected, universal backdoors remain a threat because the attacker could have used a different trigger. [Koh et al.](#page-10-15) [\(2022\)](#page-10-15) demonstrate that no detection has been shown effective against any trigger. However, evading data sanitation comes at a cost for the attacker: Less detectable triggers are less effective at equal numbers. Hence, the attacker must inject more to create an equally effective backdoor [\(Frederickson et al., 2018\)](#page-9-11). We point to Appendix [A.3](#page-12-1) showing that our attacks still remain difficult to detect using STRIP [\(Gao et al., 2019\)](#page-9-12) due to the high false positive rate. We focus on the feasibility of universal attacks and do not study the detectability-effectiveness trade-off of triggers with our attacks. Moreover, we focus on poisoning models from scratch, as opposed to poisoning pre-trained models that are fine-tuned. More research is needed to analyze the effectiveness of our attacks against large pre-trained models like ViT and CLIP [\(Dosovitskiy et al.,](#page-9-13) [2021;](#page-9-13) [Radford et al., 2021\)](#page-10-16) that are fine-tuned on poisoned data. Finally, we assume that the attacker can access similarly accurate surrogate classifiers to generate latent encodings for our attacks.
+
+# 6 CONCLUSION
+
+We introduce Universal Backdoors, a data poisoning backdoor that targets every class. We establish that our backdoor requires significantly fewer poison samples than independently attacking each class and can effectively attack web-scale datasets. We also demonstrate how compromised samples in uncritical classes can be used to reinforce poisoning attacks against other more sensitive classes. Our work exemplifies the need for practitioners who train models on untrusted data sources to protect the whole dataset, not individual classes, from data poisoning. Finally, we show that existing defenses are ineffective at defending against Universal Backdoors, indicating the need for new defenses designed to remove backdoors that target many classes.
+
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+
+# <span id="page-11-5"></span>A APPENDIX
+
+Table [4](#page-12-2) contains a complete summary of all the parameters used to evaluate defenses against our backdoor in Section [4.5.](#page-6-2) All defense parameters are adapted from [Lukas & Kerschbaum](#page-10-12) [\(2023\)](#page-10-12), where they were optimized against a BadNets [\(Gu et al., 2017\)](#page-10-3) patch trigger. When hyperparameter tuning for fine-tuning and fine-pruning defenses, we find no significant improvements over the settings described in [Lukas & Kerschbaum](#page-10-12) [\(2023\)](#page-10-12). We reduce the fine-pruning rate in Fine-pruning, as we find it degrades the model's clean accuracy below our 2% cutoff.
+
+As shown by Figure [6a,](#page-12-3) a linear trade-off exists between the effectiveness of defenses and the allowed clean accuracy cutoff. If the defender allows for more clean accuracy degradation, the effectiveness of the backdoor can be further reduced. This does not apply to all defenses, as defenses like neural cleanse [\(Wang et al., 2019\)](#page-11-2) do not significantly reduce clean accuracy.
+
+### <span id="page-11-4"></span>A.1 ANALYSIS OF CLEAN ACCURACY
+
+If a backdoor attack degrades the clean accuracy of a model, then the validation set is sufficient for the victim to recognize the presence of a backdoor [\(Gu et al., 2017\)](#page-10-3). Therefore, a model trained on the poisoned set should achieve the same clean accuracy as one trained on a comparable clean dataset. We find that our backdoored models have the same clean accuracy across all runs as a model trained on entirely clean data. We train a clean ResNet-18 model on ImageNet-1k [\(Russakovsky](#page-11-3) [et al., 2014\)](#page-11-3), which achieves 68.49% top-1 accuracy on the validation set. Table [5](#page-13-0) shows the clean accuracy of backdoored models on the ImageNet-1k dataset.
+
+Table 4: Defense Parameters on ImageNet-1K from Lukas & Kerschbaum (2023).
+
+<span id="page-12-2"></span>
+
+| <b>Neural Attention Distillation</b> |       |  |  |
+|--------------------------------------|-------|--|--|
+| n steps / N                          | 8,000 |  |  |
+| opt                                  | sgd   |  |  |
+| $lr/\alpha$                          | 5e-4  |  |  |
+| teacher steps                        | 1,000 |  |  |
+| power / p                            | 2     |  |  |
+| at lambda / $\lambda_{at}$           | 1,000 |  |  |
+| weight decay                         | 0     |  |  |
+| batch size                           | 128   |  |  |
+| Named Clause                         |       |  |  |
+
+| Fine-Tuni      | ing   |  |
+|----------------|-------|--|
+| n steps / N    | 5,000 |  |
+| opt            | sgd   |  |
+| $\ln / \alpha$ | 5e-4  |  |
+| weight decay   | 0.001 |  |
+| batch size     | 128   |  |
+|                |       |  |
+
+| <b>Neural Cleanse</b>     |       |  |  |
+|---------------------------|-------|--|--|
+| n steps / N               | 3,000 |  |  |
+| opt                       | sgd   |  |  |
+| $\ln / \alpha$            | 5e-4  |  |  |
+| steps per class / N1      | 200   |  |  |
+| norm lambda / $\lambda_N$ | 1e-5  |  |  |
+| weight decay              | 0     |  |  |
+| batch size                | 128   |  |  |
+
+| Fine-Prunir         | ng    |  |
+|---------------------|-------|--|
+| n steps / N         | 5,000 |  |
+| opt                 | sgd   |  |
+| $\ln / \alpha$      | 5e-4  |  |
+| prune rate / $\rho$ | 10%   |  |
+| sampled batches     | 10    |  |
+| weight decay        | 0     |  |
+| batch size          | 128   |  |
+|                     |       |  |
+
+<span id="page-12-3"></span>![](figures/_page_12_Figure_6.jpeg)
+
+![](figures/_page_12_Figure_7.jpeg)
+
+Figure 6: (6a) Trade-off between attack success rate and clean data accuracy when fine-tuning a backdoored model. (6b) ROC curve of our Universal Backdoor with patch and blend triggers (see Figure 2) when applying the STRIP (Gao et al., 2019) defense.
+
+### <span id="page-12-0"></span>A.2 INTER-CLASS POISON TRANSFERABILITY WITH SMALL VARIATION SETS
+
+Table 6 shows that even if the number of classes in the variation set  $\bf A$  is reduced to only 10% of classes in  $\cal Y$ , inter-class poison transferability maintains its effect on the observed set  $\bf B$ . This results in an otherwise unsuccessful attack on classes in  $\bf B$ , achieving a success rate of 67.72%. Therefore, if the attacker can strongly poison a small set of classes in the dataset, attacking other classes in the model can easily be accomplished, as inter-class poison transferability remains strong. To protect even a tiny subset of high-value classes, the victim must maintain the integrity of every class within their dataset.
+
+#### <span id="page-12-1"></span>A.3 DATA SANITATION DEFENSES
+
+Several data sanitization defenses are also poorly suited to Universal Backdoors. SPECTRE (Hayase et al., 2021) only removes samples from a single class by design, and therefore could remove at most 0.1% of our Universal Backdoor's poisoned samples on ImageNets-1K. STRIP (Gao et al., 2019) struggles to detect our trigger, resulting in a high false positive rate, as shown in Figure 6b. The area
+
+Table 5: Clean accuracy of backdoored models on ImageNet-1k dataset.
+
+<span id="page-13-0"></span>
+
+| Poison Samples (p) | Poison % | Patch  |          | Blend  |          |
+|--------------------|----------|--------|----------|--------|----------|
+|                    |          | Ours   | Baseline | Ours   | Baseline |
+| 2000               | 0.16     | 68.94% | 68.94%   | 68.51% | 69.43%   |
+| 5000               | 0.39     | 68.92% | 68.89%   | 68.77% | 68.66%   |
+| 8000               | 0.62     | 68.91% | 69.43%   | 69.78% | 69.22%   |
+
+<span id="page-13-1"></span>Table 6: Effect of the number of classes in the variation set A on attack success on the observed set B. All experiments use 4 600 poison samples.
+
+| Percentage of classes in A | ASR on classes in B |
+|----------------------------|---------------------|
+| 90%                        | 72.77%              |
+| 60%                        | 70.45%              |
+| 30%                        | 71.78%              |
+| 10%                        | 67.72%              |
+
+under the ROC curves are 0.879 and 0.687 for the patch and blend triggers, respectively. It may be difficult for defenders to detect both triggers for large datasets (1 million samples or more) due to the detection's high FPR. Considering a maximum tolerable FPR of 10%, the defender misses 39% of the patch trigger samples and 68% of the blended triggers.
+
+### A.4 CLASS-WISE ATTACK SUCCESS METRICS
+
+<span id="page-13-2"></span>Our method does not achieve even attack success across all classes in the dataset. Table [7](#page-13-2) shows statistics of our Universal Backdoor's success rate across classes in ImageNet-1K. We find that some classes are more challenging to achieve a successful attack against our backdoor. This differs from the baseline, as the baseline either performs near-perfectly or not at all.
+
+Table 7: ASR metrics across classes in ImageNet-1K
+
+| Poison Samples (p) | Min | Max (%) | Mean  | Median |
+|--------------------|-----|---------|-------|--------|
+| 2000               | 0   | 100%    | 81.0% | 98.0%  |
+| 5000               | 0   | 100%    | 95.4% | 100%   |

papers/3QkzYBSWqL/review.json

@@ -0,0 +1,91 @@
+{
+  "id": "3QkzYBSWqL",
+  "title": "Universal Backdoor Attacks",
+  "decision": "Accept",
+  "reviews": [
+    {
+      "id": "hNWh5JFvFX",
+      "rating": 6,
+      "content": {
+        "summary": "Whereas in traditional backdoor literature attacks focus on a specific target class, the proposed work introduces a method to embed backdoors from any source class to any target class. The method proceeds in three steps: 1) finding the class-wise centroids of clean-data feature extractions (using CLIP), 2) encoding each centroid into a N-dimensional bit-string, and 3) generating triggers corresponding to each bit-string (and, hence each target class). Classes with similar features are encoded to have similar embeddings. They show that their method performs and scales well with ResNets on four ImageNet-21k subsets.",
+        "soundness": "4 excellent",
+        "presentation": "4 excellent",
+        "contribution": "3 good",
+        "strengths": "- The writing was clear and easy to follow\n- Their bit-string encoding approach is a novel and elegant way to share feature information between classes while generating a class-specific backdoor trigger.\n- The experiments section was well-motivated and well-explained.",
+        "weaknesses": "- In general, each experiment should be averaged over multiple seeds for statistical significance\n- A major part of the backdoor attack regime is the preservation of clean accuracy, and there is no analysis on how well the proposed method protects a model's clean accuracy. This should certainly be included in future versions of the paper.\n- The proposed triggers in Fig. 2 seem quite obvious to the human eye and may be susceptible to input-space defenses. I would like to see some analysis on the necessary intensity of these triggers and their brittleness to input-space defenses like STRIP.\n- On the defense side, the authors \"[halt] any defense that degrades the model’s clean accuracy by more than 2%.\" I'm open to feedback here, but this has the potential to straw-man some defense mechanisms in scenarios where removing a backdoor is worth the cost of clean accuracy. Including some results without this limitation would be nice.\n- In addition to the above, the attack was not evaluated on data-cleaning defenses like SPECTRE, which I think would be particularly effective against this regime. I would like to see these defenses evaluated as well--and not limited to specific target classes.\n- The experiments are limited to ResNet variants. It would be nice to show generality by including one other architecture in the experiments section.\n  - Since most vision models rely on pretraining, one idea I would find particularly compelling would be to run the attack on a pretrained ViT.\n- In Section 4.4, only a single setting of observed percentage is tried. The analysis here would be stronger if more percentages were tried\n- I'm not sure about the timing here, but the authors claim that they \"are the first to study how to target every class in the data poisoning setting.\" However, while [1,2] address slightly different settings, they seem to be *at least* related and possibly published earlier.\n  - Depending on the nature of this relationship, I would like to see 1) these statements qualified, 2) a more thorough analysis of how the work is positioned in relation to similar work including but not limited to the papers mentioned.\n\n**Citations:**\n\n[1] Du et al., \"UOR: Universal Backdoor Attacks on Pre-trained Language Models.\"\n\n[2] Zhang et al., \"Universal backdoor attack on deep neural networks for malware detection.\"",
+        "questions": "There are a few questions embedded in the above weaknesses. In addition to those I'm curious about the effect of pretraining on the proposed attack. Could the attack be injected in a fine-tuning regime?\n\n**Note:** I'm happy to raise my score after the weaknesses and questions have been addressed.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": " - In general, each experiment should be averaged over multiple seeds for statistical significance\n- A major part of the backdoor attack regime is the preservation of clean accuracy, and there is no analysis on how well the proposed method protects a model's clean accuracy. This should certainly be included in future versions of the paper.\n- The proposed triggers in Fig. 2 seem quite obvious to the human eye and may be susceptible to input-space defenses. I would like to see some analysis on the necessary intensity of these triggers and their brittleness to input-space defenses like STRIP.\n- On the defense side, the authors \"[halt] any defense that degrades the model’s clean accuracy by more than 2%.\" I'm open to feedback here, but this has the potential to straw-man some defense mechanisms in scenarios where removing a backdoor is worth the cost of clean accuracy. Including some results without this limitation would be nice.\n- In addition to the above, the attack was not evaluated on data-cleaning defenses like SPECTRE, which I think would be particularly effective against this regime. I would like to see these defenses evaluated as well--and not limited to specific target classes.\n- The experiments are limited to ResNet variants. It would be nice to show generality by including one other architecture in the experiments section.\n  - Since most vision models rely on pretraining, one idea I would find particularly compelling would be to run the attack on a pretrained ViT.\n- In Section 4.4, only a single setting of observed percentage is tried. The analysis here would be stronger if more percentages were tried\n- I'm not sure about the timing here, but the authors claim that they \"are the first to study how to target every class in the data poisoning setting.\" However, while [1,2] address slightly different settings, they seem to be *at least* related and possibly published earlier.\n  - Depending on the nature of this relationship, I would like to see 1) these statements qualified, 2) a more thorough analysis of how the work is positioned in relation to similar work including but not limited to the papers mentioned.",
+        "suggestions": "The paper introduces an interesting approach to universal backdoor attacks, but several experimental and analytical aspects require more attention. First, the lack of statistical rigor in the experiments is concerning. Each experiment should be repeated with multiple random seeds, and the results should be presented with standard deviations or confidence intervals. This is particularly crucial for the ablation studies, where single runs might not accurately reflect the true performance of the method. Furthermore, the paper needs a more thorough investigation of the attack's impact on clean accuracy. While the authors mention it, a detailed analysis showing how different poisoning rates and trigger types affect clean accuracy is necessary. This should include a discussion of the trade-offs between attack success rate and clean accuracy degradation, as this is vital for understanding the practical implications of the attack. The current evaluation only provides a high-level overview, which is insufficient for a comprehensive analysis of the attack's stealthiness.\n\nSecond, the analysis of the proposed triggers is lacking. The paper should include a more detailed study of the trigger's sensitivity to input-space defenses. The authors should evaluate the attack's robustness against defenses like STRIP with varying trigger intensities and perturbation magnitudes. It would also be beneficial to explore more subtle triggers, as the current triggers are quite visible and may be easily detected. Furthermore, the evaluation of defenses is limited. The authors should evaluate the attack against data-cleaning defenses like SPECTRE, which are explicitly designed to remove poisoned samples. The current 2% clean accuracy cutoff for defenses is arbitrary and may unfairly disadvantage some defenses. It is necessary to include results without this limitation to provide a more complete picture of the attack's resilience. The authors should also consider adaptive attacks, where the attacker is aware of the defense mechanisms in place, to show the true potential of their attack.\n\nFinally, the experimental section needs to be expanded to include more diverse model architectures. While ResNet is a common choice, it would be beneficial to evaluate the attack on other architectures, such as ViTs, which are becoming increasingly popular. Since most vision models rely on pretraining, it would be particularly compelling to analyze the attack's effectiveness in a fine-tuning regime. This would provide a more realistic assessment of the attack's potential impact. Furthermore, the analysis in Section 4.4 needs more exploration. Varying the percentage of observed classes would provide a more detailed picture of the attack's behavior in different scenarios. The authors should also clarify the novelty of their work in relation to existing literature [1,2] by providing a more detailed comparison and discussion of the differences in methodology and scope. The current discussion is insufficient, and a more thorough analysis is needed to justify their claim of being the first to study universal attacks in the data poisoning setting."
+      }
+    },
+    {
+      "id": "1fZ60Zaof8",
+      "rating": 5,
+      "content": {
+        "summary": "This paper investigates the utilization of a small number of poisoned samples to achieve many-to-many backdoor attacks. The authors leverage inter-class poison transferability and generate triggers with salient characteristics. The proposed method is evaluated on the ImageNet dataset, demonstrating its effectiveness. The authors provide evidence of the transferability of data poisoning across different categories.",
+        "soundness": "2 fair",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "1.The paper demonstrates clear logic.\n2.The topic is intriguing and warrants further exploration.",
+        "weaknesses": "1.The design motivation of the algorithm is unclear.\n2.The concealment of the patches is poor.\n3.The comparative methods are outdated.",
+        "questions": "1.\tThe related work lacks a specific conceptual description of \"many-to-many\" and an introduction to recent works in this area.\n2.\tIn Section 3.3, the encoding method used in the latent feature space is rather simplistic, where values greater than the mean are encoded as 1 and others as 0. What is the motivation behind this encoding method, and how does it contribute to improving the transferability of inter-class data poisoning?\n3.\tThe author employs a patch and blend approach to add triggers, resulting in poor concealment of the backdoor triggers. Visually, the differences between poisoned and clean samples can be distinguished. Has the author considered more covert methods for backdoor implantation, such as injecting triggers in the latent space and decoding them back to the original samples to reduce the dissimilarity between poisoned and clean samples?\n4.\tSelection of baselines. The chosen comparative methods are both from 2017. It is recommended to include comparative experiments with the latest backdoor attack methods.\n5.\tThe experimental results in the paper compare the average attack success rates across all categories. It is suggested to provide individual attack success rates for representative categories or other statistical results such as minimum, maximum, and median values.\n6.\tThe authors validated the effectiveness of the method under model-side defense measures. It is recommended to include defense methods in data-side.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1.The design motivation of the algorithm is unclear.\n2.The concealment of the patches is poor.\n3.The comparative methods are outdated.\n4. The related work lacks a specific conceptual description of \"many-to-many\" and an introduction to recent works in this area.\n5. In Section 3.3, the encoding method used in the latent feature space is rather simplistic, where values greater than the mean are encoded as 1 and others as 0. What is the motivation behind this encoding method, and how does it contribute to improving the transferability of inter-class data poisoning?\n6. The experimental results in the paper compare the average attack success rates across all categories. It is suggested to provide individual attack success rates for representative categories or other statistical results such as minimum, maximum, and median values.\n7. The authors validated the effectiveness of the method under model-side defense measures. It is recommended to include defense methods in data-side.",
+        "suggestions": "The paper would significantly benefit from a more thorough explanation of the algorithm's design choices. The current presentation lacks a clear rationale for why the specific encoding method in the latent feature space was chosen, and how this binary encoding contributes to the transferability of the poison. A more detailed discussion of alternative encoding strategies and their potential impact on the attack's effectiveness would strengthen the paper. Furthermore, the motivation behind using a patch and blend approach for trigger injection needs to be justified, especially considering its poor concealment. The authors should explore more subtle methods, such as latent space manipulation, and provide a comparative analysis of different trigger injection techniques in terms of both attack success rate and stealthiness. It's crucial to explain why the chosen method is superior to other potential approaches, or at least acknowledge the trade-offs involved.\n\nTo improve the experimental evaluation, the authors should include a more comprehensive analysis of the attack's performance across different categories. Presenting only average attack success rates obscures the variability in performance across classes. Reporting individual success rates for representative categories, along with statistical measures like minimum, maximum, and median values, would provide a more nuanced understanding of the attack's effectiveness. It would also be valuable to investigate the reasons behind the observed variability and discuss potential factors influencing the attack's success on different classes. Additionally, the selection of baselines needs to be addressed by including more recent and relevant methods. The current baselines are outdated and do not provide a fair comparison with the proposed approach. The authors should compare their method with state-of-the-art backdoor attack techniques to demonstrate its advantages and limitations in the current landscape.\n\nFinally, the paper should address the limitations of the proposed approach in terms of its vulnerability to data-side defenses. While the authors validate their method under model-side defenses, the lack of consideration for data-side defenses is a significant oversight. The paper should include experiments evaluating the robustness of the proposed method against data sanitization techniques and other data-side defense strategies. A discussion of the potential vulnerabilities of the proposed method to these defenses and possible mitigation strategies would greatly enhance the paper's practical relevance. This would also help to better contextualize the contributions of the work and highlight areas for future research."
+      }
+    },
+    {
+      "id": "RnqJwNElWt",
+      "rating": 5,
+      "content": {
+        "summary": "This paper introduced a universal backdoor attack, a data poisoning method that targets arbitrary categories. Specifically, the authors crafted triggers by utilizing the principal components of LDA in the latent space of a surrogate classifier. Experiments showed that the generated triggers can attack any category by poisoning a certain percentage of samples in the training data.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "$\\bullet$ The authors proposed a method that was designed to poison any class, instead of targeting a single class.\n\n$\\bullet$ The proposed attack is effective than the previous method, especially when the poisoning rate is low.",
+        "weaknesses": "$\\bullet$ It is not clear why the proposed method improves the inter-class poison transferability and, in particular, how it ensures that an increase in attack success against one class improves attack success against other classes. Does the proposed method increase the transferability (attack success rate) of any two classes, even if these two classes differ significantly in the latent space?\n\n$\\bullet$ The formula in Section 3.2 needs to be formulated more appropriately and clearly. Specifically, do y' and y in the formula refer to any two categories or any two similar categories? If they refer to any two categories, please explain why categories that are very different in the latent space can also improve the success rate of the attack; otherwise, if they refer to any two similar categories, please give a clear definition of similarity.\n\n$\\bullet$ The experimental results require further discussion and analysis. For example, in Table 1, the proposed method significantly outperforms the baseline method when the poisoning samples are 5000 (i.e., the attack success rate is 95.5% vs. 2.1%), but the proposed method is suddenly worse than the baseline method when the poisoning samples are 8000 (95.7% vs. 100%). The potential reasons for the sudden improvement in the performance of the baseline method need to be discussed. Similarly, in Table 2, the attack success rate of the baseline method suddenly drops from 99.98% for ImageNet-2K to 0.03% for ImageNet-4K, which also needs to be discussed.",
+        "questions": "What are the requirements for the surrogate image classifier? The proposed method requires sampling in the latent space of the surrogate image classifier, not the original classifier. Is it possible to use any latent space of any surrogate classifier? For example, if there is a significant difference in the distribution of the hidden spaces between the surrogate classifier and the original classifier, will this result in a significant decrease in the attack success rate of the proposed method?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "$\bullet$ It is not clear why the proposed method improves the inter-class poison transferability and, in particular, how it ensures that an increase in attack success against one class improves attack success against other classes. Does the proposed method increase the transferability (attack success rate) of any two classes, even if these two classes differ significantly in the latent space? It is crucial to understand if the method's effectiveness relies on some form of similarity between classes in the latent space, and if so, how this similarity is defined and measured.\n\n$\bullet$ The formula in Section 3.2 needs to be formulated more appropriately and clearly. Specifically, do y' and y in the formula refer to any two categories or any two similar categories? If they refer to any two categories, please explain why categories that are very different in the latent space can also improve the success rate of the attack; otherwise, if they refer to any two similar categories, please give a clear definition of similarity. The current definition lacks the necessary rigor to understand the scope and limitations of the proposed method. A more precise formulation is needed to clarify the relationship between different categories and their impact on the attack's success.\n\n$\bullet$ The experimental results require further discussion and analysis. For example, in Table 1, the proposed method significantly outperforms the baseline method when the poisoning samples are 5000 (i.e., the attack success rate is 95.5% vs. 2.1%), but the proposed method is suddenly worse than the baseline method when the poisoning samples are 8000 (95.7% vs. 100%). The potential reasons for the sudden improvement in the performance of the baseline method need to be discussed. Similarly, in Table 2, the attack success rate of the baseline method suddenly drops from 99.98% for ImageNet-2K to 0.03% for ImageNet-4K, which also needs to be discussed. The lack of analysis makes it difficult to interpret the results and understand the underlying mechanisms of the attack. The paper needs to provide a more thorough investigation into these performance variations.",
+        "suggestions": "The paper should provide a more detailed explanation of how the proposed method achieves inter-class transferability. It is essential to clarify whether the method's effectiveness depends on the similarity of classes in the latent space. If so, a clear definition of similarity should be provided, along with a discussion of how this similarity is measured and how it impacts the attack's success. For example, the authors could explore the correlation between the distance of class representations in the latent space and the transferability of the attack. Furthermore, the paper should analyze the distribution of class representations in the latent space and discuss how the proposed method exploits this distribution to achieve its goals. This analysis should include visualizations or quantitative measures that support the claims made about inter-class transferability. Without this, the reader cannot fully understand the method's mechanism and its limitations.\n\nThe formulation in Section 3.2 needs to be significantly improved to provide a clear and unambiguous definition of inter-class transferability. The current formula is too vague and does not adequately capture the relationship between different categories and their impact on the attack's success. The authors should consider defining inter-class transferability in terms of the attack success rate on a set of classes given that the model has been poisoned with triggers designed for a different set of classes. This would provide a more precise and measurable definition of inter-class transferability. Furthermore, the paper should discuss the limitations of the proposed definition and explore alternative definitions that may be more appropriate for different scenarios. The authors should also provide a more detailed explanation of how the principal components in the latent space are used to generate triggers and how these triggers are associated with different classes. This explanation should include a discussion of the encoding scheme used and its impact on the attack's success.\n\nThe experimental results require a more thorough analysis to understand the performance variations observed in Tables 1 and 2. The paper should provide a detailed explanation of why the baseline method suddenly outperforms the proposed method when the number of poisoned samples is increased from 5000 to 8000. Similarly, the paper should explain why the baseline method's attack success rate drops dramatically when the dataset size is increased from ImageNet-2K to ImageNet-4K. This analysis should include a discussion of the learning dynamics of both the proposed method and the baseline method, as well as the impact of the number of poisoned samples and the dataset size on these dynamics. The authors should also explore the sensitivity of the proposed method to different hyperparameters and discuss the potential limitations of the method under different experimental conditions. Without this analysis, the reader cannot fully understand the strengths and weaknesses of the proposed method and its applicability to different scenarios."
+      }
+    },
+    {
+      "id": "Y0sigSVVqG",
+      "rating": 6,
+      "content": {
+        "summary": "The paper presents a new approach for crafting universal backdoor attacks, i.e. backdoor attacks that target several classes at inference time, as opposed to traditional backdoor attacks that target a single class. In order to mount a universal backdoor attack, the adversary crafts triggers that increase the ASR on several classes simultaneously.  To that end, the authors leverage a pretrained model to extract the feature representation of the training samples, and then craft triggers that correlate with features used by samples from several classes. \n\nThe authors evaluate their attack on several subsets of ImageNet-21k, and against BadNet's baseline presented in Guo et al. By poisoning 0.39% of the training data, the authors are able to mount an effective backdoor attack when no defense is applied. The authors then test the effectiveness of their attack when several defenses are applied, and notice a drop in ASR although the attack remains effective. \n\nFinally, in order to test how much triggers applied to a single class help triggers applied to other classes, the authors fix the number of triggers in some classes, then vary the number of triggers in other classes, and observe the ASR over the fixed classes increases as more poisoned samples are added to other classes.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "3 good",
+        "strengths": "- the paper presents an interesting approach to backdoor attacks where triggers affect several classes simultaneously\n- the authors validate the effectiveness of their attack on a large scale dataset, and against several defenses",
+        "weaknesses": "- the required number of poisoned samples seems a bit high, even for imagnet. other papers have shown that around 300-500 samples are enough to mount an effective backdoor attack [1, 2]. this is in contrast with the results observed in Table 1, where the baseline attack is not successful even with 2k poisoned samples.\n- the authors only consider a single baseline model against which their attack is compared. this comparison is helpful, however, given the large number of poisoned samples required, it would be nice to see how other baselines would compare at that scale\n- the parameters of the defenses were tuned for a simple baseline (BadNets). the effectiveness of the attack might be very different if the parameters of the defense were tuned to the authors' attack\n\n[1] POISONING AND BACKDOORING CONTRASTIVE LEARNING, Carlini et al., 2022\n[2] WITCHES’ BREW: INDUSTRIAL SCALE DATA POISONING VIA GRADIENT MATCHING, Geiping et al., 2021",
+        "questions": "- can you please look into a setup with fewer poisoned samples? it should be possible to have a successful backdoor attack with close to 500 samples on ImageNet\n- can you also tune the parameters of the defense against each attack you are considering?\n-  if possible, can you provide a good baseline for attacks to compare against?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": " - the required number of poisoned samples seems a bit high, even for imagnet. other papers have shown that around 300-500 samples are enough to mount an effective backdoor attack [1, 2]. this is in contrast with the results observed in Table 1, where the baseline attack is not successful even with 2k poisoned samples.\n- the authors only consider a single baseline model against which their attack is compared. this comparison is helpful, however, given the large number of poisoned samples required, it would be nice to see how other baselines would compare at that scale\n- the parameters of the defenses were tuned for a simple baseline (BadNets). the effectiveness of the attack might be very different if the parameters of the defense were tuned to the authors' attack",
+        "suggestions": "The paper's exploration of universal backdoor attacks is novel and significant, but the experimental setup could be strengthened to better contextualize the results. Specifically, the high number of poisoned samples required for the attack to be effective raises concerns about its practicality. While the authors achieve a high attack success rate (ASR), the fact that the baseline attack fails even with 2000 poisoned samples suggests that the comparison might not be entirely fair, and that the baseline might not be well tuned. It would be beneficial to investigate the attack's performance with a significantly reduced number of poisoned samples, closer to the 300-500 range reported in other works [1, 2]. This would not only make the attack more realistic but also provide a more robust evaluation of its effectiveness. Furthermore, it would be valuable to analyze the sensitivity of the attack to the number of poisoned samples across different classes, as the current analysis only explores the effect of varying the number of triggers in some classes while keeping the number of triggers fixed in others. This analysis could reveal whether the attack is more sensitive to poisoning certain classes than others, which could have implications for practical deployment.\n\nTo further strengthen the experimental evaluation, it is crucial to compare the proposed attack against a wider range of baselines, not just a single one. The authors' approach to selecting samples for poisoning seems to be independent of the specific attack mechanism. Therefore, it would be insightful to evaluate the effectiveness of the sample selection strategy by using it with other backdoor attacks, such as BadNets or hidden-trigger attacks. This would provide a clearer understanding of whether the observed ASR is due to the sample selection process or the specific trigger crafting method. For instance, the authors could use their sample selection method to choose samples for a BadNets attack, and then compare the ASR of this attack with the ASR of the proposed attack. This would help isolate the contribution of the sample selection strategy. Additionally, it would be beneficial to compare against other state-of-the-art backdoor attacks to ensure the proposed method is competitive and not just an improvement over a weak baseline.\n\nFinally, the evaluation of the defenses needs to be more robust. The current approach of tuning the defense parameters against a simple BadNets attack and then testing against the proposed attack might not be sufficient. The effectiveness of a defense is highly dependent on its hyperparameters, and it is possible that the current parameter settings are not optimal for the proposed attack. Therefore, it is essential to tune the defense parameters specifically against the proposed attack to obtain a more realistic assessment of its robustness. This could involve a grid search or other optimization techniques to find the best defense parameters for each attack. Furthermore, it would be beneficial to explore the transferability of the defenses, i.e., whether a defense tuned against one attack is effective against other attacks. This would provide a more comprehensive understanding of the strengths and weaknesses of the proposed attack and the defenses."
+      }
+    }
+  ]
+}

papers/3bqesUzZPH/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "3bqesUzZPH",
+  "title": "FTA: Stealthy and Adaptive Backdoor Attack with Flexible Triggers on Federated Learning",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-16",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=3bqesUzZPH"
+}

papers/3bqesUzZPH/paper.md

@@ -0,0 +1,531 @@
+# FTA: STEALTHY AND ADAPTIVE BACKDOOR ATTACK WITH FLEXIBLE TRIGGERS ON FEDERATED LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Current backdoor attacks against federated learning (FL) strongly rely on universal triggers or semantic patterns, which can be easily detected and filtered by certain defense mechanisms such as norm clipping, trigger inversion and etc. In this work, we propose a novel generator-assisted backdoor attack, FTA, against FL defenses. We for the first time consider the natural stealthiness of triggers during global inference. In this method, we build a generative trigger function that can learn to manipulate the benign samples with naturally imperceptible trigger patterns (*stealthy*) and simultaneously make poisoned samples include similar hidden features of the attacker-chosen label. Moreover, our trigger generator repeatedly produces triggers for each sample (*flexibility*) in each FL iteration (*adaptivity*), allowing it to adjust to changes of hidden features between global models of different rounds. Instead of using universal and predefined triggers of existing works, we break this wall by providing three desiderate (i.e., stealthy, flexibility and adaptivity), which helps our attack avoid the presence of backdoorrelated feature representations. Extensive experiments confirmed the effectiveness (above 98% attack success rate) and stealthiness of our attack compared to prior attacks on decentralized learning frameworks with eight well-studied defenses.
+
+# 1 INTRODUCTION
+
+Federated learning (FL) has recently provided practical performance in various real-world applications and tasks, such as prediction of oxygen requirements of symptomatic patients with COVID-19 [\(Dayan](#page-9-0) [et al., 2021\)](#page-9-0), autonomous driving [\(Nguyen et al., 2022a\)](#page-10-0), Gboard [\(Yang et al., 2018\)](#page-12-0) and Siri [\(Paulik](#page-11-0) [et al., 2021\)](#page-11-0). It supports collaborative training of an accurate global model by allowing multiple agents to upload local updates, such as gradients or weights, to a server without compromising local datasets. However, this decentralized paradigm unfortunately exposes FL to a security threat backdoor attacks [\(Bhagoji et al., 2019;](#page-9-1) [Xie et al., 2019;](#page-12-1) [Wang et al., 2020;](#page-11-1) [Zhang et al., 2022b;](#page-12-2) [Li](#page-10-1) [et al., 2023\)](#page-10-1). Existing backdoor defenses on FL possess the capability to scrutinize the anomaly of malicious model updates. Prior attacks fail to achieve adequate stealthiness under those robust FL systems due to malicious parameter perturbations introduced by the backdoor task.
+
+We summarize the following open problems from the existing backdoor attacks against FL[1](#page-0-0) :
+
+P1: The abnormality of feature extraction in convolutional layers. Existing attacks use patchbased triggers ("squares", "stripe" and etc.) [\(Bagdasaryan et al., 2020;](#page-9-2) [Xie et al., 2019;](#page-12-1) [Zhang et al.,](#page-12-2) [2022b;](#page-12-2) [Li et al., 2023\)](#page-10-1) on a fixed position or semantic backdoor triggers (shared attributes within the same class) [\(Bagdasaryan et al., 2020;](#page-9-2) [Wang et al., 2020\)](#page-11-1). Consequently, the poisoned samples are misclassified by the victim model towards the target label after backdoor training. However, we found that prior attacks manipulate the samples with universal patterns along the whole training iterations, which fails to provide enough "stealthiness" of the hidden features of the poisoned samples. The backdoor training with such triggers attaches extra hidden features to the backdoor patterns or revises current hidden features from the feature space in benign classes domain. This makes the latent representations of poisoned samples extracted from filters *standalone* compared to the benign counterparts. Figure [5](#page-8-0) (a) intuitively illustrates the statement. Therefore, unrestricted trigger patterns can cause aberrant weight changes in the filters for backdoor patterns. This abnormality induces
+
+<span id="page-0-0"></span><sup>1</sup>Due to space limit, we review prior backdoor attacks and defenses on FL in Appendix [A.1](#page-13-0)
+
+<span id="page-1-0"></span>![](figures/_page_1_Figure_1.jpeg)
+
+Figure 1: Overview of FTA. (I) Learn the optimal trigger generator gξ. (II) Train malicious model fθ. Inference/Backdoor Attack: The global model performs well on benign tasks while misclassifying the poisoned samples to the target label.
+
+weight outliers which makes the backdoor attacks vulnerable to filter-wise adversarial pruning [\(Wu &](#page-12-3) [Wang, 2021;](#page-12-3) [Liu et al., 2018;](#page-10-2) [Wu et al., 2020a\)](#page-12-4).
+
+P2: The abnormality of backdoor routing in fully connected layers. Compared with the benign model, the malicious model needs to be trained on one more task, i.e. backdoor task. Specifically, in fully connected (FC) layers, the backdoor task is to establish a *new* routing [\(Wang et al., 2018;](#page-11-2) [Carnerero-Cano et al., 2023\)](#page-9-3), separated from benign ones, between the independent hidden features of attacker's universal pattern and its corresponding target label, which yields an anomaly at the parameter level. The cause of this anomaly is natural, since the output neurons for the target label must contribute to both benign and backdoor routing, which requires significant weight/bias adjustments to the neurons involved. We note that last FC layer in the current mainstream neural networks are always with a large fraction of the total number of parameters (e.g., 98% for Classic CNN, 62% in ResNet18). As mentioned in [\(Rieger et al., 2022\)](#page-11-3), the final FC layer of the malicious classifier presents significantly greater abnormality than other FC layers, with backdoor routing being seen as the secondary source of these abnormalities. Note that these abnormalities (P1-2) would arise in existing universal trigger designs under FL.
+
+P3: The perceptible trigger for inference. Perhaps, it is not necessary to guarantee natural stealthiness of triggers on training data against FL, since its accessibility is limited to each client exclusively due to the privacy issue. However, we pay attention to the trigger stealthiness during the inference stage, in which a poisoned sample with a naturally stealthy trigger can mislead human inspection. The test input with perceptible perturbation in FL [\(Bagdasaryan et al., 2020;](#page-9-2) [Xie et al.,](#page-12-1) [2019;](#page-12-1) [Zhang et al., 2022b;](#page-12-2) [Li et al., 2023\)](#page-10-1) can be easily identified by an evaluator or a user who can distinguish the difference between 'just' an incorrect classification/prediction of the model and the purposeful wrong decision due to a backdoor in the test/use stage.
+
+P1-3 can fatally harm the stealthiness and effectiveness of prior attacks under robust FL systems. The stealthiness issue can be seen in two aspects (trigger/routing). For P3, the visible fixed triggers contain independent hidden features, and these hidden features lead to a new backdoor routing as discussed in P1-2. Meanwhile, the backdoor inference stage cannot perform properly because those triggers are not sufficiently hidden. For example, we recall that DBA [\(Xie et al., 2019\)](#page-12-1), Neurotoxin [\(Zhang et al., 2022b\)](#page-12-2) and 3DFed [\(Li et al., 2023\)](#page-10-1) use universal patterns that can be clearly filtered out by trigger inversion method such as FLIP [\(Zhang et al., 2023\)](#page-12-5). Moreover, P1-2 can cause weight dissimilarity between benign and backdoor routing. And this dissimilarity can be easily detected by cluster-based filtering, such as FLAME [\(Nguyen et al., 2022b\)](#page-10-3). Efficiency problem is also striking for P1-2 since extra computational budget is required to learn the new features of the poisoned data and to form the correspondent backdoor routing. In this work, we regard the problems P1-3 as the *stealthiness* of backdoor attacks in the context of FL.
+
+A natural question then arises: *could we eliminate the anomalies introduced by new backdoor features and routing (i.e., tackling P1-2) while making the trigger sufficiently stealthy for inference on decentralized scenario (i.e., addressing P3)?*
+
+<span id="page-2-0"></span>![](figures/_page_2_Figure_1.jpeg)
+
+Figure 2: Visualization of backdoored images. Top: the original image; backdoored samples generated by baseline/Neurotoxin, DBA, Edge-case, and FTA; Bottom: the residual maps. Our flexible triggers appear as imperceptible noise.
+
+To provide a concrete answer, we propose a stealthy generator-assisted backdoor attack, FTA, to adaptively (per FL iteration) provide triggers in a flexible manner (per sample) on decentralized setup. FTA achieves a satisfied stealthiness by producing imperceptible triggers with a generative neural network (GAN) [\(Goodfellow et al., 2014;](#page-10-4) [Arjovsky et al., 2017\)](#page-9-4) in a *flexible* way for each sample and in an *adaptive* manner during entire FL iterations. To address P3, our triggers should provide natural stealthiness to avoid inspection during inference. To solve P1, the difference of hidden features between poisoned data and benign counterparts should be minimized. Due to the imperceptibility between poisoned and benign data in latent representation, the correspondent backdoor routing will not be formed and thus P2 is effectively addressed.
+
+Specifically, the generator is learnt to produce triggers for each sample, which can ensure similar latent features of poisoned samples to benign ones with target label (P1). This idea can reduce the abnormality of creating an extra routing for backdoor in P2 since the latent features make poisoned data "look like" benign ones with target label. Thus our trigger is less perceptible and more flexible than predefined patch-based ones in prior attacks (P3). Further, to make the flexible trigger robust and adaptive to the changes in global model, the generator is continuously trained across FL iterations. Compared with existing works using fixed and universal trigger patterns, we break this wall and for the first time make the generated trigger to be stealthy, flexible and adaptive in FL setups. Compared to universal trigger-based attacks, e.g., 3DFed, our trigger-assisted attack can effectively evade (universal) trigger inversion defense such as FLIP. Since our trigger generation method forces poisoned samples to share similar hidden feature as benign one, the benign routing can be mostly reused by poisoned data and thus the backdoor task is not purely learned from scratch. Our trigger generation ensures that poisoned samples have similar hidden features to benign ones, allowing poisoned data to reuse the benign routing. As a result, the backdoor task does not need to be learned entirely from scratch, thereby achieving high attack efficiency, as shown in Figure [3.](#page-6-0) Finally, we formulate the process of finding optimal trigger generator and training malicious model in a bi-level, non-convex and constrained optimization problem, and achieve optimum by proposing a simple but practical optimization process. We illustrate learning the trigger generator, training the malicious model and testing the backdoor in Figure [1,](#page-1-0) and showcase various backdoor images in Figure [2](#page-2-0) to demonstrate the imperceptible perturbation by our generator.
+
+### Our main contributions are summarized as follows:
+
+- We propose a stealthy generator-assisted backdoor attack (FTA) against robust FL. Instead of utilizing an universal trigger pattern, we design a novel trigger generator that produces naturally imperceptible triggers during inference stage. Our flexible triggers provide hidden feature similarity of benign data and successfully lead poisoned data to reuse benign routing of target label. Hereby FTA can avoid anomaly in parameter space and improve attack effectiveness.
+- We design a new learnable and adaptive generator that can learn the flexible triggers for global model at current FL iteration to achieve the best attack effectiveness. We propose a bi-level and constrained optimization problem to find our optimal generator each iteration efficiently. We then formulate a customized learning process and solve it with reasonable complexity, making it applicable to the FL scenario.
+- Finally, we present intensive experiments to empirically demonstrate that the proposed attack provides state-of-the-art effectiveness and stealthiness against existing eight well-study defense mechanisms under four benchmark datasets.
+
+# 2 THREAT MODEL AND INTUITION
+
+### 2.1 THREAT MODEL
+
+Attacker's Knowledge & Capabilities: We consider the same threat model as in prior works [\(Bagdasaryan et al., 2020;](#page-9-2) [Bhagoji et al., 2019;](#page-9-1) [Wang et al., 2020;](#page-11-1) [Zhang et al., 2022b;](#page-12-2) [Shejwalkar](#page-11-4) [et al., 2021;](#page-11-4) [Panda et al., 2022\)](#page-11-5), where the attacker can have full access to malicious agent device(s), local training processes and training datasets. Furthermore, we do not require the attacker to know the FL aggregation rules applied in the server.
+
+Attacker's Goal: Unlike untargeted poisoning attacks [\(Jagielski et al., 2018\)](#page-10-5) preventing the convergence of the global model, the goal of our attack is to manipulate malicious agents' local training processes to achieve high accuracy in the backdoor task without undermining benign accuracy.
+
+# 2.2 OUR INTUITION
+
+Recall that prior attacks use universal predefined patterns (see Figure [2\)](#page-2-0) which cannot guarantee stealthiness (P1-3) since the poisoned samples are visually inconsistent with natural inputs. These universal triggers (including tail data) used in whole FL iterations with noticeable modification can introduce new hidden features during extraction and further influence the process of backdoor routing. Consequently, this makes prior attacks be easily detected by current robust defenses due to P1-2. Also, the inconsistency between benign and poisoned samples tends to be detected by defenders during the global inference (P3) and the triggers can be inversed in decentralized setup.
+
+Compared to prior attacks that focus on manipulating parameters, we bridge the gap and focus on designing stealty triggers. To address P1-3, a well-designed trigger should provide 4 superiorities: *i*) the poisoned sample is naturally stealthy to the original benign sample; *ii*) the trigger is able to achieve hidden feature similarity between poisoned and benign samples of target label; *iii*) the trigger can eliminate the anomaly between backdoor and benign routing during learning; *iv*) the trigger design framework can evade robust FL defenses. A practical and effective solution that provides these advantages over prior works simultaneously is the design of *flexible* triggers. The optimal flexible triggers are learnt to make latent representations of poisoned samples similar to benign ones, thereby making the reuse of benign routing possible, which can naturally diminish the presence of outlier at parameter level. We propose a learnable and adaptive trigger generator to produce flexible and stealthy triggers.
+
+- v.s. Trigger generators in centralized setting. One may argue that the attacker can simply apply a similar (trigger) generator in centralized setup [\(Doan et al., 2021b;](#page-9-5)[a;](#page-9-6) [Zhao et al., 2022b;](#page-12-6) [Li et al.,](#page-10-6) [2021b;](#page-10-6) [Zhong et al., 2022\)](#page-12-7) on FL to achieve imperceptible trigger and stealthy model update.
+- Stealthiness. For example, the attacker can use a generator to produce imperceptible triggers for poisoned samples and make their hidden features similar to original benign samples' as in [\(Zhao](#page-12-6) [et al., 2022b;](#page-12-6) [Zhong et al., 2022\)](#page-12-7). This, however, cannot ensure the indistinguishable perturbation of model parameters (caused by backdoor routing) during malicious training and fail to capture the stealthiness (in P1-2) in FL setup. This is so because it only constrains the distinction of the input domain and the hidden features between poisoned and benign samples other than the hidden features between poisoned and benign samples of target label. In other words, a centralized generator masks triggers in the input domain and feature space of benign samples, conceals the poisoned sample for visibility and feature representation, whereas this cannot ensure the absence of backdoor routing for poisoned data. A stealthy backdoor attack on FL should mitigate the routing introduced by backdoor task and guarantee the stealthiness of model parameters instead of just the hidden features of poisoned samples compared to their original inputs.
+
+Learning. The centralized learning process of existing trigger generators cannot directly apply to decentralized setups due to the continuously changing of global model and time consumption of training trigger generator. As an example, IBA [\(Zhong et al., 2022\)](#page-12-7) directly constrains the distance of feature representation between benign and poisoned samples. This approach cannot achieve satisfied attack effectiveness due to inaccurate hidden features of benign samples before global model convergence. In contrast, we propose a customized optimization method for FL scenarios that can learn the optimal trigger generator for global model of current iteration to achieve the best attack effectiveness and practical computational cost as depicted in Section [3.3](#page-5-0) and Appendix [A.10.](#page-22-0)
+
+• Defenses. We note that the robust FL aggregator can only access local updates of all agents other
+
+than local training datasets. The centralized backdoor attack does not require consideration of the magnitude of the malicious parameters. However, in reality, the magnitude of malicious updates is usually larger than that of benign updates under FL setups. In that regard, norm clipping can effectively weaken and even eliminate the impact of the backdoor (Sun et al., 2019; Shejwalkar et al., 2021). Based on the flexibility of our triggers, we advance the state-of-the-art by enhancing the stealthiness and effectiveness of the backdoor attack even against well-studied defenses such as trigger inversion method on FL, e.g. FLIP. We note that FLIP is effective in removing backdoors with patch-based triggers, whereas our proposed attack can effectively evade this SOTA defense.
+
+### 3 Proposed Methodology: FTA
+
+#### 3.1 PROBLEM FORMULATION
+
+ $f(x) = y, f(\mathcal{T}(x)) = \eta(y).$ 
+
+Based on the federated scenario in Appendix A.1.1, the attacker m trains the malicious models to alter the behavior of the global model  $\theta$  under ERM as follows:  $\theta_m^* = \underset{\theta}{\operatorname{argmin}} \sum_{(x,y) \in D^{cln} \cup D^{bd}} \mathcal{L}(f_{\theta}(x),y)$ , where  $D^{cln}$  is clean training set and  $D^{bd}$  is a small fraction of clean samples in  $D^{cln}$  to produce poisoned data by the attacker. Each clean sample (x,y) in the selected subset is transformed into a poisoned sample as  $(\mathcal{T}(x), \eta(y))$ , where  $\mathcal{T}: \mathcal{X} \to \mathcal{X}$  is the trigger function and  $\eta$  is the target labeling function. And the poison fraction is defined as
+
+ $|D^{bd}|/|D^{cln}|$ . During inference, for a clean input x and its true label y, the learned f behaves as:
+
+To generate a stealthy backdoor, our main goal is to learn a stealthy trigger function  $\mathcal{T}:\mathcal{X}\to\mathcal{X}$  to craft poisoned samples and a malicious backdoor model  $f_{\theta_m^*}$  to inject backdoor behavior into the global model with the followings: 1) the poisoned sample  $\mathcal{T}(x)$  provides an imperceptible perturbation to ensure that we do not bring distribution divergences between clean and backdoor datasets; 2) the injected global classifier simultaneously performs indifferently on test input x compared to its vanilla version but changes its prediction on the poisoned image  $\mathcal{T}(x)$  to the target class  $\eta(y)$ ; 3) the latent representation of backdoor sample  $\mathcal{T}(x)$  is similar to its benign input x. Inspired by recent works in learning trigger function backdoor attacks (Cheng et al., 2021; Doan et al., 2021b; Nguyen & Tran, 2020; Zhao et al., 2022b), we propose to jointly learn  $\mathcal{T}(\cdot)$  and poison  $f_{\theta}$  via the following constrained optimization:
+
+<span id="page-4-0"></span>
+$$\min_{\theta} \sum_{(x,y)\in D^{cln}} \mathcal{L}(f_{\theta}^{t}(x), y) + \sum_{(x,y)\in D^{bd}} \mathcal{L}(f_{\theta}^{t}(\mathcal{T}_{\xi^{*}(\theta)}(x)), \eta(y))$$
+
+$$s.t. \quad (i) \quad \xi^{*} = \underset{\xi}{\operatorname{argmin}} \sum_{(x,y)\in D^{bd}} \mathcal{L}(f_{\theta}^{t}(\mathcal{T}_{\xi}(x)), \eta(y))$$
+
+$$(ii) \quad d(\mathcal{T}_{\xi}(x), x) \leq \epsilon$$
+(1)
+
+where t is FL round, d is a distance measurement function,  $\epsilon$  is a constant threshold value to ensure a small perturbation by  $l_2$ -norm constraint,  $\xi$  is the parameters of trigger function  $\mathcal{T}(\cdot)$ . In the above bilevel problem, we optimize a generative trigger function  $\mathcal{T}_{\xi^*}$  that is associated with an optimally malicious classifier. The poisoning training finds the optimal parameters  $\theta$  of the malicious classifier to minimize the linear combination of the benign and backdoor objectives. Meanwhile, the generative trigger function is trained to manipulate poisoned samples with imperceptible perturbation, while also finding the optimal trigger that can cause misclassification to the target label. The optimization in Equation (1) is a challenging task in FL scenario since the target classification model  $f_{\theta}$  varies in each iteration and its non-linear constraint. Thus, the learned trigger function  $\mathcal{T}_{\xi}$  is unstable based on dynamic  $f_{\theta}$ . For the optimization, we consider two steps: learning trigger generator and poisoning training, and further execute these steps respectively (not alternately) to optimize  $f_{\theta}$  and  $\mathcal{T}_{\xi}$ . The details are depicted in Algorithm 1 (please see Appendix A.2 for more optimization details).
+
+### 3.2 FTA TRIGGER FUNCTION
+
+We train  $\mathcal{T}_{\xi}$  based on a given generative network  $g_{\xi}$ , i.e., our FTA trigger generator. Similar to the philosophy of generative trigger technology (Doan et al., 2021b; Zhao et al., 2022b), we design our
+
+trigger function to guarantee: 1) The perturbation of poisoned sample is imperceptible; 2) The trigger generator can learn features of input domain of target label to fool the global model. Given a benign sample x and corresponding label y, we formally model  $\mathcal{T}_{\xi}$  with restricted perturbation as follows:
+
+<span id="page-5-2"></span>
+$$\mathcal{T}_{\xi}(x) = x + g_{\xi}(x), \quad \|g_{\xi}(x)\|_{2} \le \epsilon \quad \forall x, \quad \eta(y) = c, \tag{2}$$
+
+where  $\xi$  is the learnable parameters of the FTA trigger generator and  $\epsilon$  is the trigger norm bound to constrain the value of the generative trigger norm. We use the same neural network architecture as (Doan et al., 2021b) to build our trigger generator  $g_{\xi}$ , i.e., an autoencoder or more complex U-Net structure (Ronneberger et al., 2015). The  $l_2$ -norm of the imperceptible trigger noise generated by  $g_{\xi}$  is strictly limited within  $\epsilon$  by:  $\frac{g_{\xi}(x)}{\max(1,||g_{\xi}(x)||_2/\epsilon)}$ . Note that, under Equation (2), the distance d in Equation (1) is  $l_2$ -norm on the image-pixel space between  $\mathcal{T}_{\xi}(x)$  and x.
+
+#### <span id="page-5-0"></span>3.3 FTA'S OPTIMIZATION
+
+To address the constrained optimization in Equation (1), existing function based attacks alternately updating  $f_{\theta}$  while keeping  $\mathcal{T}_{\xi}$  unchanged, or the other way round, for many iterations. However, according to our trials, we find that simply updating parameters makes the training process unstable and harms the backdoor performance. Inspired by (Doan et al., 2022), one local round of FTA attack is divided into two phases, and each phase is executed for only one iteration with fewer epochs. In phase one, we fix the classification model  $f_{\theta}$  and only learn the trigger function  $\mathcal{T}_{\xi}$ . In phase two, we use the pre-trained  $\mathcal{T}_{\xi^*}$  to generate the poisoned dataset and train the malicious classifier  $f_{\theta}$ . Since the number of poisoning epochs of malicious agents is fairly small, which means  $f_{\theta}$  would not vary too much during poisoning training process, the hidden features of samples in target label extracted from  $f_{\theta}$  will also remain similarly. The pre-trained  $\mathcal{T}_{\xi^*}$  can still match with the final locally trained  $f_{\theta}$ .
+
+In order to make flexible triggers generated by  $g_{\xi}$  adaptive to global models in different rounds,  $g_{\xi}$  should be continuously trained. If a malicious agent is selected more than one round to participate in FL iterations, it can keep training on previous pre-trained  $g_{\xi}$  under new global model to make our flexible triggers match with hidden features of benign samples with target label from new model.
+
+#### <span id="page-5-1"></span>**Algorithm 1** FTA Backdoor Attack
+
+**Input**: Clean dataset  $D_{cln}$ , Global model  $f_{\theta}^t$  at round t, Learning rate of malicious model  $\gamma_f$  and trigger function  $\gamma_{\mathcal{T}}$ , Batch of clean dataset  $B_{cln}$  and poisoned dataset  $B_{bd}$ , Epochs to train trigger function  $e_{\mathcal{T}}$  and malicious model  $e_f$ .
+
+**Output**: Malicious model update  $\delta^*$ .
+
+- 1: Initialize parameters of trigger function  $\xi$  and global model:  $f_a^t$ .
+- 2: Sample subset  $D_{bd}$  from  $D_{cln}$ .
+- 3: // Stage I: Update flexible  $\mathcal{T}$ .
+- 4: Sample minibatch  $(x, y) \in B_{bd}$  from  $D_{bd}$
+- 5: for  $i=1,2,\cdots,e_{\mathcal{T}}$  do
+
+- 6: Optimize  $\xi$  by using SGD with fixed  $f_{\theta}^{t}$  on  $B_{bd}$ :  $\xi \leftarrow \xi \gamma_{\mathcal{T}} \nabla_{\xi} \mathcal{L}(f_{\theta}^{t}(\mathcal{T}_{\xi}(x)), \eta(y))$
+- 7: end for
+- 8:  $\xi^* \leftarrow \xi$
+- 9: // Stage II: Train malicious model  $f^t$ .
+- 10: Sample minibatch  $(x, y) \in B_{cln}$  from  $D_{cln}$  and  $(x_m, y_m) \in B_{bd}$  from  $D_{bd}$
+- 11: **for**  $i = 1, 2, \cdots, e_f$  **do**
+- 12: Optimize  $\theta$  by using SGD with fixed  $\mathcal{T}_{\xi^*}$  on  $B_{cln}$ ,  $B_{bd}$ :  $\theta \leftarrow \theta \gamma_f \nabla_{\theta} (\mathcal{L}(f_{\theta}^t(x,y)) + \mathcal{L}(f_{\theta}^t(\mathcal{T}_{\xi}(x_m)), \eta(y_m)))$
+- 13: **end for**
+- 14:  $\theta^* \leftarrow \theta$
+- 15: Compute malicious update:  $\delta^* \leftarrow \theta^* \theta$
+
+### 4 ATTACK EVALUATION
+
+# 4.1 EXPERIMENTAL SETUP
+
+**Datasets and Models.** We demonstrate the effectiveness of FTA backdoor through comprehensive experiments on four publicly available datasets, namely Fashion-MNIST (Xiao et al., 2017), FEM-NIST (Caldas et al., 2018), CIFAR-10 (Krizhevsky et al., 2009), and Tiny-ImageNet (Le & Yang, 2015). The classification model used in the experiments includes Classic CNN, VGG11 (Simonyan & Zisserman, 2015), and ResNet18 (He et al., 2016). These datasets and models are representative
+
+<span id="page-6-0"></span>![](figures/_page_6_Figure_1.jpeg)
+
+Figure 3: Fixed-frequency attack performance under FedAvg. FTA is more effective than others.
+
+and commonly used in existing backdoor and FL research works. The overview of our models is described in Appendix [A.6.](#page-19-0) The details of tasks are depicted in Appendix [A.3.](#page-15-0)
+
+Attack Settings. As in Neurotoxin [\(Zhang et al., 2022b\)](#page-12-2), we assume that the attacker can only compromise a limited number of agents (<1% ) in practice [\(Shejwalkar et al., 2021\)](#page-11-4) and uses them to launch the attack by uploading manipulated gradients to the server. Malicious agents can only participate in a constrained number of training rounds in FL settings. Note even if the attacker has above restrictions, our attack can still be effective, stealthy and robust against defenses (see Figures [3](#page-6-0) and [4\)](#page-7-0). Also, the attack effectiveness should last even though the attacker stops the attack under robust FL aggregators (see Figure [6](#page-16-0) in Appendix [A.4.1\)](#page-16-1). We test stealthiness and durability of FTA with two attack modes respectively, i.e., fixed-frequency and few-shot as Neurotoxin. *i*) Fixed-frequency mode: The server randomly chooses 10 agents among all agents. The attacker controls exactly one agent in each round in which they participate. For other rounds, 10 benign agents are randomly chosen among all agents. *ii*) Few-shot mode: The attacker participates only in Attack\_num rounds. During these rounds, we ensure that one malicious agent is selected for training. After Attack\_num rounds or backdoor accuracy has reached 95%, the attack will stop. Under this setting, the attack can take effect quickly, and gradually weaken by benign updates after the attack is stopped.
+
+Evaluation Metrics. We evaluate the performance based on backdoor accuracy (BA) and benign accuracy according to the following criteria: effectiveness and stealthiness against current SOTA defense methods under fixed-frequency mode, durability evaluated under few-shot mode.
+
+Comparison. We compare FTA with three SOTA attacks, namely DBA, Neurotoxin and Edge-case [\(Wang et al., 2020\)](#page-11-1), and the baseline attack method described in [\(Zhang et al., 2022b\)](#page-12-2) under different settings and ten defenses (a variant of norm clipping based on [\(Sun et al., 2019\)](#page-11-6), FLAME, Multi-Krum [\(Blanchard et al., 2017\)](#page-9-10), Trimmed-mean [\(Yin et al., 2018\)](#page-12-9), RFA [\(Pillutla et al., 2022\)](#page-11-9), SparseFed [\(Panda et al., 2022\)](#page-11-5), SignSGD [\(Bernstein et al., 2019\)](#page-9-11), Foolsgold [\(Fung et al., 2020\)](#page-9-12)), RLR [\(Ozdayi](#page-11-10) [et al., 2021\)](#page-11-10) and Pruning [\(Wu et al., 2020b\)](#page-12-10). We show that FTA outperforms 3 SOTA attacks (under 10 robust FL defenses) by conducting experiments on different computer vision tasks (please see Appendix [A.7](#page-19-1) for more experimental setup details).
+
+# 4.2 ATTACK EFFECTIVENESS
+
+Attack effectiveness under fixed-frequency mode. Compared to the attacks with unified triggers, FTA converges much faster and delivers the best BA in all cases since our poisoned data can reuse benign routing of target label, see Figure [3.](#page-6-0) It can yield a high backdoor accuracy on the server model within very few rounds (<50) and maintain above 97% accuracy on average. Especially in Tiny-ImageNet, FTA reaches 100% accuracy extremely fast, with at least 25% advantage compared to others. In CIFAR-10, FTA achieves nearly 83% BA after 50 rounds which is 60% higher than other attacks on average. There is only <5% BA gap between FTA and Edge-case on FEMNIST in the beginning and later, they reach the same BA after 100 rounds. We note that the backdoor task of Edge-case in FEMNIST is relatively easy, mapping 7-like images to the target label of digit "1", which makes its convergence slightly faster than ours.
+
+Attack effectiveness under few-shot mode. As an independent interest, we test the durability of the attacks during training stage in this setting. According to Appendix [A.4.1,](#page-16-1) FTA has long-term attack effectiveness even if we stop attacking early since the poisoned data with our well-learned triggers contain similar features to benign data and can be naturally misclassified into the target label with certain confidence by server model. Due to space limit, please see Appendix [A.4.1](#page-16-1) for more details.
+
+Influence on Benign accuracy and computational cost. We include all benign accuracy results across tasks in Appendix [A.5.](#page-18-0) Like other SOTA attacks, FTA has a minor effect (no more than 1.5%)
+
+<span id="page-7-0"></span>![](figures/_page_7_Figure_1.jpeg)
+
+Figure 4: Attack stealthiness against defenses. (a)-(d): The variant of norm clipping; (e)-(h): FLAME. on benign accuracy. Our attack does not significantly increase the computational and time cost due to our optimization procedure (see Appendix [A.10](#page-22-0) for details).
+
+# 4.3 STEALTHINESS AGAINST DEFENSIVE MEASURES
+
+We test the stealthiness (P1-2) and robustness of FTA and other attacks using 8 SOTA robust FL defenses introduced in Appendix [A.1.3,](#page-14-1) such as norm clipping and FLAME, under fixed-frequency scenarios. All four tasks are involved in this defense evaluation. The results, see Figure [4](#page-7-0) show that FTA can break the listed defenses. Beyond this, we also evaluate different tasks on Multi-Krum, Trimmed-mean, RFA, SignSGD, Foolsgold and SparseFed. FTA maintains its stealthiness and robustness under these defenses. We put results of compared attacks under defenses in Appendix [A.4.](#page-15-1)
+
+# 4.3.1 RESISTANCE TO VECTOR-WISE SCALING
+
+We use the norm clipping as the vector-wise scaling defense method, which is regarded as a potent defense and has proven effective in mitigating prior attacks [\(Shejwalkar et al., 2021\)](#page-11-4). On the server side, norm clipping is applied on all updates before performing FedAvg. Inspired by [\(Sun et al.,](#page-11-6) [2019\)](#page-11-6), we utilize the variant of this method in our experiments. As introduced in Appendix [A.3,](#page-15-0) if we begin the attack from scratch, the norm of benign updates will be unstable and keep fluctuating, making us hard to set a fixed norm bound for all updates. We here filter out the biggest and smallest updates and compute the average norm magnitude based on the rest updates, and set it as the norm bound in current FL iteration.
+
+As shown in Figure [4](#page-7-0) (a)-(d), this variant of norm clipping can effectively undermine prior attacks in Fashion-MNIST, CIFAR-10, and Tiny-ImageNet. It fails in FEMNIST because benign updates have a larger norm (for example, 1.2 in FEMNIST at round 10, but only 0.3 in Fashion-MNIST), which cannot effectively clip the norm of malicious updates, thus resulting in a higher BA of existing attacks. We see that FTA provides the best BA which is less influenced by clipping than others. FTA only needs a much smaller norm to effectively fool the global model. Although converging a bit slowly in FEMNIST, FTA can finally output a similar performance (above 98%) compared to others.
+
+# 4.3.2 RESISTANCE TO CLUSTER-BASED FILTERING
+
+The cluster-based filtering defense method is FLAME, which has demonstrated its effectiveness in mitigating SOTA attacks against FL. It mainly uses HDBSCAN clustering algorithm based on cosine similarity between all updates and strains the updates with the least similarity compared with other updates. In Figure [4](#page-7-0) (e)-(h), we see that FLAME can effectively sieve malicious updates of other attacks in Fashion-MNIST and CIFAR-10, but provides relatively weak effectiveness in FEMNIST and Tiny-ImageNet. This is so because data distribution among different agents are fairly in non-i.i.d. manner. Cosine similarity between benign updates is naturally low, making malicious update possibly evade from the clustering filter.
+
+Similar to result of Multi-Krum (see Appendix [A.4.2\)](#page-16-2), FTA achieves >99% BA and finishes the convergence within 50 rounds in CIFAR-10 and Tiny-ImageNet, while delivering an acceptable
+
+<span id="page-8-0"></span>![](figures/_page_8_Figure_1.jpeg)
+
+Figure 5: (a)-(b): T-SNE visualization of hidden features of input samples in CIFAR-10. The hidden features between poisoned and benign samples of target label is indistinguishable in FTA framework. (c)-(d): Similarity comparison between benign & malicious updates. FTA's malicious updates is more similar to benign updates than the baseline attack's.
+
+degradation of accuracy, <20%, in Fashion-MNIST. In FEMNIST, FTA converges slightly slower than baseline and Neurotoxin but eventually maintains a similar accuracy with only 2% difference. The result proves that FTA enforces malicious updates to have highly cosine-similarity against benign updates due to same reason in Appendix [A.4.2,](#page-16-2) so it can bypass defenses based on model similarity.
+
+# 4.4 EXPLANATION VIA FEATURE VISUALIZATION BY T-SNE
+
+We use t-SNE [\(Van der Maaten & Hinton, 2008\)](#page-11-11) visualization result on CIFAR-10 to illustrate why FTA is more stealthy than the attacks without "flexible" triggers. We select 1,000 images from different classes uniformly and choose another 100 images randomly from the dataset and add triggers to them (in particular, patch-based trigger "square" in baseline method, flexible triggers in FTA). To analyze the hidden features of these samples, we use two global poisoned models injected by baseline attack and FTA respectively. We exploit the output of each sample in the last convolutional layer as the feature representation. Next, we apply dimensionality reduction techniques and cluster the latent representations of these samples using t-SNE. From Figure [5](#page-8-0) (a)-(b), We see that in the baseline, the distance of clusters between images of the target label "7" and the poisoned images are clearly distinguishable. So the parameters responsible for backdoor routing should do adjustments to map the hidden representations of poisoned images to target label. In FTA, the hidden features of poisoned data overlapped with benign data of target label, which eliminates the anomaly in feature extraction (P1). FTA can reuse the benign routing in FC layers for backdoor tasks, resulting in much less abnormality in backdoor routing (P2), thus the malicious updates can be more similar to benign ones, see Figure [5](#page-8-0) (c)-(d), producing a natural parameter stealthiness.
+
+# 4.5 NATURAL STEALTHINESS
+
+We evaluate natural stealthiness of our poisoned data by SSIM [\(Wang et al., 2004\)](#page-12-11) and LPIPS [\(Zhang](#page-12-12) [et al., 2018\)](#page-12-12) to indicate that P3 is well addressed by flexible triggers (see Appendix [A.9](#page-22-1) for results).
+
+# 4.6 ABLATION STUDY IN FTA ATTACK
+
+We here analyze several hyperparameters that are critical for the FTA's performance including trigger size, poison fraction and batch size of our generator (please see Appendix [A.8](#page-20-0) for details).
+
+# 5 CONCLUSION
+
+We design an effective and stealthy backdoor attack against FL called FTA by learning an adaptive generator to produce imperceptible and flexible triggers, making poisoned samples have similar hidden features to benign samples with target label. FTA can provide stealthiness and robustness in making hidden features of poisoned samples consistent with benign samples of target label; reducing the abnormality of parameters during backdoor task training; manipulating triggers with imperceptible perturbation for training/testing stage; learning the adaptive trigger generator across different FL rounds to generate flexible triggers with best performance. The empirical experiments demonstrate that FTA can achieve a practical performance to evade SOTA FL defenses. Due to the space limit, we present discussions on the proposed attack and experiments in Appendix [A.12.](#page-23-0) We hope this work can inspire follow-up studies that provide more secure and robust FL aggregation algorithms.
+
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+
+### A APPENDIX
+
+#### <span id="page-13-0"></span>A.1 RELATED WORK
+
+#### <span id="page-13-1"></span>A.1.1 FEDERATED LEARNING
+
+Consider the empirical risk minimization (ERM) in FL setting where the goal is to learn a global classifier  $f_{\theta}: \mathcal{X} \to \mathcal{Y}$  that maps an input  $x \in \mathcal{X}$  to a target label  $y \in \mathcal{Y}$ . Recall that the FL server cannot access to training dataset. It aggregates the parameters/gradients from local agents performing centralized training with local datasets. The de-facto standard rule for aggregating the updates is so-called FedAvg (McMahan et al., 2017). The training task is to learn the global parameters  $\theta$  by solving the finite-sum optimization:  $\min_{\theta} f_{\theta} = \frac{1}{n} \sum_{i=1}^{n} f_{\theta_i}$ , where n is the number of participating
+
+agents. At round t, the server S randomly selects  $n^t \in \{1,2,...,n\}$  agents to participate in the aggregation and sends the global model  $\theta^t$  to them. Each of the agents i trains its local classifier  $f_{\theta_i}: \mathcal{X}_i \to \mathcal{Y}_i$  with its local dataset  $D_i = \{(x_j,y_j): x_j \in \mathcal{X}_i, y_j \in \mathcal{Y}_i, j=1,2,...,N\}$  for some epochs, where  $N = |D_i|$ , by certain optimization algorithm, e.g., stochastic gradient descent (SGD). The objective of agent i is to train a local model as:  $\theta^*_i = \underset{t}{\operatorname{argmin}} \sum_{(x_j,y_j) \in D_i} \mathcal{L}(f_{\theta^t}(x_j),y_j)$ , where
+
+ $\mathcal L$  stands for the classification loss, e.g., cross-entropy loss. Then agent i computes its local update as  $\delta_i^t = \theta_i^* - \theta^t$ , and sends back to S. Finally, the server aggregates all updates and produces the new global model with an average  $\theta^{t+1} = \theta^t + \frac{\gamma}{|n^t|} \sum_{i \in n^t} \delta_i^t$ . where  $\gamma$  is the global learning rate. When the global model  $\theta$  converges or the training reaches a specific iteration upper bound, the aggregation process terminates and outputs a final global model. During inference, given a benign sample x and its true label y, the learned global classifier  $f_\theta$  will behave well as:  $f_\theta(x) = y$ .
+
+Optimizations of FL have been proposed for various purposes, e.g., privacy (Bonawitz et al., 2016), security (Blanchard et al., 2017; Zhao et al., 2022a), heterogeneity (Li et al., 2020), communication efficiency (Liu et al., 2019; Jiang et al., 2020) and personalization issues (Li et al., 2021a; Yu et al., 2020).
+
+#### A.1.2 BACKDOOR ATTACKS
+
+**Backdoor Attacks on FL.** Current backdoor attacks can poison data and models. In data poisoning (Shen et al., 2016; Xie et al., 2019), the attacker poisons the benign samples with a trigger pattern and marks them as a target label in order to induce the model to misbehave by training this poisoned dataset. As for model poisoning (Bagdasaryan et al., 2020; Wang et al., 2020), the attacker manipulates the training process by modifying parameters and scaling the malicious update to maximize the attack effectiveness while evading anomaly detection of robust FL aggregators (Blanchard et al., 2017; Sun et al., 2019; Panda et al., 2022; Nguyen et al., 2022b; Rieger et al., 2022; Yin et al., 2018; Bernstein et al., 2019).
+
+The most well-known backdoor attack on FL is introduced in (Bagdasaryan et al., 2020), where the adversary scales up the weights of malicious model updates to maximize attack impact and replace the global model with its malicious local model. To fully exploit the distributed learning methodology of FL, the local trigger patterns are used in (Xie et al., 2019) to generate poisoned images for different malicious models, while the data from the tail of the input data distribution is leveraged in (Wang et al., 2020). Durable backdoor attacks are proposed in (Zhang et al., 2022b; Dai & Li, 2023), and make attack itself more persistent in the federated scenarios. We state that this kind of attacks mainly focuses on the persistence, whereas our focus is on stealthiness.
+
+Existing works reply on a universal trigger or tail data, which do not fully exploit the "attribute" of trigger. Our design is fully applicable and complementary to prior attacks. By learning a stealthy trigger generator and injecting the sample-specific triggers, we can significantly decrease the anomalies in **P1-3** and reinforce the stealthiness of backdoor attacks.
+
+**Function-based Backdoor Attacks.** Existing backdoor attacks can leverage generative functions to produce triggers. (Nguyen & Tran, 2020) implements a trigger generator to make triggers vary from input to input. To improve the invisibility of triggers, (Doan et al., 2021b) proposes a bi-level problem to learn a generator to produce invisible sample-specific triggers. Further, (Doan et al., 2021a) extends the concept of imperceptible backdoors from the input to feature space, which learns a trigger generator to constrain the similarity of hidden features between posioned and clean data. To
+
+improve the stealthiness of triggers on latent representations, (Zhao et al., 2022b) adaptively learns the generator by constraining the latent layers, which makes triggers more invisible in both input and latent feature space. Moreover, (Doan et al., 2022) proposed a generator that can learn invisible triggers with arbitrary target class. Most works propose their customized bi-level optimization problems and solve them by alternatively learning their generative and classification models. There is less literature considering function-based attacks against FL, we thus propose a stealthy backdoor attack to eliminate the abnormality of parameters and bridge the gap between the centralized and federated scenarios.
+
+#### <span id="page-14-1"></span>A.1.3 BACKDOOR DEFENSES ON FL
+
+There are a number of defenses that provide empirical robustness against backdoor attacks.
+
+**Dimension-wise filtering.** Trimmed-mean (Yin et al., 2018) aggregates each dimension of model updates of all agents independently. It sorts the parameters of the  $j^{th}$ -dimension of all updates and removes m of the largest and smallest parameters in that dimension. Finally, it computes the arithmetic mean of the rest parameters as the aggregate of dimension j. Similarly, Median (Yin et al., 2018) takes the arithmetic median value of each dimension for aggregation. SignSGD (Bernstein et al., 2019) only aggregates the signs of the gradients (of all agents) and returns the sign to agents for updating the local models.
+
+**Vector-wise scaling.** Norm clipping (Sun et al., 2019) bounds the  $l_2$ -norm of all updates to a fixed threshold due to high norms of malicious updates. For a threshold  $\tau$  and an update  $\nabla$ , if the norm of the update  $||\nabla|| > \tau$ ,  $\nabla$  is scaled by  $\frac{\tau}{||\nabla||}$ . The server averages all the updates, scaled or not, for aggregation.
+
+**Vector-wise filtering.** Krum (Blanchard et al., 2017) selects a local model, with the smallest Euclidean distance to n-f-1 of other local models, as the global model. A variant of Krum called Multi-Krum (Blanchard et al., 2017) selects a local model using Krum and removes it from the remaining models repeatedly. The selected model is added to a selection S until S has c models such that n-c>2m+2, where n is the number of selected models and m is the number of malicious models. Finally, Multi-Krum averages the selected model updates. RFA (Pillutla et al., 2022) aggregates model updates and makes FedAvg robust to outliers by replacing the averaging aggregation with an approximate geometric median.
+
+**Certification.** CRFL (Xie et al., 2021) provides certified robustness in FL frameworks. It exploits parameter clipping and perturbing during federated averaging aggregation. In the test stage, it constructs a "smoothed" classifier using parameter smoothing. The robust accuracy of each test sample can be certified by this classifier when the number of compromised clients or perturbation to the test input is below a certified threshold.
+
+**Sparsification.** SparseFed (Panda et al., 2022) performs norm clipping to all local updates and averages the updates as the aggregate.  $Top_k$  values of the aggregation update are extracted and returned to each agent who locally updates the models using this sparse update.
+
+Cluster-based filtering. Recently, (Nguyen et al., 2022b) proposed a defending framework FLAME based on the clustering algorithm (HDBSCAN) which can cluster dynamically all local updates based on their cosine distance into two groups separately. FLAME uses weight clipping for scaling-up malicious weights and noise addition for smoothing the boundary of clustering after filtering malicious updates. By using HDBSCAN, (Rieger et al., 2022) designed a robust FL aggregation rule called DeepSight. Their design leverages the distribution of labels for the output layer, output of random inputs, and cosine similarity of updates to cluster all agents' updates and further applies the clipping method.
+
+### <span id="page-14-0"></span>A.2 THE PROCEDURE OF FTA OPTIMIZATION
+
+In case of collusion between more than one malicious agent device, the local datasets owned by these devices are in non-i.i.d. manner. Their local trigger generators  $g_{\xi_i}$  are trained by these local datasets. This kind of dataset bias can degrade attack effectiveness since their malicious updates are for local triggers from different  $g_{\xi_i}$  and cannot be merged together to yield a better attack performance. To resolve this problem, we develop a practical solution. Before starting the FTA backdoor attack, the
+
+malicious agents can share a portion of their local datasets to form a universal poisoned dataset (for all the malicious agents), so that their local generators gξ<sup>i</sup> can produce the same triggers.
+
+### <span id="page-15-0"></span>A.3 DETAILS OF THE TASKS
+
+The details of 4 computer vision tasks are described in Table [1.](#page-15-2) To prove the stealthiness and further robustness against defenses of FTA, we use a decentralized setting with non-i.i.d. data distribution among all agents. The attacker chooses the all-to-one type of backdoor attack (except Edge-case [\(Wang et al., 2020\)](#page-11-1)), fooling the global model to misclassify the poisoned images of any label to an attacker-chosen target label. Following a practical scenario for the attacker given in [\(Zhang et al.,](#page-12-2) [2022b\)](#page-12-2), *10* agents among thousands of agents are selected for training in each round and their updates are used for aggregation and updating the server model. We apply backdoor attacks from different phases of training. In FEMNIST task, we follow the same setting as [\(Xie et al., 2019\)](#page-12-1), where the attacker begins to attack when the benign accuracy of global models starts to converge. For other tasks, we perform backdoor attacks at the beginning of FL training. In this sense, as mentioned in [\(Xie et al., 2019\)](#page-12-1), benign updates are more likely to share common patterns of gradients and have a larger magnitude than malicious updates, which can significantly restrict the effectiveness of malicious updates. Note we consider such a setting for the bottom performance of attacks and further, we still see that our attack performs more effectively than prior works in this case (see Figure [3\)](#page-6-0).
+
+Table 1: The datasets, and their corresponding models and hyperparameters.
+
+<span id="page-15-2"></span>
+
+|                                    | Fahion-MNIST                     | FEMNIST                  | CIFAR-10            | Tiny-ImageNet       |  |  |
+|------------------------------------|----------------------------------|--------------------------|---------------------|---------------------|--|--|
+| Classes                            | 62                               | 10                       | 10                  | 200                 |  |  |
+| Size of training set               | 60000                            | 737837                   | 50000               | 100000              |  |  |
+| Size of testing set                | 10000                            | 80014                    | 10000               | 10000               |  |  |
+| Total agents                       | 2000                             | 3000                     | 1000                | 2000                |  |  |
+| Malicious agents                   | 2                                | 3                        | 1                   | 2                   |  |  |
+| Agents per FL round                | 10                               | 10                       | 10                  | 10                  |  |  |
+| Phase to start attack              | Attack from scratch              | Attack after convergence | Attack from scratch | Attack from scratch |  |  |
+| Poison fraction                    | 0.2                              |                          |                     |                     |  |  |
+| Trigger size                       | 1                                | 1.5                      |                     | 3                   |  |  |
+| Dataset size of trigger generator  | 256                              |                          |                     |                     |  |  |
+| Epochs of benign task              | 2                                | 4                        | 5                   | 5                   |  |  |
+| Epochs of backdoor task            | 5 (FTA: 2)                       | 10 (FTA: 4)              | 10 (FTA: 5)         | 10 (FTA: 5)         |  |  |
+| Learning rate of trigger generator | 0.01                             | 0.01                     | 0.001               | 0.01                |  |  |
+| Epochs of trigger generator        | 20                               | 20                       | 30                  | 30                  |  |  |
+| Local data distribution            | non-i.i.d.                       |                          |                     |                     |  |  |
+| Classification model               | Classic CNN                      | Classic CNN              | ResNet-18           | ResNet-18           |  |  |
+| Trigger generator model            | Autoencoder                      | Autoencoder              | U-Net               | Autoencoder         |  |  |
+| Learning rate of benign task       | 0.1                              | 0.01                     | 0.01                | 0.001               |  |  |
+| Learning rate of backdoor task     | 0.1                              | 0.01                     | 0.01                | 0.01                |  |  |
+| Edge-case                          | FALSE                            | TRUE                     | TRUE                | FALSE               |  |  |
+| Other hyperparameters              | Momentum:0.9, Weight Decay: 10−4 |                          |                     |                     |  |  |
+
+### <span id="page-15-1"></span>A.4 FTA AGAINST OTHER DEFENSES
+
+Besides the defense methods used in the main body, we test the performance of FTA under Multi-Krum, Trimmed-mean, RFA, SignSGD, Foolsgold and SparsedFed. The results prove that FTA is able to evade the defenses.
+
+<span id="page-16-0"></span>![](figures/_page_16_Figure_1.jpeg)
+
+Figure 6: Few-shot attack performance under FedAvg. FTA is more durable than baseline.
+
+# <span id="page-16-1"></span>A.4.1 ATTACK EFFECTIVENESS UNDER FEW-SHOT MODE.
+
+In our experiments, the Attack\_num is 100 for all attacks, and the total FL round is 1000 for CIFAR-10, and 500 for other datasets. The results under few-shot settings are shown in Figure [6.](#page-16-0) All attacks reach a high BA rapidly after consistently poisoning the server model, then BA gradually drops after stopping attacking and the backdoor injected into the server model is gradually weakened by the aggregation of benign updates. FTA's performance drops much slower than the baseline attack. For example, in Fashion-MNIST and after 500 rounds, FTA still remains 73% BA, which is only 9% less than Neurotoxin, 61% higher than the baseline. Moreover, FTA can beat DBA and the baseline on Tiny-ImageNet. After 500 rounds, FTA maintains 37% accuracy while the baseline and DBA only have 5%, which is 45% less than Neurotoxin. However, Neurotoxin cannot provide the same stealthiness as shown in following comparison under robust FL defenses. Since malicious and benign updates have a similar direction by FTA, the effectiveness of FTA's backdoor can survive after few-shot attack. The results prove the durability of FTA.
+
+# <span id="page-16-3"></span><span id="page-16-2"></span>A.4.2 RESISTANCE TO VECTOR-WISE FILTERING
+
+![](figures/_page_16_Figure_6.jpeg)
+
+Figure 7: The effectiveness of attack under Multi-Krum in 4 tasks.
+
+Multi-Krum is used as the vector-wise defense method. As described in Appendix [A.1.3,](#page-14-1) it calculates the Euclidean distance between all updates and selects n − f − 1 updates with the smallest Euclidean distances for aggregation. In Figure [7,](#page-16-3) the defense manages to filter out almost all malicious updates of prior attacks and effectively degrade their attacks' performance. In contrast, local update of FTA cannot be easily filtered and thus FTA outperforms others. In CIFAR-10 and Tiny-ImageNet, the attack performance is steady for FTA (nearly 100%) within 40 rounds to converge. In FEMNIST, Multi-Krum only results in a 10% BA degradation for FTA while BAs of others are restricted to 0%. In Fashion-MNIST, Multi-Krum can sieve malicious updates of FTA occasionally, leading to a longer convergence time, but still fails to completely defend the FTA. Malicious updates produced by FTA (which successfully eliminates the anomalies in P1-2) are with a similar Euclidean distance compared to benign updates, making them more stealthy than other attacks'.
+
+# A.4.3 RESISTANCE TO DIMENSION-WISE FILTERING
+
+We choose Trimmed-mean as the representative of dimension-wise filtering. As mentioned in Appendix [A.1.3,](#page-14-1) the dimensions of updates are sorted respectively, and the top m highest and smallest updates are removed, and the arithmetic mean of the rest parameters is computed for aggregated updates. In our experiments, m is set as 2 because we assume there is no more than one malicious agent during FL iteration, and setting a higher m can result in lower convergence. As shown in Figure [8,](#page-17-0) Trimmed-mean successfully filters out the compared attacks in Fashion-MNIST and Tiny-ImageNet, and its effects are weakened in CIFAR-10 and FEMNIST. However, FTA survives in all
+
+<span id="page-17-0"></span>![](figures/_page_17_Figure_1.jpeg)
+
+Figure 8: The effectiveness of attack under Trimmed-mean in 4 tasks.
+
+four tasks and performs the best under trimmed-mean. In CIFAR-10, it completes the convergence within 30 rounds and remains 99.9% BA. In Fashion-MNIST and FEMNIST, FTA takes above 50 rounds to fully converge, and the final accuracy manages to reach 96%. The performance of FTA is significantly degraded in Tiny-ImageNet, but still with 30% advantage over other attacks on average. The update of FTA shares a similar weights/biases distribution of benign updates. This ensures our attack to defeat the defenses based on dimension-wise filtering.
+
+# A.4.4 RESISTANCE TO RFA
+
+In Figure [9,](#page-17-1) FTA provides the best performance among others in Fashion-MNIST, CIFAR-10 and Tiny-ImageNet. In FEMNIST, it converges much faster than prior attacks. Although its accuracy is 8% lower than the baseline in the middle of training, FTA achieves the same performance at the end (of training).
+
+<span id="page-17-1"></span>![](figures/_page_17_Figure_6.jpeg)
+
+Figure 9: The effectiveness of attack under RFA in 4 tasks.
+
+# A.4.5 RESISTANCE TO SIGNSGD AND RLR
+
+As shown in Figure [10](#page-17-2) (a)-(b), SignSGD mitigates prior backdoor attacks with a universal trigger pattern. However, FTA still defeats it and remains 94% and 99% BA on Fashion-MNIST and Tiny-ImageNet, respectively.
+
+<span id="page-17-2"></span>![](figures/_page_17_Figure_10.jpeg)
+
+Figure 10: (a)-(b): The effectiveness of attack under SignSGD in Fashion-MNIST and Tiny-ImageNet. (c): The effectiveness of attack under Foolsgold in Fashion-MNIST. (d): The effectiveness of attack under SparseFed in Tiny-ImageNet.
+
+RLR can effectively filter out malicious updates, we test FTA under RLR as the variant of SignSGD. As shown in Figure [11](#page-18-1) (a)-(b), FTA achieves above 98% backdoor accuracy in both i.i.d and non-i.i.d manners.
+
+<span id="page-18-1"></span>![](figures/_page_18_Figure_2.jpeg)
+
+Figure 11: (a)-(b): The effectiveness of attack under RLR in FEMNIST and Tiny-ImageNet. (c)-(d): The effectiveness of attack under Pruning in FEMNIST and CIFAR-10.
+
+# A.4.6 RESISTANCE TO FOOLSGOLD
+
+From Figure [10](#page-17-2) (c), we see that Foolsgold hinders the convergence speed of FTA in Fashion-MNIST, which requires FTA to perform extra 25 rounds for convergence. In this sense, FTA still converges much faster than others.
+
+# A.4.7 RESISTANCE TO SPARSIFICATION
+
+We choose SparseFed as the representative of the sparsification defense. In Figure [10](#page-17-2) (d), only Neurotoxin and FTA are capable of breaking through SparseFed on Tiny-ImageNet. The BA of Neurotoxin exhibits fluctuations (between 22% and 36%) throughout the training process, unable to maintain a continuous rise. In contrast, FTA demonstrates the ability to consistently poison the global model and later achieves an impressive accuracy of 90% by round 150. The reason for the above performance difference is that the backdoor task of FTA captures imperceptible perturbations on model parameters, which eliminates the anomalies of poisoning training. The backdoor tasks trained by FTA are more likely to contribute to the same dimensions of gradients as benign updates. Consequently, the top-k filtering mechanism implemented in the server side is ineffective to filter out FTA's backdoor effect.
+
+### A.4.8 RESISTANCE TO POST-TRAINING STAGE DEFENSE
+
+We choose Pruning as a strong post-training stage defense. The attack effectiveness of FTA under Pruning is illustrated in Figure [11](#page-18-1) (c)-(d). Figure [11](#page-18-1) (c) demonstrates that even with a 50% prune ratio, FTA maintains 80% backdoor accuracy in FEMNIST. To reduce the backdoor accuracy to below 40%, it must prune 90% of neurons in CIFAR-10, as depicted in Figure [11](#page-18-1) (d). However, this setting significantly compromises benign accuracy, rendering global model unusable. This is because the poisoned data shares similar hidden features as the clean data with the target label, allowing FTA to reuse benign neurons for the backdoor task. Specifically, the baseline attack heavily depends on certain fine-tuned malicious parameters, making it susceptible to Pruning based on the activation of clean data. In contrast, FTA does not rely on the fine-tuned malicious parameters too much.
+
+# <span id="page-18-0"></span>A.5 BENIGN ACCURACY OF FTA
+
+We showcase the benign accuracy of both the baseline attack and FTA, and also consider the accuracy without backdoor attacks under FedAvg. We start FTA and the baseline from a specific round (e.g., 0 or 200 for different datasets) and perform the attacks during Attack\_num rounds. We record the accuracy once the attacks have ended. From Table [2,](#page-19-2) it is evident that FTA results in a slightly smaller decrease in the benign accuracy compared to baseline attack.
+
+<span id="page-19-2"></span>Table 2: Benign accuracy of the baseline attack. FTA and no attackers circumstance under different datasets. Benign accuracy drops by ≤ 1.5% in FTA compared to the accuracy without attack.
+
+| Dataset       | Attack start epoch | Attack_num | No attack (%) | Baseline attack (%) | FTA (%) |
+|---------------|--------------------|------------|---------------|---------------------|---------|
+| Fashion-MNIST | 0                  | 50         | 90.21         | 85.14               | 90.02   |
+| FEMNIST       | 200                | 50         | 92.06         | 91.27               | 92.05   |
+| CIFAR-10      | 0                  | 100        | 61.73         | 56.34               | 60.61   |
+| Tiny-ImageNet | 0                  | 100        | 25.21         | 19.06               | 25.13   |
+
+## <span id="page-19-0"></span>A.6 THE STRUCTURE OF OUR MODELS
+
+### A.6.1 THE STRUCTURE OF CLASSIFICATION MODELS FOR FASHION-MNIST AND FEMNIST
+
+<span id="page-19-3"></span>We use an 8-layer classic CNN architecture for training Fashion-MNIST and FEMNIST datasets. The details are shown in Table [3.](#page-19-3)
+
+Table 3: The structure of classic CNN model.
+
+| Parameters                | Shape     | Hyperparameters of layer |
+|---------------------------|-----------|--------------------------|
+| Conv2d                    | 1*32*3*3  | stride = (1, 1)          |
+| GroupNorm                 | 32*32     | eps = 10−5               |
+| Conv2d                    | 32*64*3*3 | stride = (1, 1)          |
+| GroupNorm                 | 32*64     | eps = 10−5               |
+| Dropout2d                 |           | p = 0.25                 |
+| Linear                    | 9216*128  | bias = True              |
+| Linear(For Fashion-MNIST) | 128*10    | bias = True              |
+| Linear(For FEMNIST)       | 128*62    | bias = True              |
+
+### A.6.2 THE STRUCTURE OF TRIGGER GENERATOR
+
+In the FTA framework, the trigger generator plays a crucial role in feature extraction in the sense that it aims to align the hidden features of poisoned samples with the target label samples. We utilize the Autoencoder as the trigger generator due to its ability to capture essential features of input and generate outputs satisfying our needs. Moreover, we find that U-Net exhibits comparable performance for trigger generation while requiring less training data, as stated in [\(Doan et al., 2021b\)](#page-9-5). Therefore, we include U-Net in our experiments. Both U-Net and autoencoder architectures used to train the trigger generator g<sup>ξ</sup> are similar to those presented in [\(Doan et al., 2021b\)](#page-9-5).
+
+### A.6.3 THE STRUCTURE OF CLASSIFICATION MODELS FOR CIFAR-10 AND TINY-IMAGENET
+
+We use a similar ResNet-18 architecture as in [\(Xie et al., 2019\)](#page-12-1) for training CIFAR-10 and Tiny-ImageNet.
+
+### <span id="page-19-1"></span>A.7 OTHER EXPERIMENT SETTINGS
+
+The implementation of all the compared attacks and FL framework are based on PyTorch [\(Paszke](#page-11-13) [et al., 2019\)](#page-11-13). We test the experiments on a server with one Intel Xeon E5-2620 CPU and one NVIDIA A40 GPU with 32G RAM.
+
+In Fashion-MNIST, CIFAR-10 and Tiny-ImageNet, a Dirichlet distribution is used to divide training data for the number of total agent parties, and the hyperparameter for distribution is 0.7 for the datasets. For FEMNIST, we randomly choose data of 3000 users from the dataset and randomly distribute every training agent with the training data from 3 users. All parties use SGD as an optimizer and train for local training epochs with a batch size of 256. A global model is shared by all agents, and updates of 10 agents will be selected for aggregating the global model. Benign agents train with a benign learning rate for benign epochs. The attacker's local training dataset is mixed with 80% correct labeled data and 20% poisoned data. The target labels are "sneaker" in Fashion-MNIST, "digit 1" in FEMNIST, "truck" in CIFAR-10 and "tree frog" in Tiny-ImageNet. The attacker has its own local malicious learning rate and epochs to maximize its backdoor performance. It also needs to train its local trigger generator with learning rate and epochs before performing local malicious training on the downloaded global model.
+
+Regarding the attack methods, we set the top-k ratio of 0.95 for Neurotoxin, in line with the recommended settings in [\(Zhang et al., 2022b\)](#page-12-2). For DBA, we use 4 distributed strips as backdoor trigger patterns. Both the baseline attack and Neurotoxin employ a "square" trigger pattern on the top left as the backdoor trigger. We conduct Edge-case attack on CIFAR-10 and FEMNIST. Specifically, for CIFAR-10, we use the southwest airplane as the backdoored images and set the target label as "bird". For FEMNIST, we use images of "7" in ARDIS [\(Kusetogullari et al., 2020\)](#page-10-16) as poisoned samples with the target label set as the digit "1". The dataset settings of the experiments are the same as those used in [\(Wang et al., 2020\)](#page-11-1).
+
+### <span id="page-20-2"></span>A.7.1 VISUALIZATION OF DIFFERENT TRIGGER SIZES
+
+The benign and poisoned samples with flexible triggers of different sizes generated by FTA are presented in Figure [12.](#page-20-1) For Tiny-ImageNet and CIFAR-10, it is hard for human inspection to immediately identify the triggers, which proves the stealthiness in P3. In Fashion-MNIST and FEMNIST, the triggers are easier to distinguish because there is only one channel of the input samples in the datasets. But those flexible triggers are still much more stealthy compared to those produced by prior attacks on FL (see Figure [2\)](#page-2-0).
+
+<span id="page-20-1"></span>![](figures/_page_20_Figure_5.jpeg)
+
+Figure 12: Visualization of backdoored images of different trigger sizes.
+
+# <span id="page-20-0"></span>A.8 ABLATION STUDIES IN FTA ATTACK
+
+Trigger Size. This size refers to the l2-norm bound of the trigger generated by the generator, corresponding to ϵ in Algorithm [1.](#page-5-1) If the size is set too large, the poisoned image can be easily distinguished (i.e., no stealthiness) by human inspection in test/evaluation stage. On the other hand, if we set it too small, the trigger will have a low proportion of features in the input domain. In this sense, the global model will encounter difficulty in catching and learning these features of trigger pattern, resulting in a drop of attack performance.
+
+In Figure [13](#page-21-0) (a)-(d), the trigger size significantly influences the attack performance in all the tasks. The accuracies of FTA drop seriously and eventually reach closely to 0% while we keep decreasing the size of the trigger, in which evidences can be seen in CIFAR-10, FEMNIST, and Tiny-ImageNet.
+
+The sample-specific trigger with l2-norm bound of 2 in CIFAR-10 and Tiny-ImageNet is indistinguishable from human inspection (see Figure [12](#page-20-1) in Appendix [A.7.1\)](#page-20-2), while for Fashion-MNIST and FEMNIST (images with back-and-white backgrounds), additional noise can be still easily detected. Thus, a balance between visual stealthiness and effectiveness should be considered before conducting an FTA.
+
+<span id="page-21-0"></span>![](figures/_page_21_Figure_3.jpeg)
+
+Figure 13: Different hyperparameters on backdoor accuracy. (a)-(d): trigger size; (e)-(h): poison fraction; (i)-(l): dataset size of trigger generator.
+
+Poison Fraction. This is the fraction of poisoned training samples in the training dataset of the attacker. Setting a low poison fraction can benefit the attack's stealthiness by having less abnormality in parameters and less influence on benign tasks. But this can slow down the attack effectiveness, as a side effect. Fortunately, we find that FTA can still take effect under a low poison fraction. We set the local training batch size to 256 for all the tasks, follow the standard settings of other FL frameworks, and set the poison fraction as 0.2. As stated in Appendix [A.5,](#page-18-0) this fraction setting cannot degrade the performance of benign accuracy and meanwhile, we would like to explore further to examine the lower bound of the fraction which FTA's performance can tolerate. In Figure [13](#page-21-0) (e)-(h), FTA is still effective whilst the fraction drops to 0.05. We also find that sensitivities to poison fraction can vary among tasks. In Fashion-MNIST and CIFAR-10, FTA remains its performance even if poison fraction = 0.01, in which only 3 samples are posoined in each batch. As for FEMNIST and Tiny-ImageNet, under the same rate, the backdoor tasks are dramatically weakened by the benign ones.
+
+Dataset Size of Trigger Generator. Theoretically, if this dataset is small-scale, the trigger generator could not be properly trained, thus resulting in bad quality and further endangering the attack performance. During the training, if the attacker controls multiple agents, it can merge all local datasets into one for generator training. However, in many cases, the attacker can only control relatively limited agents and is provided by a small-scale dataset for training. Recall that in Algorithm [1](#page-5-1) we use the same dataset for the malicious model and trigger generator training. We set the size of dataset for learning trigger generator to 1024 for all tasks in default. From Figure [13](#page-21-0) (i)-(l) in Appendix [A.8,](#page-21-0) we see that this concern should not be crucial for FTA. Even if the size of the dataset is only set to 32, FTA can provide a high attack performance. We note that the training process here is somewhat similar to generative adversarial networks, in which we do not require a large amount of samples in the training dataset.
+
+<span id="page-22-2"></span>Table 4: Experimental results on trigger stealthiness (SSIM↑ and LPIPS↓).
+
+| Dataset       | Metric        | Baseline         | DBA              | Neurotoxin       | Edge-case | FTA(Ours)        |
+|---------------|---------------|------------------|------------------|------------------|-----------|------------------|
+| Fashion-MNIST | SSIM          | 0.9376           | 0.9052           | 0.9359           | -         | <b>0.9967</b>    |
+|               | LPIPS         | NA               | NA               | NA               | NA        | NA               |
+| CIFAR-10      | SSIM          | 0.9612           | 0.9440           | 0.9638           | 0.7354    | 0.9978           |
+|               | LPIPS         | 0.0058           | 0.0091           | 0.0075           | 0.3171    | 0.0008           |
+| Tiny-ImageNet | SSIM<br>LPIPS | 0.9851<br>0.0072 | 0.9734<br>0.0149 | 0.9810<br>0.0086 | -         | 0.9881<br>0.0029 |
+
+<span id="page-22-3"></span>Table 5: Time consumption and computational cost (MEAN±SD) of different attack methods in one FL iteration under Fashion-MNIST, CIFAR-10 and Tiny-ImageNet.
+
+| $Dataset \rightarrow$ | Fashion-MNIST |               | CIFAR-10         |               | Tiny-ImageNet    |               |
+|-----------------------|---------------|---------------|------------------|---------------|------------------|---------------|
+| Attack↓               | Time (s)      | Memories (MB) | Time (s)         | Memories (MB) | Time (s)         | Memories (MB) |
+| Benign                | 1.62±0.19     | 76.8          | 14.11±1.45       | 125.1         | 37.92±2.71       | 233.5         |
+| Baseline Attack       | 1.67±0.25     | 81.6          | $14.81\pm2.10$   | 127.2         | $38.52\pm2.19$   | 226.4         |
+| DBA                   | 1.57±0.31     | 81.7          | $14.91 \pm 1.86$ | 124.7         | $38.74 \pm 1.92$ | 248.5         |
+| Neurotoxin            | $3.39\pm0.66$ | 120.4         | $27.85 \pm 1.74$ | 279.3         | $76.38\pm3.46$   | 478.7         |
+| FTA                   | 2.04±0.52     | 86            | $18.38 \pm 1.89$ | 169.1         | $46.98{\pm}2.14$ | 298.4         |
+
+#### <span id="page-22-1"></span>A.9 NATURAL STEALTHINESS
+
+For each dataset, we randomly select 500 sample images from test dataset to evaluate the trigger stealthiness. As the SSIM value increases, the poisoned sample looks more stealthy. But for LPIPS, that is the other way round. Table 4 shows that FTA achieves excellent stealthiness in all cases. Specifically, SSIM values of FTA are the highest in these datasets, which are close to 1. LPIPS values of FTA are 2-7× improvement to that of baseline attack. Although the baseline attack and Neurotoxin, which uses a universal square pattern, performs well on more complex datasets, using such a patch-based pattern can make the original image look "unnatural".
+
+### <span id="page-22-0"></span>A.10 COMPUTATIONAL COST
+
+We understand the significance of the external computational cost and time consumption of backdoor training on malicious devices in our proposed attack under FL scenario. Training with GANs in federated systems introduces extra time consumption. However, our attack does not significantly increase the computational and time cost due to our optimization procedure. Compared to training benign task and baseline backdoor task, FTA only needs to train an additional trigger generator which is actually a small generative neural network. Our generator only consists of several convolutional layers in total. It is worth noting that the datasets used to train both two network structures comprise only 1024 poisoned samples as shown in Table 1 whose size are relatively small compared to the entire training dataset. For instance, the training dataset for our trigger generator accounts for approximately 0.14% of the FEMNIST dataset Therefore, the time consumption and computational cost for training this generative network are very minimal. The remaining time consumption is comparable to training a benign local model. As shown in Table 5, Neurotoxin requires approximately  $2\times$  the time and memory compared to benign training to complete backdoor training for one FL round. This is attributed to an additional local benign training requirement in Neurotoxin. However, FTA consumes less than 30% additional time and 25% additional computational cost for backdoor training compared to benign ones. Given that FTA remains under 70% of the cost of Neurotoxin, it is practical to conduct an FTA attack in decentralized scenario.
+
+#### A.11 THE IMPORTANCE OF ADAPTABILITY OF FTA TRIGGER GENERATOR
+
+We understand and verify the significance of adaptability in our proposed attack. Figure 14 (a)-(b) demonstrate that the non-adaptive generator provides a lower convergence speed, approximately 70 rounds to achieve 96% backdoor accuracy under CIFAR-10, compared to the adaptive variant. Also, as shown in Figure 14 (c)-(d), the non-adaptive variant cannot evade norm clipping (vector-wise scaling) since it needs to significantly tune malicious parameters to achieve high backdoor accuracy. Our findings provide evidence that the adaptive variant indeed enhances the stealthiness of FTA in the parameter space.
+
+<span id="page-23-1"></span>![](figures/_page_23_Figure_1.jpeg)
+
+Figure 14: (a)-(b): The comparison between FTA and its restricted version under no defense in FEMNIST and CIFAR-10. (c)-(d): The comparison between FTA and its restricted version under norm clipping in FEMNIST and CIFAR-10.
+
+### <span id="page-23-0"></span>A.12 DISCUSSION
+
+In this work, we concentrate on the computer vision tasks, which have been the focus of numerous existing works [\(Xie et al., 2019;](#page-12-1) [Wang et al., 2020;](#page-11-1) [Doan et al., 2021b;](#page-9-5) [Zhao et al., 2022b;](#page-12-6) [Ozdayi](#page-11-10) [et al., 2021\)](#page-11-10). In the future, we intend to expand the scope of this work by applying our design to other real-world applications, such as natural language processing (NLP) and reinforcement learning (RL), as well as other vision tasks, e.g., object detection.
+
+The primary focus of FTA is to achieve stealthiness rather than durability, in contrast to other attacks such as Neurotoxin [\(Zhang et al., 2022b\)](#page-12-2). Neurotoxin manipulates malicious parameters based on gradients in magnitude, which yields a clear increase in the dissimilarity of parameters and thus harms the stealthiness of the attack. FTA addresses the dissimilarity difference of weights/biases introduced by backdoor training by using a stealthy and adaptive trigger generator, which makes the hidden features of poisoned samples similar to benign ones. We emphasize that the durability of backdoor attacks on FL is orthogonal to the main focus of this work, and we leave it as an open problem. A possible solution to achieve persistence could be to decelerate the learning rate of malicious agents, as proposed in [\(Bagdasaryan et al., 2020\)](#page-9-2).
+
+Comparison. In addition to the defenses evaluated in this paper, we discuss our attack effectiveness under other defenses below. As depicted in FLDetector [\(Zhang et al., 2022a\)](#page-12-16), in a typical FL scenario where the server does not have a validation dataset that Fltrust [\(Cao et al., 2021\)](#page-9-15) requires, the global model remains susceptible to backdoor attacks. However, the stringent demand by FLtrust for an extra validation dataset could not be practical for conventional FL frameworks and applications. Furthermore, Fltrust eliminates backdoor effectiveness based on cosine dissimilarity which is similar to the approach used in FLAME. As shown in Figure [5,](#page-8-0) FTA's malicious updates have less dissimilarity to benign updates than the baseline attack's. Therefore, we can state that FTA can evade Fltrust according to the results obtained under FLAME. DnC [\(Shejwalkar & Houmansadr,](#page-11-14) [2021\)](#page-11-14) primarily focuses on untargeted poisoning attacks rather than backdoor attacks, and its main objective is to reduce the accuracy of FL models. Accordingly, we do not consider it as a "proper" SOTA backdoor defense (to our attack). In particular, DnC is a kind of vector-wise filtering defense. In our experiments, conducted under Multi-krum and RFA, we ascertain that FTA is robust against vector-wise filtering. In conclusion, FTA can also successfully evade DnC, much like Multi-krum and RFA. As for certified defense like Flcert [\(Cao et al., 2022\)](#page-9-16), while it is a promising approach to robustness certification, it is not intended to detect and filter out malicious updates in FL. As outlined in Flcert, the certified accuracy of the global model experiences a decline with the increase of malicious agents. Fortunately, FTA can cope with a very challenging threat model, where the attacker is allowed to control merely one malicious agent out of thousands. We thus can achieve a certified accuracy almost on par with the original global model accuracy against Flcert. FLIP [\(Zhang et al.,](#page-12-5) [2023\)](#page-12-5) only considers static backdoors as potential attacks, i.e. patch-based patterns, whereas FTA can use flexible triggers to break FLIP's threat model. Using the flexible trigger generator, FTA can produce sample-specific triggers which pose challenges when applying universal trigger inversion method in FLIP's step 1.

papers/3bqesUzZPH/review.json

@@ -0,0 +1,70 @@
+{
+  "id": "3bqesUzZPH",
+  "title": "FTA: Stealthy and Adaptive Backdoor Attack with Flexible Triggers on Federated Learning",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "PQ7SNEG3qn",
+      "rating": 6,
+      "content": {
+        "summary": "The authors propose a generator-assisted backdoor attack (FTA) against robust FL. The newly designed generator is flexible and adaptive, where a bi-level optimization problem is formed to find the optimal generator.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "1. Clear model and algorithm\n\n1. T-SNE visualization of hidden features and similarity comparison are helpful.",
+        "weaknesses": "1. To emphasis the importance of flexibility and adaptability, the authors may consider add some experiments compared with their restricted version attacks against fixed batch of data and under non-adaptive setting.\n\n2. The current baselines are all fixed and non-adaptive. I suggest the authors compare their results with SOTA trigger generated based attacks as [1] and [2].\n\n3. The post-training stage defenses play a vital role in countering backdoor attacks. Even within the context of FL, certain techniques such as Neuron Clipping [3] and Pruning [4] have demonstrated their effectiveness in detecting and mitigating the impact of backdoor attacks. Consequently, I am curious to know how the proposed FTA performs when subjected to these post-training stage defenses.\n\n\n[1] Salem, Ahmed, et al. \"Dynamic backdoor attacks against machine learning models.\" 2022 IEEE 7th European Symposium on Security and Privacy (EuroS&P). IEEE, 2022. [2] Doan, Khoa D., Yingjie Lao, and Ping Li. \"Marksman backdoor: Backdoor attacks with arbitrary target class.\" Advances in Neural Information Processing Systems 35 (2022): 38260-38273. [3] Wang, Hang, et al. \"Universal post-training backdoor detection.\" arXiv preprint arXiv:2205.06900 (2022). [4] Wu, Chen, et al. \"Mitigating backdoor attacks in federated learning.\" arXiv preprint arXiv:2011.01767 (2020).",
+        "questions": "1. How to choose/tune a good or even an optimal (is it exist?) $\\epsilon$?\n\n2. The structure of generator network is crucial to balance the tradeoff between effectiveness and efficiency since the authors want to achieve flexible (each training example) and adaptive (every FL epoch). In the centralized setting in [1] [2], trigger generators specific to every label need be trained one time before machine learning, and it still require some training time. I wonder is there any modifications the authors made to increase the efficiency of the training to achieve a flexible and adaptive attack? \n\n\n[1] Doan, Khoa, et al. \"Lira: Learnable, imperceptible and robust backdoor attacks.\" Proceedings of the IEEE/CVF international conference on computer vision. 2021. [2] Doan, Khoa D., Yingjie Lao, and Ping Li. \"Marksman backdoor: Backdoor attacks with arbitrary target class.\" Advances in Neural Information Processing Systems 35 (2022): 38260-38273.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. To emphasis the importance of flexibility and adaptability, the authors may consider add some experiments compared with their restricted version attacks against fixed batch of data and under non-adaptive setting.\n\n2. The current baselines are all fixed and non-adaptive. I suggest the authors compare their results with SOTA trigger generated based attacks as [1] and [2].\n\n3. The post-training stage defenses play a vital role in countering backdoor attacks. Even within the context of FL, certain techniques such as Neuron Clipping [3] and Pruning [4] have demonstrated their effectiveness in detecting and mitigating the impact of backdoor attacks. Consequently, I am curious to know how the proposed FTA performs when subjected to these post-training stage defenses.",
+        "suggestions": "The authors should conduct a more thorough investigation into the flexibility and adaptability of their proposed attack. Specifically, they should compare the performance of their flexible generator-based attack against a version that uses a fixed, non-adaptive trigger. This could involve training a generator on a fixed batch of data and then using that same generator across all FL rounds, or using a universal patch-based trigger. Such experiments would provide a clearer understanding of the benefits of the proposed approach. Furthermore, the authors should explore the impact of different levels of adaptability, perhaps by varying the frequency with which the generator is updated during FL. This would help to determine the optimal balance between attack effectiveness and computational cost. The current experiments do not fully isolate the impact of flexibility and adaptability, and additional experiments are needed to validate these claims.\n\nIt is also crucial to compare the proposed method against state-of-the-art trigger generation-based attacks, particularly those that are designed for centralized settings. While the authors argue that these methods are not directly applicable to FL, it is important to understand how the proposed method compares in terms of stealthiness and effectiveness. For example, the authors could adapt the trigger generation techniques from [1] and [2] to the FL setting, even if this requires some modifications. This would provide a more robust evaluation of the proposed method. The authors should also consider the computational cost of their approach compared to these baselines, as this is a key factor in practical applications. A detailed comparison of the computational resources required for each approach would be beneficial.\n\nFinally, the authors should evaluate the robustness of their attack against post-training defense mechanisms, such as Neuron Clipping and Pruning. While the authors mention these defenses, they do not provide any experimental results. It is essential to understand how the proposed method performs under these conditions. For example, the authors could evaluate the backdoor accuracy of their attack after applying Neuron Clipping or Pruning to the trained model. This would provide a more realistic assessment of the attack's effectiveness. Furthermore, the authors should consider other post-training defenses, such as fine-tuning or adversarial training, to provide a comprehensive evaluation of the attack's robustness. The lack of experimental results against post-training defenses is a significant limitation of the current study."
+      }
+    },
+    {
+      "id": "6BkNqXlUwm",
+      "rating": 5,
+      "content": {
+        "summary": "This paper proposes a backdoor attack in the federated learning scenario, using a generative model that optimizes the perturbation to achieve stealthiness. The trigger is optimized during the training to be flexible and adaptive. The evaluation shows that it can achieve a 98% attack success rate.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "The paper focuses on an important problem, and the solution is clear. It is easy\nto follow and understand. \n\nThe evaluation uses multiple datasets and models, also compares with multiple\nbaselines.",
+        "weaknesses": "The core idea of the paper is to leverage a generative model to add adaptive\nperturbations, which has been studied in many existing works, e.g., Cheng et al.\nAAAI 2021, Dynamic attack, etc. The paper applies this idea in the federated\nlearning domain, but there is nothing that the method is specific to this\ndomain. Namely, I do not see any challenges because of federated learning that\nprevents existing work from being used. Thus, I do not think the paper is novel.\n\nRelated to the previous question, there has been studies in detecting function\nbased attacks, and the paper does not discuss that.",
+        "questions": "What is the main technical contribution of the paper?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "The core idea of the paper is to leverage a generative model to add adaptive\nperturbations, which has been studied in many existing works, e.g., Cheng et al.\nAAAI 2021, Dynamic attack, etc. The paper applies this idea in the federated\nlearning domain, but there is nothing that the method is specific to this\ndomain. Namely, I do not see any challenges because of federated learning that\nprevents existing work from being used. Thus, I do not think the paper is novel.\n\nRelated to the previous question, there has been studies in detecting function\nbased attacks, and the paper does not discuss that.",
+        "suggestions": "The paper would benefit from a more detailed explanation of how the proposed method specifically addresses the challenges of federated learning. While the use of a generative model for adaptive perturbations is not novel, the authors could highlight how their approach is tailored to the decentralized nature of federated learning, which introduces unique constraints compared to centralized settings. For example, the paper could discuss the impact of limited communication rounds and the heterogeneity of local datasets on the training of the trigger generator. It would be beneficial to see a discussion on how the proposed method handles the potential drift in the global model over federated learning rounds, and how the trigger generator adapts to these changes. A more in-depth analysis of the computational cost and communication overhead of the proposed approach in the federated setting would also be valuable, especially in comparison to existing centralized methods.\n\nFurthermore, the paper should include a more comprehensive discussion of existing defense mechanisms, particularly those designed to detect function-based attacks. The authors should analyze how their proposed attack might evade such defenses, or if it is susceptible to them. This analysis should go beyond simply stating that the attack achieves stealthiness in the parameter space, and should provide a more detailed explanation of how the attack manipulates the model's parameters to avoid detection. For example, the authors could discuss how the attack affects the distribution of weights and biases in the model, and whether these changes are detectable by existing anomaly detection techniques. The paper could also benefit from a discussion of the limitations of the proposed attack, such as the potential for the trigger to be ineffective if the global model changes significantly, or if the target class is not well-represented in the local datasets.\n\nFinally, the evaluation could be strengthened by including experiments that specifically target the challenges of federated learning. For example, the authors could evaluate the performance of the attack under different levels of client heterogeneity, or with varying numbers of malicious clients. It would also be beneficial to see experiments that compare the proposed method to existing backdoor attacks that are specifically designed for federated learning. The evaluation should also include a more detailed analysis of the trade-off between attack success rate and stealthiness, and how this trade-off is affected by the different parameters of the proposed method. The authors should also consider evaluating the attack's robustness to different types of defenses, such as gradient clipping or robust aggregation techniques."
+      }
+    },
+    {
+      "id": "aPOXeZMYV1",
+      "rating": 5,
+      "content": {
+        "summary": "This paper proposes a stealthy and adaptive backdoor attack with flexible triggers for federated learning.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "The studied problem of backdoor attack in federated learning is important.\n\nThe experiment results show that the generated trigger is less perceptible in human eyes, and comprehensive experiments are done to verify the success of the attack.",
+        "weaknesses": "1. The novelty of the formulated problem, as well as the method design is limited.  Specifically, the problem formulation in Eq. (1)  is mostly the same with Eq. (3) of Lira [A], except for some minor differences like separating poisoned and clean datasets.  The solution to solve the proposed problem is also quite standard by alternating optimization of the two variables, which is also adopted by  Wasserstein Backdoor [B]. The generator of the trigger is also following the autoencoder structure as adopted by [A].   In this sense, the proposed attack seems to be a direct migration of Lira into a federated learning setting, which looks quite incremental.  \n\n2. The defense baselines are not comprehensive. The authors can consider adding more defense baselines, e.g., RLR [C], Crfl [D],  to show that the attack can successfully break through defenses other than cluster-based filtering.\n\n3. It is unclear why optimizing the triggers can guarantee a better attack towards cluster-based filtering (or minimizing the distance of updates with the poisoned update), as this is not reflected in the problem formulation. See details in my questions part.\n\n4. There are some issues with the experiment results and the setup. The baseline benign accuracy is very low (shown in Table 2, 61.73% benign accuracy for CIFAR10 with ResNet, and also low for TinyImagNet), which makes the correctness of the experiment implementation questionable.  The setup of local epochs is also strange, in that the malicious clients run more epochs than the benign clients. This might introduce bias to other baselines because this would make the malicious updates significantly larger than other benign updates, which may affect the performance of other attack baselines when against filtering-based defense.   Also, the authors should test the results in IID setting as well as various Non-IID parameters to show its effectiveness. \n\n\n[A] Doan K, Lao Y, Zhao W, et al. Lira: Learnable, imperceptible and robust backdoor attacks[C]//Proceedings of the IEEE/CVF international conference on computer vision. 2021: 11966-11976.\n\n[B] Doan K, Lao Y, Li P. Backdoor attack with imperceptible input and latent modification[J]. Advances in Neural Information Processing Systems, 2021, 34: 18944-18957.\n\n[C] Ozdayi M S, Kantarcioglu M, Gel Y R. Defending against backdoors in federated learning with robust learning rate[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2021, 35(10): 9268-9276.\n \n[D] Xie C, Chen M, Chen P Y, et al. Crfl: Certifiably robust federated learning against backdoor attacks[C]//International Conference on Machine Learning. PMLR, 2021: 11372-11382.",
+        "questions": "It is suggested in Section 3.3 \"one may consider alternately updating fθ while keeping Tξ unchanged, or the other way round... (but this couldn't work well)\". However, it is later claimed that \"Inspired by (Doan et al., 2022), we divide local malicious training into two phases. In\nphase one, we fix the classification model fθ and only learn the trigger function Tξ. In phase two, we use the pre-trained Tξ∗ to generate the poisoned dataset and train the malicious classifier fθ\". In my understanding, the two descriptions of alternating optimization are identical. Can the authors elaborate on it?\n\nIt is claimed on page 4 that \"A stealthy backdoor attack on FL should mitigate the routing introduced by backdoor task and guarantee the stealthiness of model parameters instead of just the hidden features of poisoned samples compared to their original inputs\". However, it is unknown how the authors are achieving this goal with their problem formulation in Eq. (1).",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. The novelty of the formulated problem, as well as the method design is limited.  Specifically, the problem formulation in Eq. (1)  is mostly the same with Eq. (3) of Lira [A], except for some minor differences like separating poisoned and clean datasets.  The solution to solve the proposed problem is also quite standard by alternating optimization of the two variables, which is also adopted by  Wasserstein Backdoor [B]. The generator of the trigger is also following the autoencoder structure as adopted by [A].   In this sense, the proposed attack seems to be a direct migration of Lira into a federated learning setting, which looks quite incremental.  \n\n2. The defense baselines are not comprehensive. The authors can consider adding more defense baselines, e.g., RLR [C], Crfl [D],  to show that the attack can successfully break through defenses other than cluster-based filtering. Specifically, the evaluation lacks a thorough investigation into defenses that focus on gradient manipulation or robust aggregation techniques, which are highly relevant to federated learning scenarios.\n\n3. It is unclear why optimizing the triggers can guarantee a better attack towards cluster-based filtering (or minimizing the distance of updates with the poisoned update), as this is not reflected in the problem formulation. See details in my questions part. The connection between the optimization objective and the claimed stealthiness against cluster-based defenses is not explicitly established. The authors need to provide a more rigorous justification for this claim, possibly through theoretical analysis or more detailed empirical evidence.\n\n4. There are some issues with the experiment results and the setup. The baseline benign accuracy is very low (shown in Table 2, 61.73% benign accuracy for CIFAR10 with ResNet, and also low for TinyImagNet), which makes the correctness of the experiment implementation questionable.  The setup of local epochs is also strange, in that the malicious clients run more epochs than the benign clients. This might introduce bias to other baselines because this would make the malicious updates significantly larger than other benign updates, which may affect the performance of other attack baselines when against filtering-based defense.   Also, the authors should test the results in IID setting as well as various Non-IID parameters to show its effectiveness. ",
+        "suggestions": "The core weakness of this paper lies in its limited novelty and incremental contribution over existing backdoor attacks, particularly Lira [A]. While the authors adapt the attack to a federated learning setting, the fundamental approach of using an autoencoder-based trigger generator and alternating optimization remains largely unchanged. To strengthen the paper, the authors should explore more novel techniques for generating stealthy triggers that are specifically tailored to the federated learning environment. This could involve incorporating federated-specific constraints into the optimization process or exploring alternative trigger generation methods that are less susceptible to detection in the parameter space. Furthermore, the paper should provide a more in-depth analysis of the attack's stealthiness, going beyond just visual imperceptibility and considering the impact on model parameters and gradients.\n\nTo address the lack of comprehensive defense baselines, the authors should include a wider range of state-of-the-art defenses, particularly those that are designed to mitigate backdoor attacks in federated learning. This should include defenses that focus on gradient manipulation, robust aggregation, and anomaly detection. The evaluation should not only focus on the attack's success rate but also on its ability to evade these defenses. A thorough analysis of the attack's limitations and vulnerabilities against different defense mechanisms would significantly enhance the paper's contribution. Furthermore, the authors should clarify the connection between their optimization objective and the stealthiness against cluster-based defenses. A more rigorous justification, possibly through theoretical analysis or more detailed empirical evidence, is needed to support their claims. This could involve demonstrating how the learned trigger minimizes the distance between poisoned updates and benign updates in the parameter space, making it harder for cluster-based defenses to distinguish them.\n\nFinally, the experimental setup needs to be carefully reviewed and improved. The low baseline accuracy raises concerns about the correctness of the implementation. The authors should ensure that the benign model achieves reasonable accuracy before introducing the backdoor attack. The setup of local epochs should also be standardized across malicious and benign clients to avoid introducing bias. The authors should also conduct experiments under various IID and non-IID settings to demonstrate the attack's effectiveness in different scenarios. This would provide a more comprehensive evaluation of the attack's performance and its robustness to different data distributions. Additionally, the authors should provide more details on the hyperparameter settings and the training process to ensure reproducibility."
+      }
+    }
+  ]
+}

papers/3mdCet7vVv/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "3mdCet7vVv",
+  "title": "Maestro: Uncovering Low-Rank Structures via Trainable Decomposition",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2024-05-26",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=3mdCet7vVv"
+}

papers/3mdCet7vVv/paper.md

@@ -0,0 +1,353 @@
+# <span id="page-0-4"></span>MAESTRO: UNCOVERING LOW-RANK STRUCTURES VIA TRAINABLE DECOMPOSITION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+<span id="page-0-5"></span><span id="page-0-0"></span>Deep Neural Networks (DNNs) have been a large driver and enabler for AI breakthroughs in recent years. These models have been getting larger in their attempt to become more accurate and tackle new upcoming use-cases, including AR/VR and intelligent assistants. However, the training process of such large models is a costly and time-consuming process, which typically yields a single model to fit all targets. To mitigate this, various techniques have been proposed in the literature, including pruning, sparsification or quantization of the model weights and updates. While able to achieve high compression rates, they often incur computational overheads or accuracy penalties. Alternatively, factorization methods have been leveraged to incorporate low-rank compression in the training process. Similarly, such techniques (e.g., SVD) frequently rely on the computationally expensive decomposition of layers and are potentially sub-optimal for non-linear models, such as DNNs. In this work, we take a further step in designing efficient low-rank models and propose MAESTRO, a framework for trainable low-rank layers. Instead of regularly applying a priori decompositions such as SVD, the low-rank structure is built into the training process through a generalized variant of Ordered Dropout. This method imposes an importance ordering via sampling on the decomposed DNN structure. Our theoretical analysis demonstrates that our method recovers the SVD decomposition of linear mapping on uniformly distributed data and PCA for linear autoencoders. We further apply our technique on DNNs and empirically illustrate that MAESTRO enables the extraction of lower footprint models that preserve model performance while allowing for graceful accuracy-latency tradeoff for the deployment to devices of different capabilities.
+
+# <span id="page-0-1"></span>1 INTRODUCTION
+
+Deep Learning has been experiencing an unprecedented uptake, with models achieving a (super-)human level of performance in several tasks across modalities, giving birth to even more intelligent assistants and next-gen visual perception and generation systems. However, the price of this performance is that models are getting significantly larger, with training and deployment becoming increasingly costly. Therefore, techniques from Efficient ML become evermore relevant [\(Laskaridis](#page-10-0) [et al., 2022\)](#page-10-0), and a requirement for deployment in constrained devices, such as smartphones or IoT devices.
+
+<span id="page-0-3"></span>Typical techniques to compress the network involve *i) quantization*, i.e., reducing precision of the model [\(Wang et al., 2019\)](#page-11-0) or communicated updates [\(Seide et al., 2014;](#page-11-1) [Alistarh et al., 2017\)](#page-9-0), *ii) pruning* the model during training, e.g., through Lottery Ticket Hypothesis (LTH) [\(Frankle &](#page-9-1) [Carbin, 2019\)](#page-9-1), *iii) sparsification* of the network representation and updates, i.e., dropping the subset of coordinates [\(Suresh et al., 2017;](#page-11-2) [Alistarh et al., 2018\)](#page-9-2) or *iv) low-rank approximation [\(Wang et al.,](#page-11-3) [2021;](#page-11-3) [Dudziak et al., 2019\)](#page-9-3)*, i.e. keeping the most relevant ranks of the decomposed network. Despite the benefits during deployment, that is a lower footprint model, in many cases, the overhead during training time or the accuracy degradation can be non-negligible. Moreover, many techniques can introduce mutliple hyperparameters or the need to fine-tune to recover the lost accuracy.
+
+<span id="page-0-2"></span>In this work, we focus on training low-rank factorized models. Specifically, we pinpoint the challenges of techniques [\(Wang et al., 2021;](#page-11-3) [2023\)](#page-11-4) when decomposing the parameters of each layer in low-rank space and the need to find the optimal ranks for each one at training time. To solve this, we adopt and non-trivially extend the Ordered Dropout technique from [\(Horváth et al., 2021\)](#page-9-4) and apply it to
+
+<span id="page-1-0"></span>![](figures/_page_1_Figure_1.jpeg)
+
+**Figure 1:** MAESTRO's construction. To obtain low-rank approximation, the given linear map is decomposed and trained with ordered dropout to obtain an ordered representation that can be efficiently pruned.
+
+progressively find the optimal decomposition for each layer of a DNN while training (Fig. 1). Critical differences to prior work include *i*) the non-uniformity of the search space (i.e. we allow for different ranks per layer), *ii*) the trainable aspect of the decomposition to reflect the data distribution, and *iii*) the gains to training and deployment time without sacrificing accuracy. Nevertheless, we also provide a latency-accuracy trade-off mechanism to deploy the model on more constrained devices.
+
+Our contributions can be summarized as follows:
+
+- We propose MAESTRO, a novel layer decomposition technique that enables learning low-rank layers in a progressive manner while training. We fuse layer factorization and an extended variant of the ordered dropout, in a novel manner, by embedding OD directly into the factorized weights. By decomposing layers and training on stochastically sampled low-rank models, we apply ordered importance decomposed representation of each layer. We combine this with a hierarchical group-lasso term (Yuan & Lin 2006) in the loss function to zero out redundant ranks and progressively shrink the rank space. This way, we enable computationally efficient training achieved by the proposed decomposition without relying on inexact and potentially computationally expensive decompositions such as Singular Value Decomposition (SVD).
+- MAESTRO is a theoretically motivated approach that embeds decomposition into training. First, we show that our new objective is able to recover *i*) the SVD of the target linear mapping for the particular case of uniform data distribution and *ii*) the Principal Component Analysis (PCA) of the data in the case of identity mapping.
+- As MAESTRO's decomposition is part of the training procedure, it also accounts for data distribution
+  and the target function, contrary to SVD, which operates directly on learned weights. We show
+  that this problem *already arises* for a simple linear model and empirically generalize our results in
+  the case of DNNs, by applying our method to different types of layers (including fully-connected,
+  convolutional, and attention) spanning across three datasets and modalities. We illustrate that our
+  technique achieves better results than SVD-based baselines at a lower cost.
+
+#### 2 Related work
+
+The topic of Efficient ML has received a lot of attention throughout the past decade as networks have been getting increasingly computationally expensive. Towards this end, we distinguish between training and deployment time, with the latter having a more significant impact and thus amortizes the potential overhead during training. Nevertheless, with the advent of Federated Learning (McMahan et al., 2017), efficient training becomes increasingly relevant to remain tractable.
+
+Efficient inference. For efficient deployment, various techniques have been proposed that either optimize the architecture of the DNN in a hand-crafted (Howard et al., 2017) or automated manner (i.e. NAS) (Tan & Le, 2019), they remove redundant computation by means of pruning parts of the network (Han et al., 2015; Carreira-Perpinán & Idelbayev, 2018; Frankle & Carbin, 2019; Chen et al., 2021; Sreenivasan et al., 2022; Li et al., 2016; Wen et al., 2016; Hu et al., 2016; Wen et al., 2016; Zhu & Gupta, 2017; He et al., 2017; Yang et al., 2017; Liu et al., 2018; Yu & Huang, 2019b), in a structured or unstructured manner, or utilise low-precision representation (Wang et al., 2019) of the neurons and activations. However, such techniques may involve non-negligible training overheads or lack flexibility of variable footprint upon deployment. Closer to our method, there have been techniques leveraging low-rank approximation (e.g. SVD) for efficient inference (Xue et al., 2013; Sainath et al., 2013; Jaderberg et al., 2014; Wiesler et al., 2014; Dudziak et al., 2019). Last, there is a category of techniques that dynamically resize the network at runtime for compute, memory or energy efficiency, based on early-exiting (Laskaridis et al., 2021) or dynamic-width (Yu et al., 2019) and leverage the accuracy-latency tradeoff.
+
+Efficient training. On the other hand, techniques for efficient training become very relevant nowadays when scaling DNNs sizes Hu et al. (2021) or deploying to embedded devices (Lin et al., 2022), and oftentimes offer additional gains at deployment time. Towards this goal, there have been employed methods where part of the network is masked (Sidahmed et al., 2021) or dropped (Alam et al., 2022). Caldas et al., 2019) during training, with the goal of minimizing the training footprint. Similarly to early-exiting, multi-exit variants for efficient training (Kim et al., 2023) [Liu et al., 2022) have been proposed, and the same applies for width-based scaling [Horváth et al., (2021); Diao et al., (2021). Last but not least, in the era of transformers and LLMs, where networks have scaled exponentially in size, PEFT-based techniques, such as adapter-based fine-tuning (Houlsby et al., 2019) (such as LoRA (Hu et al., 2021)), become increasingly important and make an important differentiator for tackling downstream tasks.
+
+Learning ordered representation. Originally, Ordered Dropout (OD) was proposed as a mechanism for importance-based pruning for the easy extraction of sub-networks devised to allow for heterogeneous federated training (Horváth et al., 2021). The earlier work that aims to learn ordered representation includes a similar technique to OD—Nested Dropout, which proposed a similar construction, applied to the representation layer in autoencoders (Rippel et al., 2014) to enforce identifiability of the learned representation or the last layer of the feature extractor (Horváth et al., 2021) to learn an ordered set of features for transfer learning. We leverage and non-trivially extend OD in our technique as a means to order ranks in terms of importance in a nested manner during training of a decomposed network that is progressively shrunk as redundant ranks converge to 0. Ranks selection is ensured through hierarchical group lasso penalty, as described in Sec. 3.3 Moreover, contrary to (Horváth et al., 2021), which assumed a uniform width, our formulation allows for heterogeneous ranks per layer. Last, we leverage the ordered representation of ranks at inference time to further compress the model, allowing a graceful degradation of performance as a mechanism for the accuracy-latency trade-off.
+
+#### 3 MAESTRO
+
+In this work, we focus on low-rank models as a technique to reduce the computational complexity and memory requirements of the neural network model. The main challenge that we face is the selection of the optimal rank or the trade-off between the efficiency and the rank for the given layer represented by linear mapping. Therefore, we devise an importance-based training technique, MAESTRO, which not only learns a mapping between features and responses, but also learns the decomposition of the trained network. This is achieved by factorizing all the layers in the network.
+
+### 3.1 FORMULATION
+
+**Low-rank approximation.** Our inspiration comes from the low-rank matrix approximation of a matrix  $A \in \mathbb{R}^{m \times n}$ . For simplicity, we assume that A has rank  $r = \min\{m, n\}$  with  $k \le r$  distinct non-zero singular values  $\tilde{\sigma}_1 > \tilde{\sigma}_2 > \ldots > \tilde{\sigma}_k > 0$ , with corresponding left and right singular vectors  $\tilde{u}_1, \tilde{u}_2, \ldots, \tilde{u}_k \in R^m$  and  $\tilde{v}_1, \tilde{v}_2, \ldots, \tilde{v}_k \in R^n$ , respectively. For such a matrix, we can rewrite its best l-rank approximation as the following minimization problem
+
+<span id="page-2-0"></span>
+$$\min_{U \in \mathbb{R}^{m \times l}, V \in \mathbb{R}^{n \times l}} \left\| \sum_{i=1}^{l} u_i v_i^{\top} - A \right\|_F^2 \tag{1}$$
+
+where  $c_i$  denotes the i-th row of matrix C and  $\|\cdot\|_F$  denotes Frobenius norm. We note that Problem (I) is non-convex and non-smooth. However, Ye & Du (2021) showed that the randomly initialized gradient descent algorithm solves this problem in polynomial time. In this work, we consider the best rank approximation across all the ranks that leads us to the following objective
+
+$$\min_{U \in \mathbb{R}^{m \times r}, V \in \mathbb{R}^{n \times r}} \frac{1}{r} \sum_{b=1}^{r} \left\| U_{:b} V_{:b}^{\top} - A \right\|_{F}^{2}, \tag{2}$$
+
+where  $C_{:b}$  denotes the first b columns of matrix C. This objective, up to scaling, recovers SVD of A exactly, and for the case of distinct non-zero singular values, the solution is, up to scaling, unique Horváth et al. (2021). This formulation, however, does not account for the data distribution, i.e., it cannot tailor the decomposition to capture specific structures that appear in the dataset.
+
+**Data-dependent low-rank approximation.** Therefore, the next step of our construction is to extend this problem formulation with data that can further improve compression, reconstruction, and
+
+generalization, and incorporate domain knowledge. We assume that data comes from the distribution  $x \sim \mathcal{X}$  centered around zero, i.e.,  $\mathbf{E}_{x \sim \mathcal{X}}[x] = 0$  and the response is given by y = Ax. In this particular case, we can write the training loss as
+
+<span id="page-3-4"></span><span id="page-3-1"></span>
+$$\min_{U \in \mathbb{R}^{m \times r}, V \in \mathbb{R}^{n \times r}} \mathbf{E}_{x, y \sim \mathcal{X}} \left[ \sum_{b=1}^{r} \frac{1}{r} \left\| U_{:b} V_{:b}^{\top} x - y \right\|^{2} \right]. \tag{3}$$
+
+It is important to note that the introduced problem formulation (3) is the same as the Ordered Dropout formulation of Horváth et al. (2021) for the neural network with a single hidden layer and no activations, and it can be solved using stochastic algorithms by sampling from the data distribution  $\mathcal{X}$  (subsampling) and rank distribution  $\mathcal{D}$ . However, there is an important distinction when we apply MAESTRO for deep neural networks. While FjORD applies uniform dropout across the width of the network for each layer, we propose to decompose each layer independently to uncover its – potentially different – optimal rank for deployment. We discuss details in the next paragraph.
+
+**DNN low-rank approximation.** For Deep Neural Networks (DNNs), we seek to uncover the optimal ranks for a set of d linear mappings  $W^1 \in \mathbb{R}^{m_1 \times n_1}, \dots, W^d \in \mathbb{R}^{m_d \times n_d}$ , where  $W^i$ 's are model parameters and d is model depth, e.g., weights corresponding to linear layers by decomposing them as  $W^i = U^i \left(V^i\right)^\top$ . We discuss how these are selected in the next section. To decompose the network, we aim to minimize the following objective:
+
+$$\mathbf{E}_{x,y\sim\mathcal{X}}\left[\frac{1}{\sum_{i=1}^{d}r_{i}}\sum_{i=1}^{d}\sum_{b=1}^{r_{i}}l(h(U^{1}(V^{1})^{\top},\ldots,U_{:b}^{i}(V_{:b}^{i})^{\top},\ldots,U^{d}(V^{d})^{\top},W^{o},x),y)\right],\quad(4)$$
+
+where  $r_i = \min\{m_i, n_i\}$ , l is a loss function, h is a DNN, and  $W^o$  are the other weights that we do not decompose. We note that our formulation aims to decompose each layer, while decompositions across layers do not directly interact. The motivation for this approach is to uncover low-rank structures within each layer that are not affected by inaccuracies from other layers due to multiple low-rank approximations.
+
+#### <span id="page-3-3"></span>3.2 Layer factorization
+
+The following sections discuss how we implement model factorization for different architectures.
+
+**FC layers.** A 2-layer fully connected (FC) neural network can be expressed as  $f(x) = \sigma(\sigma(xW_1)W_2)$ , where Ws are weight matrices of each FC layer, and  $\sigma(\cdot)$  is any arbitrary activation function, e.g., ReLU. The weight matrix W can be factorized as  $UV^{\top}$ .
+
+**CNN layers.** For a convolution layer with dimension,  $W \in \mathbb{R}^{m \times n \times k \times k}$  where m and n are the number of input and output channels, and k is the size of the convolution filters. Instead of directly factorizing the 4D weight of a convolution layer, we factorize the unrolled 2D matrix. Unrolling the 4D tensor W leads to a 2D matrix with shape  $W_{\text{unrolled}} \in \mathbb{R}^{mk^2 \times n}$ , where each column represents the weight of a vectorized convolution filter. Factorization can then be conducted on the unrolled 2D matrix; see (Wang et al., [2021]) for details.
+
+**Transformers.** A Transformer layer consists of a stack of encoders and decoders Vaswani et al. (2017). The encoder and decoder contain three main building blocks: the multi-head attention layer, position-wise feed-forward networks (FFN), and positional encoding. We factorize all trainable weight matrices in the multi-head attention (MHA) and the FFN layers. The FFN layer factorization can directly adopt the strategy from the FC factorization. A p-head attention layer learns p attention mechanisms on the key, value, and query (K, V, Q) of each input token:
+
+$$MHA(Q, K, V) = Concat(head_1, \dots, head_p)W^O.$$
+
+Each head performs the computation of:
+
+$$\operatorname{head}_i = \operatorname{Attention}(QW_Q^{(i)}, KW_K^{(i)}, VW_V^{(i)}) = \operatorname{softmax}\left(\frac{QW_Q^{(i)}W_K^{(i)\top}K^\top}{\sqrt{d/p}}\right)VW_V^{(i)}.$$
+
+where d is the hidden dimension. The trainable weights  $W_Q^{(i)}, W_K^{(i)}, W_V^{(i)}, i \in \{1, 2, \dots, p\}$  can be factorized by simply decomposing all learnable weights  $W \cdot$  in an attention layer and obtaining  $U \cdot V^{\top} \cdot \text{Vaswani}$  et al. (2017).
+
+<span id="page-3-0"></span><sup>&</sup>lt;sup>1</sup>We make this assumption for simplicity. It can be simply overcome by adding a bias term into the model.
+
+<span id="page-3-2"></span><sup>&</sup>lt;sup>2</sup>We can apply our decomposition on different types of layers, such as Linear, Convolutional and Transformers as shown in Sec. 3.2
+
+#### <span id="page-4-0"></span>3.3 Training techniques
+
+Having defined the decomposition of typical layers found in DNNs, we move to formulate the training procedure of our method, formally described in Algorithm II. Training the model comprises an iterative process of propagating forward on the model by sampling a rank  $b_i$  per decomposed layer i up to maximal rank  $r_i$  (line 3). We calculate the loss, which integrates an additional hierarchical group lasso component (lines 4) and backpropagate on the sampled decomposed model (line 5). At the end of each epoch, we progressively shrink the network by updating the maximal rank  $r_i$ , based on an importance threshold  $\varepsilon_{ps}$  (line 11). We provide more details about each component below.
+
+#### Algorithm 1: MAESTRO (Training Process)
+
+```
+Input: epochs E, dataset \mathcal{D}, model h parametrized by U^1 \in \mathbb{R}^{m_1 \times r_1}, V^1 \in \mathbb{R}^{n_1 \times r_1}, ..., U^d \in \mathbb{R}^{m_d \times r_d}, V^d \in \mathbb{R}^{n_d \times r_d}, W^o, and hyperparameters \lambda_{gl}, \varepsilon_{ps}
+  1 for t \leftarrow 0 to E - 1 do // Epochs
+                 for (x,y) \in \mathcal{D} do // Iterate over dataset
+  2
+                         Sample (i,b) \sim \left\{ \left\{ (i,b) \right\}_{b=1}^{r_i} \right\}_{i=1}^d;
+L = l(h(U^1(V^1)^\top, \dots, U^i_{:b}(V^i_{:b})^\top, \dots, U^d(V^d)^\top, W^o, x), y) + \frac{1}{2} \sum_{i=1}^d \sum_{b=1}^{r_i} \left( \left\| U^i_{b:} \right\| + \left\| V^i_{b:} \right\| \right) \text{ } || \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text
+  5
+                 end
+  6
+                 for i \leftarrow 1 to d do
+  7
+                           for b \leftarrow 1 to r_i do
+                                     // rank importance thresholding
+                                     if \left\|V_{b:}^{i}\right\|\left\|U_{b:}^{i}\right\|\leq \varepsilon_{ps} then
+10
+                                               r_i = b - 1 // progressive shrinking
+11
+                                     end
+14
+                           end
+                 end
+15
+16 end
+```
+
+<span id="page-4-1"></span>Efficient training via sampling. In Sec. 4 we show that for the linear case (3), the optimal solution corresponds to PCA over the linearly transformed dataset. This means that the obtained solution contains orthogonal directions. This property is beneficial because it directly implies that when we employ gradient-based optimization, not only is the gradient zero at the optimum, but the gradient with respect to each summand in Equation (3) is also zero. The same property is directly implied by overparametrization Ma et al. (2018) or strong growth condition Schmidt & Roux (2013). As a consequence, this enables us to sample only one summand at a time and obtain the same quality solution. When considering (4) as an extension to (3), it is unclear whether this property still holds, which would also imply that the set of stationary points of (3) is a subset of stationary points of the original objective without decomposition. However, in the experiments, we observed that sampling is sufficient to converge to a good-quality solution. If this only holds approximately, one could leverage fine-tuning to recover the loss in performance.
+
+Efficient rank extraction via hierarchical group-lasso. By definition, (3) leads to an ordered set of ranks for each layer. This ordered structure enables efficient rank extraction and selection. To effectively eliminate unimportant ranks while retaining the important ones, thus leading to a more efficient model, we consider Hierarchical Group Lasso (HGL) Lim & Hastie (2015) in the form
+
+$$\lambda_{gl} \sum_{i=1}^{d} \sum_{b=1}^{r_i} (\|U_{b:}^i\| + \|V_{b:}^i\|), \tag{5}$$
+
+where  $C_b$ : denotes the matrix that contains all the columns of C except for the first b-1 columns.
+
+**Progressive shrinking.** HGL encourages that unimportant ranks become zero and can be effectively removed from the model. To account for this, for each layer we remove  $V_{b:}^i$  and  $U_{b:}^i$  (i.e., set  $r_i = b-1$ ) if  $\|V_{b:}^i\|\|U_{b:}^i\| \le \varepsilon_{ps}$ , where  $\varepsilon_{ps}$  is a pre-selected threshold – and a hyperparameter of our method.
+
+Initialization. Initialization is a key component of the training procedure He et al. (2015); Mishkin & Matas (2015). To adopt the best practices from standard non-factorized training, we follow a similar approach to Khodak et al. (2021); Wang et al. (2021), where we first initialize the non-factorized model using standard initialization. For initializing factorized layers, we use the Singular Value
+
+<span id="page-5-2"></span>![](figures/_page_5_Figure_1.jpeg)
+
+(a) Verification that MAESTRO recovers SVD for linear mapping with uniform data. The plot displays the L2 distance between the best rank k and MAESTRO's approximation of mapping A. The target matrix was randomly generated  $9\times 6$  matrix with rank 3. p and k represent relative and actual rank.
+
+![](figures/_page_5_Figure_3.jpeg)
+
+(b) Verification that MAESTRO recovers PCA for identity mapping. The plot displays the estimates of singular values. The data distribution has only 3 directions. It is expected that the top 3 ranks will converge to value one and the rest to zero. p and k stand for relative and actual rank, respectively.
+
+Figure 2: Empirical showcase of theoretical properties of the MAESTRO's formulation.
+
+Decomposition of the non-factorized initialization – in a full-rank form – to ensure that the resulting product matrix is the same as the original parameter decomposition. In addition, SVD is an optimal decomposition for the linear case with uniform data. However, in contrast with the adaptive baseline method (Wang et al., |2023|) we only decompose once, rather than on every training iteration.
+
+#### <span id="page-5-3"></span>3.4 Train-once, deploy-everywhere
+
+Up until now, we have described how our method works for training low-rank models, which yield computational, memory, network, and energy ( $\overline{\text{Wu et al.}}$ ) ( $\overline{\text{2022}}$ ) bandwidth benefits during training. At deployment time, one can directly deploy the final model (rank  $r_i$  for each layer) on the device, which we acquire from performing a threshold sweep of  $\varepsilon_{ps}$  over the effective range of rank importance across layers. However, in case we want to run on even more constrained devices, such as mobile ( $\overline{\text{Almeida et al.}}$ ) or embedded ( $\overline{\text{Almeida et al.}}$ ) systems, the learned decomposition also gives us the flexibility to further compress the model in a straightforward manner, effectively trading off accuracy for a smaller model footprint. Inspired by  $\overline{\text{Yu \& Huang}}$  ( $\overline{\text{2019a}}$ ), we propose to use greedy search. We begin with the current model and compare model performance across various low-rank models, each created by removing a certain percentage of ranks from each layer. We then eliminate the ranks that cause the least decrease in performance. This process is iterated until we reach the desired size or accuracy constraint. To make this approach efficient, we estimate the loss using a single mini-batch with a large batch size, for example, 2048. This also avoids issues with BatchNorm layers; see  $\overline{\text{Yu \& Huang}}$  ( $\overline{\text{2019a}}$ ) for details.
+
+In summary, MAESTRO comprises a technique for trainable low-rank approximation during training time that progressively compresses the model, reflecting the data distribution, and a method that enables a graceful trade-off between accuracy and latency for embedded deployment, by selecting the most important parts of the network. We validate these claims in Sec. 5.2 and 5.5 respectively.
+
+#### <span id="page-5-0"></span>4 THEORETICAL GUARANTEES
+
+In this section, we further investigate the theoretical properties of MAESTRO for the linear mappings, i.e., the setup of the problem formulation (3).
+
+<span id="page-5-1"></span>**Theorem 4.1** (Informal). Let  $A = \tilde{U}\tilde{\Sigma}\tilde{V}^{\top}$  be a SVD decomposition of A. Then, the minimization problem [3] is equivalent to PCA applied to the transformed dataset  $x \to \tilde{\Sigma}\tilde{V}^{\top}x$ ,  $x \sim \mathcal{X}$  projected on the column space of  $\tilde{U}$ .
+
+The formal statement can be found in Appendix  $\boxed{D}$ . Theorem  $\boxed{4.1}$  shows that MAESTRO can adapt to data distribution by directly operating on data  $x \sim \mathcal{X}$  and also to the target mapping by projecting data to its right singular vectors scaled by singular values. In particular, we show that in the special case, when  $\mathcal{X}$  is the uniform distribution on the unit ball,  $\boxed{3}$ , i.e., MAESTRO, exactly recovers truncated SVD of A, which is consistent with the prior results  $\boxed{\text{Horváth et al.}}$  ( $\boxed{2021}$ ). In the case A is the identity, it is straightforward to see that MAESTRO is equivalent to PCA. We can see that MAESTRO can efficiently extract low-rank solutions by filtering out directions corresponding to the null space of the target mapping A and directions with no data. We also numerically verify both of the special cases–PCA and SVD, by minimizing  $\boxed{3}$  using stochastic gradient descent (SGD) with  $\mathcal{D}$  being the uniform distribution. These preliminary experiments are provided in Fig.  $\boxed{2}$  and  $\boxed{2}$ b.
+
+We showed that MAESTRO could recover SVD in a particular case of the linear model and the uniform data distribution on the unit ball. We note that in this case, SVD is optimal, and we cannot acquire better decomposition. Therefore, it is desired that MAESTRO is equivalent to SVD in this scenario. In the more general setting, we argue that MAESTRO decomposition should be preferable to SVD due to the following reasons:
+
+- MAESTRO formulation is directly built into the training and tailored to obtain the best low-rank decomposition, while SVD relies on linearity assumption.
+- SVD does not account for data, and even in the linear NN case, the learned singular vectors might exhibit wrong ordering. We demonstrate this issue using a simple example where we take matrix *A* with rank 3. We construct the dataset *X* in such a way that the third singular vector is the most important, the second one is the second, and the first is the third most important direction. Clearly, SVD does not look at data. Therefore, it cannot capture this phenomenon. We showcase that MAESTRO learns the correct order; see Fig. [5](#page-0-1) of the Appendix.
+- Pre-factorizing models allow us to apply hierarchical group-lasso penalty [\(Yuan & Lin, 2006\)](#page-12-0) for decomposed weights to directly regularize the rank of different layers.
+- SVD is computationally expensive and can only run rarely, while MAESTRO is directly built into the training and, therefore, does not require extra computations. In addition, MAESTRO supports rank sampling so training can be made computationally efficient.
+
+# 5 EXPERIMENTS
+
+We start this section by describing the setup of our experiments, including the models, datasets and baselines with which we compare MAESTRO. We then compare MAESTRO against the baselines on accuracy and training Multiply-Accumulate operations (MACs) and discuss the results. Subsequently, we analyze the behaviour of our system in-depth and provide additional insights on the performance of our technique, along with an ablation study and sensitivity analysis to specific hyperparameters. Finally, we showcase the performance of models upon deployment and how we can derive a smaller footprint model with some accuracy trade-off, without the need to fine-tune.
+
+#### 5.1 EXPERIMENTAL SETUP
+
+Models & datasets. The datasets and models considered in our experiments span across four datasets, concisely presented along with the associated models on Tab. [1.](#page-6-1) We have implemented our solution with PyTorch [\(Paszke et al., 2017\)](#page-10-16)(v1.13.0) trained our models on NVidia A100 (40G) GPUs. Details for the learning tasks and hyperparameters used are presented in the Appendix.
+
+Baselines. We have selected various baselines from the literature that we believe are closest to aspects of our system. On the *pruning* front, we compare with the IMP [\(Paul et al., 2023\)](#page-11-16) and RareGems [\(Sreenivasan et al., 2022\)](#page-11-6) techniques, themselves based on the LTH [\(Frankle & Carbin,](#page-9-1) [2019\)](#page-9-1). On the *quantization* front, we compare
+
+<span id="page-6-1"></span>Table 1: Datasets and models for evaluation. The network footprints depict the vanilla variants of the models.
+
+| Dataset      | Model               | # GMACs | # Params (M) | Task                 |
+|--------------|---------------------|---------|--------------|----------------------|
+| MNIST        | LeNet               | 2e4     | 0.04         | Image classification |
+| CIFAR10      | ResNet-18           | 0.56    | 11.18        | Image classification |
+| CIFAR10      | VGG-19              | 0.40    | 20.00        | Image classification |
+| TinyImageNet | ResNet-50           | 5.19    | 53.9         | Image classification |
+| Multi30k     | 6-layer Transformer | 1.37    | 48.98        | Translation (en-ge)  |
+
+with XNOR-Net [\(Rastegari et al., 2016\)](#page-11-17). With respect to *low-rank* methods, we compare with Spectral Initialisation [Khodak et al.](#page-10-15) [\(2021\)](#page-10-15), Pufferfish [\(Wang et al., 2021\)](#page-11-3) and Cuttlefish [\(Wang et al., 2023\)](#page-11-4).
+
+## <span id="page-6-0"></span>5.2 PERFORMANCE COMPARISON
+
+We start off by comparing MAESTRO with various baselines from the literature across different datasets and types of model[s3.](#page-6-2) Results are depicted in Tab. [2](#page-7-0) and [3,](#page-7-0) while additional performance points of MAESTRO for different model footprints are presented in the Appendix [F.2](#page-0-2) and [F.3.](#page-0-3)
+
+Comparisons with low-rank methods. The low-rank methods we are comparing against are Pufferfish [\(Wang et al., 2021\)](#page-11-3) and Cuttlefish [\(Wang et al., 2023\)](#page-11-4). These methods try to reduce training and inference runtime while preserving model accuracy by leveraging low-rank approximations. For ResNet-18, we achieve 94.19*±*0*.*07% for 4.08M parameters and 93.97*±*0*.*25% for 2.19M parameters compared to the 94.17% of Pufferfish at 3.3M parameters. For VGG-19, we achieve +0.41pp (percentage points) higher accuracy compared to Pufferfish and -0.29pp to Cuttlefish at 44.8% and
+
+<span id="page-6-2"></span><sup>3</sup> The operating points we select for MAESTRO are the closest lower to the respective baseline in terms of footprint. Where the result is not present in the Tab. [2,](#page-7-0) we provide the *gp* value so that it can be referenced from the Appendix, Tab. [11,](#page-0-4) [12.](#page-0-5)
+
+Table 2: Maestro vs. baselines on CIFAR10.
+
+**Table 3:** Maestro vs. baselines on Multi30k.
+
+<span id="page-7-0"></span>
+
+| Variant                                          | Model     | Acc. (%)                       | GMACs                         | Params. $(M)$                 |
+|--------------------------------------------------|-----------|--------------------------------|-------------------------------|-------------------------------|
+| Non-factorized                                   | ResNet-18 | 93.86±0.20                     | 0.56                          | 11.17                         |
+| Pufferfish                                       | ResNet-18 | 94.17                          | 0.22                          | 3.336                         |
+| Cuttlefish                                       | ResNet-18 | 93.47                          | 0.3                           | 3.108                         |
+| IMP                                              | ResNet-18 | 92.12                          | -                             | 0.154                         |
+| RareGems                                         | ResNet-18 | 92.83                          | -                             | 0.076                         |
+| XNOR-Net                                         | ResNet-18 | 90.06                          | -                             | $0.349^{\dagger}$             |
+| Maestro <sup>†</sup> $(\lambda_{qp} = 16e^{-6})$ | ResNet-18 | $94.19 \scriptstyle{\pm 0.07}$ | $0.39{\scriptstyle \pm 0.00}$ | $4.08{\scriptstyle\pm0.02}$   |
+| Maestro <sup>†</sup> $(\lambda_{gp} = 64e^{-6})$ | ResNet-18 | 93.86±0.11                     | $0.15{\scriptstyle\pm0.00}$   | $1.23{\scriptstyle \pm 0.00}$ |
+| Non-factorized                                   | VGG-19    | 92.94±0.17                     | 0.40                          | 20.56                         |
+| Pufferfish                                       | VGG-19    | 92.69                          | 0.29                          | 8.37                          |
+| Cuttlefish                                       | VGG-19    | 93.39                          | 0.15                          | 2.36                          |
+| RareGems                                         | VGG-19    | 86.28                          | -                             | 5.04                          |
+| IMP                                              | VGG-19    | 92.86                          | -                             | 5.04                          |
+| XNOR-Net                                         | VGG-19    | 88.94                          | -                             | $0.64^{\dagger}$              |
+| Spectral Init.*                                  | VGG-19    | 83.27                          | -                             | $\approx 0.4$                 |
+| MAESTRO <sup>†</sup> $(\lambda_{gp} = 32e^{-6})$ | VGG-19    | $93.10{\scriptstyle\pm0.10}$   | $0.13{\scriptstyle\pm0.00}$   | $2.20{\scriptstyle \pm 0.03}$ |
+| MAESTRO <sup>†</sup> $(\lambda = 512e^{-6})$     | VGG-19    | 88.53±0.13                     | $0.03{\scriptstyle \pm 0.00}$ | $0.35{\scriptstyle \pm 0.00}$ |
+
+| Variant             | Model       | Perplexity                          | GMACs                                          | Params. $(M)$     |
+|---------------------|-------------|-------------------------------------|------------------------------------------------|-------------------|
+| Non-factorized      | Transformer | $9.85_{\pm 0.10}$                   | 1.370                                          | 53.90             |
+| Pufferfish*         | Transformer | $7.34 \pm 0.12$                     | 0.996                                          | 26.70             |
+| $Maestro^{\dagger}$ | Transformer | $\pmb{6.90} \scriptstyle{\pm 0.07}$ | $\boldsymbol{0.248} {\scriptstyle \pm 0.0032}$ | $13.80 \pm 0.113$ |
+| 1.70                |             |                                     | Cai (400 1                                     | 0 03              |
+
+\*Results from original work; † tuned  $\lambda_{gp}$  from  $\{2^i/100; i \in 0, \dots, 9\}$ 
+
+**Table 4:** Ablation study for ResNet18 on CIFAR10
+
+| Variant                      | Acc. (%)   | GMACs                           | Params. $(M)$                    |
+|------------------------------|------------|---------------------------------|----------------------------------|
+| MAESTRO                      |            | $0.39 \scriptstyle{\pm 0.0008}$ | $4.08{\scriptstyle\pm0.020}$     |
+| w/out GL                     |            | $0.56 \pm 0.0000$               | 11.2±0.000                       |
+| w/out PS<br>w/ full-training |            | $0.39 \pm 0.0010$               | $4.09\pm0.027$<br>$4.09\pm0.032$ |
+| w/ run-training              | 94.03±0.32 | U.39±0.0004                     | 4.09±0.032                       |
+
+\*Results from original work; †: XNOR-Net employs binary weights and activations; although the overall #trainable parameters remain the same as the vanilla network, each model weight is quantized from 32-bit to 1-bit. Therefore, we report a compression rate of 3.125%(1/32).
+
+93.2% of the sizes, respectively. Finally, comparing with the spectral initialization (Khodak et al.) 2021) for VGG-19, we achieve +5.26pp higher accuracy for 87.5% of parameter size. Detailed results are shown in Tab. 2 This performance benefits also apply in the case of Transformers (Tab. 3), where MAESTRO performs 6% better in terms of perplexity at 25% of the cost (MACs) and 51.7% of the size (parameters) compared to Pufferfish.
+
+Comparisons with pruning methods. The next family of baselines is related to the LTH (Frankle & Carbin, 2019). Specifically, we compare against IMP (Paul et al.) 2023) and witness from Tab. 2 that MAESTRO can achieve +1.25pp ( $\lambda_{gp}=128e^{-6}$ ) and +0.24pp ( $\lambda_{gp}=32e^{-6}$ ) higher accuracy for ResNet-18 and VGG-19 respectively. Although we cannot scale to the size that RareGems (Sreenivasan et al.) 2022) for ResNet-18, the sparsity that they achieve is unstructured, which most modern hardware cannot take advantage of. In contrast, our technique performs ordered structured sparsity, compatibly with most computation targets. On the other hand, for VGG-19, we achieve +6.82pp higher accuracy at 43.6% of the footprint.
+
+Comparisons with quantized models. We also compare against XNOR-Net (Rastegari et al., 2016), which binarizes the network to achieve efficient inference. Training continues to happen in full precision, and inference performance is dependent on the operation implementation of the target hardware. Nonetheless, assuming a compression rate of 3.125%, for the same model size, we achieve +1.08pp ( $\lambda_{qp}=512e^{-6}$ ) and +2.18pp ( $\lambda_{qp}=256e^{-6}$ ) higher accuracy on ResNet-18 and VGG-19.
+
+#### 5.3 Training behaviour of Maestro
+
+Having shown the relative performance of our framework to selected baselines, we now move to investigate how our method behaves, with respect to its convergence and low-rank approximations.
+
+Model and rank convergence. In Fig.  $\boxed{3}$ , we present the training dynamics for MAESTRO. Fig.  $\boxed{3}$ a illustrates the evolution of total rank throughout the training steps. We observe that the ranks are pruned incrementally. This aligns with the observations made during Pufferfish Wang et al. (2021) training, where the authors suggest warm-start training with full precision to enhance the final model performance. In our situation, we do not need to integrate this heuristic because MAESTRO automatically prunes rank. Fig.  $\boxed{3}$ b reveals the ranks across layers after training. We notice an intriguing phenomenon: the ranks are nested for increasing  $\lambda_{gl}$ . This could imply apart from a natural order of ranks within each layer, a global order. We briefly examine this captivating occurrence in the following section, and we plan to investigate it more thoroughly in future work, as we believe this might contribute to a superior rank selection and sampling process. Lastly, Fig.  $\boxed{3}$ c depicts the progression of training loss. We find that our hypothesis, that sampling does not adversely impact training, is also supported empirically.
+
+#### 5.4 ABLATION STUDY
+
+In this section, we examine the impact of each component on the performance of MAESTRO. Specifically, we run variants of our method i) without the *hierarchical group lasso regularization* (HGL), ii) without progressive *shrinking* (PS). Additionally, we integrate iii) an *extra full low-rank* pass  $(b = r_i)$  into the training at each step to assess whether extra sampling would be beneficial.
+
+<span id="page-8-1"></span>![](figures/_page_8_Figure_1.jpeg)
+
+Figure 3: Training dynamics of MAESTRO for ResNet18 on CIFAR10.
+
+<span id="page-8-2"></span>![](figures/_page_8_Figure_3.jpeg)
+
+Figure 4: Accuracy-latency trade-off of MAESTRO under different settings for VGG19 on CIFAR10. The results are displayed in Tab. [4.](#page-7-0) As anticipated, our findings confirm that neither inclusion of hierarchical group lasso with a tuned *gl* nor progressive shrinking impair the final performance, but they do significantly enhance the efficiency of MAESTRO. Moreover, sampling more ranks at each training step does not improve the final performance, and, in fact, it hampers training efficiency, making it approximately twice as computationally demanding.
+
+#### <span id="page-8-0"></span>5.5 ACCURACY-LATENCY TRADE-OFF AT TRAINING AND DEPLOYMENT TIME
+
+In Fig. [4,](#page-8-2) we illustrate various approaches to balance latency (proxied through MACs operations) and accuracy in model training and deployment. Fig. [4a](#page-8-2) demonstrates how MAESTRO (*gl* = 0) can be pruned effectively for deployment using the greedy search method discussed in Section [3.4.](#page-5-3) We contrast this with the greedy pruning of a non-factorized model that has been factorized using SVD. We reveal that this straightforward baseline does not measure up to the learned decomposition of MAESTRO and results in a significant performance decrease. Next, Fig. [4b](#page-8-2) portrays the final accuracy and the number of model parameters for varying hierarchical group lasso penalties. This leads to the optimal latency-accuracy balance for both training and inference. However, it's crucial to point out that each model was trained individually, while greedy pruning only necessitates a single training cycle. Lastly, we delve into the observation of nested ranks across increasing *gl*. Fig. [4c](#page-8-2) displays the performance of MAESTRO (*gl* = 0) across different ranks selected by smaller models MAESTRO (*gl >* 0). Intriguingly, we observe that MAESTRO (*gl* = 0) performs very well—for instance, we can decrease its operations in half (and parameters by 10⇥) and still maintain an accuracy of 87*.*7% without fine-tuning, just by reusing rank structure from independent runs. As aforementioned, we intend to further explore this in the future.
+
+# 6 CONCLUSION AND FUTURE WORK
+
+In this work, we have presented MAESTRO, a method for trainable low-rank approximation of DNNs that leverages progressive shrinking by applying a generalized variant of Ordered Dropout to the factorized weights. We have shown the theoretical guarantees of our work in the case of linear models and empirically demonstrated its performance across different types of models, datasets, and modalities. Our evaluation has demonstrated that MAESTRO outperforms competitive compression methods at a lower cost. In the future, we plan to expand our technique to encompass more advanced sampling techniques and apply it to different distributed learning scenarios, such as Federated Learning, where data are natively non-independent or identically distributed (non-IID).
+
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papers/3mdCet7vVv/review.json

@@ -0,0 +1,91 @@
+{
+  "id": "3mdCet7vVv",
+  "title": "Maestro: Uncovering Low-Rank Structures via Trainable Decomposition",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "hi0mIdcLFJ",
+      "rating": 5,
+      "content": {
+        "summary": "The paper proposes MAESTRO, which is a trainable low-rank approximation technique for deep neural networks. It proposes a progressive shrinking approach that decomposes the weights of each layer into low-rank components using an extended version of Ordered Dropout. This allows for efficient compression and trade-off between model size and accuracy. The method is evaluated on various models, datasets, and modalities, showing superior performance compared to other compression methods.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "- The paper extends the Ordered Dropout technique to handle non-uniformity in the search space by allowing different ranks per layer. \n\n- It introduces a trainable aspect to the decomposition, which enables the model to reflect the data distribution. \n\n- It provides a latency-accuracy trade-off mechanism for deploying the network on constrained devices.",
+        "weaknesses": "- The citation style seems not correct. It should include the author's names in place of numerical references.\n\n- Why the method named after \"Maestro\"? It is never introduced and seems weird to me.\n\n- The proposed technique appears as a logical improvement from Ordered Dropout. Its effectiveness, however, is primarily demonstrated through toy architectures and datasets, such as ResNet18 and Cifar10. For the method to gain practical and impactful validation, I recommend conducting additional experiments on more complex datasets like ImageNet to substantiate its superiority.\n\n- Building on the previous point, there are alternative methods that report better accuracy with more compact architectures. For instance, the OTOv2 framework:\n\nChen, Tianyi, et al. \"Only train once: A one-shot neural network training and pruning framework.\" Advances in Neural Information Processing Systems 34 (2021): 19637-19651.\n\nIt structurally prunes the model during training (hence still training efficient), and it achieves a 93.3% accuracy with only 0.55M parameters on Cifar10 using VGG16. This is in contrast to the 93.10% accuracy with 2.20M parameters reported by the proposed method. This comparison casts doubt on the practical utility and the advantages of the low-rank based method presented.",
+        "questions": "See the weaknesses part above.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": " - The citation style seems not correct. It should include the author's names in place of numerical references.\n\n- Why the method named after \"Maestro\"? It is never introduced and seems weird to me.\n\n- The proposed technique appears as a logical improvement from Ordered Dropout. Its effectiveness, however, is primarily demonstrated through toy architectures and datasets, such as ResNet18 and Cifar10. For the method to gain practical and impactful validation, I recommend conducting additional experiments on more complex datasets like ImageNet to substantiate its superiority.\n\n- Building on the previous point, there are alternative methods that report better accuracy with more compact architectures. For instance, the OTOv2 framework:\n\nChen, Tianyi, et al. \"Only train once: A one-shot neural network training and pruning framework.\" Advances in Neural Information Processing Systems 34 (2021): 19637-19651.\n\nIt structurally prunes the model during training (hence still training efficient), and it achieves a 93.3% accuracy with only 0.55M parameters on Cifar10 using VGG16. This is in contrast to the 93.10% accuracy with 2.20M parameters reported by the proposed method. This comparison casts doubt on the practical utility and the advantages of the low-rank based method presented.",
+        "suggestions": "The paper's core idea of using a trainable low-rank approximation through a progressive shrinking approach is interesting, however, the experimental validation is not sufficiently convincing. The current results are limited to relatively simple architectures and datasets. To demonstrate the practical value of the proposed method, the authors should conduct experiments on more challenging datasets such as ImageNet, which would provide a more robust evaluation of the method's scalability and effectiveness. Furthermore, it would be beneficial to compare the proposed method against more recent state-of-the-art compression techniques, particularly those that achieve higher compression rates with comparable or better accuracy. The current comparison with OTOv2 is not entirely fair, as it compares VGG-19 with VGG-16. However, the fact that OTOv2 achieves better accuracy with fewer parameters on Cifar10 using VGG16 raises concerns about the practical advantages of the proposed low-rank method. A more comprehensive comparison against other pruning and compression techniques, including those that achieve higher compression rates with comparable or better accuracy, is necessary to establish the method's true potential.\n\nTo strengthen the paper, the authors should provide a more detailed analysis of the training process and the impact of different hyperparameters on the final model performance. For example, the paper could explore how the learning rate, rank selection strategy, and the shrinking schedule affect the accuracy-compression trade-off. A sensitivity analysis of these hyperparameters would provide valuable insights into the method's robustness and help practitioners to effectively apply it to different tasks. Furthermore, the paper should include a more in-depth discussion of the computational overhead of the proposed method, including the training time and memory requirements. This is particularly important for practical applications, where computational resources are often limited. A clear understanding of the computational cost would allow practitioners to make informed decisions about whether to use the proposed method or alternative compression techniques.\n\nFinally, the paper should clearly articulate the novelty of the proposed method compared to existing low-rank approximation techniques. While the paper extends Ordered Dropout, it is not immediately clear how this extension leads to a significant improvement over existing methods. A more detailed explanation of the technical contributions and the advantages of the proposed method over existing techniques would be beneficial. The authors should also discuss the limitations of the proposed method and potential directions for future research. This would help to place the method in the context of the broader research landscape and provide a more balanced perspective on its strengths and weaknesses. In summary, the paper needs more comprehensive experimental validation, a more detailed analysis of the training process, and a clearer articulation of the method's novelty and limitations."
+      }
+    },
+    {
+      "id": "ML8evsHc8c",
+      "rating": 5,
+      "content": {
+        "summary": "This paper proposes a low-rank compression scheme for deep neural networks, which factorizes fully connected, convolutional, and attention layers in the form A=UV, and progressively reduces the rank of the U and V matrices. For convolutional layers the factorization is applied to the unrolled 2D matrix, while for attention layers it is applied to the Q, K, V matrices. They use ordered dropout and hierarchical group-lasso to facilitate the reduction of the rank of U/V matrices.",
+        "soundness": "3 good",
+        "presentation": "4 excellent",
+        "contribution": "1 poor",
+        "strengths": "Unlike unstructured pruning methods, low-rank compression can preserve the dense structure of matrices, which can extract more performance from GPUs. For the training of transformers on the Multi30k dataset shown in Table 3, the proposed method is able to reduce the number of parameters by more than half compared to the baseline (Pufferfish), while also reducing the perplexity.",
+        "weaknesses": "Low-rank compression and Lasso have been around for a very long time, and the only novelty seems to be the use of ordered dropout. The improvement over existing methods is marginal for the experiments with CNNs. The proposed method is obviously very sensitive to the choice of the Lasso coefficient lambda, but there is no theory behind how it can be chosen effectively.",
+        "questions": "How is the initial factorized mapping performed without SVD? How is the initial maximal rank r chosen?\n\nHow does the proposed method compare with other structured pruning methods?\n\nTypos\np.4 “multi-head attention (HMA)” > “multi-head attention (MHA)”\np.5 “we one could leverage” > “one could leverage”\np.5 “Singular Value Decomposition (SVD)” Why define this here when it has been repeatedly used in previous sections?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "Low-rank compression and Lasso have been around for a very long time, and the only novelty seems to be the use of ordered dropout. The improvement over existing methods is marginal for the experiments with CNNs. The proposed method is obviously very sensitive to the choice of the Lasso coefficient lambda, but there is no theory behind how it can be chosen effectively. Furthermore, the method's reliance on SVD for initialization, while common, introduces a computational overhead that is not fully addressed. The paper does not explore alternative initialization strategies that could potentially reduce this overhead or offer a more efficient starting point for the optimization process. The lack of a clear theoretical framework for selecting the Lasso coefficient, coupled with the sensitivity of the method to this parameter, makes it difficult to apply the method in practice without extensive hyperparameter tuning.",
+        "suggestions": "The paper should explore alternative initialization strategies that do not rely on SVD, or at least provide a detailed analysis of the computational cost associated with SVD initialization and how it scales with network size. For example, the authors could investigate random initialization of the factorized matrices, or explore techniques like K-means clustering to initialize the factors based on the data distribution. This would not only reduce the initial computational overhead but could also potentially lead to better convergence properties. Furthermore, the authors should provide a more rigorous analysis of the impact of the Lasso coefficient on the performance of the method, and develop a more principled approach for selecting this parameter. This could involve deriving theoretical bounds on the optimal value of lambda, or developing adaptive strategies that adjust the value of lambda during training based on the network's performance. A more detailed analysis of the sensitivity of the method to the choice of lambda, including a study of the landscape of the loss function with respect to lambda, would be beneficial.\n\nTo improve the practical applicability of the method, the authors should provide a more detailed analysis of the computational cost associated with the proposed approach, including the cost of ordered dropout and hierarchical group-lasso. This analysis should include a comparison with other low-rank compression methods, and should consider both training and inference time. The authors should also explore techniques for reducing the computational cost of the method, such as using more efficient implementations of ordered dropout or hierarchical group-lasso. Additionally, the paper should include a more comprehensive comparison with other structured pruning methods, including channel-based pruning, to better understand the strengths and weaknesses of the proposed approach. This comparison should not only focus on the performance of the methods, but also on their computational cost and memory footprint. A more thorough comparison would help to better position the proposed method within the broader landscape of model compression techniques.\n\nFinally, while the paper demonstrates the effectiveness of the proposed method on a few datasets, it would be beneficial to evaluate the method on a wider range of datasets and tasks, including more complex and challenging problems. This would help to assess the generalizability of the method and its robustness to different types of data and network architectures. The authors should also consider evaluating the method on larger-scale models, to demonstrate its scalability and its ability to compress large and complex networks. This would help to establish the practical relevance of the method and its potential for real-world applications. The paper should also include a more detailed analysis of the impact of the proposed method on the interpretability of the model, and whether the low-rank compression affects the ability to understand the model's decision-making process."
+      }
+    },
+    {
+      "id": "hoNfoK0O6U",
+      "rating": 8,
+      "content": {
+        "summary": "This work mainly focuses on incorporating trainable low-rank layer decompositions in deep-learning models. The authors propose MAESTRO, which progressively finds the optimal rank of each layer during the training by imposing importance ordering via the existing Ordered Dropout technique. The redundant ranks are zeroed out by using the hierarchical group lasso term as the regularizer in the loss function. MAESTRO accounts for data distributions and the target function rather than applying SVD on pre-learned model weights.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "3 good",
+        "strengths": "The novelty of the work lies in applying the existing Ordered Dropout technique from Federated Learning (FjORD) to optimally order the heterogeneous ranks of various layers in DNNs based on importance criterion, which results in discovering layer-wise low-rank decompositions. In contrast to uniform dropout across the width in each layer ( FjORD), MAESTRO independently decomposes each layer to uncover optimal rank. The authors provide applications of MAESTRO to various layer types in CNNs, FC, and Transformers. \n\nThe paper is easy to understand and is well-structured. The experiments are comprehensive and justify theoretical insights.",
+        "weaknesses": "1. The paper suffers from typos. The authors are encouraged to review and proofread the draft.\n- Page 1: …*find progressively*…\n- Page 2: …*novelly fuse*…\n- Page 3: ..*have been proposed*… (multiple instances)\n- Page 4: …*HMA*….\n- Page 5: ….*orthoghonal*….\n\n2. It is recommended that authors explore a better illustration for Figure 1. For instance, there is not much difference visually in Factorized mapping and Ordered Representation when printed in black/white. It might be helpful to provide a better illustration for the Ordered Dropout process (it is challenging to understand it with symbols without any reference in the figure caption. In current form, it is assumed that the readers will be familiar with OD). Since MAESTRO provides layer-wise decomposition and is generally applicable to various DNN layers, it might be useful to incorporate the various layer types of the DNN network (Sec 3.2) in Figure 1 as an overall summary of the proposed work and its applicability.",
+        "questions": "Suggestions are provided in the above section.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "1. The paper suffers from typos. The authors are encouraged to review and proofread the draft.\n- Page 1: …*find progressively*…\n- Page 2: …*novelly fuse*…\n- Page 3: ..*have been proposed*… (multiple instances)\n- Page 4: …*HMA*….\n- Page 5: ….*orthoghonal*….\n\n2. It is recommended that authors explore a better illustration for Figure 1. For instance, there is not much difference visually in Factorized mapping and Ordered Representation when printed in black/white. It might be helpful to provide a better illustration for the Ordered Dropout process (it is challenging to understand it with symbols without any reference in the figure caption. In current form, it is assumed that the readers will be familiar with OD). Since MAESTRO provides layer-wise decomposition and is generally applicable to various DNN layers, it might be useful to incorporate the various layer types of the DNN network (Sec 3.2) in Figure 1 as an overall summary of the proposed work and its applicability.",
+        "suggestions": "The visual clarity of Figure 1 needs significant improvement to effectively communicate the core concepts of MAESTRO. The current depiction of 'Factorized mapping' and 'Ordered Representation' lacks sufficient visual distinction, particularly when printed in black and white, which makes it hard to grasp the difference between the two. A more effective approach would involve using distinct visual cues, such as different line styles, shading, or color-coding (if color printing is an option), to highlight the structural differences between these representations. Furthermore, the illustration of the Ordered Dropout (OD) process is too abstract, relying solely on symbols without sufficient context or explanation within the figure itself. Given that the OD technique is not universally known, the authors should consider adding a step-by-step visual breakdown of the OD process, perhaps using a simplified example with a small matrix or tensor to show how the importance ordering and rank selection works. This could involve showing how the dropout masks are applied and how the low-rank structure is progressively learned. A clearer visual representation of this process is crucial for readers to understand the core mechanism of MAESTRO.\n\nTo further enhance the paper's clarity and impact, the authors should consider incorporating a visual representation of how MAESTRO is applied across different layer types within a DNN architecture. While the text mentions that MAESTRO is applicable to CNNs, FC layers, and Transformers, this generality is not visually conveyed. Figure 1 could be expanded to include a high-level overview of a typical DNN architecture, highlighting how MAESTRO is applied to different layer types. For example, the figure could show a convolutional layer being decomposed into low-rank form, followed by a fully connected layer and a transformer layer, each with its respective decomposition. This would provide a more complete and intuitive understanding of the method's flexibility and broad applicability. This addition would also serve as a concise summary of the entire proposed approach, making it easier for readers to grasp the overall contribution of the paper.\n\nFinally, the authors should provide more details on the practical implications of the hierarchical group lasso regularization. While the paper mentions that this regularization term is used to zero out redundant ranks, it would be beneficial to provide more insights into how the regularization parameter is chosen and how it impacts the final low-rank decomposition. Adding a small experiment or a visual example showing how different regularization strengths affect the resulting rank of the layers would also be beneficial. Furthermore, it would be useful to discuss the computational overhead of using the hierarchical group lasso and how it compares to other regularization techniques. This would help readers understand the practical trade-offs of using MAESTRO in real-world applications. The authors should also discuss the sensitivity of MAESTRO to hyperparameter choices, such as the learning rate, batch size, and regularization parameter, as well as provide guidelines for selecting these parameters."
+      }
+    },
+    {
+      "id": "KPLklSOFhK",
+      "rating": 5,
+      "content": {
+        "summary": "The authors introduce Maestro, a technique designed for efficient layer-wise low-rank factorization during training. This method incorporates an ordered drop strategy combined with group lasso regularization, encouraging the progressive adoption of lower-rank weights during training. The evaluation is conducted on CIFAR10, MNIST, and Multi-30k, comparing Maestro against various low-rank approaches and several pruning and quantization techniques. Furthermore, the paper offers multiple ablation studies and provides theoretical analysis for specific problems.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "2 fair",
+        "strengths": "1. The paper is easy to follow. \n2. The theoretical properties are sound with the proposed method.\n3. The algorithm seems reasonable.",
+        "weaknesses": "The algorithm seems reasonable to me. However, for the experiments, ImageNet results are missing. As an important benchmark, ImageNet is often used to compare performance between the compression-related tasks. For instance, Cutterfish presented their ResNet-50 results using the ImageNet dataset. To highlight effectiveness, it would be beneficial to include evaluations based on the ImageNet dataset. Additionally, tests on larger models would enhance the comprehensiveness of the study.\n\nIs the #GMACs the training cost? If not, please show the training cost.",
+        "questions": "How does the proposed method perform on ViT and other larger models using the ImageNet dataset?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": "The algorithm seems reasonable to me. However, for the experiments, ImageNet results are missing. As an important benchmark, ImageNet is often used to compare performance between the compression-related tasks. For instance, Cutterfish presented their ResNet-50 results using the ImageNet dataset. To highlight effectiveness, it would be beneficial to include evaluations based on the ImageNet dataset. Additionally, tests on larger models would enhance the comprehensiveness of the study. \n\nIs the #GMACs the training cost? If not, please show the training cost.",
+        "suggestions": "The absence of ImageNet results significantly limits the impact of the paper, as it is a crucial benchmark for evaluating compression techniques, especially for models like ResNet-50. The paper should include a comprehensive evaluation on ImageNet, including both accuracy and computational cost (GMACs) at different compression levels. This should involve a detailed comparison with existing state-of-the-art methods, not just Cutterfish, but also other relevant low-rank and pruning techniques. The evaluation should also explore the trade-offs between accuracy and computational cost, providing a clear picture of the method's performance characteristics on a large-scale dataset. Furthermore, the paper should include an analysis of the training time and memory requirements for the proposed method on ImageNet, which is crucial for practical applications.\n\nTo strengthen the paper, the authors should extend their evaluation to larger models, such as ViT or other transformer-based architectures. These models have become increasingly important in computer vision, and assessing the method's performance on them would provide a more complete understanding of its capabilities. The evaluation should include a detailed analysis of the method's performance across different model sizes and architectures, providing insights into its scalability and robustness. This would also help identify potential limitations of the method and guide future research directions. Moreover, the study should explore the impact of different hyperparameter settings on the performance of the proposed method on these larger models, as well as the sensitivity of the method to different choices of the rank reduction strategy and regularization parameters.\n\nFinally, the paper needs to clarify the meaning of #GMACs. If it does not represent training cost, a detailed analysis of the training cost should be provided. This should include the number of floating-point operations (FLOPs) and the time required for training, as well as the memory requirements. This information is crucial for assessing the practical applicability of the proposed method. The authors should also compare the training cost of their method with other low-rank and pruning approaches, to show the efficiency of their method. A detailed breakdown of the computational cost of each step of the training process would also be beneficial to understand the bottleneck and potential areas for optimization."
+      }
+    }
+  ]
+}

papers/4VGEeER6W9/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "4VGEeER6W9",
+  "title": "Towards Non-Asymptotic Convergence for Diffusion-Based Generative Models",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Accept",
+  "date": "2023-09-22",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=4VGEeER6W9"
+}

papers/4VGEeER6W9/paper.md

@@ -0,0 +1,379 @@
+# TOWARDS NON-ASYMPTOTIC CONVERGENCE FOR DIFFUSION-BASED GENERATIVE MODELS
+
+Gen Li<sup>∗</sup> Yuting Wei† Yuxin Chen†‡ Yuejie Chi§
+
+# ABSTRACT
+
+Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain far from mature. In this work, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to `2-accurate estimates of the (Stein) score functions. For a popular deterministic sampler (based on the probability flow ODE), we establish a convergence rate proportional to 1/T (with T the total number of steps), improving upon past results; for another mainstream stochastic sampler (i.e., a type of the denoising diffusion probabilistic model), we derive a convergence rate proportional to 1/ √ T, matching the stateof-the-art theory. Imposing only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), our results characterize how `<sup>2</sup> score estimation errors affect the quality of the data generation process. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach without resorting to toolboxes for SDEs and ODEs.
+
+# 1 INTRODUCTION
+
+Diffusion models have emerged as a cornerstone in contemporary generative modeling, a task that learns to generate new data instances (e.g., images, text, audio) that look similar in distribution to the training data [\(Ho et al., 2020;](#page-10-0) [Sohl-Dickstein et al., 2015;](#page-11-0) [Song & Ermon, 2019;](#page-11-1) [Dhariwal &](#page-9-0) [Nichol, 2021;](#page-9-0) [Jolicoeur-Martineau et al., 2021;](#page-10-1) [Chen et al., 2021;](#page-9-1) [Kong et al., 2021;](#page-10-2) [Austin et al.,](#page-9-2) [2021\)](#page-9-2). Originally proposed by [Sohl-Dickstein et al.](#page-11-0) [\(2015\)](#page-11-0) and later popularized by [Song & Ermon](#page-11-1) [\(2019\)](#page-11-1); [Ho et al.](#page-10-0) [\(2020\)](#page-10-0), the mainstream diffusion generative models — e.g., denoising diffusion probabilistic models (DDPMs) [\(Ho et al., 2020\)](#page-10-0) and denoising diffusion implicit models (DDIMs) [\(Song et al., 2020a\)](#page-11-2) — have underpinned major successes in content generators like DALL·E 2 [\(Ramesh et al., 2022\)](#page-11-3), Stable Diffusion [\(Rombach et al., 2022\)](#page-11-4) and Imagen [\(Saharia et al., 2022\)](#page-11-5), claiming state-of-the-art performance in the now broad field of generative artificial intelligence (AI). See [Yang et al.](#page-11-6) [\(2022\)](#page-11-6); [Croitoru et al.](#page-9-3) [\(2023\)](#page-9-3) for overviews of recent development.
+
+In a nutshell, a diffusion generative model is based upon two stochastic processes in R d :
+
+1) a forward process
+
+<span id="page-0-1"></span>
+$$X_0 \to X_1 \to \dots \to X_T$$
+ (1)
+
+that starts from a sample drawn from the target data distribution (e.g., of natural images) and gradually diffuses it into a noise-like distribution (e.g., standard Gaussians);
+
+2) a reverse process
+
+<span id="page-0-0"></span>
+$$Y_T \to Y_{T-1} \to \dots \to Y_0 \tag{2}$$
+
+<sup>∗</sup>Department of Statistics, The Chinese University of Hong Kong, Hong Kong.
+
+<sup>†</sup>Department of Statistics and Data Science, Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA.
+
+<sup>‡</sup>Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
+
+<sup>§</sup>Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
+
+that starts from pure noise (e.g., standard Gaussians) and successively converts it into new samples sharing similar distributions as the target data distribution.
+
+Transforming data into noise in the forward process is straightforward, often hand-crafted by increasingly injecting more noise into the data at hand. What is challenging is the construction of the reverse process: how to generate the desired information out of pure noise? To do so, a diffusion model learns to build a reverse process [\(2\)](#page-0-0) that imitates the dynamics of the forward process [\(1\)](#page-0-1) in a time-reverse fashion; more precisely, the design goal is to ascertain distributional proximity[1](#page-1-0)
+
+$$Y_t \stackrel{\mathrm{d}}{\approx} X_t, \qquad t = T, \cdots, 1$$
+ (3)
+
+through proper learning based on how the training data propagate in the forward process. Encouragingly, there often exist feasible strategies to achieve this goal as long as faithful estimates about the (Stein) score functions — the gradients of the log marginal density of the forward process are available, an intriguing fact that can be illuminated by the existence and construction of reversetime stochastic differential equations (SDEs) [\(Anderson, 1982;](#page-9-4) [Haussmann & Pardoux, 1986\)](#page-10-3) (see Section [2.2](#page-3-0) for more precise discussions). Viewed in this light, a diverse array of diffusion models are frequently referred to as *score-based generative modeling (SGM)*. The popularity of SGM was initially motivated by, and has since further inspired, numerous recent studies on the problem of learning score functions, a subroutine that also goes by the name of score matching (e.g., [Hyvärinen](#page-10-4) [\(2005;](#page-10-4) [2007\)](#page-10-5); [Vincent](#page-11-7) [\(2011\)](#page-11-7); [Song et al.](#page-11-8) [\(2020b\)](#page-11-8); [Koehler et al.](#page-10-6) [\(2023\)](#page-10-6)).
+
+Nonetheless, despite the mind-blowing empirical advances, a mathematical theory for diffusion generative models is still in its infancy. Given the complexity of developing a full-fledged end-to-end theory, a divide-and-conquer approach has been advertised, decoupling the score learning phase (i.e., how to estimate score functions from training data) and the generative sampling phase (i.e., how to generate new data given the score estimates). In particular, the past two years have witnessed growing interest and remarkable progress from the theoretical community towards understanding the sampling phase [\(Block et al., 2020;](#page-9-5) [De Bortoli et al., 2021;](#page-9-6) [Liu et al., 2022;](#page-11-9) [De Bortoli, 2022;](#page-9-7) [Lee et al., 2023;](#page-10-7) [Pidstrigach, 2022;](#page-11-10) [Chen et al., 2022b;](#page-9-8)[a;](#page-9-9) [Tang, 2023;](#page-11-11) [Chen et al., 2023c;](#page-9-10) [Tang &](#page-11-12) [Zhao, 2024;](#page-11-12) [Li et al., 2024a\)](#page-10-8). For instance, polynomial-time convergence guarantees have been established for stochastic samplers (e.g., [Chen et al.](#page-9-8) [\(2022b](#page-9-8)[;a\)](#page-9-9); [Benton et al.](#page-9-11) [\(2023a\)](#page-9-11)) and deterministic samplers (e.g., [Chen et al.](#page-9-10) [\(2023c\)](#page-9-10); [Benton et al.](#page-9-12) [\(2023b\)](#page-9-12)), both of which accommodated a fairly general family of data distributions.
+
+This paper. The present paper contributes to this growing list of theoretical endeavors by developing a new suite of non-asymptotic theory for several score-based generative modeling algorithms. We concentrate on two types of samplers [\(Song et al., 2021b\)](#page-11-13) in discrete time: (i) a deterministic sampler based on a sort of ordinary differential equations (ODEs) called probability flow ODEs (which is closely related to the DDIM); and (ii) a DDPM-type stochastic sampler motivated by reverse-time SDEs. We impose only minimal assumptions on the target data distribution (e.g., no smoothness condition is needed), and would like to quantify the impact of `<sup>2</sup> score estimation errors. In comparisons to past works, our main contributions are three-fold.
+
+*Non-asymptotic convergence guarantees.* For a popular deterministic sampler, we demonstrate that the number of steps needed to yield ε-accuracy — meaning that the total variation (TV) distance between the distribution of X<sup>1</sup> and that of Y<sup>1</sup> is no larger than ε — is proportional to 1/ε (in addition to other polynomial dimension dependency). This improves upon prior convergence guarantees [\(Chen et al., 2023c\)](#page-9-10) and does not exhibit exponential dependency on the smoothness assumption as in [Chen et al.](#page-9-10) [\(2023c\)](#page-9-10); [Benton et al.](#page-9-12) [\(2023b\)](#page-9-12). For another DDPM-type stochastic sampler, we establish an iteration complexity proportional to 1/ε<sup>2</sup> , matching existing theory [Chen et al.](#page-9-8) [\(2022b](#page-9-8)[;a\)](#page-9-9); [Benton et al.](#page-9-11) [\(2023a\)](#page-9-11) in terms of the ε-dependency.
+
+*Score estimation errors for the determinstic sampler.* In our convergence guarantees for the deterministic sampler, the TV distance between X<sup>1</sup> and Y<sup>1</sup> are shown to be proportional to the `<sup>2</sup> score estimation error as well as the associated Jacobian errors. As far as we know, this is the first result for this deterministic sampler that accounts for score estimation errors in discrete time. In comparison, other theoretical results that accommodate score errors for the probability flow ODE approach
+
+<span id="page-1-0"></span><sup>1</sup>Two random vectors X and Y are said to obey X <sup>d</sup>= Y (resp. X d ≈ Y ) if they are equivalent (resp. close) in distribution.
+
+either study certain stochastic variations of this deterministic sampler (Chen et al., 2023b) or fall short of accommodating discretization errors (Benton et al., 2023b).
+
+An elementary non-asymptotic analysis framework. From the technical viewpoint, the analysis framework laid out in this paper is fully non-asymptotic in nature. In contrast to prior analyses that take a detour to study the continuum limits and then control the discretization error, our approach tackles the discrete-time processes directly using elementary analysis strategies. No knowledge of SDEs or ODEs is required for establishing our theory, thereby resulting in a more versatile framework and sometimes lowering the technical barrier towards understanding diffusion models.
+
+**Notation.** For any two functions f(d,T) and g(d,T), we adopt the notation  $f(d,T) \lesssim g(d,T)$  or f(d,T) = O(g(d,T)) (resp.  $f(d,T) \gtrsim g(d,T)$ ) to mean that there exists some universal constant  $C_1 > 0$  such that  $f(d,T) \leq C_1 g(d,T)$  (resp.  $f(d,T) \geq C_1 g(d,T)$ ) for all d and T; moreover, the notation  $f(d,T) \asymp g(d,T)$  indicates that  $f(d,T) \lesssim g(d,T)$  and  $f(d,T) \gtrsim g(d,T)$  hold at once. The notation  $O(\cdot)$  is defined similar to  $O(\cdot)$  except that it hides the logarithmic dependency. Additionally, the notation f(d,T) = o(g(d,T)) means that  $f(d,T)/g(d,T) \to 0$  as d,T tend to infinity. For any two probability measures P and Q, the total variation (TV) distance between them is defined to be  $V(P,Q) := \frac{1}{2} \int |dP - dQ|$ . Throughout the paper,  $p_X(\cdot)$  (resp.  $p_{X|Y}(\cdot|\cdot)$ ) denotes the probability density function of X (resp. X given Y). For any matrix A, we denote by  $\|A\|$  (resp.  $\|A\|_F$ ) the spectral norm (resp. Frobenius norm) of A. Also, for any vector-valued function A, we let A or A represent the Jacobian matrix of A.
+
+## 2 Preliminaries
+
+In this section, we introduce the basics of diffusion generative models. The ultimate goal of a generative model can be concisely stated: given data samples drawn from an unknown distribution of interest  $p_{\text{data}}$  in  $\mathbb{R}^d$ , we wish to generate new samples whose distributions closely resemble  $p_{\text{data}}$ .
+
+## 2.1 DIFFUSION GENERATIVE MODELS
+
+Towards achieving the above goal, a diffusion generative model typically encompasses two Markov processes: a forward process and a reverse process, as described below.
+
+The forward process. In the forward chain, one progressively injects noise into the data samples to diffuse and obscure the data. The distributions of the injected noise are often hand-picked, with the standard Gaussian distribution receiving widespread adoption. Specifically, the forward Markov process produces a sequence of d-dimensional random vectors  $X_1 \to X_2 \to \cdots \to X_T$  as follows:
+
+<span id="page-2-0"></span>
+$$X_0 \sim p_{\mathsf{data}},$$
+ (4a)
+
+$$X_t = \sqrt{1 - \beta_t} X_{t-1} + \sqrt{\beta_t} W_t, \qquad 1 \le t \le T, \tag{4b}$$
+
+where  $\{W_t\}_{1 \leq t \leq T}$  indicates a sequence of independent noise vectors drawn from  $W_t \overset{\text{i.i.d.}}{\sim} \mathcal{N}(0, I_d)$ . The hyper-parameters  $\{\beta_t \in (0,1)\}$  represent prescribed learning rate schedules that control the variance of the noise injected in each step. If we define
+
+$$\alpha_t := 1 - \beta_t, \qquad \overline{\alpha}_t := \prod_{k=1}^t \alpha_k, \qquad 1 \le t \le T,$$
+ (5)
+
+then it can be straightforwardly verified that for every  $1 \le t \le T$ ,
+
+$$X_t = \sqrt{\overline{\alpha}_t} X_0 + \sqrt{1 - \overline{\alpha}_t} \overline{W}_t$$
+ for some  $\overline{W}_t \sim \mathcal{N}(0, I_d)$ . (6)
+
+Clearly, if the covariance of  $X_0$  is also equal to  $I_d$ , then the covariance of  $X_t$  is preserved throughout the forward process; for this reason, this forward process (4) is sometimes referred to as *variance-preserving* (Song et al., 2021b). Throughout this paper, we employ the notation
+
+$$q_t := \mathsf{law}(X_t) \tag{7}$$
+
+to denote the distribution of  $X_t$ . As long as  $\overline{\alpha}_T$  is vanishingly small, one has the following property for a general family of data distributions:
+
+$$q_T \approx \mathcal{N}(0, I_d).$$
+ (8)
+
+**The reverse process.** The reverse chain  $Y_T \to Y_{T-1} \to \ldots \to Y_1$  is designed to (approximately) revert the forward process, allowing one to transform pure noise into new samples with matching distributions as the original data. To be more precise, by initializing it as
+
+$$Y_T \sim \mathcal{N}(0, I_d),$$
+ (9a)
+
+we seek to design a reverse-time Markov process with nearly identical marginals as the forward process, namely,
+
+(goal) 
+$$Y_t \stackrel{\mathrm{d}}{\approx} X_t, \quad t = T, T - 1, \dots, 1.$$
+ (9b)
+
+Throughout the paper, we often employ the following notation to indicate the distribution of  $Y_t$ :
+
+$$p_t := \mathsf{law}(Y_t). \tag{10}$$
+
+## <span id="page-3-0"></span>2.2 DETERMINISTIC VS. STOCHASTIC SAMPLERS: A CONTINUOUS-TIME INTERPRETATION
+
+Evidently, the most crucial step of the diffusion model lies in effective design of the reverse process. Two mainstream approaches stand out:
+
+• Deterministic samplers. Starting from  $Y_T \sim \mathcal{N}(0, I_d)$ , this approach selects a set of functions  $\{\Phi_t(\cdot)\}_{1 \le t \le T}$  and computes:
+
+$$Y_{t-1} = \Phi_t(Y_t), \qquad t = T, \dots, 1.$$
+ (11)
+
+Clearly, the sampling process is fully deterministic except for the initialization  $Y_T$ .
+
+• Stochastic samplers. Initialized again at  $Y_T \sim \mathcal{N}(0, I_d)$ , this approach computes another collection of functions  $\{\Psi_t(\cdot, \cdot)\}_{1 < t < T}$  and performs the updates:
+
+$$Y_{t-1} = \Psi_t(Y_t, Z_t), \qquad t = T, \dots, 1,$$
+ (12)
+
+where the  $Z_t$ 's are independent noise vectors obeying  $Z_t \overset{\text{i.i.d.}}{\sim} \mathcal{N}(0, I_d)$ .
+
+In order to elucidate the feasibility of the above two approaches, we find it helpful to look at the continuum limit through the lens of SDEs and ODEs. It is worth emphasizing, however, that the development of our main theory does *not* rely on any knowledge of SDEs and ODEs.
+
+• The forward process. A continuous-time analog of the forward process can be modeled as
+
+<span id="page-3-2"></span>
+$$dX_t = f(X_t, t)dt + g(t)dW_t \quad (0 \le t \le T), \qquad X_0 \sim p_{\mathsf{data}} \tag{13}$$
+
+for some functions  $f(\cdot, \cdot)$  and  $g(\cdot)$  (denoting respectively the drift and diffusion coefficient), where  $W_t$  denotes a d-dimensional standard Brownian motion. As a special example, the continuum limit of (4) takes the following form<sup>2</sup> (Song et al., 2021b)
+
+$$dX_t = -\frac{1}{2}\beta(t)X_tdt + \sqrt{\beta(t)}\,dW_t \quad (0 \le t \le T), \qquad X_0 \sim p_{\mathsf{data}}$$
+ (14)
+
+for some function  $\beta(t)$ . As before, we denote by  $q_t$  the distribution of  $X_t$  in (13).
+
+- The reverse process. As it turns out, the following two reverse processes are both capable of reconstructing the distribution of the forward process, motivating the design of two distinctive samplers. Here and throughout, we use  $\nabla \log q_t(X)$  to abbreviate  $\nabla_X \log q_t(X)$  for notational simplicity.
+  - One feasible approach is to the so-called *probability flow ODE* (Song et al., 2021b)
+
+$$dY_t^{\mathsf{ode}} = \left(-f(Y_t^{\mathsf{ode}}, T - t) + \frac{1}{2}g(T - t)^2 \nabla \log q_{T - t}(Y_t^{\mathsf{ode}})\right) dt \quad (0 \le t \le T),$$
+(15)
+
+with  $Y_0^{\text{ode}} \sim q_T$ , which exhibits matching distributions as follows:
+
+<span id="page-3-3"></span>
+$$Y_{T-t}^{\text{ode}} \stackrel{\mathrm{d}}{=} X_t, \qquad 0 < t < T.$$
+
+The deterministic nature of this approach often enables faster sampling. It has been shown that this family of deterministic samplers is closely related to the DDIM sampler (Karras et al., 2022; Song et al., 2021b).
+
+<span id="page-3-1"></span><sup>&</sup>lt;sup>2</sup>To see its connection with (4), it suffices to derive from (4) that  $X_t - X_{t-\mathrm{d}t} = \sqrt{1-\beta_t}X_{t-\mathrm{d}t} - X_{t-\mathrm{d}t} + \sqrt{\beta_t}W_t \approx -\frac{1}{2}\beta_tX_{t-\mathrm{d}t} + \sqrt{\beta_t}W_t$ .
+
+ In view of the classical results Anderson (1982); Haussmann & Pardoux (1986), one can also construct a "reverse-time" SDE
+
+$$dY_t^{\mathsf{sde}} = \left(-f\left(Y_t^{\mathsf{sde}}, T - t\right) + g(T - t)^2 \nabla \log q_{T - t}\left(Y_t^{\mathsf{sde}}\right)\right) dt + g(T - t) dZ_t^{\mathsf{sde}}$$
+(16)
+
+for  $0 \le t \le T$ , with  $Y_0^{\rm sde} \sim q_T$  and  $Z_t^{\rm sde}$  being a standard Brownian motion. Strikingly, this process also satisfies
+
+<span id="page-4-0"></span>
+$$Y_{T-t}^{\mathsf{sde}} \stackrel{\mathrm{d}}{=} X_t, \qquad 0 \le t \le T.$$
+
+The popular DDPM sampler (Ho et al., 2020) falls under this category.
+
+Interestingly, in addition to the functions f and g that define the forward process, construction of both (15) and (16) relies only upon the knowledge of the gradient of the log density  $\nabla \log q_t(\cdot)$  of the intermediate steps of the forward diffusion process — often referred to as the (Stein) score function. Consequently, a key enabler of the above paradigms lies in reliable learning of the score function, and hence the name *score-based generative modeling*.
+
+## 3 ALGORITHMS AND MAIN RESULTS
+
+In this section, we analyze a couple of diffusion generative models, including both deterministic and stochastic samplers. While the proofs for our main theory are all postponed to the appendix, it is worth emphasizing upfront that our analysis framework directly tackles the discrete-time processes without resorting to any toolbox of SDEs and ODEs tailored to the continuous-time limits. This elementary approach might potentially be versatile for analyzing a broad class of variations of these samplers. For instance, prior ODE-based theory (e.g., Chen et al. (2023b;c)) encountered certain technical challenges when analyzing the deterministic sampler directly, and our elementary approach is able to shed new light on the convergence of this important sampler.
+
+## 3.1 Assumptions and Learning rates
+
+Before proceeding, we impose some assumptions on the score estimates and the target data distributions, and specify the hypter-parameters  $\{\alpha_t\}$ , which shall be adopted throughout all cases.
+
+**Score estimates.** Given that the score functions are an essential component in score-based generative modeling, we assume access to faithful estimates of the score functions  $\nabla \log q_t(\cdot)$  across all intermediate steps t, thus disentangling the score learning phase and the data generation phase. Towards this end, let us first formally introduce the true score function as follows.
+
+<span id="page-4-1"></span>**Definition 1** (Score function). The score function, denoted by  $s_t^{\star}: \mathbb{R}^d \to \mathbb{R}^d$ , is defined as
+
+$$s_t^{\star}(X) := \nabla \log q_t(X), \qquad 1 \le t \le T. \tag{17}$$
+
+As has been pointed out by previous works concerning score matching (e.g., Hyvärinen (2005); Vincent (2011); Chen et al. (2022b)), the score function  $s_t^*$  admits an alternative form as follows (owing to properties of Gaussian distributions):
+
+$$s_t^{\star} := \arg\min_{s:\mathbb{R}^d \to \mathbb{R}^d} \mathbb{E}_{W \sim \mathcal{N}(0, I_d), X_0 \sim p_{\mathsf{data}}} \left[ \left\| s \left( \sqrt{\overline{\alpha}_t} X_0 + \sqrt{1 - \overline{\alpha}_t} W \right) + \frac{1}{\sqrt{1 - \overline{\alpha}_t}} W \right\|_2^2 \right], \quad (18)$$
+
+which takes the form of the minimum mean square error estimator for  $-\frac{1}{\sqrt{1-\overline{\alpha}_t}}W$  given  $\sqrt{\overline{\alpha}_t}X_0 + \sqrt{1-\overline{\alpha}_t}W$  and is often more amenable to training.
+
+With Definition 1 in place, we can readily introduce the following assumptions that capture the quality of the score estimate  $\{s_t\}_{1 \le t \le T}$  we have available.
+
+<span id="page-4-2"></span>**Assumption 1.** Suppose that the score function estimate  $\{s_t\}_{1 \leq t \leq T}$  obeys
+
+$$\frac{1}{T} \sum_{t=1}^{T} \underset{X \sim q_t}{\mathbb{E}} \left[ \left\| s_t(X) - s_t^{\star}(X) \right\|_2^2 \right] \le \varepsilon_{\mathsf{score}}^2. \tag{19}$$
+
+<span id="page-5-0"></span>**Assumption 2.** For each  $1 \le t \le T$ , assume that  $s_t(\cdot)$  is continuously differentiable, and denote by  $J_{s_t^\star} = \frac{\partial s_t^\star}{\partial x}$  and  $J_{s_t} = \frac{\partial s_t}{\partial x}$  the Jacobian matrices of  $s_t^\star(\cdot)$  and  $s_t(\cdot)$ , respectively. Assume that the score function estimate  $\{s_t\}_{1 \le t \le T}$  obeys
+
+$$\frac{1}{T} \sum_{t=1}^{T} \underset{X \sim q_t}{\mathbb{E}} \left[ \left\| J_{s_t}(X) - J_{s_t^*}(X) \right\| \right] \le \varepsilon_{\mathsf{Jacobi}}. \tag{20}$$
+
+In a nutshell, Assumption 1 reflects the  $\ell_2$  score estimation error, whereas Assumption 2 concerns the estimation error in terms of the corresponding Jacobian matrix. Both assumptions consider the *average* estimation errors over all T steps. Our theory for the deterministic sampler relies on both Assumptions 1 and 2, while the theory for the stochastic sampler requires only Assumption 1. We shall discuss in Section 3.2 the insufficiency of Assumption 1 alone for the deterministic sampler.
+
+**Target data distributions.** Our goal is to uncover the effectiveness of diffusion models in generating a broad family of data distributions. Throughout this paper, the only assumptions we need to impose on the target data distribution  $p_{\mathsf{data}}$  are the following:
+
+•  $X_0$  is an absolutely continuous random vector, and
+
+<span id="page-5-4"></span><span id="page-5-3"></span>
+$$\mathbb{P}(\|X_0\|_2 \le T^{c_R} \mid X_0 \sim p_{\mathsf{data}}) = 1 \tag{21}$$
+
+for some arbitrarily large constant  $c_R > 0$ .
+
+This assumption allows the radius of the support of  $p_{data}$  to be exceedingly large (given that the exponent  $c_R$  can be arbitrarily large).
+
+**Learning rate schedule.** Let us also take a moment to specify the learning rates to be used for our theory and analyses. For some large enough numerical constants  $c_0$ ,  $c_1 > 0$ , we set
+
+$$\beta_1 = 1 - \alpha_1 = \frac{1}{T^{c_0}};\tag{22a}$$
+
+$$\beta_t = 1 - \alpha_t = \frac{c_1 \log T}{T} \min \left\{ \beta_1 \left( 1 + \frac{c_1 \log T}{T} \right)^t, 1 \right\}. \tag{22b}$$
+
+**Remark 1.** As we shall see in our analysis, the discretization error depends crucially upon the quantity  $\frac{1-\alpha_t}{1-\overline{\alpha}_t}$ , whereas the initialization error relies heavily upon  $\overline{\alpha}_1$  and  $\overline{\alpha}_T$ . Based on these observations, our learning rate schedule (22) is designed to make  $\frac{1-\alpha_t}{1-\overline{\alpha}_t}$  as small as possible, while making sure  $\overline{\alpha}_1$  (resp.  $\overline{\alpha}_T$ ) is close to 1 (resp. 0). These properties will be shown in (43). Moreover, it is worth noting that our analysis can be easily extended to accommodate a much broader class of learning rates, although the resulting convergence rates might vary.
+
+#### <span id="page-5-1"></span>3.2 AN ODE-BASED DETERMINISTIC SAMPLER
+
+We begin by analyzing a deterministic sampler: a discrete-time version of the probability flow ODE.
+
+Armed with the score estimates  $\{s_t\}_{1 \le t \le T}$ , a discrete-time version of the probability flow ODE approach (cf. (15)) adopts the following update rule:
+
+$$Y_T \sim \mathcal{N}(0, I_d), \qquad Y_{t-1} = \Phi_t(Y_t) \quad \text{for } t = T, \dots, 1,$$
+ (23a)
+
+where  $\Phi_t(\cdot)$  is taken to be
+
+<span id="page-5-2"></span>
+$$\Phi_t(x) := \frac{1}{\sqrt{\alpha_t}} \left( x + \frac{1 - \alpha_t}{2} s_t(x) \right). \tag{23b}$$
+
+This approach, based on the probability flow ODE (15), often achieves faster sampling compared to the stochastic counterpart (Song et al., 2021b). Despite the empirical advances, however, the theoretical understanding of this type of deterministic samplers remained far from mature.
+
+We first derive non-asymptotic convergence guarantees — measured by the total variation distance between the forward and the reverse processes — for the above deterministic sampler (23). The proof of this result can be found in Li et al. (2023, Section 5.2).
+
+<span id="page-6-0"></span>**Theorem 1.** Suppose that (21) holds true. Assume that the score estimates  $s_t(\cdot)$   $(1 \le t \le T)$  satisfy Assumptions 1 and 2. Then the sampling process (23) with the learning rate schedule (22) satisfies
+
+$$\mathsf{TV}\big(q_1, p_1\big) \le C_1 \frac{d^2 \log^4 T}{T} + C_1 \frac{d^6 \log^6 T}{T^2} + C_1 \sqrt{d \log^3 T} \varepsilon_{\mathsf{score}} + C_1 d(\log T) \varepsilon_{\mathsf{Jacobi}} \tag{24}$$
+
+for some universal constants  $C_1 > 0$ , where  $p_1$  (resp.  $q_1$ ) represents the distribution of  $Y_1$  (resp.  $X_1$ ).
+
+**Implications.** Let us highlight the main implications of Theorem 1. Before proceeding, note that our theory is concerned with convergence to  $q_1$ . Given that  $X_1 \sim q_1$  and  $X_0 \sim q_0$  are very close due to the choice of  $\alpha_1$ , focusing on the convergence w.r.t.  $q_1$  instead of  $q_0$  remains practically relevant.
+
+(a) Iteration complexity. Consider first the scenario that has access to perfect score estimates (i.e.,  $\varepsilon_{\text{score}} = 0$ ). In order to achieve  $\varepsilon$ -accuracy (in the sense that  $\mathsf{TV}(q_1, p_1) \leq \varepsilon$ ), the number of steps T only needs to exceed
+
+$$\widetilde{O}(d^2/\varepsilon + d^3/\sqrt{\varepsilon}). \tag{25}$$
+
+- (b) Stability. Turning to the more general case with imperfect score estimates (i.e.,  $\varepsilon_{\text{score}} > 0$ ), the deterministic sampler (23) yields a distribution whose distance to the target distribution (measured again by the TV distance) scales proportionally with  $\varepsilon_{\text{score}}$  and  $\varepsilon_{\text{Jacobi}}$ . It is noteworthy that in addition to the score estimation errors, we are in need of an assumption on the stability of the associated Jacobian matrices, which plays a pivotal in ensuring that the reverse-time deterministic process does not deviate considerably from the desired process.
+- (c) Insufficiency of the score estimation error assumption alone. The careful reader might wonder why we are in need of additional assumptions beyond the  $\ell_2$  score error stated in Assumption 1. To answer this question, we find it helpful to look at a simple example below.
+  - Example. Consider the case where  $X_0 \sim \mathcal{N}(0,1)$ , and hence  $X_1 \sim \mathcal{N}(0,1)$ . Suppose that the reverse process for time t=2 can lead to the desired distribution if exact score function is employed, namely,
+
+$$Y_1^* := \frac{1}{\sqrt{\alpha_2}} \left( Y_2 - \frac{1 - \alpha_2}{2} s_2^*(Y_2) \right) \sim \mathcal{N}(0, 1).$$
+
+Now, suppose that the score estimate  $s_2(\cdot)$  we have available obeys
+
+$$s_2(y_2) = s_2^\star(y_2) + \frac{2\sqrt{\alpha_2}}{1-\alpha_2} \left\{ y_1^\star - L \left\lfloor \frac{y_1^\star}{L} \right\rfloor \right\} \quad \text{with } y_1^\star := \frac{1}{\sqrt{\alpha_2}} \left( y_2 - \frac{1-\alpha_2}{2} s_2^\star(y_2) \right)$$
+
+for L > 0, where |z| is the greatest integer not exceeding z. It follows that
+
+$$Y_1 = Y_1^* + \frac{1 - \alpha_2}{2\sqrt{\alpha_2}} \left[ s_2^*(Y_2) - s_2(Y_2) \right] = L \left| \frac{Y_1^*}{L} \right|.$$
+
+Clearly, the score error  $\mathbb{E}_{X_2 \sim \mathcal{N}(0,1)} \left[ |s_2(X_2) - s_2^\star(X_2)|^2 \right]$  can be made arbitrarily small by taking  $L \to 0$ . However, the discrete nature of  $Y_1$  forces  $\mathsf{TV}(Y_1, X_1) = 1$ .
+
+This example demonstrates that, for the deterministic sampler, the TV distance between  $Y_1$  and  $X_1$  might not improve as the score error decreases. If we wish to relax Assumption 2, one potential way is to resort to other metrics (e.g., Wasserstein distance) instead of TV distance between  $Y_1$  and  $X_1$ .
+
+(d) Relaxing the boundedness assumption on  $X_0$ . As it turns out, the assumption (21) can also be relaxed. Supposing that  $\mathbb{P}(\|X_0\|_2 \leq B \mid X_0 \sim p_{\mathsf{data}}) = 1$  for some quantity B > 0 (which is allowed to grow faster than a polynomial in T), we can readily extend our analysis to obtain
+
+$$\mathsf{TV}\big(q_1, p_1\big) \leq C_1 \frac{d^2 \log^4 T \log^2 B}{T} + C_1 \frac{d^6 \log^6 T \log^3 B}{T^2} + C_1 \sqrt{d \log^3 T \log B} \varepsilon_{\mathsf{score}} + C_1 d (\log T) \varepsilon_{\mathsf{Jacobi}}.$$
+
+Importantly, the convergence rate depends only logarithmically in B.
+
+Comparisons with past works. To the best of our knowledge, the only non-asymptotic analysis for the discretized probability flow ODE approach in prior literature was derived by a very recent work Chen et al. (2023c), which established the first non-asymptotic convergence guarantees that exhibit
+
+polynomial dependency in both d and  $1/\varepsilon$  (see, e.g., Chen et al. (2023c, Theorem 4.1)). However, it fell short of providing concrete polynomial dependency in d and  $1/\varepsilon$ , suffered from exponential dependency in the Lipschitz constant of the score function, and relied on exact score estimates. In contrast, our result in Theorem 1 uncovers a concrete  $d^2/\varepsilon$  scaling (ignoring lower-order and logarithmic terms) without imposing any smoothness assumption on the target data distribution, and makes explicit the effect of score estimation errors, both which were previously unavailable for such discrete-time deterministic samplers. Another recent work Benton et al. (2023b) studied the convergence of the probability flow ODE approach without accounting for the discretization error; the result therein also exhibited exponential dependency on the Lipschitz constant. Finally, while we were wrapping up the current paper, we became aware of the independent work Chen et al. (2023b) establishing improved polynomial dependency for two variants of the probability flow ODE. By inserting an additional stochastic corrector step — based on overdamped (resp. underdamped) Langevin diffusion — in each iteration of the probability flow ODE (so strictly speaking, these variations are no longer deterministic samplers), Chen et al. (2023b) showed that  $O(L^3d/\varepsilon^2)$  (resp.  $O(L^2\sqrt{d}/\varepsilon)$ ) steps are sufficient, where L denotes the Lipschitz constant of the score function. In comparison, our result demonstrates for the first time that the plain probability flow ODE already achieves the  $1/\varepsilon$  scaling without requiring either a corrector step; one limitation of our result, however, is the sub-optimal d-dependency compared to the variants studied in Chen et al. (2023b).
+
+#### 3.3 A DDPM-TYPE STOCHASTIC SAMPLER
+
+Armed with the score estimates  $\{s_t\}$ , we can readily introduce the following stochastic sampler that operates in discrete time, motivated by the reverse-time SDE (16):
+
+<span id="page-7-0"></span>
+$$Y_T \sim \mathcal{N}(0, I_d), \qquad Y_{t-1} = \Psi_t(Y_t, Z_t) \quad \text{ for } t = T, \dots, 1$$
+ (26a)
+
+where  $Z_t \overset{\text{i.i.d.}}{\sim} \mathcal{N}(0, I_d)$ , and
+
+$$\Psi_t(y,z) = \frac{1}{\sqrt{\alpha_t}} \left( y + (1 - \alpha_t) s_t(y) \right) + \sigma_t z \quad \text{with } \sigma_t^2 = \frac{1}{\alpha_t} - 1.$$
+ (26b)
+
+The key difference between this sampler and the deterministic sampler (23) is that: (i) there exists an additional pre-factor of 1/2 on  $s_t$  in the deterministic sampler; and (ii) the stochastic sampler injects additional noise  $Z_t$  in each step.
+
+In contrast to deterministic samplers, the stochastic samplers have received more theoretical attention, with the state-of-the-art results established by Chen et al. (2022b;a) as well as a very recent paper Benton et al. (2023a). The elementary approach developed in the current paper is also applicable towards understanding this type of samplers, leading to the following non-asymptotic theory.
+
+<span id="page-7-1"></span>**Theorem 2.** Suppose (21) holds true. Equipped with the estimates in Assumption 1 and the learning rate schedule (22), the stochastic sampler (26) achieves, for some universal constants  $C_1 > 0$ ,
+
+$$\mathsf{TV}\big(q_1, p_1\big) \le \sqrt{\frac{1}{2}\mathsf{KL}\big(q_1 \parallel p_1\big)} \le C_1 \frac{d^2 \log^3 T}{\sqrt{T}} + C_1 \sqrt{d}\varepsilon_{\mathsf{score}} \log^2 T. \tag{27}$$
+
+Theorem 2 establishes non-asymptotic convergence guarantees for the stochastic sampler (26). As asserted by the theorem, if we have access to perfect score estimates, then the number of steps needed to attain  $\varepsilon$ -accuracy (measured by the TV distance between  $p_1$  and  $q_1$ ) is proportional to  $1/\varepsilon^2$ , matching the state-of-the-art  $\varepsilon$ -dependency derived in Chen et al. (2022a), albeit exhibiting a worse dimensional dependency. In addition, in the presence of score estimation error, the sampler achieves a TV distance proportional to  $\varepsilon_{\text{score}}$ , again consistent with prior results. Our analysis follows a completely different path compared with the SDE-based approach in Chen et al. (2022a), thus offering complementary interpretations for this important sampler.
+
+## 4 OTHER RELATED WORKS
+
+**Theory for SGMs.** Early theoretical efforts in understanding the convergence of score-based stochastic samplers suffered from being either not quantitative (De Bortoli et al., 2021; Liu et al., 2022; Pidstrigach, 2022), or the curse of dimensionality (e.g., exponential dependencies in the convergence guarantees) (Block et al., 2020; De Bortoli, 2022). Lee et al. (2022) provided the first
+
+polynomial convergence guarantees with L2-accurate score estimates, for any smooth distribution satisfying the log-Sobelev inequality. [Chen et al.](#page-9-8) [\(2022b\)](#page-9-8); [Lee et al.](#page-10-7) [\(2023\)](#page-10-7); [Chen et al.](#page-9-9) [\(2022a\)](#page-9-9) subsequently lifted such a stringent data distribution assumption. More concretely, [Chen et al.](#page-9-8) [\(2022b\)](#page-9-8) accommodated a broad family of data distributions under the premise that the score functions over the entire trajectory of the forward process are Lipschitz; [Lee et al.](#page-10-7) [\(2023\)](#page-10-7) only required certain smoothness assumptions but came with worse dependence on the problem parameters; and more recent results in [Chen et al.](#page-9-9) [\(2022a\)](#page-9-9) applied to literally any data distribution with bounded secondorder moment. In addition, [Wibisono & Yang](#page-11-14) [\(2022\)](#page-11-14) also established a convergence theory for score-based generative models, assuming that the error of the score estimator has a bounded moment generating function and that the data distribution satisfies the log-Sobelev inequality. Turning attention to samplers based on the probability flow ODE, [Chen et al.](#page-9-10) [\(2023c\)](#page-9-10) derived the first nonasymptotic bounds for this type of samplers. Improved convergence guarantees have recently been provided by a concurrent work [Chen et al.](#page-9-13) [\(2023b\)](#page-9-13), with the assistance of additional corrector steps inerspersed in each iteration of the probability flow ODE. It is worth noting that the corrector steps proposed therein are based on Langevin-type diffusion and inject additive noise, and hence the resulting sampling processes are not deterministic. Additionally, theoretical justifications for DDPM in the context of image in-painting have been developed by [Rout et al.](#page-11-15) [\(2023\)](#page-11-15). Moreover, convergence results based on the Wasserstein distance have recently been derived as well [\(Tang, 2023;](#page-11-11) [Benton et al., 2023b\)](#page-9-12), although these results typically exhibit exponential dependency on the Lipschitz constants of the score functions. Theoretical guarantees are also extended to accommodate popular methods like consistency models and diffusion guidance [\(Li et al., 2024b;](#page-10-12) [Wu et al., 2024\)](#page-11-16).
+
+Score matching. [Hyvärinen](#page-10-4) [\(2005\)](#page-10-4) showed that the score function can be estimated via integration by parts, a result that was further extended in [Hyvärinen](#page-10-5) [\(2007\)](#page-10-5). [Song et al.](#page-11-8) [\(2020b\)](#page-11-8) proposed sliced score matching to tame the computational complexity in high dimension. The consistency of the score matching estimator was studied in [Hyvärinen](#page-10-4) [\(2005\)](#page-10-4), with asymptotic normality established in [Forbes & Lauritzen](#page-10-13) [\(2015\)](#page-10-13). Optimizing the score matching loss has been shown to be intimately connected to minimizing upper bounds on the Kullback-Leibler divergence [\(Song et al., 2021a\)](#page-11-17) and Wasserstein distance [\(Kwon et al., 2022\)](#page-10-14) between the generated distribution and the target data distribution. From a non-asymptotic perspective, [Koehler et al.](#page-10-6) [\(2023\)](#page-10-6) studied the statistical efficiency of score matching by connecting it with the isoperimetric properties of the distribution.
+
+Other theory for diffusion models. [Oko et al.](#page-11-18) [\(2023\)](#page-11-18) studied the approximation and generalization capabilities of diffusion modeling for distribution estimation. Assuming that the data are supported on a low-dimensional linear subspace, [Chen et al.](#page-9-14) [\(2023a\)](#page-9-14) developed a sample complexity bound for diffusion models. Moreover, [Ghimire et al.](#page-10-15) [\(2023\)](#page-10-15) adopted a geometric perspective and showed that the forward and backward processes of diffusion models are essentially Wasserstein gradient flows. Recently, the idea of stochastic localization, which is closely related to diffusion models, is adopted to sample from posterior distributions [\(Montanari & Wu, 2023;](#page-11-19) [El Alaoui et al., 2022\)](#page-10-16), which has been implemented using approximate message passing [\(Donoho et al., 2009;](#page-10-17) [Li & Wei, 2022\)](#page-10-18).
+
+# 5 DISCUSSION
+
+In this paper, we have developed a new suite of non-asymptotic theory for establishing the convergence and faithfulness of diffusion generative modeling, assuming access to reliable estimates of the (Stein) score functions. Our analysis framework seeks to track the dynamics of the reverse process directly using elementary tools, which eliminates the need to look at the continuous-time limit and invoke the SDE and ODE toolboxes. Only the very minimal assumptions on the target data distribution are imposed. The analysis framework laid out in the current paper might shed light on how to analyze other variants of score-based generative models as well. Moving forward, there are plenty of questions that require in-depth theoretical understanding. For instance, the dimension dependency in our convergence results remains sub-optimal; can we further refine our theory in order to reveal tight dependency in this regard? Can we establish sharp convergence results in terms of the Wasserstein distance, which could sometimes be "closer" to how humans differentiate pictures and might potentially help relax Assumption [2](#page-5-0) in the case of deterministic samplers? It would also be of paramount interest to establish end-to-end performance guarantees that take into account both the score learning phase and the sampling phase.
+
+# ACKNOWLEDGEMENTS
+
+Y. Wei is supported in part by the the NSF grants DMS-2147546/2015447, CAREER award DMS-2143215, CCF-2106778, and the Google Research Scholar Award. Y. Chen is supported in part by the Alfred P. Sloan Research Fellowship, the Google Research Scholar Award, the AFOSR grant FA9550-22-1-0198, the ONR grant N00014-22-1-2354, and the NSF grants CCF-2221009 and CCF-1907661. Y. Chi is supported in part by the grants ONR N00014-19-1-2404, NSF CCF-2106778, DMS-2134080 and ECCS-2126634.
+
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papers/4VGEeER6W9/review.json

@@ -0,0 +1,92 @@
+{
+  "id": "4VGEeER6W9",
+  "title": "Towards Non-Asymptotic Convergence for Diffusion-Based Generative Models",
+  "decision": "Accept",
+  "reviews": [
+    {
+      "id": "31R2kSZkbC",
+      "rating": 6,
+      "content": {
+        "summary": "The paper delves into the intricacies of diffusion models, a unique class of models capable of converting noise into fresh data instances through the reversal of a Markov diffusion process. While the practical applications and capabilities of these models are well-acknowledged, there remains a gap in the comprehensive theoretical understanding of their workings. Addressing this, the authors introduce a novel non-asymptotic theory, specifically tailored to grasp the data generation mechanisms of diffusion models in a discrete-time setting. A significant contribution of their research is the establishment of convergence rates for both deterministic and stochastic samplers, given a score estimation oracle. The study underscores the importance of score estimation accuracies. Notably, this research stands apart from prior works by adopting a non-asymptotic approach, eschewing the traditional reliance on toolboxes designed for SDEs and ODEs.",
+        "soundness": "4 excellent",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "This paper offers a significant theoretical advancement by providing the convergence bounds for both stochastic and deterministic samplers of diffusion processes. I'm particularly struck by the elegance of their results, especially given the minimal assumptions required—for instance, the results for stochastic samplers rely solely on Assumption 1. These theoretical findings provide a clear understanding of the effects of score estimation inaccuracies. Furthermore, the emphasis on the estimation accuracies of Jacobian matrices for deterministic samplers sheds light on potential training strategies, suggesting the incorporation of penalties in objective functions when learning the score function for these samplers. Additionally, the proof presented is elementary, and potentially useful in a broader context.",
+        "weaknesses": "- While this paper doesn't present any algorithmic advancements, it's understandable considering the depth of their theoretical contributions.\n\n- The proof appears to be procedural. I was hoping for deeper insights into how the proof was constructed. It might be beneficial for the authors to include a subsection detailing the outline and insights behind their proof.",
+        "questions": "- Eq. (14), just want to confirm: should it be $dX_t = \\sqrt{1-\\beta_t}X_td_t$ instead of $-\\frac{1}{2}\\beta(t)X_t d_t$? \n- Eq. (15), maybe I am missing something, but should it be $dY = (-f(...) + \\frac{1}{2}g^2 \\nabla) d_t$? The original paper was taking a reverse form. \n- Eq. (16), similar question to Eq. (15). \n- Eq. (21), I feel a bit weird about the notation: maybe remove the $R$. \n- The results for deterministic samplers may motivate a better training strategy (i.e., incorporating the requirement for Jacobian matrices accuracy). The first step is to verify that this phenomenon exists in experiments (i.e., a worse $\\epsilon_{Jacobi}$ does imply a worse sampling result). It may be worth adding a numerical experiment to confirm this if time permits.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "- While this paper doesn't present any algorithmic advancements, it's understandable considering the depth of their theoretical contributions.\n\n- The proof appears to be procedural. I was hoping for deeper insights into how the proof was constructed. It might be beneficial for the authors to include a subsection detailing the outline and insights behind their proof.\n\n- Eq. (14), just want to confirm: should it be $dX_t = \\sqrt{1-\\beta_t}X_td_t$ instead of $-\\frac{1}{2}\\beta(t)X_t d_t$?\n- Eq. (15), maybe I am missing something, but should it be $dY = (-f(...) + \\frac{1}{2}g^2 \\nabla) d_t$? The original paper was taking a reverse form. \n- Eq. (16), similar question to Eq. (15). \n- Eq. (21), I feel a bit weird about the notation: maybe remove the $R$. \n- The results for deterministic samplers may motivate a better training strategy (i.e., incorporating the requirement for Jacobian matrices accuracy). The first step is to verify that this phenomenon exists in experiments (i.e., a worse $\\epsilon_{Jacobi}$ does imply a worse sampling result). It may be worth adding a numerical experiment to confirm this if time permits.",
+        "suggestions": "The paper makes a valuable theoretical contribution by establishing convergence bounds for both stochastic and deterministic samplers in diffusion processes. However, the presentation of the proof could be significantly improved to enhance the reader's understanding. Currently, the proof feels like a sequence of steps without a clear narrative or explanation of the underlying intuition. Including a section that outlines the key ideas and strategies behind the proof would greatly benefit the reader. For example, it would be helpful to explain the motivation behind the specific mathematical techniques used, and how these techniques relate to the overall goal of establishing convergence bounds. This would transform the proof from a procedural exercise into a more insightful and educational experience. Furthermore, highlighting the connections between the different steps and explaining the high-level strategy would make the proof more accessible and easier to follow.\n\nRegarding the practical implications of the theoretical results, the paper correctly points out that the Jacobian accuracy is crucial for deterministic samplers. However, the paper could delve deeper into the practical implications of this finding. For instance, the authors could discuss how this requirement could be incorporated into the training process of diffusion models. One approach could be to introduce a penalty term in the loss function that encourages the accurate estimation of the Jacobian matrix. This would involve exploring different methods for estimating the Jacobian and analyzing their impact on the sampling quality. Furthermore, the authors could investigate how the Jacobian accuracy interacts with other training parameters, such as the learning rate and batch size. This would provide a more comprehensive understanding of the practical challenges and opportunities associated with training deterministic samplers.\n\nFinally, while the theoretical results are elegant, the paper would benefit from a more thorough discussion of the limitations. For example, the paper could explore the assumptions that are made in the analysis and discuss how these assumptions might affect the applicability of the results in practice. Specifically, it would be useful to analyze the sensitivity of the convergence bounds to the choice of parameters and the quality of the score estimation. This would provide a more nuanced perspective on the strengths and weaknesses of the proposed theory. Additionally, the authors could consider exploring alternative metrics, such as the Wasserstein distance, which might be more suitable for analyzing the convergence of deterministic samplers. This would broaden the scope of the analysis and provide a more complete picture of the behavior of diffusion models."
+      }
+    },
+    {
+      "id": "9MWDNny1bC",
+      "rating": 8,
+      "content": {
+        "summary": "This paper aims to provide a systematic analysis of the convergence rate of both deterministic and stochastic samplers of the diffusion models in the context of generative modeling. The authors proves, under certain assumptions, the former has a rate of $T^{-1}$\nwhile the latter has a rate $\\sqrt{T}$ which is consistent with the previous empirical observations. The authors also proposed some improvements, leading to a rate of $T^{-2}$ in the deterministic case, and a rate of $T^{-1}$ in the stochastic case.",
+        "soundness": "4 excellent",
+        "presentation": "3 good",
+        "contribution": "4 excellent",
+        "strengths": "This paper provides an early systematic analysis on the convergence rate of samplers in the diffusion models. Both deterministic and stochastic cases are considered, and their results are almost optimal under the assumptions made. The presentation of the paper is good, and I really enjoyed reading it. Especially, I like Theorem 1.",
+        "weaknesses": "As for every (good) paper, there are always plenty of things remained to be done. For instance,\n\n(1) It is worthy to comment on the learning rate (22a)-(22b). I understand these rates are carefully chosen in order to match the rates in the theorems. The author may mention this, or provide some explanations/insights on it.\n\n(2) The paper, like Chen et al., deals with the TV (or KL) divergence. I understand that under these metrics, one can prove \"nice\" theoretical results using some specific algebraic identities (flow...) On the other hand, practitioners may care more about the FID (or Wasserstein distance) -- part of the reason is that Wasserstein distance is \"closer\" to how humans distinguish pictures. The authors may want to add a few remarks on this.",
+        "questions": "See the weaknesses.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "details_of_ethics_concerns": "NA",
+        "rating": "8: accept, good paper",
+        "confidence": "5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.",
+        "code_of_conduct": "Yes",
+        "weakness": "As for every (good) paper, there are always plenty of things remained to be done. For instance,\n\n(1) It is worthy to comment on the learning rate (22a)-(22b). I understand these rates are carefully chosen in order to match the rates in the theorems. The author may mention this, or provide some explanations/insights on it. Specifically, the choice of $\\alpha_t$ and $\\overline{\\alpha}_t$ seems crucial for achieving the stated convergence rates, and a more detailed discussion on how these parameters are derived and their impact on the overall performance would be beneficial. For instance, how sensitive are the results to small perturbations in these parameters? What is the intuition behind the specific functional forms chosen?\n\n(2) The paper, like Chen et al., deals with the TV (or KL) divergence. I understand that under these metrics, one can prove \"nice\" theoretical results using some specific algebraic identities (flow...) On the other hand, practitioners may care more about the FID (or Wasserstein distance) -- part of the reason is that Wasserstein distance is \"closer\" to how humans distinguish pictures. The authors may want to add a few remarks on this. Furthermore, while TV and KL divergence provide useful theoretical insights, their practical relevance in image generation tasks is limited. The Wasserstein distance, and metrics derived from it such as FID, are more aligned with perceptual quality. It would be valuable to discuss the limitations of the current analysis in this context and suggest potential avenues for extending the theoretical framework to these metrics.",
+        "suggestions": "The paper provides a solid theoretical foundation for understanding the convergence rates of diffusion model samplers. However, to enhance its practical impact, several points could be further explored. First, a more detailed sensitivity analysis of the learning rate parameters, specifically $\\alpha_t$ and $\\overline{\\alpha}_t$, is needed. The current analysis assumes a specific form for these parameters, but it would be beneficial to investigate how deviations from this form affect the convergence rates. For example, one could explore the impact of using different functional forms or introducing small perturbations to the chosen parameters. This would provide a more robust understanding of the practical implications of the theoretical results. Furthermore, it would be valuable to provide some intuition behind the specific choices of these parameters, explaining why they are optimal for achieving the stated convergence rates. This could involve discussing the trade-offs between different parameter choices and their impact on the discretization and initialization errors.\n\nSecondly, the paper's focus on TV and KL divergence, while theoretically tractable, limits its practical relevance. A discussion on the limitations of these metrics in the context of image generation is necessary. Specifically, the authors should acknowledge that metrics like FID and Wasserstein distance are more aligned with human perception and are widely used in practice. It would be beneficial to explore the challenges of extending the current theoretical framework to these metrics. This could involve discussing the difficulties in establishing similar algebraic identities or flow properties under these metrics. Furthermore, the authors could suggest potential avenues for future research, such as exploring alternative proof techniques or making additional assumptions that would allow for the analysis of convergence rates under Wasserstein distance. This would significantly enhance the practical impact of the paper and make it more relevant to the broader community.\n\nFinally, while the paper provides a comprehensive analysis of convergence rates, it would be valuable to discuss the computational cost associated with achieving these rates. For example, the improved rates of $T^{-2}$ and $T^{-1}$ for deterministic and stochastic samplers, respectively, might come at the cost of increased computational complexity. A discussion on the trade-offs between convergence rate and computational cost would provide valuable insights for practitioners. This could involve analyzing the number of iterations required to achieve a certain level of accuracy and comparing the computational cost of different sampling methods. Furthermore, the authors could discuss potential techniques for reducing the computational cost without sacrificing the convergence rate, such as using adaptive step sizes or more efficient numerical integration methods."
+      }
+    },
+    {
+      "id": "NdlScvNTfm",
+      "rating": 8,
+      "content": {
+        "summary": "This paper studies the deterministic probability flow ODE-based sampler often used in practice for score-based diffusion. It shows that the ODE-based sampler gets a $1/T$ convergence rate, improving upon the SDE-based sampling rate of $1/\\sqrt{T}$. The techniques are elementary, and do not rely on Girsanov's theorem and other techniques from the SDE/ODE toolboxes. While there was prior work (Chen et. al. 2023b) that obtains an improved guarantee for the ODE-based sampler, their analysis required the use of stochastic \"corrector steps\", while in practice, even just the ODE-based sampler without corrector steps seems to perform well. This is the first work that provides theoretical evidence that the vanilla ODE-based sampler can outperform the SDE-based sampler in practice.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "- Provides the first analysis of the (vanilla) ODE-based sampler for score-based diffusion models that gives some theoretical evidence for why it outperforms the SDE-based sampler in practice ($1/T$ convergence instead of $1/\\sqrt{T}$)\n- New analysis that doesn't make use of Girsanov's theorem/other results from the ODE/SDE literature.\n- Doesn't require Lipschitzness of score unlike (Chen et al 2023b), but pays in d dependence",
+        "weaknesses": "- $d$ dependence is worse than (Chen et al 2023b). In particular, Chen gets a $\\sqrt{d}$ dependence for the ODE-based sampler when using stochastic corrector steps, which is better than the previous bound of $d$ for the SDE-based sampler. This paper on the other hand gets a $d^3$ dependence, which is significantly worse than both these bounds. \n- Requires Jacobian of score to be estimated accurately, rather than just the score\n- Requires the distribution $q_0$ to be bounded, and bound is stated in terms of this bound. In contrast, some of the prior works only required the second moment of $q_0$ to be bounded.\n- While new analysis is \"elementary\" in that it doesn't require SDE/ODE machinery, it seems much longer/more complicated than the previous analyses. Would really appreciate a condensation/proof overview in the main paper.",
+        "questions": "- Is it clear that $1/\\sqrt{T}$ is tight for the SDE-based sampler, and $1/T$ is impossible?\n- What are the barriers to getting a $d$ or $\\sqrt{d}$ dependence? Can you write something about this in the main paper?\n- Can you include a proof overview in the main paper?\n- Why is the proof so long? Can it be condensed?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes",
+        "weakness": " - $d$ dependence is worse than (Chen et al 2023b). In particular, Chen gets a $\\sqrt{d}$ dependence for the ODE-based sampler when using stochastic corrector steps, which is better than the previous bound of $d$ for the SDE-based sampler. This paper on the other hand gets a $d^3$ dependence, which is significantly worse than both these bounds. The $d^3$ dependence arises from the need to control the error propagation through the Jacobian of the score function, which is a significant limitation in high-dimensional settings. This makes the theoretical results less applicable to practical scenarios where $d$ is very large.\n- Requires Jacobian of score to be estimated accurately, rather than just the score. This is a strong requirement, as accurate Jacobian estimation is often more difficult than score estimation, and may require additional computational overhead or stronger assumptions on the score function. The paper does not provide sufficient justification for why this is a necessary condition, or discuss the practical implications of this requirement. It would be helpful to see a more detailed analysis of the impact of Jacobian estimation errors on the overall performance of the sampler.\n- Requires the distribution $q_0$ to be bounded, and bound is stated in terms of this bound. In contrast, some of the prior works only required the second moment of $q_0$ to be bounded. This boundedness assumption is quite restrictive, and may not hold for many real-world datasets. The paper should discuss the implications of this assumption and how it might affect the applicability of the results. It would also be beneficial to explore if the analysis can be extended to cases where $q_0$ has unbounded support, perhaps by using alternative metrics or assumptions.\n- While new analysis is \"elementary\" in that it doesn't require SDE/ODE machinery, it seems much longer/more complicated than the previous analyses. Would really appreciate a condensation/proof overview in the main paper. The current presentation makes it difficult to grasp the core ideas and techniques used in the analysis, and a high-level overview would greatly improve the readability and accessibility of the paper.",
+        "suggestions": "The paper makes a valuable contribution by providing a theoretical analysis of the vanilla ODE-based sampler, demonstrating its $1/T$ convergence rate. However, the practical impact of the results is limited by the strong assumptions and suboptimal $d$ dependence. To enhance the paper, it would be beneficial to explore alternative analysis techniques that can reduce the $d$ dependence, perhaps by leveraging more advanced tools from SDE/ODE theory. Additionally, the paper should provide a more detailed discussion of the practical implications of the Jacobian estimation requirement, including potential methods for mitigating the impact of errors in the Jacobian estimate. It would also be helpful to investigate the possibility of relaxing the boundedness assumption on $q_0$, perhaps by considering alternative metrics like the Wasserstein distance, which might be more robust to unbounded distributions. Furthermore, a more detailed discussion of the limitations of the current analysis and potential directions for future research would be valuable. \n\nTo address the issue of the complicated proof, the authors should include a detailed proof overview in the main paper, even if the full proofs are deferred to the supplementary material. This overview should highlight the key steps and techniques used in the analysis, and explain the intuition behind the main results. The overview should also clearly state the assumptions made and their implications. The authors should also consider reorganizing the proof to make it more modular and easier to follow. This could involve breaking the proof into smaller, more manageable lemmas, and providing clear explanations for each step. The goal should be to make the analysis more accessible to a wider audience, without sacrificing technical rigor. It would be helpful to include a diagram or flowchart that illustrates the logical flow of the proof. \n\nFinally, the paper should explore the possibility of obtaining convergence guarantees under weaker assumptions, such as using the Wasserstein distance instead of the total variation distance. This could potentially eliminate the need for the Jacobian error assumption and allow for a more robust analysis. The authors should also investigate the possibility of obtaining a better $d$ dependence by using different analysis techniques. For example, it might be possible to adapt some of the techniques used in the analysis of stochastic gradient descent to analyze the ODE-based sampler. It would also be helpful to provide a more detailed comparison with existing results, highlighting the advantages and disadvantages of the proposed approach. This would help to clarify the contribution of the paper and its place within the existing literature."
+      }
+    },
+    {
+      "id": "La3vs3IDeZ",
+      "rating": 8,
+      "content": {
+        "summary": "This paper develops theoretical analyses for two variants of score-based generative models, those with deterministic (known as the probability flow ODE) and stochastic (known as denoising diffusion probabilistic models) reverse time processes, respectively. The deterministic variant is of particular interest because it has been difficult to analyze with existing techniques, despite being successful in practice. The main contribution of this work is to derive convergence guarantees for each of these processes under mild assumptions on the data distribution and the score function. Briefly, they provide an analysis of the deterministic algorithm which is the first to provide explicit rates of convergence, when the data distribution has bounded support (with only logarithmic dependence on the diameter) and when the score function and its Jacobian have been estimated. For the stochastic algorithm they recover similar results to the state-of-the-art, albeit with worse dimension dependence and stronger assumptions on the data distribution (compact support vs finite second moment).",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "This work studies an important problem, that of developing theoretical understanding of the efficacy of score-based methods, and focuses in particular on deterministic methods, which are not well understood theoretically. They develop the first analysis to achieve explicit rates of convergence for these methods in the literature, and achieve a strong bound under assumptions which are quite mild (except for the Jacobian assumption). For the stochastic method, they gain results which are close to the best known. Their analysis is necessarily novel and avoids technical difficulties that have forced previous works [1] to study (stochastic) modifications of the fully deterministic methods.\n\n[1] The Probability Flow ODE Is Provably Fast, by Chen et al 2023",
+        "weaknesses": "From my point of view, the main weakness of the results is that they involve the error of the differential of the score function, and it is not clear why this would be well-controlled in general (since the score-matching objective doesn't involve the Jacobian). The prior work [2] didn't use such conditions, but then again achieved far weaker guarantees. It would be good to comment on the importance and plausibility of this condition. Less significant but nonetheless important is the authors' use of very specific step-size schemes, a remark on this would also be helpful. Finally, their convergence results are proved in TV (weaker than KL) and are not for the true data distribution, but for the distribution of the first step of the forward diffusion process.\n\nWith regard to correctness of their arguments, I was not able to carefully check this point due to the long and involved natured of their proofs but everything that I did read in the supplementary material seems correct.\n\n[2] \"Restoration-degradation beyond linear diffusions: A non-asymptotic analysis for DDIM-type samplers\" by Chen, Daras, and Dimakis 2023",
+        "questions": "- Please add a remark about the fact that you prove your guarantees for convergence to the first step of the forward process (rather than the true data distribution). Of course, this is what allows for guarantees in TV with minimal assumptions on the data distribution since otherwise the data distribution could be singular, but I wonder how much this changes your results.\n- Are the step-size schemes you consider similar to those used in practice? How robust are your results to variations in the step-sizes?\n- Please discuss the utility and plausibility of the bound on the difference of Jacobians\n- Could you please clarify the meaning of \"continuous\" in the assumption on the data distribution when it is says \"$X_0$ is a continuous random vector, and\". In particular, are you assuming the data distribution has a density wrt Lebesgue here?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "8: accept, good paper",
+        "confidence": "2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes",
+        "weakness": "From my point of view, the main weakness of the results is that they involve the error of the differential of the score function, and it is not clear why this would be well-controlled in general (since the score-matching objective doesn't involve the Jacobian). The prior work [2] didn't use such conditions, but then again achieved far weaker guarantees. It would be good to comment on the importance and plausibility of this condition. Specifically, it's unclear how the error in the Jacobian of the score function relates to the training objective, which only involves the score itself. This discrepancy raises concerns about the practical relevance of the theoretical results, as controlling the Jacobian error might require a different training procedure or objective than standard score matching. Less significant but nonetheless important is the authors' use of very specific step-size schemes, a remark on this would also be helpful. Finally, their convergence results are proved in TV (weaker than KL) and are not for the true data distribution, but for the distribution of the first step of the forward diffusion process. It is not clear how much this simplification impacts the practical relevance of the results, since the first step of the forward process is an approximation of the true data distribution, and the convergence is only guaranteed to this approximation rather than the true data distribution.",
+        "suggestions": "The authors should provide a more detailed discussion on the practical implications of their assumption regarding the Jacobian error. Specifically, they should address how one might control this error during the training process, given that standard score-matching objectives do not directly involve the Jacobian. It would be beneficial to explore alternative training objectives or regularization techniques that could help ensure the Jacobian of the learned score function is well-behaved. Furthermore, a comparison with other methods that do not require such assumptions, even if they provide weaker guarantees, would help to contextualize the importance and limitations of their approach. For example, it would be helpful to discuss if there are known conditions under which the Jacobian error is naturally controlled by the score matching objective, or if there are specific architectures or training procedures that tend to produce score functions with well-behaved Jacobians.\n\nRegarding the step-size schemes, while the authors mention that their analysis can be extended to a broader class of learning rates, it would be helpful to provide more concrete examples of such learning rates and discuss how they might affect the convergence rates. A more detailed analysis of the robustness of their results to variations in the step-sizes would also be valuable. In particular, it would be useful to understand if there are specific ranges of step-sizes that are more likely to lead to good performance and if there are any practical guidelines for choosing appropriate step-sizes. This discussion should also include a comparison with step-size schemes used in practice and an explanation of how the theoretical choices relate to practical implementations. \n\nFinally, the authors should clarify the implications of proving convergence to the first step of the forward process rather than the true data distribution. While it is acknowledged that this simplification allows for guarantees in TV with minimal assumptions on the data distribution, a more detailed discussion of the potential impact on the practical relevance of the results is needed. Specifically, it would be helpful to explore the conditions under which the distribution of the first step of the forward process is a good approximation of the true data distribution, and how the convergence results might be affected if this approximation is not accurate. Furthermore, it would be useful to discuss if there are any techniques to bridge the gap between convergence to the first step of the forward process and convergence to the true data distribution."
+      }
+    }
+  ]
+}

papers/532tcx7IHF/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "532tcx7IHF",
+  "title": "RLLTE: Long-Term Evolution Project of Reinforcement Learning",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2025-05-13",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=532tcx7IHF"
+}

papers/532tcx7IHF/paper.md

@@ -0,0 +1,693 @@
+# RLLTE: LONG-TERM EVOLUTION PROJECT OF REIN-FORCEMENT LEARNING
+
+### Anonymous authors
+
+Paper under double-blind review
+
+# ABSTRACT
+
+We present RLLTE: a long-term evolution, extremely modular, and open-source framework for reinforcement learning (RL) research and application. Beyond delivering top-notch algorithm implementations, RLLTE also serves as a toolkit for developing algorithms. More specifically, RLLTE decouples the RL algorithms completely from the exploitation-exploration perspective, providing a large number of components to accelerate algorithm development and evolution. In particular, RLLTE is the first RL framework to build a complete and luxuriant ecosystem, which includes model training, evaluation, deployment, benchmark hub, and large language model (LLM)-empowered copilot. RLLTE is expected to set standards for RL engineering practice and be highly stimulative for industry and academia.
+
+# 1 INTRODUCTION
+
+Reinforcement learning (RL) has emerged as a highly significant research topic, garnering considerable attention due to its remarkable achievements in diverse fields, including smart manufacturing and autonomous driving [\(Mnih et al., 2015;](#page-10-0) [Duan et al., 2016;](#page-9-0) [Schulman et al., 2017;](#page-11-0) [Haarnoja et al., 2018;](#page-10-1) [Yarats et al., 2021\)](#page-11-1). However, the efficient and reliable engineering implementation of RL algorithms remains a long-standing challenge. These algorithms often possess sophisticated structures, where minor code variations can substantially influence their practical performance. Academia requires a stable baseline for algorithm comparison, while the industry seeks convenient interfaces for swift application development [\(Raffin et al., 2021\)](#page-10-2). However, the design and maintenance of an RL library prove costly, involving substantial computing resources, making it prohibitive for most research teams.
+
+To tackle this problem, several open-source projects were proposed to offer reference implementations of popular RL algorithms [\(Liang et al., 2018;](#page-10-3) [D'Eramo et al., 2021;](#page-9-1) [Fujita et al., 2021;](#page-10-4) [Raffin](#page-10-2) [et al., 2021;](#page-10-2) [Huang et al., 2022\)](#page-10-5). For instance, [Raffin et al.](#page-10-2) [\(2021\)](#page-10-2) developed a stable-baselines3 (SB3) framework, which encompasses seven model-free deep RL algorithms, including proximal policy optimization (PPO) [\(Schulman et al., 2017\)](#page-11-0) and asynchronous actor-critic (A2C) [\(Mnih et al.,](#page-10-6) [2016\)](#page-10-6). SB3 prioritizes stability and reliability, and rigorous code testing has been conducted to minimize implementation errors and ensure the reproducibility of results. [Weng et al.](#page-11-2) [\(2022a\)](#page-11-2) introduced Tianshou, a highly modularized library emphasizing flexibility and training process standardization. Tianshou also provides a unified interface for various algorithms, such as offline and imitation learning. In contrast, [Huang et al.](#page-10-5) [\(2022\)](#page-10-5) introduced CleanRL, which focuses on single-file implementations to facilitate algorithm comprehension, new features prototyping, experiment analysis, and scalability.
+
+Despite their achievements, most of the existing benchmarks have not established a long-term evolution plan and have proven to be short-lived. Firstly, the consistent complexity of RL algorithms naturally results in distinct coding styles, posing significant obstacles to open-source collaborations. Complete algorithm decoupling and modularization have yet to be well achieved, making maintenance challenging and limiting extensibility. Secondly, these projects are deficient in establishing a comprehensive application ecosystem. They primarily concentrate on model training, disregarding vital aspects like model evaluation and deployment. Furthermore, they frequently lack exhaustive benchmark testing data, including essential elements like learning curves and trained models. This deficiency makes replicating algorithms demanding in terms of computational resources.
+
+![](figures/_page_1_Figure_1.jpeg)
+
+Figure 1: Overview of the architecture of RLLTE.
+
+<span id="page-1-0"></span>Inspired by the discussions above, we propose RLLTE, a long-term evolution, extremely modular, and open-source framework of RL. We summarize the highlighted features of RLLTE as follows:
+
+- Module-oriented. RLLTE decouples RL algorithms from the *exploitation-exploration* perspective and breaks them down into minimal primitives, such as *encoder* for feature extraction and *storage* for archiving and sampling experiences. RLLTE offers a rich selection of modules for each primitive, enabling developers to utilize them as building blocks for constructing algorithms. As a result, the focus of RLLTE shifts from specific algorithms to providing more handy modules like PyTorch. In particular, each module in RLLTE is customizable and plug-and-play, empowering users to develop their own modules. This decoupling process also contributes to advancements in interpretability research, allowing for a more in-depth exploration of RL algorithms.
+- Long-term evolution. RLLTE is a long-term evolution project, continually involving advanced algorithms and tools in RL. RLLTE will be updated based on the following tenet: (i) generality; (ii) improvements in generalization ability and sample efficiency; (iii) excellent performance on recognized benchmarks; (iv) promising tools for RL. Therefore, this project can uphold the right volume and high quality resources, thereby inspiring more subsequent projects.
+- Data augmentation. Recent approaches have introduced data augmentation techniques at the *observation* and *reward* levels to improve the sample efficiency and generalization ability of RL agents, which are cost-effective and highly efficient. In line with this trend, RLLTE incorporates built-in support for data augmentation operations and offers a wide range of observation augmentation modules and intrinsic reward modules.
+- Abundant ecosystem. RLLTE considers the needs of both academia and industry and develops an abundant project ecosystem. For instance, RLLTE designed an evaluation toolkit to provide statistical and reliable metrics for assessing RL algorithms. Additionally, the deployment toolkit enables the seamless execution of models on various inference devices. In particular, RLLTE attempts to introduce the large language model (LLM) to build an intelligent copilot for RL research and applications.
+- Comprehensive benchmark data. Existing RL projects typically conduct testing on a limited number of benchmarks and often lack comprehensive training data, including learning
+
+curves and test scores. While this limitation is understandable, given the resource-intensive nature of RL training, it hampers the advancement of subsequent research. To address this issue, RLLTE has established a data hub utilizing the Hugging Face platform. This data hub provides extensive testing data for the included algorithms on widely recognized benchmarks. By offering complete and accessible testing data, RLLTE will facilitate and accelerate future research endeavors in RL.
+
+• Multi-hardware support. RLLTE has been thoughtfully designed to accommodate diverse computing hardware configurations, including graphic processing units (GPUs) and neural network processing units (NPUs), in response to the escalating global demand for computing power. This flexibility enables RLLTE to support various computing resources, ensuring optimal trade-off of performance and scalability for RL applications.
+
+#### 2 ARCHITECTURE
+
+Figure 1 illustrates the overall architecture of RLLTE, which contains the core layer, application layer, and tool layer. The following sections will detail the design concepts and usage of the three layers.
+
+#### 2.1 CORE LAYER
+
+In the core layer, we decouple an RL algorithm from the *exploitation-exploration* perspective and break them down into minimal primitives. Figure 2 illustrates a typical forward and update workflow of RL training. At each time step, an encoder first processes the observation to extract features. Then, the features are passed to a policy module to generate actions. Finally, the transition will be inserted into the storage, and the agent will sample from the storage to perform the policy update. In particular, we can use data augmentation techniques such as observation augmentation and intrinsic reward shaping to improve the sample efficiency and generalization ability.
+
+![](figures/_page_2_Figure_7.jpeg)
+
+<span id="page-2-0"></span>Figure 2: Forward and update workflow of an RL algorithm. **Aug.**: Augmentation. **Dist.**: Distribution for sampling actions. **Int.**: Intrinsic. **Obs.**: Observation.
+
+We categorize these fundamental components into two parts: xploit and xplore, and Table 1 illustrates their architectures. The modules within the xploit component primarily focus on exploiting the current collected experiences. For instance, the storage module defines the methods for storing and sampling experiences, while the policy module is updated based on the sampled data. In contrast, modules in xplore focus on exploring unknown domains. When policy is stochastic, distribution specifies the methods for sampling actions from the action space. In the case of a deterministic policy, the distribution module introduces noise to the current action to enhance the exploration of the action space. The augmentation and reward modules contribute to exploring the state and action space by augmenting observations and providing additional intrinsic rewards, respectively. Each submodule in Table 1 is accompanied by many pre-defined components, which are listed in Appendix A.
+
+<span id="page-3-0"></span>Table 1: Six primitives in RLLTE. Note that the action noise is implemented via a distribution manner to keep unification in RLLTE.
+
+| Module       | Submodule                              | Remark                                                                                                            |
+|--------------|----------------------------------------|-------------------------------------------------------------------------------------------------------------------|
+| rllte.xploit | policy<br>encoder<br>storage           | Policies for interaction and learning.<br>Encoders for feature extraction.<br>Storages for collected experiences. |
+| rllte.xplore | distribution<br>augmentation<br>reward | Distributions for sampling actions.<br>Observation augmentation modules.<br>Intrinsic reward modules.             |
+
+### 2.2 APPLICATION LAYER
+
+Equipped with modules of the core layer, we can efficiently develop RL algorithms and applications with simple steps, and Table [2](#page-3-1) illustrates the architecture of the application layer. See all the corresponding code examples in Appendix [C.](#page-15-0)
+
+Table 2: Architecture of the application layer in RLLTE.
+
+<span id="page-3-1"></span>
+
+| Module       | Remark                                                                                                                                                                                                                                                                                                                                                          |
+|--------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| rllte.agent  | Top-notch implementations of highly-recognized RL algorithms, in<br>which convenient interfaces are designed to realize fast application<br>construction. In particular, the module-oriented design allows devel<br>opers to replace settled modules of implemented algorithms to make<br>performance comparisons and algorithm improvements.                   |
+| Pre-training | Since RLLTE is designed to support intrinsic reward modules na<br>tively, developers can conveniently realize pre-training.<br>The pre<br>trained weights will be saved automatically after training, and it suf<br>fices to perform fine-tuning by loading the weights in the .train()<br>function.                                                            |
+| Deployment   | A toolkit that helps developers run their RL models on inference de<br>vices, which consistently have lower computational power.<br>RLLTE<br>currently supports two inference frameworks: NVIDIA TensorRT and<br>HUAWEI CANN. RLLTE provides a fast API for model transforma<br>tion and inference, and developers can invoke it directly with their<br>models. |
+| Copilot      | A promising attempt to introduce the LLM into an RL framework.<br>The copilot can help users reduce the time required for learning<br>frameworks and assist in the design and development of RL appli<br>cations.<br>We are developing more advanced features to it, including<br>RL-oriented code completion and training control.                             |
+
+# 2.2.1 FAST ALGORITHM CONSTRUCTION
+
+Developers only need three steps to implement an RL algorithm with RLLTE: (i) select an algorithm prototype; (ii) select desired modules; (iii) define an update function. Currently, RLLTE provides three algorithm prototypes: **OnPolicyAgent**, **OffPolicyAgent**, and **DistributedAgent**. Figure [3](#page-4-0) demonstrates how to write an A2C agent for discrete control tasks with RLLTE:
+
+As shown in this example, developers can effortlessly choose the desired modules and create an **.update()** function to implement a new algorithm. At present, the framework includes a collection of 13 algorithms, such as data-regularized actor-critic (DrAC) [\(Raileanu et al., 2021\)](#page-11-3) and data regularized Q-v2 (DrQ-v2), and the detailed introduction can be found in Appendix [B.](#page-14-0)
+
+```
+from rllte.common.prototype import OnPolicyAgent
+from rllte.xploit.encoder import MnihCnnEncoder
+from rllte.xploit.policy import OnPolicySharedActorCritic
+from rllte.xploit.storage import VanillaRolloutStorage
+from rllte.xplore.distribution import Categorical
+class A2C(OnPolicyAgent):
+    def __init__(self, ...) -> None:
+        super().__init__(...)
+        policy = OnPolicySharedActorCritic(...)
+        storage = VanillaRolloutStorage(...)
+        dist = Categorical()
+        # set all the modules
+        self.set(encoder=encoder, policy=policy, 
+                 storage=storage, distribution=dist)
+    def update(self) -> Dict[str, float]:
+        batch = self.storage.sample()
+```
+
+```
+# import `env` and `agent`
+from rllte.env import make_dmc_env
+from rllte.agent import DrQv2
+if __name__ == "__main__":
+    env = make_dmc_env(env_id="cartpole_balance", 
+                       device=device)
+    eval_env = make_dmc_env(env_id="cartpole_balance", 
+                            device=device)
+    agent = DrQv2(env=env, 
+                  eval_env=eval_env, 
+                  device=device, 
+                  tag="drqv2_dmc_pixel")
+    agent.train(num_train_steps=500000, 
+                log_interval=1000)
+```
+
+<span id="page-4-0"></span>Figure 3: Left: Implement A2C algorithm with dozens of lines of code, and the complete code example can be found in Appendix [C.1.](#page-15-1) Right: Simple interface to invoke implemented RL algorithms.
+
+### 2.2.2 MODULE REPLACEMENT
+
+For an implemented algorithm, developers can replace its settled modules using the **.set()** method to realize performance comparisons and algorithm improvements. Moreover, developers can utilize custom modules as long as they inherit from the base class, as demonstrated in the code example in Appendix [C.2.](#page-16-0) By decoupling these elements, RLLTE also empowers developers to construct prototypes and perform quantitative analysis of algorithm performance swiftly.
+
+### 2.2.3 COPILOT
+
+![](figures/_page_4_Figure_7.jpeg)
+
+<span id="page-4-1"></span>Figure 4: Left: The workflow of the copilot. Right: A conversation example of training an PPO agent using RLLTE.
+
+**Copilot** is the first attempt to integrate an LLM into an RL framework, which aims to help developers reduce the learning cost and facilitate application construction. We follow the design of [\(Toro,](#page-11-4) [2023\)](#page-11-4) that interacts privately with documents using the power of GPT, and Figure [4](#page-4-1) illustrates its architecture. The source documents are first ingested by an instructor embedding tool to create a local vector database. After that, a local LLM is used to understand questions and create answers based on the database. In practice, we utilize Vicuna-7B [\(Chiang et al., 2023\)](#page-9-2) as the base model and build the database using various corpora, including API documentation, tutorials, and RL references. The powerful understanding ability of the LLM model enables the copilot to accurately answer questions about the use of the framework and any other questions of RL. Moreover, no additional training is required, and users are free to replace the base model according to their computing power. In future work, we will further enrich the corpus and add the code completion function to build a more intelligent copilot for RL.
+
+# 2.3 TOOL LAYER
+
+The tool layer provides practical toolkits for task design, model evaluation, and benchmark data. **rllte.env** allows users to design task environments following the natural Gymnasium pattern with-
+
+Table 3: Architecture of the tool layer in RLLTE. Code example for each toolkit can be found in Appendix D.
+
+| Toolkit          | Remark                                                                                                                                                                                                                                                                                                                                               |
+|------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| rllte.env        | Provides a large number of packaged environments (e.g., Atari games) for fast invocation. RLLTE is designed to natively support Gymnasium (Towers et al., 2023), which is a maintained fork of the Gym library of OpenAI (Brockman et al., 2016). Moreover, developers are allowed to use their custom environments with built-in wrappers in RLLTE. |
+| rllte.evaluation | Provides reasonable and reliable metrics for algorithm evaluation following (Agarwal et al., 2021). Performance module for evaluating a single algorithm. Comparison module for comparing multiple algorithms. Visualization for visualizing computed metrics.                                                                                       |
+| rllte.hub        | Provides a large number of reusable datasets (.datasets) and trained models (.models) of supported RL algorithms. Developers can also reproduce the training process via the pre-defined RL applications (.applications).                                                                                                                            |
+
+![](figures/_page_5_Figure_3.jpeg)
+
+(a) Aggregate metrics with 95% confidence intervals (CIs). IQM: Interquartile mean. OG: Optimality gap.
+
+![](figures/_page_5_Figure_5.jpeg)
+
+<span id="page-5-0"></span>(b) **Left**: Each row shows the probability of improvement, with 95% bootstrap CIs, that the algorithm X on the left outperforms algorithm Y on the right. **Right**: Sample-efficiency of agents as a function of number of frames measured via IQM human-normalized scores.
+
+Figure 5: Performance metrics computed and visualized by rllte.evaluation, and the code example can be found in Appendix D.2.
+
+out additional effort. All the environments in RLLTE are set to be vectorized to guarantee sample efficiency, and many different observation and action spaces (e.g., box, discrete, multi-binary, etc.) are supported. In particular, users can also use EnvPool (Weng et al., 2022b) to realize ultra-fast operational acceleration. See code example in Appendix D.1.
+
+Beyond providing efficient task design and training interfaces, RLLTE further investigates the model evaluation problem in RL and develops a simple evaluation toolkit. RLLTE reconstructs and improves the code of (Agarwal et al., 2021) to realize a more convenient and efficient interface. Figure 5 illustrates several metrics computed and visualized by the toolkit.
+
+Finally, rllte.hub can accelerate academic research by providing practically available benchmark data, including training data and trained models. This toolkit will save much time and computational resources for researchers, and the code example can be found in Appendix D.3. RLLTE is the first open-source RL project that aims to build a complete ecosystem. Developers can perform task design, model training, model evaluation, and model deployment within one framework. As a result, RLLTE is highly stimulative for both industry and academia.
+
+#### 3 Project Evolution
+
+As a long-term evolution project, RLLTE is expected to consistently provide high-quality and timely engineering standards and development components for RL. To that end, RLLTE sets the following tenet for updating new features:
+
+- Generality is the most important;
+- Improvements in sample efficiency or generalization ability;
+- Excellent performance on recognized benchmarks;
+- Promising tools for RL.
+
+Firstly, RLLTE only accepts general algorithms that can be applied in many distinct scenarios and tasks. For example, PPO is a general RL algorithm that can solve tasks with arbitrary action spaces, and random network distillation (RND) (Burda et al., 2019) is a general intrinsic reward module that can be combined with arbitrary RL agents. This rule can effectively control the volume of the project while ensuring its adaptability to a wide range of requirements. Moreover, generality exemplifies the potential for future enhancements (e.g., the various variants of PPO), which can also reduce the difficulty of open-source collaboration and maintain community vitality. Furthermore, the algorithm is expected to improve sample efficiency or generalization ability (e.g., better intrinsic reward shaping approaches), two long-standing and critical problems in RL. Accordingly, the algorithm must be evaluated on multiple recognized benchmarks like Atari (Bellemare et al., 2013) and Procgen games (Cobbe et al., 2020) to guarantee practical performance across tasks. In particular, RLLTE also accepts various promising tools (e.g., operational efficiency optimization, model evaluation, and deployment) to maintain a comprehensive ecosystem. In summary, RLLTE will keep evolving to adapt to changing needs and produce a positive impact on the RL community.
+
+Table 4: Architecture comparison with existing projects. **Modularized**: The project adopts a modular design with reusable components. **Parallel**: The project supports parallel learning. **Decoupling**: The project supports algorithm decoupling and module replacement. **Backend**: Which machine learning framework to use? **License**: Which open-source protocol to use? Note that the short line represents partial support.
+
+| Framework  | Modularized | Parallel | Decoupling | Backend    | License    |
+|------------|-------------|----------|------------|------------|------------|
+| Baselines  | <b>✓</b>    | Х        | -          | TensorFlow | MIT        |
+| SB3        | ✓           | ×        | -          | PyTorch    | MIT        |
+| CleanRL    | -           | ×        | X          | PyTorch    | MIT        |
+| Ray/rllib  | ✓           | ✓        | -          | TF/PyTorch | Apache-2.0 |
+| rlpyt      | ✓           | ✓        | X          | PyTorch    | MIT        |
+| Tianshou   | ✓           | ✓        | -          | PyTorch    | MIT        |
+| ElegantRL  | ✓           | ✓        | -          | PyTorch    | Apache-2.0 |
+| SpinningUp | X           | ×        | ×          | PyTorch    | MIT        |
+| ACME       | X           | ✓        | ×          | TF/JAX     | Apache-2.0 |
+| RLLTE      | ✓           | ✓        | ✓          | PyTorch    | MIT        |
+
+### 4 RELATED WORK
+
+We compare RLLTE with eleven representative open-source RL projects, namely Baselines (Dhariwal et al., 2017), SB3 (Raffin et al., 2021), CleanRL (Huang et al., 2022), Ray/rllib (Liang et al.,
+
+2018), and rlpyt (Stooke & Abbeel, 2019), Tianshou (Weng et al., 2022a), ElegantRL (Liu et al., 2021), SpinningUp (Achiam, 2018), and ACME (Hoffman et al., 2020), respectively. The following comparison is conducted from three aspects: architecture, functionality, and engineering quality. This project references some other open-source projects and adheres to their open-source protocols.
+
+Table 5: Functionality comparison with existing projects. **Custom Env.**: Support custom environments? Since Gym (Brockman et al., 2016) is no longer maintained, it is critical to make the project adapt to Gymnasium (Towers et al., 2023). **Custom Module**: Support custom modules? **Data Aug.**: Support data augmentation techniques like intrinsic reward shaping and observation augmentation? **Data Hub**: Have a data hub to store benchmark data? **Deploy.**: Support model deployment? **Eval.**: Support model evaluation? **Multi-Device**: Support hardware acceleration of different computing devices (e.g., GPU and NPU)? Note that the short line represents partial support.
+
+| Framework  | Number of Algo. | Custom<br>Env.       | Custom<br>Module | Data<br>Aug. |   | Deploy. | Eval. | Multi-<br>Device |
+|------------|-----------------|----------------------|------------------|--------------|---|---------|-------|------------------|
+| Baselines  | 9               | <b>√</b> (gym)       | -                | X            | - | Х       | Х     | X                |
+| SB3        | 7               | <b>√</b> (gymnasium) | -                | -            | ✓ | X       | X     | X                |
+| CleanRL    | 9               | X                    | ✓                | -            | ✓ | X       | X     | X                |
+| Ray/rllib  | 16              | <b>√</b> (gym)       | -                | -            | - | X       | X     | X                |
+| rlpyt      | 11              | X                    | -                | X            | - | X       | X     | X                |
+| Tianshou   | 20              | <b>√</b> (gymnasium) | X                | -            | - | X       | X     | X                |
+| ElegantRL  | 9               | <b>√</b> (gym)       | X                | X            | - | X       | X     | X                |
+| SpinningUp | 6               | <b>√</b> (gym)       | X                | X            | - | X       | X     | X                |
+| ACME       | 14              | <b>√</b> (dm_env)    | X                | X            | - | X       | X     | X                |
+| RLLTE      | 13 7            | <b>✓</b> (gymnasium) | ✓                | ✓            | ✓ | ✓       | ✓     | ✓                |
+
+Table 6: Engineering quality comparison with existing projects. Note that the short line represents unknown.
+
+| Framework  | Documentation | <b>Code Coverage</b> | <b>Type Hints</b> | Last Update | Used by |
+|------------|---------------|----------------------|-------------------|-------------|---------|
+| Baselines  | ×             | Х                    | Х                 | 01/2020     | 508     |
+| SB3        | ✓             | 96%                  | ✓                 | 09/2023     | 3.3k    |
+| CleanRL    | ✓             | -                    | X                 | 09/2023     | 27      |
+| Ray/rllib  | ✓             | -                    | ×                 | 09/2023     | -       |
+| rlpyt      | ✓             | 15%                  | ×                 | 09/2020     | -       |
+| Tianshou   | ✓             | 91%                  | ✓                 | 09/2023     | 169     |
+| ElegantRL  | ✓             | -                    | ✓                 | 07/2023     | 256     |
+| SpinningUp | ✓             | X                    | ×                 | 02/2020     | -       |
+| ACME       | ✓             | -                    | ×                 | 07/2023     | 149     |
+| RLLTE      | ✓             | 97%                  | ✓                 | 09/2023     | 2 /     |
+
+# 5 DISCUSSION
+
+In this paper, we introduced a novel RL framework entitled RLLTE, which is a long-term evolution, extremely modular, and open-source project for advancing RL research and applications. With a rich and comprehensive ecosystem, RLLTE enables developers to accomplish task design, model training, evaluation, and deployment within one framework seamlessly, which is highly stimulative for both academia and industry. Moreover, RLLTE is an ultra-open framework where developers can freely use and try many built-in or custom modules, contributing to the research of decoupling and interpretability of RL. As a long-term evolution project, RLLTE will keep tracking the latest research progress and provide high-quality implementations to inspire more subsequent research.
+
+In particular, there are some remaining issues that we intend to work on in the future. Firstly, RLLTE plans to add more algorithm prototypes to meet the task requirements of different scenarios, including multi-agent RL, inverse RL, imitation learning, and offline RL. Secondly, RLLTE will enhance
+
+the functionality of the pre-training module, which includes more prosperous training methods and more efficient training processes, as well as providing downloadable model parameters. Thirdly, RLLTE will further explore the combination of RL and LLM, including using LLM to control the construction of RL applications and improving the performance of existing algorithms (e.g., reward function design and data generation). Finally, RLLTE will optimize the operational efficiency of modules at the hardware level to reduce the computational power threshold, promoting the goal of RL for everyone.
+
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+
+# <span id="page-12-0"></span>A FUNCTION LIST
+
+### A.1 XPLOIT: MODULES THAT FOCUS ON EXPLOITATION IN RL.
+
+Table 7: **rllte.xploit.policy**: Policies for interaction and learning.
+
+| Module                           | Type        | Remark                                                    |
+|----------------------------------|-------------|-----------------------------------------------------------|
+| OnPolicySharedActorCritic        | On-policy   | Actor-Critic networks<br>with a shared encoder.           |
+| OnPolicyDecoupledActorCritic     | On-policy   | Actor-Critic networks<br>with two separate encoders.      |
+| OffPolicyDoubleQNetwork          | Off-policy  | Double Q-network.                                         |
+| OffPolicyDetActorDoubleCritic    | Off-policy  | Deterministic actor network<br>and double-critic network. |
+| OffPolicyDoubleActorDoubleCritic | Off-policy  | Double-actor network<br>and double-critic network.        |
+| OffPolicyStochActorDoubleCritic  | Off-policy  | Stochastic actor network<br>and double-critic network.    |
+| DistributedActorLearner          | Distributed | Memory-shared actor and<br>learner networks.              |
+
+Table 8: **rllte.xploit.encoder**: Neural nework-based encoders for processing observations. Naming Rule: Surname of the first author + Backbone + Encoder. Target Task: The testing tasks reported in their paper or potential tasks.
+
+| Module                                          | Input  | Target Task             |
+|-------------------------------------------------|--------|-------------------------|
+| EspeholtResidualEncoder (Espeholt et al., 2018) | Images | Atari or Procgen games  |
+| MnihCnnEncoder (Mnih et al., 2013)              | Images | Atari games             |
+| TassaCnnEncoder (Tassa et al., 2018)            | Images | DMC Suite: pixel        |
+| PathakCnnEncoder (Pathak et al., 2017)          | Images | Atari or MiniGrid games |
+| IdentityEncoder                                 | States | DMC Suite: state        |
+| VanillaMlpEncoder                               | States | DMC Suite: state        |
+| RaffinCombinedEncoder (Raffin et al., 2021)     | Dict   | Highway                 |
+
+Table 9: **rllte.xploit.storage**: Experience storage and sampling.
+
+| Module                                         | Type        |
+|------------------------------------------------|-------------|
+| VanillaRolloutStorage                          | On-policy   |
+| DictRolloutStorage                             | On-policy   |
+| VanillaReplayStorage                           | Off-policy  |
+| DictReplayStorage                              | Off-policy  |
+| NStepReplayStorage (Sutton & Barto, 2018)      | Off-policy  |
+| PrioritizedReplayStorage (Schaul et al., 2016) | Off-policy  |
+| HerReplayStorage (Andrychowicz et al., 2017)   | Off-policy  |
+| VanillaDistributedStorage                      | Distributed |
+
+### A.2 XPLORE: MODULES THAT FOCUS ON EXPLORATION IN RL.
+
+Table 10: **rllte.xploit.augmentation**: PyTorch.nn-like modules for observation augmentation.
+
+| Module                                       | Input  |
+|----------------------------------------------|--------|
+| GaussianNoise (Laskin et al., 2020)          | States |
+| RandomAmplitudeScaling (Laskin et al., 2020) | States |
+| GrayScale (Laskin et al., 2020)              | Images |
+| RandomColorJitter (Laskin et al., 2020)      | Images |
+| RandomConvolution (Laskin et al., 2020)      | Images |
+| RandomCrop (Laskin et al., 2020)             | Images |
+| RandomCutout (Laskin et al., 2020)           | Images |
+| RandomCutoutColor (Laskin et al., 2020)      | Images |
+| RandomFlip (Laskin et al., 2020)             | Images |
+| RandomRotate (Laskin et al., 2020)           | Images |
+| RandomShift (Yarats et al., 2021)            | Images |
+| RandomTranslate (Laskin et al., 2020)        | Images |
+
+Table 11: **rllte.xploit.distribution**: Distributions for sampling actions. In RLLTE, the action noise is implemented via a distribution manner to realize unification.
+
+| Module                 | Type         |
+|------------------------|--------------|
+| NormalNoise            | Noise        |
+| OrnsteinUhlenbeckNoise | Noise        |
+| TruncatedNormalNoise   | Noise        |
+| Bernoulli              | Distribution |
+| Categorical            | Distribution |
+| MultiCategorical       | Distribution |
+| DiagonalGaussian       | Distribution |
+| SquashedNormal         | Distribution |
+
+Table 12: **rllte.xploit.reward**: Intrinsic reward modules for enhancing exploration.
+
+| Type                     | Modules                                                                                                  |
+|--------------------------|----------------------------------------------------------------------------------------------------------|
+| Count-based              | PseudoCounts (Badia et al., 2020), RND (Burda et al., 2019)                                              |
+| Curiosity-driven         | ICM (Pathak et al., 2017) (Pathak et al., 2017),<br>GIRM (Yu et al., 2020), RIDE (Raileanu et al., 2020) |
+| Memory-based             | NGU (Badia et al., 2020)                                                                                 |
+| Information theory-based | RE3 (Seo et al., 2021), RISE (Yuan et al., 2022b),<br>REVD (Yuan et al., 2022a)                          |
+
+### <span id="page-14-0"></span>B IMPLEMENTED RL ALGORITHMS
+
+Table 13: Implemented RL algorithms using RLLTE modules. **Dis., M.B., and M.D.**: Discrete, multi-binary, and multi-discrete action space. **M.P.**: Multi processing. **I.R.**: Support intrinsic reward shaping. **O.A.**: Support observation augmentation.
+
+| Type        | Algo.        | Box | Dis. | M.B. | M.D. | M.P. | NPU | I.R. | O.A. |
+|-------------|--------------|-----|------|------|------|------|-----|------|------|
+| On-Policy   | A2C          | 1   | 1    | 1    | 1    | 1    | 1   | 1    | ×    |
+| On-Policy   | PPO          | ✓   | 1    | 1    | 1    | ✓    | ✓   | ✓    | X    |
+| On-Policy   | DrAC         | 1   | 1    | ✓    | ✓    | ✓    | ✓   | ✓    | /    |
+| On-Policy   | DAAC         | 1   | 1    | ✓    | ✓    | ✓    | ✓   | ✓    | X    |
+| On-Policy   | DrDAAC       | ✓   | 1    | 1    | 1    | ✓    | ✓   | ✓    | ✓    |
+| On-Policy   | PPG          | ✓   | ✓    | 1    | X    | ✓    | 1   | 1    | ✓    |
+| Off-Policy  | DQN          | ✓   | X    | X    | X    | ✓    | ✓   | ✓    | X    |
+| Off-Policy  | DDPG         | ✓   | X    | X    | X    | ✓    | ✓   | ✓    | X    |
+| Off-Policy  | TD3          | ✓   | X    | X    | X    | ✓    | 1   | 1    | X    |
+| Off-Policy  | SAC          | ✓   | X    | X    | X    | ✓    | 1   | 1    | X    |
+| Off-Policy  | SAC-Discrete | X   | ✓    | X    | X    | ✓    | 1   | 1    | X    |
+| Off-Policy  | DrQ-v2       | ✓   | X    | X    | X    | X    | ✓   | ✓    | ✓    |
+| Distributed | IMPALA       | ✓   | ✓    | X    | X    | ✓    | ×   | X    | X    |
+
+Full names and references of all algorithms:
+
+- A2C: Advantage Actor-Critic (Mnih et al., 2016).
+- **PPO**: Proximal Policy Optimization (Schulman et al., 2017).
+- **DrAC**: Data-Regularized Actor-Critic (Raileanu et al., 2021).
+- DAAC: Decoupled Advantage Actor-Critic (Raileanu & Fergus, 2021).
+- DrDAAC: The combination of DrAC and DAAC.
+- **PPG**: Phasic Policy Gradient (Cobbe et al., 2021).
+- **DQN**: Deep Q-Network (Mnih et al., 2013).
+- **DDPG**: Deep Deterministic Policy Gradient (Lillicrap et al., 2016).
+- TD3: Twin Delayed DDPG (Fujimoto et al., 2018).
+- SAC: Soft Actor-Critic (Haarnoja et al., 2018).
+- SAC-Discrete: Soft Actor-Critic (Discrete) (Christodoulou, 2019).
+- DrQ-v2: Data-Regularized Q-v2 (Yarats et al., 2021).
+- IMPALA: Importance Weighted Actor-Learner Architecture (Espeholt et al., 2018).
+
+# <span id="page-15-0"></span>C CODE EXAMPLES OF THE APPLICATION LAYER
+
+### <span id="page-15-1"></span>C.1 FAST ALGORITHM CONSTRUCTION
+
+```
+from rllte.common.prototype import OnPolicyAgent
+from rllte.xploit.encoder import MnihCnnEncoder
+from rllte.xploit.policy import OnPolicySharedActorCritic
+from rllte.xploit.storage import VanillaRolloutStorage
+from rllte.xplore.distribution import Categorical
+from torch import nn
+import torch as th
+class A2C(OnPolicyAgent):
+   def __init__(self, env, tag, seed, device, num_steps) -> None:
+       super().__init__(env=env, tag=tag, seed=seed, device=device, num_steps=num_steps)
+       encoder = MnihCnnEncoder(observation_space=env.observation_space, feature_dim=512)
+       policy = OnPolicySharedActorCritic(observation_space=env.observation_space,
+                                         action_space=env.action_space,
+                                         feature_dim=512,
+                                         opt_class=th.optim.Adam,
+                                         opt_kwargs=dict(lr=2.5e-4, eps=1e-5),
+                                         init_fn="xavier_uniform"
+                                         )
+       storage = VanillaRolloutStorage(observation_space=env.observation_space,
+                                      action_space=env.action_space,
+                                      storage_size=self.num_steps,
+                                      num_envs=self.num_envs,
+                                      batch_size=256
+       dist = Categorical()
+       self.set(encoder=encoder, policy=policy, storage=storage, distribution=dist)
+   def update(self):
+       for _ in range(4):
+           for batch in self.storage.sample():
+               new_values, new_log_probs, entropy = \
+                   self.policy.evaluate_actions(obs=batch.observations, actions=batch.actions)
+               policy_loss = - (batch.adv_targ * new_log_probs).mean()
+               value_loss = 0.5 * (new_values.flatten() - batch.returns).pow(2).mean()
+               self.policy.optimizers['opt'].zero_grad(set_to_none=True)
+               (value_loss * 0.5 + policy_loss - entropy * 0.01).backward()
+               nn.utils.clip_grad_norm_(self.policy.parameters(), 0.5)
+               self.policy.optimizers['opt'].step()
+```
+
+Figure 6: Implement A2C algorithm with dozens of lines of code.
+
+### <span id="page-16-0"></span>C.2 MODULE REPLACEMENT
+
+### C.2.1 USE BUILT-IN MODULES
+
+```
+from rllte.agent import PPO
+from rllte.env import make_atari_env
+if __name__ == "__main__":
+    env = make_atari_env(device=device)
+    eval_env = make_atari_env(device=device)
+    # create agent
+    agent = PPO(env=env, 
+                eval_env=eval_env, 
+                device=device,
+                tag="ppo_atari")
+    agent.train(num_train_steps=5000)
+```
+
+```
+from rllte.agent import PPO
+from rllte.env import make_atari_env
+from rllte.xploit.encoder import EspeholtResidualEncoder
+if __name__ == "__main__":
+    env = make_atari_env(device=device)
+    eval_env = make_atari_env(device=device)
+    feature_dim = 512
+    agent = PPO(env=env, 
+                eval_env=eval_env, 
+                device=device,
+                tag="ppo_atari",
+                feature_dim=feature_dim)
+    encoder = EspeholtResidualEncoder(
+        observation_space=env.observation_space,
+        feature_dim=feature_dim)
+    agent.set(encoder=encoder)
+    agent.train(num_train_steps=5000)
+```
+
+Figure 7: Left: Train an PPO agent on the Atari games. Right: Replace the default encoder with **EspeholtResidualEncoder**.
+
+### C.2.2 USE CUSTOM MODULES
+
+```
+from rllte.agent import PPO
+from rllte.env import make_atari_env
+from rllte.common.prototype import BaseEncoder
+from gymnasium.spaces import Space
+from torch import nn
+import torch as th
+class CustomEncoder(BaseEncoder):
+   """Custom encoder.
+   Args:
+       observation_space (Space): The observation space of environment.
+       feature_dim (int): Number of features extracted.
+   Returns:
+       The new encoder instance.
+   def __init__(self, observation_space: Space, feature_dim: int = 0) -> None:
+       super().__init__(observation_space, feature_dim)
+       obs_shape = observation_space.shape
+       assert len(obs_shape) == 3
+       self.trunk = nn.Sequential(
+           nn.Conv2d(obs_shape[0], 32, 3, stride=2), nn.ReLU(),
+           nn.Conv2d(32, 32, 3, stride=2), nn.ReLU(),
+           nn.Flatten(),
+       )
+       with th.no_grad():
+           sample = th.ones(size=tuple(obs_shape)).float()
+           n_flatten = self.trunk(sample.unsqueeze(0)).shape[1]
+       self.trunk.extend([nn.Linear(n_flatten, feature_dim), nn.ReLU()])
+   def forward(self, obs: th.Tensor) -> th.Tensor:
+       h = self.trunk(obs / 255.0)
+       return h.view(h.size()[0], -1)
+```
+
+Figure 8: Define a custom CNN-based encoder with RLLTE. This encoder can automatically compute the dimension of the extracted features of observations.
+
+# <span id="page-17-0"></span>D CODE EXAMPLES OF THE TOOL LAYER
+
+### <span id="page-17-1"></span>D.1 ENVIRONMENT DESIGN
+
+```
+from rllte.agent import DrQv2
+from rllte.env.utils import make_rllte_env
+import gymnasium as gym
+import numpy as np
+class CustomEnv(gym.Env):
+   def __init__(self, total_length) -> None:
+       super().__init__()
+       self.observation_space = gym.spaces.Box(shape=(9, 84, 84),
+           high=255.0, low=0., dtype=np.uint8)
+       self.action_space = gym.spaces.Box(shape=(7,),
+           high=1., low=-1., dtype=np.float32)
+       self.total_length = total_length
+       self.count = 0
+   def step(self, action):
+       obs = self.observation_space.sample()
+       reward = np.random.rand()
+       if self.count < self.total_length:
+           terminated = truncated = False
+           terminated = truncated = True
+       info = {"discount": 0.99}
+       self.count += 1
+       return obs, reward, terminated, truncated, info
+   def reset(self, seed=None, options=None):
+       self.count = 0
+       return self.observation_space.sample(), {"discount": 0.99}
+if __name__ == "__main__":
+   device = "cuda:0"
+   env = make_rllte_env(env_id=CustomEnv, 
+                       device=device, 
+                       env_kwargs={'total_length': 499} # set env arguments
+                       )
+   eval_env = make_rllte_env(env_id=CustomEnv, 
+                           device=device, 
+                           env_kwargs={'total_length': 499} # set env arguments
+                           )
+   agent = DrQv2(env=env, 
+               eval_env=eval_env, 
+               device=device,
+               tag="drqv2_dmc_pixel")
+   agent.train(num_train_steps=5000)
+```
+
+Figure 9: Define a custom environment and perform training using DrQ-v2 agent.
+
+### <span id="page-18-0"></span>D.2 MODEL EVALUATION
+
+Firstly, Suppose we want to evaluate algorithm performance on the Procgen [\(Cobbe et al., 2020\)](#page-9-7) benchmark. First, download the data from **rllte.hub**:
+
+```
+from rllte.evaluation import Performance, Comparison, min_max_normalize
+from rllte.hub.datasets import Procgen, Atari
+import numpy as np
+procgen = Procgen()
+procgen_scores = procgen.load_scores()
+print(procgen_scores.keys())
+# get ppo-normalized scores
+ppo_norm_scores = dict()
+MIN_SCORES = np.zeros_like(procgen_scores['ppo'])
+MAX_SCORES = np.mean(procgen_scores['ppo'], axis=0)
+for algo in procgen_scores.keys():
+   ppo_norm_scores[algo] = min_max_normalize(procgen_scores[algo],
+                                            min_scores=MIN_SCORES,
+                                            max_scores=MAX_SCORES)
+```
+
+Figure 10: Download benchmark data from **rllte.hub**.
+
+```
+perf = Performance(scores=ppo_norm_scores['ppo'], 
+                  get_ci=True # get confidence intervals
+                  )
+print(perf.aggregate_mean())
+print(perf.aggregate_median())
+# computes optimality gap across all runs and tasks
+print(perf.aggregate_og())
+print(perf.aggregate_iqm())
+```
+
+Figure 11: Performance evaluation of single algorithm.
+
+```
+comp = Comparison(scores_x=ppo_norm_scores['ppg'],
+                 scores_y=ppo_norm_scores['ppo'],
+                 get_ci=True)
+print(comp.compute_poi())
+```
+
+Figure 12: Performance comparison of multiple algorithms.
+
+```
+from rllte.evaluation import (plot_interval_estimates,
+                            plot_probability_improvement,
+                            plot_sample_efficiency_curve,
+                            plot_performance_profile)
+aggregate_performance_dict = {
+   "MEAN": {},
+   "MEDIAN": {},
+   "IQM": {},
+   "OG": {}
+}
+for algo in ppo_norm_scores.keys():
+   perf = Performance(scores=ppo_norm_scores[algo], get_ci=True)
+   aggregate_performance_dict['MEAN'][algo] = perf.aggregate_mean()
+   aggregate_performance_dict['MEDIAN'][algo] = perf.aggregate_median()
+   aggregate_performance_dict['IQM'][algo] = perf.aggregate_iqm()
+   aggregate_performance_dict['OG'][algo] = perf.aggregate_og()
+fig, axes = plot_interval_estimates(aggregate_performance_dict,
+                                  metric_names=['MEAN', 'MEDIAN', 'IQM', 'OG'],
+                                  algorithms=['ppg', 'mixreg', 'ppo', 'idaac', 'plr', 'ucb-drac'],
+                                  xlabel="PPO-Normalized Score")
+fig.savefig('./plot_interval_estimates1.png', format='png', bbox_inches='tight')
+pairs = [['idaac', 'ppg'], ['idaac', 'ucb-drac'], ['idaac', 'ppo'],
+   ['ppg', 'ppo'], ['ucb-drac', 'plr'], 
+   ['plr', 'mixreg'], ['ucb-drac', 'mixreg'], ['mixreg', 'ppo']]
+probability_of_improvement_dict = {}
+for pair in pairs:
+   comp = Comparison(scores_x=ppo_norm_scores[pair[0]], 
+                     scores_y=ppo_norm_scores[pair[1]],
+                     get_ci=True)
+   probability_of_improvement_dict['_'.join(pair)] = comp.compute_poi()
+fig, ax = plot_probability_improvement(poi_dict=probability_of_improvement_dict)
+fig.savefig('./plot_probability_improvement.png', format='png', bbox_inches='tight')
+```
+
+Figure 13: Two examples of the visualization tool of **rllte.evaluation**.
+
+### <span id="page-20-0"></span>D.3 RLLTE HUB
+
+```
+from rllte.hub.datasets import Procgen
+procgen = Procgen()
+# For each algorithm, this will return a `NdArray` of size (10 x 16) 
+procgen_scores = procgen.load_scores()
+print(procgen_scores['ppo'].shape)
+# this will return the learning curves by a Python `Dict` like:
+# }
+curves = procgen.load_curves()
+print(curves['ppo']['train']['bigfish'].shape)
+print(curves['ppo']['eval']['bigfish'].shape)
+```
+
+Figure 14: **rllte.hub.datasets** provides test scores and learning cures of various RL algorithms on different benchmarks.
+
+```
+from rllte.hub.models import Procgen
+from rllte.env import make_procgen_env
+import torch as th
+import numpy as np
+if __name__ == "__main__":
+   device = "cuda:0"
+   env_id = "starpilot"
+   seed = 1
+   procgen = Procgen()
+   agent = procgen.load_models(agent="ppo",
+                               env_id=env_id,
+                               seed=seed,
+                               device=device)
+   # create env
+   env = make_procgen_env(env_id=env_id, device=device, num_envs=1, seed=seed)
+   obs, infos = env.reset(seed=seed)
+   episode_rewards, episode_steps = list(), list()
+   while len(episode_rewards) < 10:
+       action = th.softmax(agent(obs), dim=1).argmax(dim=1)
+       obs, rewards, terminateds, truncateds, infos = env.step(action)
+       if "episode" in infos:
+           indices = np.nonzero(infos["episode"]["l"])
+           episode_rewards.extend(infos["episode"]["r"][indices].tolist())
+           episode_steps.extend(infos["episode"]["l"][indices].tolist())
+   print(f"mean episode reward: {np.mean(episode_rewards)}")
+   print(f"mean episode length: {np.mean(episode_steps)}")
+# mean episode reward: 30.0
+```
+
+Figure 15: **rllte.hub.models** provides trained models of various RL algorithms on different benchmarks.

papers/532tcx7IHF/review.json

@@ -0,0 +1,64 @@
+{
+  "id": "532tcx7IHF",
+  "title": "RLLTE: Long-Term Evolution Project of Reinforcement Learning",
+  "decision": "Reject",
+  "reviews": [
+    {
+      "id": "j7NIQLu6Mg",
+      "rating": 6,
+      "content": {
+        "summary": "The paper presents RLLTE, a long-term evolution, extremely modular, and open-source framework for reinforcement learning (RL) research and application. RLLTE decouples RL algorithms from the exploitation-exploration perspective and provides a large number of components to accelerate algorithm development and evolution. The framework serves as a toolkit for developing algorithms and is the first RL framework to build a complete ecosystem, including model training, evaluation, deployment, benchmark hub, and large language model (LLM)-empowered copilot. RLLTE is expected to set standards for RL engineering practice and be highly stimulative for industry and academia.",
+        "soundness": "3 good",
+        "presentation": "3 good",
+        "contribution": "3 good",
+        "strengths": "* Modular and customizable design, allowing for easy algorithm development and improvement.\n* Long-term evolution plan, ensuring the framework stays up-to-date with the latest research.\n* Comprehensive ecosystem, covering various aspects of RL research and application.\n* Built-in support for data augmentation techniques, improving sample efficiency and generalization ability.\n* Multi-hardware support, accommodating diverse computing hardware configurations.",
+        "weaknesses": "* The paper does not provide a thorough comparison of RLLTE with other existing RL frameworks.\n* The proposed LLM-empowered copilot is in its early stages and may not be as effective as expected.\n* The paper does not discuss potential limitations or challenges in implementing the proposed framework.",
+        "questions": "* How does RLLTE compare to other existing RL frameworks in terms of performance, modularity, and ease of use?\n* What are the specific advantages of using RLLTE over other RL frameworks for different types of RL problems?\n* How does the proposed LLM-empowered copilot improve the overall RL research and application process?\n* Are there any potential limitations or challenges in implementing the proposed RLLTE framework that the authors have not discussed?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "6: marginally above the acceptance threshold",
+        "confidence": "3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.",
+        "code_of_conduct": "Yes"
+      }
+    },
+    {
+      "id": "cNvAFpoXTi",
+      "rating": 5,
+      "content": {
+        "summary": "The authors have created a modular, open-source framework for reinforcement learning. It includes a number of different modular layers each of which is highly flexible in how they are combined leading to easy to write code for efficient, easily-parallelisable model training and evaluation.",
+        "soundness": "3 good",
+        "presentation": "2 fair",
+        "contribution": "2 fair",
+        "strengths": "The framework is clearly presented, and there are good comparisons to other frameworks trying to do achieve similar goals. The evaluation modules in particular are well-thought out  and follow standards which are being pursued by the community.",
+        "weaknesses": "While there are comparisons to other frameworks, it is not clear that all of the comparisons are up-to-date and this is a major issue. In particular SB3 does support parallel learning and hardware acceleration and while it doesn't natively support model deployment, it is explained in the documentation how to export models. With a user base of over 3k users, it clearly has a lot of momentum within the community, and so the authors would have to make a strong case that their system is genuinely superior to SB3. In addition, RL-Baselines3-zoo provides a training framework for SB3.\n\nIn addition to this, much of the language used within the paper feels like it is trying to oversell the framework. While I am sure that this is not the authors intensions, phrases such as \"RLLTE has been thoughtfully designed\", \"Beyond delivering top-notch algorithm implementations\", \"RLLTE is the first RL framework to build a complete and luxuriant ecosystem\". Such ideas should come through in the technical details, and not have to be sold using overly-confident language.",
+        "questions": "It would be useful to see a side-by-side comparison between RLLTE and SB3 to see precisely why it is superior. If this can be shown unequivocally, then I believe that there is a lot more merit.",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "5: marginally below the acceptance threshold",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes"
+      }
+    },
+    {
+      "id": "mAEx7upvhj",
+      "rating": 3,
+      "content": {
+        "summary": "The work introduces RLLTE, a framework for RL research. It provides a modular approach to designing RL agents and additionally provides modules for evaluation, comparison and an interface to Huggingface to share benchmarking results.",
+        "soundness": "2 fair",
+        "presentation": "2 fair",
+        "contribution": "1 poor",
+        "strengths": "* The idea of a modular RL framework is neat.\n* The framework has implementations for many well-known algorithms.\n* Using a Datahub is a great idea (as also shown by SB3 and CleanRL)",
+        "weaknesses": "* The work does not present novel ideas\n* The paper does not show any experiments showing the advantage of a modular framework. Neither are any experiments included that would show why one should prefer RLLTE over something like SB3. \n* I don’t see how “RLLTE decouples RL algorithms from the exploitation-exploration perspective”. This claim seems wholly false.\n* The work states multiple times that RLLTE is open-source or even ultra-open, but no link to code is given nor is a supplementary archive uploaded.\n* The introduced modularity seems to simply introduce many more hyperparameters, thus offloading a lot of critical choices to a potential user. The work fails to discuss how this affects users or how hyperparameters should be treated in RLLTE.",
+        "questions": "* Why is there no code available?\n* How much better/worse is hyperparameter tuning with RLLTE?",
+        "flag_for_ethics_review": [
+          "No ethics review needed."
+        ],
+        "rating": "3: reject, not good enough",
+        "confidence": "4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.",
+        "code_of_conduct": "Yes"
+      }
+    }
+  ]
+}

papers/5xKixQzhDE/metadata.json

@@ -0,0 +1,9 @@
+{
+  "id": "5xKixQzhDE",
+  "title": "Calibrated Dataset Condensation for Faster Hyperparameter Search",
+  "venue": "ICLR",
+  "venue_year": 2024,
+  "decision": "Reject",
+  "date": "2023-09-21",
+  "openreview_pdf_url": "https://openreview.net/pdf?id=5xKixQzhDE"
+}

papers/5xKixQzhDE/paper.md

@@ -0,0 +1,332 @@
+# <span id="page-0-0"></span>CALIBRATED DATASET CONDENSATION FOR FASTER HYPERPARAMETER SEARCH
+
+Anonymous authors Paper under double-blind review
+
+## ABSTRACT
+
+Dataset condensation can be used to reduce the computational cost of training multiple models on a large dataset by condensing the training dataset into a small synthetic set. State-of-the-art approaches rely on matching model gradients between the real and synthetic data. However, there is no theoretical guarantee on the generalizability of the condensed data: data condensation often generalizes poorly *across hyperparameters/architectures* in practice. In this paper, we consider a different condensation objective specifically geared toward *hyperparameter search*. We aim to generate a synthetic validation dataset so that the validation-performance rankings of models, with different hyperparameters, on the condensed and original datasets are comparable. We propose a novel *hyperparameter-calibrated dataset condensation* (HCDC) algorithm, which obtains the synthetic validation dataset by matching the *hyperparameter gradients* computed via implicit differentiation and efficient inverse Hessian approximation. Experiments demonstrate that the proposed framework effectively maintains the validation-performance rankings of models and speeds up hyperparameter/architecture search for tasks on both images and graphs.
+
+## 1 INTRODUCTION
+
+Deep learning has achieved great success in various fields, such as computer vision and graph related tasks. However, the computational cost of training state-of-the-art neural networks is rapidly increasing due to growing model and dataset sizes. Moreover, designing deep learning models usually requires training numerous models on the same data to obtain the optimal hyperparameters and architecture [\(Elsken et al.,](#page-10-0) [2019\)](#page-10-0), posing significant computational challenges. Thus, reducing the computational cost of repeatedly training on the same dataset is crucial. We address this problem from a data-efficiency perspective and consider the following question: how can one reduce the training data size for faster *hyperparameter search/optimization* with minimal performance loss?
+
+Recently, *dataset distillation/condensation* [\(Wang et al.,](#page-12-0) [2018\)](#page-12-0) is proposed as an effective way to reduce sample size. This approach involves producing a small *synthetic* dataset to replace the original larger one, so that the test performance of the model trained on the synthetic set is comparable to that trained on the original. Despite the state-of-the-art performance achieved by recent dataset condensation methods when used to train a single pre-specified model, it remains challenging to utilize such methods effectively for hyperparameter search. Current dataset condensation methods perform poorly when applied to neural architecture search (NAS) [\(Elsken et al.,](#page-10-0) [2019\)](#page-10-0) and when used to train deep networks beyond the pre-specified architecture [\(Cui et al.,](#page-9-0) [2022\)](#page-9-0). Moreover, there is little or even a negative correlation between the performance of models trained on the synthetic vs. the full dataset, across architectures: often, one architecture achieves higher validation accuracy when trained on the original data relative to a second architecture, but obtains lower validation accuracy than the second when trained on the synthetic data. Since architecture performance ranking is not preserved when the original data is condensed, current data condensation methods are inadequate for NAS. This issue stems from the fact that existing condensation methods are designed on top of a single pre-specified model, and thus the condensed data may overfit this model.
+
+We ask: *is it possible to preserve the architecture/hyperparameter search outcome when the original data is replaced by the condensed data?*
+
+<span id="page-1-1"></span><span id="page-1-0"></span>![](figures/_page_1_Figure_1.jpeg)
+
+Figure 1: Hyperparameter Calibrated Dataset Condensation (HCDC) aims to find a small validation dataset such that the validation-performance rankings of the models with different hyperparameters are comparable to the large original dataset's. Our method realizes this goal (Eq. (HCD)) by learning the synthetic validation set to match the hypergradients w.r.t the hyperparameters (Eq. (HCDC) in the "Loss" box). Our contribution is depicted within the big black dashed box: the algorithm flow is indicated through the red dashed arrows. The synthetic training set is predetermined by any standard dataset condensation (SDC) methods (e.g., Eq. (SDC)). The synthetic training and validation datasets obtained can later be used for hyperparameter search using only a fraction of the original computational load. A more detailed diagram is depicted in Fig. 5 in Appendix A.
+
+To answer this question, we reformulate the dataset condensation problem using a hyperparameter optimization (HPO) framework (Feurer & Hutter, 2019), with the goal of preserving architecture/hyperparameter search outcomes over *multiple* architectures/hyperparameters, just as standard dataset condensation preserves generalization performance results for a *single pre-specified* architecture. This is illustrated in Fig. 1's "Goal" box. However, solving the resulting nested optimization problem is tremendously difficult. Therefore, we consider an alternative objective and show that architecture performance ranking preservation is equivalent to aligning the *hyperparameter gradients* (or *hypergradients* for short), of this objective, in the context of dataset condensation. This is illustrated as the "Loss" box in Fig. 1. Thus, we propose *hyperparameter calibrated dataset condensation* (HCDC), a novel condensation method that preserves hyperparameter performance rankings by aligning the hypergradients computed using the condensed data to those computed using the original dataset, see Fig. 1.
+
+Our implementation of HCDC is efficient and scales linearly with respect to the size of hyperparameter search space. Moreover, hypergradients are efficiently computed with constant memory overhead, using the implicit function theorem (IFT) and the Neumann series approximation of an inverse Hessian (Lorraine et al., 2020). We also specifically consider how to apply HCDC to the practical architecture search spaces for image and graph datasets.
+
+Experiments demonstrate that our proposed HCDC algorithm drastically increases the correlation between the architecture rankings of models trained on the condensed dataset and those trained on the original dataset, for both image and graph data. Additionally, the test performance of the highest ranked architecture determined by the condensed dataset is comparable to that of the true optimal architecture determined by the original dataset. Thus, HCDC can enable faster hyperparameter search and obtain high performance accuracy by choosing the highest ranked hyperparameters, while the other condensation and coreset methods cannot. We also demonstrate that condensed datasets obtained with HCDC are compatible with off-the-shelf architecture search algorithms with or without parameter sharing.
+
+We summarize our contributions as follows: (1) We study the data condensation problem for hyperparameter search and show that performance ranking preservation is equivalent to hypergradient alignment in this context. (2) We propose HCDC, which synthesizes condensed data by aligning the hypergradients of the objectives associated with the condensed and original datasets for faster hyperparameter search. (3) We present experiments, for which HCDC drastically reduces the search time and complexity of off-the-shelf NAS algorithms, for both image and graph data, while preserving the search outcome with high accuracy.
+
+#### 2 STANDARD DATASET CONDENSATION
+
+Consider a classification problem where the original dataset  $\mathcal{T}^{\text{train}} = \{(x_i, y_i)\}_{i=1}^n$  consists of n (input, label) pairs sampled from the original data distribution  $P_{\mathcal{D}}$ . To simplify notation, we replace  $\mathcal{T}^{\text{train}}$  with  $\mathcal{T}$  when the context is clear. The classification task goal is to train a function  $f_{\theta}$  (e.g., a deep neural network), with parameter  $\theta$ , to correctly predict labels y from inputs x. Obtaining  $f_{\theta}$ 
+
+<span id="page-2-1"></span>involves optimizing an empirical loss objective determined by  $\mathcal{T}^{\text{train}}$ :
+
+$$\theta^{\mathcal{T}} = \arg\min_{\theta} \mathcal{L}_{\mathcal{T}}^{\text{train}}(\theta, \lambda), \text{ where } \mathcal{L}_{\mathcal{T}}^{\text{train}}(\theta, \lambda) \coloneqq \frac{1}{|\mathcal{T}^{\text{train}}|} \sum_{(x, y) \in \mathcal{T}^{\text{train}}} l(f_{\theta}(x), y, \lambda),$$
+ (1)
+
+where  $\lambda$  denotes the model hyperparameter (e.g., the neural network architecture that characterizes  $f_{\theta}$ ), and  $l(\cdot, \cdot, \cdot)$  is a task-specific loss function that depends on  $\lambda$ .
+
+Dataset condensation involves generating a small set of  $c \ll n$  synthesized samples  $\mathcal{S} = \{x_i', y_i'\}_{i=1}^c$ , with which to replace the original training dataset  $\mathcal{T}$ . Using the condensed dataset  $\mathcal{S}$ , one can obtain  $f_{\theta}$  with parameter  $\theta = \theta^{\mathcal{S}} = \arg\min_{\theta} \mathcal{L}_{\mathcal{S}}^{\mathrm{train}}(\theta, \lambda)$ , where  $\mathcal{L}_{\mathcal{S}}^{\mathrm{train}} = \frac{1}{|\mathcal{S}|} \sum_{(x,y) \in \mathcal{S}} l(f_{\theta}(x), y, \lambda)$ . The goal is for the generalization performance of the model  $f_{\theta^{\mathcal{S}}}$  obtained using the condensed data to approximate that of  $f_{\theta^{\mathcal{T}}}$ , i.e.,  $\mathbb{E}_{(x,y) \sim P_{\mathcal{D}}}[l(f_{\theta^{\mathcal{T}}}(x), y, \lambda)] \approx \mathbb{E}_{(x,y) \sim P_{\mathcal{D}}}[l(f_{\theta^{\mathcal{S}}}(x), y, \lambda)]$ .
+
+Next, we review the bi-level optimization formulation of the *standard dataset condensation* (SDC) (Wang et al., 2018) and one of its efficient solutions using gradient matching (Zhao et al., 2020).
+
+**SDC's objective.** By posing the optimal parameters  $\theta^{\mathcal{S}}(\mathcal{S})$  as a function of the condensed dataset  $\mathcal{S}$ , SDC can be formulated as a bi-level optimization problem as follows,
+
+<span id="page-2-0"></span>
+$$\mathcal{S}^* = \arg\min_{\mathcal{S}} \mathcal{L}^{\mathrm{train}}_{\mathcal{T}}(\theta^{\mathcal{S}}(\mathcal{S}), \lambda), \text{ s.t. } \theta^{\mathcal{S}}(\mathcal{S}) \coloneqq \arg\min_{\theta} \mathcal{L}^{\mathrm{train}}_{\mathcal{S}}(\theta, \lambda). \tag{SDC}$$
+
+In other words, the optimization problem in Eq. (SDC) aims to find the optimal synthetic dataset  $\mathcal{S}$  such that the model  $\theta^{\mathcal{S}}(\mathcal{S})$  trained on it minimizes the training loss over the original data  $\mathcal{T}^{\text{train}}$ . However, directly solving the optimization problem in Eq. (SDC) is difficult since it involves a nested-loop optimization and solving the inner loop for  $\theta^{\mathcal{S}}(\mathcal{S})$  at each iteration requires unrolling the recursive computation graph for  $\mathcal{S}$  over multiple optimization steps for  $\theta$  (Domke, 2012), which is computationally expensive.
+
+**SDC in a gradient matching formulation.** Zhao et al. (2020) alleviate this computational issue by introducing a *gradient matching* (GM) formulation. Firstly, they formulate the condensation objective as not only achieves comparable generalization performance to  $\theta^{\mathcal{T}}$  but also converges to a similar solution in the parameter space, i.e.,  $\theta^{\mathcal{S}}(\mathcal{S}, \theta_0) \approx \theta_{\mathcal{T}}(\theta_0)$ , where  $\theta_0$  indicates the initialization. The resulting formulation is still a bilevel optimization but can be simplified via several approximations.
+
+(1)  $\theta^{\mathcal{S}}(\mathcal{S}, \theta_0)$  is approximated by the output of a series of gradient-descent updates,  $\theta^{\mathcal{S}}(\mathcal{S}, \theta_0) \approx \theta_{t+1}^{\mathcal{S}} \leftarrow \theta_t^{\mathcal{S}} - \eta \nabla_{\theta} \mathcal{L}_{\mathcal{S}}^{\mathrm{train}}(\theta_t^{\mathcal{S}}, \lambda)$ . In addition, Zhao et al. (2020) propose to match  $\theta_{t+1}^{\mathcal{S}}$  with incompletely optimized  $\theta_{t+1}^{\mathcal{T}}$  at each iteration t. Consequently, the dataset condensation objective is now  $\mathcal{S}^* = \arg\min_{\mathcal{S}} \mathbb{E}_{\theta_0 \sim P_{\theta_0}}[\sum_{t=0}^{T-1} D(\theta_t^{\mathcal{S}}, \theta_t^{\mathcal{T}})]$ .
+
+(2) If we assume  $\theta_t^{\mathcal{S}}$  can always track  $\theta_t^{\mathcal{T}}$  (i.e.,  $\theta_t^{\mathcal{S}} \approx \theta_t^{\mathcal{T}}$ ) from the initialization  $\theta_0$  up to iteration t, then we can replace  $D(\theta_{t+1}^{\mathcal{S}}, \theta_{t+1}^{\mathcal{T}})$  by  $D(\nabla_{\theta} \mathcal{L}_{\mathcal{S}}^{\text{train}}(\theta_t^{\mathcal{S}}, \lambda), \nabla_{\theta} \mathcal{L}_{\mathcal{T}}^{\text{train}}(\theta_t^{\mathcal{T}}, \lambda))$ . The final objective for the GM formulation is,
+
+$$\min_{\mathcal{S}} \mathbb{E}_{\theta_0 \sim P_{\theta_0}} \Big[ \sum_{t=0}^{T-1} D\Big( \nabla_{\theta} \mathcal{L}_{\mathcal{S}}^{\text{train}}(\theta_t^{\mathcal{S}}, \lambda), \nabla_{\theta} \mathcal{L}_{\mathcal{T}}^{\text{train}}(\theta_t^{\mathcal{S}}, \lambda) \Big) \Big]. \tag{2}$$
+
+Challenge of varying hyperparameter  $\lambda$ . In the formulation of the SDC, the condensed data S is learned with a fixed hyperparameter  $\lambda$ , e.g., a pre-specified neural network architecture. As a result, the condensed data trained with SDC's objective performs poorly on hyperparameter search (Cui et al., 2022), which requires the performance of models under varying hyperparameters to behave consistently on the original and condensed dataset. In the following, we tackle this issue by reformulating the dataset condensation problem under the hyperparameter optimization framework.
+
+## 3 HYPERPARAMETER CALIBRATED DATASET CONDENSATION
+
+In this section, we would like to develop a condensation method specifically for preserving the outcome of *hyperparameter optimization* (HPO) on the condensed dataset across different architectures/hyperparameters for faster hyperparameter search. This requires dealing with varying choices of hyperparameters so that the relative performances of different hyperparameters on the condensed and
+
+original datasets are consistent. We first formulate the data condensation for hyperparameter search in the HPO framework below and then propose the hyperparameter calibrated dataset condensation framework in Section 4 by using the equivalence relationship between preserving the performance ranking and the hypergradient alignment.
+
+**HPO's objective.** Given  $\mathcal{T} = \mathcal{T}^{\mathrm{train}} \bigcup \mathcal{T}^{\mathrm{val}} \bigcup \mathcal{T}^{\mathrm{test}}$ , HPO aims to find the optimal hyperparameter  $\lambda^{\mathcal{T}}$  that minimizes the validation loss of the model optimized on the training dataset  $\mathcal{T}^{\mathrm{train}}$  with hyperparameter  $\lambda^{\mathcal{T}}$ , i.e.,
+
+<span id="page-3-2"></span>
+$$\lambda^{\mathcal{T}} = \arg\min_{\lambda \in \Lambda} \mathcal{L}_{\mathcal{T}}^{*}(\lambda), \text{ where } \mathcal{L}_{\mathcal{T}}^{*}(\lambda) \coloneqq \mathcal{L}_{\mathcal{T}}^{\mathrm{val}}(\theta^{\mathcal{T}}(\lambda), \lambda) \text{ and } \theta^{\mathcal{T}}(\lambda) \coloneqq \arg\min_{\theta} \mathcal{L}_{\mathcal{T}}^{\mathrm{train}}(\theta, \lambda).$$
+(HPO)
+
+Here  $\mathcal{L}^{\mathrm{val}}_{\mathcal{T}}(\theta,\lambda) \coloneqq \frac{1}{|\mathcal{T}^{\mathrm{val}}|} \sum_{(x,y) \in \mathcal{T}^{\mathrm{val}}} l(f_{\theta}(x),y,\lambda)$ . HPO is a bi-level optimization where both the optimal parameter  $\theta^{\mathcal{T}}(\lambda)$  and the optimized validation loss  $\mathcal{L}^*_{\mathcal{T}}(\lambda)$  are viewed as a function of the hyperparameter  $\lambda$ .
+
+**Dataset condensation for HPO.** We would like to synthesize a condensed training dataset  $\mathcal{S}^{\text{train}}$  and a condensed validation dataset  $\mathcal{S}^{\text{val}}$  to replace the original  $\mathcal{T}^{\text{train}}$  and  $\mathcal{T}^{\text{val}}$  for hyperparameter search. Denote the synthetic dataset as  $\mathcal{S} = \mathcal{S}^{\text{train}} \bigcup \mathcal{S}^{\text{val}}$ . Similar to Eq. (HPO), the optimal hyperparameter  $\lambda^{\mathcal{S}}$  is defined for a given dataset  $\mathcal{S}$ . Naively, one can formulate such a problem as finding the condensed dataset  $\mathcal{S}$  to minimize the validation loss on the original dataset  $\mathcal{T}^{\text{val}}$  as follows, which is an optimization problem similar to the standard dataset condensation in Eq. (SDC):
+
+$$S^* = \arg\min_{S} \mathcal{L}_{\mathcal{T}}^* (\lambda^S(S)) \quad \text{s.t.} \quad \lambda^S(S) := \arg\min_{\lambda \in \Lambda} \mathcal{L}_{\mathcal{S}}^*(\lambda), \tag{3}$$
+
+where the optimized validation losses  $\mathcal{L}_{\mathcal{T}}^*(\cdot)$  and  $\mathcal{L}_{\mathcal{S}}^*(\cdot)$  are defined following Eq. (HPO).
+
+However, **two challenges** exist for such a formulation. **Challenge (1)**: Eq. (3) is a nested optimization (for dataset condensation) over another nested optimization (for HPO), which is computationally expensive. **Challenge (2)**: the search space  $\Lambda$  of the hyperparameters can be complicated. In contrast to parameter optimization, where the search space is usually assumed to be the continuous and unbounded Euclidean space, the search space of the hyperparameters can be compositions of discrete and continuous spaces. Having such discrete components in the search space poses challenges for gradient-based optimization methods.
+
+To address **Challenge** (1), we propose an alternative objective based on the alignment of hypergradients that can be computed efficiently in Section 4. For **Challenge** (2), we construct the extended search space in Section 5.
+
+## <span id="page-3-1"></span>4 HYPERPARAMETER CALIBRATION VIA HYPERGRADIENT ALIGNMENT
+
+In this section, we introduce Hyperparameter-Calibrated Dataset Condensation (HCDC), a novel condensation method designed to align *hyperparameter gradients* – referred to as *hypergradients* – thus preserving the validation performance ranking of various hyperparameters.
+
+**Hyperparameter calibration.** To tackle the computational challenges inherent in hyperparameter optimization (HPO) as expressed in Eq. (3), we propose an efficient yet sufficient alternative. Rather than directly solving the HPO problem, we aim to identify a condensed dataset that maintains the outcomes of HPO on the hyperparameter set  $\Lambda$ . We refer to this process as hyperparameter calibration, formally defined as follows.
+
+<span id="page-3-3"></span>**Definition 1** (Hyperparameter Calibration). Given original dataset  $\mathcal{T}$ , generic model  $f_{\theta}^{\lambda}$ , and hyperparameter search space  $\Lambda$ , we say a condensed dataset  $\mathcal{S}$  is hyperparameter calibrated, if for any  $\lambda_1 \neq \lambda_2 \in \Lambda$ , it holds that,
+
+<span id="page-3-0"></span>
+$$\left(\mathcal{L}_{\mathcal{T}}^{*}(\lambda_{1}) - \mathcal{L}_{\mathcal{T}}^{*}(\lambda_{2})\right) \left(\mathcal{L}_{\mathcal{S}}^{*}(\lambda_{1}) - \mathcal{L}_{\mathcal{S}}^{*}(\lambda_{2})\right) > 0 \tag{HC}$$
+
+In other words, changes of the optimized validation loss on T and S always have the same sign, between any pairs of hyperparameters  $\lambda_1 \neq \lambda_2$ .
+
+It is evident that if hyperparameter calibration (HC) is satisfied, the outcomes of HPO on both the original and condensed datasets will be identical. Consequently, our objective shifts to *ensuring hyperparameter calibration across all pairs of hyperparameters*.
+
+<span id="page-4-4"></span>**HCDC:** hypergradient alignment objective for dataset condensation. To move forward, we make the assumption that there exists a continuous extension of the search space. Specifically, the (potentially discrete) search space  $\Lambda$  can be extended to a compact and connected set  $\tilde{\Lambda} \supset \Lambda$ . Within this extended set, we define a continuation of the generic model  $f_{\theta}^{\lambda}$  such that  $f_{\theta}^{\lambda}$  is differentiable anywhere in  $\tilde{\Lambda}$ . In Section 5, we will elaborate on how to construct such an extended search space  $\tilde{\Lambda}$ .
+
+To establish a new objective for hyperparameter calibration, consider the case when  $\lambda_1$  is in the neighborhood of  $\lambda_2$ , denoted as  $\lambda_1 \in B_r(\lambda_2)$  for some r>0. In this situation, the change in validation loss can be approximated up to first-order by the hypergradients, as follows:  $\mathcal{L}_{\mathcal{T}}^*(\lambda_1) - \mathcal{L}_{\mathcal{T}}^*(\lambda_2) \approx \langle \nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^*(\lambda_2), \Delta \lambda \rangle$ . Here,  $\Delta \lambda = \lambda_1 - \lambda_2$  with  $r \geq \|\Delta \lambda\|_2 \to 0^+$ . Analogously, for the synthetic dataset we have:  $\mathcal{L}_{\mathcal{S}}^*(\lambda_1) - \mathcal{L}_{\mathcal{S}}^*(\lambda_2) \approx \langle \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^*(\lambda_2), \Delta \lambda \rangle$ . Hence, the hyperparameter calibration condition simplifies to  $\langle \nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^*(\lambda_2), \Delta \lambda \rangle \cdot \langle \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^*(\lambda_2), \Delta \lambda \rangle > 0$ . Further simplification leads to  $\nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^*(\lambda) \| \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^*(\lambda)$ , indicating *alignment* of the two hypergradient vectors. We formally define this hypergradient alignment and establish its equivalence to hyperparameter calibration.
+
+<span id="page-4-1"></span>**Definition 2** (Hypergradient Alignment). We say hypergradients are aligned in an extended search space  $\tilde{\Lambda}$ , if for any  $\lambda \in \tilde{\Lambda}$ , it holds that  $\nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^{*}(\lambda) \parallel \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^{*}(\lambda)$ , i.e.,  $D_{c}(\nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^{*}(\lambda), \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^{*}(\lambda)) = 0$ , where  $D_{c}(\cdot, \cdot) = 1 - \cos(\cdot, \cdot)$  represents the cosine distance.
+
+<span id="page-4-2"></span>Theorem 1 (Equivalence between Hypergradient Alignment and Hypergrameter Calibration). Hypergradient alignment (Definition 2) is equivalent to hyperparameter calibration (Definition 1) on a connected and compact set, e.g., the extended search space  $\tilde{\Lambda}$ .
+
+The implication is straightforward: if hyperparameter calibration holds in  $\tilde{\Lambda}$ , it also holds in  $\Lambda$ . According to Theorem 1, achieving hypergradient alignment in  $\tilde{\Lambda}$  is sufficient to ensure hyperparameter calibration in  $\Lambda$ . Therefore, the integrity of the HPO outcome over  $\Lambda$  is maintained.
+
+Consequently, the essence of our hyperparameter calibrated dataset condensation (HCDC) is to align/match the hypergradients calculated on both the original and condensed datasets within the extended search space  $\tilde{\Lambda}$ :
+
+$$S^* = \arg\min_{\mathcal{S}} \sum_{\lambda \in \tilde{\Lambda}} \frac{D_c}{D_c} \Big( \nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^{\text{val}} \big( \theta^{\mathcal{T}}(\lambda), \lambda \big), \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^{\text{val}} \big( \theta^{\mathcal{S}}(\lambda), \lambda \big) \Big), \tag{HCDC}$$
+
+where the cosine distance  $D_c(\cdot,\cdot) = 1 - \cos(\cdot,\cdot)$  is used without loss of generality.
+
+#### <span id="page-4-0"></span>5 IMPLEMENTATIONS OF HCDC
+
+In this section, we focus on implementing the hyperparameter calibrated dataset condensation (HCDC) algorithm. We address two primary challenges: (1) efficient approximate computation of hyperparameter gradients, often called hypergradients, using implicit differentiation techniques; and (2) the efficient formation of the extended search space  $\tilde{\Lambda}$ . The complete pseudocode for HCDC will be provided at the end of this section.
+
+#### 5.1 EFFICIENT EVALUATION OF HYPERGRADIENTS
+
+The efficient computation of hypergradients is well-addressed in existing literature (see Section 6). In our HCDC implementation, we utilize the implicit function theorem (IFT) and the Neumann series approximation for inverse Hessians, as proposed by Lorraine et al. (2020).
+
+Computing hypergradients via IFT. The hypergradients are the gradients of the optimized validation loss  $\mathcal{L}^*_{\mathcal{T}}(\lambda) = \mathcal{L}^{\mathrm{val}}_{\mathcal{T}}(\theta^{\mathcal{T}}(\lambda), \lambda)$  with respect to the hyperparameters  $\lambda$ ; see Appendix E for further details. The implicit function theorem (IFT) provides an efficient approximation to compute the hypergradients  $\nabla_{\lambda}\mathcal{L}^*_{\mathcal{T}}(\lambda)$  and  $\nabla_{\lambda}\mathcal{L}^*_{\mathcal{S}}(\lambda)$ .
+
+<span id="page-4-3"></span>
+$$\nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^{*}(\lambda) \approx - \left[ \frac{\partial^{2} \mathcal{L}_{\mathcal{T}}^{train}(\theta, \lambda)}{\partial \lambda \partial \theta^{T}} \right] \left[ \frac{\partial^{2} \mathcal{L}_{\mathcal{T}}^{train}(\theta, \lambda)}{\partial \theta \partial \theta^{T}} \right]^{-1} \nabla_{\theta} \mathcal{L}_{\mathcal{T}}^{val}(\theta, \lambda) + \nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^{val}(\theta, \lambda), \quad (IFT)$$
+
+where we consider the direct gradient  $\nabla_{\lambda}\mathcal{L}^{\mathrm{val}}_{\mathcal{T}}(\theta,\lambda)$  is 0, since in most cases the hyperparameter  $\lambda$  only affects the validation loss  $\mathcal{L}^{\mathrm{val}}_{\mathcal{T}}(\theta,\lambda)$  through the model function  $f_{\theta,\lambda}$ . The first term consists of the mixed partials  $\left[\frac{\partial^2 \mathcal{L}^{\mathrm{train}}_{\mathcal{T}}(\theta,\lambda)}{\partial \lambda \partial \theta^T}\right]$ , the inverse Hessian  $\left[\frac{\partial^2 \mathcal{L}^{\mathrm{train}}_{\mathcal{T}}(\theta,\lambda)}{\partial \theta \partial \theta^T}\right]^{-1}$ , and the validation gradients  $\nabla_{\theta}\mathcal{L}^{\mathrm{val}}_{\mathcal{T}}(\theta,\lambda)$ . While the other parts can be calculated efficiently through a single back-propagation,
+
+<span id="page-5-3"></span>approximating the inverse Hessian is required. Lorraine et al. (2020) propose a stable, tractable, and efficient Neumann series approximation of the inverse Hessian as follows:
+
+$$\textstyle \big[\frac{\partial^2 \mathcal{L}_{\mathcal{T}}^{\mathrm{train}}(\theta, \lambda)}{\partial \theta \partial \theta^T}\big]^{-1} = \lim_{i \to \infty} \sum_{j=0}^{i} \big[I - \frac{\partial^2 \mathcal{L}_{\mathcal{T}}^{\mathrm{train}}(\theta, \lambda)}{\partial \theta \partial \theta^T}\big]^j,$$
+
+which requires only constant memory. When combined with Eq. (IFT), the approximated hypergradients can be evaluated by employing efficient vector-Jacobian products (Lorraine et al., 2020).
+
+Optimizing hypergradient alignment loss in Eq. (HCDC). To optimize the objective defined in HCDC (Eq. (HCDC)), we learn the synthetic validation set  $\mathcal{S}^{\mathrm{val}}$  from scratch. This is crucial as the hypergradients with respect to the validation losses in Eq. (HCDC), are significantly influenced by the synthetic validation examples, which are free learnable parameters during the condensation process. In contrast, we maintain the synthetic training set  $\mathcal{S}^{\mathrm{train}}$  as fixed. For generating  $\mathcal{S}^{\mathrm{train}}$ , we employ the standard dataset condensation (SDC) algorithm, as described in Eq. (2). To optimize the synthetic validation set  $\mathcal{S}^{\mathrm{val}}$  with respect to the hyper-gradient loss in Eq. (HCDC), we compute the gradients of  $\nabla_{\theta}\mathcal{L}^{\mathrm{val}}_{\mathcal{S}}(\theta,\lambda)$  and  $\nabla_{\lambda}\mathcal{L}^{\mathrm{val}}_{\mathcal{S}}(\theta,\lambda)$  w.r.t.  $\mathcal{S}^{\mathrm{val}}$ . This is handled using an additional back-propagation step, akin to the one in SDC that calculates the gradients of  $\nabla_{\theta}\mathcal{L}^{\mathrm{train}}_{\mathcal{S}}(\theta,\lambda)$  w.r.t.  $\mathcal{S}^{\mathrm{train}}$ .
+
+### 5.2 EFFICIENT DESIGN OF EXTENDED SEARCH SPACE
+
+HCDC's objective (Eq. (HCDC)) necessitates the alignment of hypergradients across all hyperparameters  $\lambda$ 's in an extended space  $\tilde{\Lambda}$ . This space is a compact and connected superset of the original search space  $\Lambda$ . For practical implementation, we evaluate the hypergradient matching loss using a subset of  $\lambda$  values randomly sampled from  $\tilde{\Lambda}$ . To enhance HCDC's efficiency within a predefined search space  $\lambda$ , our goal is to minimally extend this space to  $\tilde{\Lambda}$  for sampling.
+
+In the case of continuous hyperparameters,  $\Lambda$  is generally both compact and connected, rending  $\tilde{\Lambda}$  identical to  $\Lambda$ . For discrete search spaces  $\Lambda$  consisting of p candidate hyperparameters, we propose a linear-complexity construction for  $\tilde{\Lambda}$  (in which the linearity is in terms of p). Specifically, for each  $i \in [p]$ , we formulate an "i-th HPO trajectory", a representative path that originates from  $\lambda_{i,0}^{\mathcal{S}} = \lambda_i \in \Lambda$  and evolves via the update rule  $\lambda_{i,t+1}^{\mathcal{S}} \leftarrow \lambda_{i,t}^{\mathcal{S}} - \eta \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^*(\lambda_{i,t}^{\mathcal{S}})$ , see Appendix H for details and Fig. 8 for illustration. We assume that all p trajectories converge to the same or equivalent optima  $\lambda^{\mathcal{S}}$ , thus forming "connected" paths. Consequently, the extended search space  $\tilde{\Lambda}$  comprises these p connected trajectories, allowing us to evaluate the hypergradient matching loss along each trajectory  $\{\lambda_{i,t}^{\mathcal{S}}\}_{t=0}^T$  during the iterative update of  $\lambda$ .
+
+#### 5.3 PSEUDOCODE
+
+We conclude this section by outlining the HCDC algorithm in Algorithm 1, assuming a discrete and finite hyperparameter search space  $\Lambda$ . In Line 7, we calculate the hypergradients  $\nabla_{\lambda}\mathcal{L}_{\mathcal{S}}^{*}(\lambda)$  using Eq. (IFT). For computing the gradient  $\nabla_{\mathcal{S}^{\mathrm{val}}}D\big(\nabla_{\lambda}\mathcal{L}_{\mathcal{T}}^{*}(\lambda),\nabla_{\lambda}\mathcal{L}_{\mathcal{S}}^{*}(\lambda)\big)$  in Line 8, we note that only  $\nabla_{\lambda}\mathcal{L}_{\mathcal{S}}^{*}(\lambda)$  is depends on  $\mathcal{S}^{\mathrm{val}}$ . Employing Eq. (IFT), we find that  $\nabla_{\lambda}\mathcal{L}_{\mathcal{S}}^{*}(\lambda)=-\left[\frac{\partial^{2}\mathcal{L}_{\mathcal{S}}^{\mathrm{train}}(\theta,\lambda)}{\partial \partial \partial \theta^{S}}\right]\left[\frac{\partial^{2}\mathcal{L}_{\mathcal{S}}^{\mathrm{train}}(\theta,\lambda)}{\partial \theta \partial \theta^{S}}\right]^{-1}\nabla_{\theta}\mathcal{L}_{\mathcal{S}}^{\mathrm{val}}(\theta,\lambda)$ . Note that there are no direct gradients, as  $\lambda$  influences the loss solely through the model  $f_{\theta}^{\lambda}$ . Therefore, to obtain  $\nabla_{\mathcal{S}^{\mathrm{val}}}D\big(\nabla_{\lambda}\mathcal{L}_{\mathcal{T}}^{*}(\lambda),\nabla_{\lambda}\mathcal{L}_{\mathcal{S}}^{*}(\lambda)\big)$ , we simply need to compute the gradient  $\nabla_{\mathcal{S}^{\mathrm{val}}}\nabla_{\theta}\mathcal{L}_{\mathcal{S}}^{\mathrm{val}}(\theta,\lambda)$  through standard back-propagation methods, since only the validation loss term  $\nabla_{\theta}\mathcal{L}_{\mathcal{S}}^{\mathrm{val}}(\theta,\lambda)$  depends on  $\mathcal{S}^{\mathrm{val}}$ .
+
+## Algorithm 1: Hyperparameter Calibrated Dataset Condensation (HCDC)
+
+```
+Input: Original dataset \mathcal{T}, a set of NN architectures f_{\theta}, hyperparameter search space \lambda \in \Lambda = \{\lambda_1, \dots, \lambda_p\}, predetermined condensed training data \mathcal{S}^{\text{train}} learned by standard dataset condensation (e.g., Eq. (2)), randomly initialized synthetic examples \mathcal{S}^{\text{val}} of C classes.
+
+1 for repeat k = 0, \dots, K - 1 do
+
+2 | foreach hyperparameters \lambda = \lambda_1, \dots, \lambda_p in \Lambda do
+
+3 | Initialize model parameters \theta \leftarrow \theta_0 \sim P_{\theta_0}
+4 | for epoch t = 0, \dots, T_{\theta} - 1 do
+
+5 | Update model parameters \theta \leftarrow \theta - \eta_{\theta} \nabla_{\theta} \mathcal{L}_{\mathcal{S}}^{\text{train}}(\theta, \lambda)
+6 | Update model parameters \theta \leftarrow \theta - \eta_{\theta} \nabla_{\theta} \mathcal{L}_{\mathcal{S}}^{\text{train}}(\theta, \lambda)
+6 | Initialize model parameters \theta \leftarrow \theta - \eta_{\theta} \nabla_{\theta} \mathcal{L}_{\mathcal{S}}^{\text{train}}(\theta, \lambda)
+8 | Update the synthetic validation set \mathcal{S}^{\text{val}} \leftarrow \mathcal{S}^{\text{val}} - \eta_{\mathcal{S}} \nabla_{\mathcal{S}^{\text{val}}} D(\nabla_{\lambda} \mathcal{L}_{\mathcal{T}}^*(\lambda), \nabla_{\lambda} \mathcal{L}_{\mathcal{S}}^*(\lambda))
+9 return Condensed validation set \mathcal{S}^{\text{val}}.
+```
+
+<span id="page-5-2"></span><span id="page-5-1"></span>For a detailed complexity analysis of Algorithm 1 and further discussions, refer to Appendix I.
+
+### <span id="page-6-2"></span><span id="page-6-0"></span>6 RELATED WORK
+
+The traditional way to simplify a dataset is **coreset selection** (Toneva et al., 2018; Paul et al., 2021), where critical training data samples are chosen based on heuristics like diversity (Aljundi et al., 2019), distance to the dataset cluster centers (Rebuffi et al., 2017; Chen et al., 2010) and forgetfulness (Toneva et al., 2018). However, the performance of coreset selection methods is limited by the assumption of the existence of representative samples in the original data, which may not hold in practice.
+
+To overcome this limitation, dataset distillation/condensation (Wang et al., 2018) has been proposed as a more effective way to reduce sample size. Dataset condensation (or dataset distillation) is first proposed in (Wang et al., 2018) as a learning-to-learn problem by formulating the network parameters as a function of synthetic data and learning them through the network parameters to minimize the training loss over the original data. This approach involves producing a small synthetic dataset to replace the original larger one, so that the test/generalization performance of the model trained on the synthetic set is comparable to that trained on the original. However, the nested-loop optimization precludes it from scaling up to large-scale in-the-wild datasets. Zhao et al. (2020) alleviate this issue by enforcing the gradients of the synthetic samples w.r.t. the network weights to approach those of the original data, which successfully alleviates the expensive unrolling of the computational graph. Based on the meta-learning formulation in (Wang et al., 2018), Bohdal et al. (2020) and Nguyen et al. (2020; 2021) propose to simplify the inner-loop optimization of a classification model by training with ridge regression which has a closed-form solution, while Such et al. (2020) model the synthetic data using a generative network. To improve the data efficiency of synthetic samples in the gradient-matching algorithm, Zhao & Bilen (2021a) apply differentiable Siamese augmentation, and Kim et al. (2022) introduce efficient synthetic-data parametrization.
+
+**Implicit differentiation** methods apply the implicit function theorem (IFT) (Eq. (IFT)) to nested-optimization problems (Wang et al., 2019). Lorraine et al. (2020) approximated the inverse Hessian by Neumann series, which is a stable alternative to conjugate gradients (Shaban et al., 2019) and scales IFT to large networks with constant memory.
+
+**Differentiable NAS** methods, e.g., DARTS (Liu et al., 2018) explore the possibility of transforming the discrete neural architecture space into a continuously differentiable form and further uses gradient optimization to search the neural architecture. SNAS (Xie et al., 2018) points out that DARTS suffers from the unbounded bias issue towards its objective, and it remodels the NAS and leverages the Gumbel-softmax trick (Jang et al., 2017; Maddison et al., 2017) to learn the architecture parameter.
+
+In addition, we summarize more dataset condensation and coreset selection methods as well as graph reduction methods in Appendix B.
+
+Table 1: The Spearman's rank correlation of architecture's performance (Corr.) and the test performance of the best architecture selected on the condensed dataset (Perf.) on two **image datasets**. Grid search is applied to find the best architecture.
+
+<span id="page-6-1"></span>
+
+| Dataset   | Coresets  |                |                 |                 |                | Ours           | Oracle         |                |                |                              |         |
+|-----------|-----------|----------------|-----------------|-----------------|----------------|----------------|----------------|----------------|----------------|------------------------------|---------|
+| Datasci   |           | Random         | K-Center        | Herding         | DC             | DSA            | DM             | KIP            | TM             | HCDC                         | Optimal |
+| CIFAR-10  | Corr.     | $-0.12\pm0.07$ | $0.19 \pm 0.12$ | $-0.05\pm0.08$  | $-0.21\pm0.15$ | $-0.33\pm0.09$ | $-0.10\pm0.15$ | $-0.27\pm0.15$ | $-0.07\pm0.04$ | $\boldsymbol{0.74 \pm 0.21}$ | _       |
+|           | Perf. (%) | $91.3 \pm 0.2$ | $91.4 \pm 0.3$  | $90.2 \pm 0.9$  | $89.2 \pm 3.3$ | $73.5 \pm 7.2$ | $92.2 \pm 0.4$ | $91.8 \pm 0.2$ | $75.2 \pm 4.3$ | $92.9 \pm 0.7$               | 93.5    |
+| CIFAR-100 | Corr.     | $-0.05\pm0.03$ | $-0.07\pm0.05$  | $0.08 \pm 0.11$ | $-0.13\pm0.02$ | $-0.28\pm0.05$ | $-0.15\pm0.07$ | $-0.08\pm0.04$ | $-0.09\pm0.03$ | $0.63 \pm 0.13$              | _       |
+|           | Perf. (%) | $71.1 \pm 1.4$ | $69.5 \pm 2.8$  | $67.9 \pm 1.8$  | $64.9 \pm 2.2$ | $59.0 \pm 4.1$ | $70.1 \pm 0.6$ | $68.8 \pm 0.6$ | $51.3 \pm 6.1$ | $72.4 \pm 1.7$               | 72.9    |
+
+## 7 EXPERIMENTS
+
+In this section, we validate the effectiveness of hyperparameter calibrated dataset condensation (HCDC) when applied to speed up architecture/hyperparameter search on two types of data: **images** and **graphs**. For an ordered list of architectures, we calculate Spearman's rank correlation coefficient  $-1 \le \text{Corr.} \le 1$ , between the rankings of their validation performance on the original and condensed datasets. This correlation coefficient (denoted by **Corr.**) indicates how similar the performance ranking on the condensed dataset is to that on the original dataset. We also report the test accuracy (referred to as **Perf.**) evaluated on the original dataset of the architectures selected on the condensed dataset. If the test performance is close to the true optimal performance among all architectures, we say the architecture search outcome is preserved with high accuracy. See Appendix G and Appendix J for more discussions on implementation and experimental setups.
+
+<span id="page-7-3"></span>Table 2: Spearman's rank correlation of convolution filters in GNNs (Corr.) and the test performance of the best convolution filter selected on the condensed graph (Pref.) on four **graph datasets**. Continuous hyperparameter optimization (Lorraine et al., 2020) is applied to find the best convolution filter, while Spearman's rank correlation coefficients are evaluated on 80 sampled hyperparameter configurations. n is the total number of nodes in the original graph, and  $c_{\rm train}$  is the number of training nodes in the condensed graph.
+
+<span id="page-7-2"></span>
+
+| Dataset    | Ratio $(c_{\text{train}}/n)$ | Ran<br>Corr.                                                                | dom<br>Perf. (%)                                                            | GCo<br>Corr.                                                                | nd-X<br>Perf. (%)                                                           | GC<br>Corr.                                                                 | ond<br>Perf. (%)                                                            | HC<br>Corr.                                                                 | DC<br>Perf. (%)                                                                                                                   | Whole Graph<br>Perf. (%) |
+|------------|------------------------------|-----------------------------------------------------------------------------|-----------------------------------------------------------------------------|-----------------------------------------------------------------------------|-----------------------------------------------------------------------------|-----------------------------------------------------------------------------|-----------------------------------------------------------------------------|-----------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------|--------------------------|
+| Cora       | 0.9%<br>1.8%<br>3.6%         | $\begin{array}{c} 0.29 \pm .08 \\ 0.40 \pm .04 \\ 0.51 \pm .04 \end{array}$ | $\begin{array}{c} 81.2 \pm 1.1 \\ 81.9 \pm 0.5 \\ 82.2 \pm 0.6 \end{array}$ | $0.16 \pm .07$<br>$0.21 \pm .07$<br>$0.23 \pm .04$                          | $79.5 \pm 0.7$<br>$80.3 \pm 0.4$<br>$80.9 \pm 0.6$                          | $0.61 \pm .03$<br>$0.76 \pm .06$<br>$0.81 \pm .04$                          | $81.9 \pm 1.6$<br>$83.2 \pm 0.9$<br>$83.2 \pm 1.1$                          | $\begin{array}{c} 0.80 \pm .03 \\ 0.85 \pm .03 \\ 0.90 \pm .01 \end{array}$ | $\begin{array}{c} 83.0 \pm 0.2 \\ 83.4 \pm 0.2 \\ 83.4 \pm 0.3 \end{array}$                                                       | $83.8 \pm 0.4$           |
+| Citeseer   | 1.3%<br>2.6%<br>5.2%         | $\begin{array}{c} 0.38 \pm .11 \\ 0.56 \pm .06 \\ 0.71 \pm .05 \end{array}$ | $71.9 \pm 0.8 72.2 \pm 0.4 73.0 \pm 0.3$                                    | $\begin{array}{c} 0.15 \pm .07 \\ 0.29 \pm .05 \\ 0.35 \pm .08 \end{array}$ | $\begin{array}{c} 70.7 \pm 0.9 \\ 70.8 \pm 0.5 \\ 70.2 \pm 0.4 \end{array}$ | $0.68 \pm .03$<br>$0.79 \pm .05$<br>$0.83 \pm .03$                          | $\begin{array}{c} 71.3 \pm 1.2 \\ 71.5 \pm 0.7 \\ 71.1 \pm 0.8 \end{array}$ | $\begin{array}{c} 0.79 \pm .01 \\ 0.83 \pm .02 \\ 0.89 \pm .02 \end{array}$ | $\begin{array}{c} \textbf{73.1} \pm \textbf{0.2} \\ \textbf{73.3} \pm \textbf{0.5} \\ \textbf{73.4} \pm \textbf{0.4} \end{array}$ | $73.7 \pm 0.6$           |
+| Ogbn-arxiv | 0.1%<br>0.25%<br>0.5%        | $0.59 \pm .08$<br>$0.63 \pm .05$<br>$0.68 \pm .07$                          | $70.1 \pm 1.7 \\ 70.3 \pm 1.3 \\ 70.9 \pm 1.0$                              | $\begin{array}{c} 0.39 \pm .06 \\ 0.44 \pm .03 \\ 0.47 \pm .05 \end{array}$ | $\begin{array}{c} 69.8 \pm 1.4 \\ 70.1 \pm 0.7 \\ 70.0 \pm 0.7 \end{array}$ | $\begin{array}{c} 0.59 \pm .07 \\ 0.64 \pm .05 \\ 0.67 \pm .05 \end{array}$ | $\begin{array}{c} 70.3 \pm 1.4 \\ 70.5 \pm 1.0 \\ 71.1 \pm 0.6 \end{array}$ | $\begin{array}{c} 0.77 \pm .04 \\ 0.83 \pm .03 \\ 0.88 \pm .03 \end{array}$ | $\begin{array}{c} 71.9 \pm 0.8 \\ 72.4 \pm 1.0 \\ 72.6 \pm 0.6 \end{array}$                                                       | $73.2 \pm 0.8$           |
+| Reddit     | 0.1%<br>0.25%<br>0.5%        | $\begin{array}{c} 0.42 \pm .09 \\ 0.50 \pm .06 \\ 0.58 \pm .06 \end{array}$ | $\begin{array}{c} 92.1 \pm 1.6 \\ 92.7 \pm 1.3 \\ 92.8 \pm 0.7 \end{array}$ | $\begin{array}{c} 0.39 \pm .04 \\ 0.41 \pm .05 \\ 0.42 \pm .03 \end{array}$ | $\begin{array}{c} 90.9 \pm 0.8 \\ 90.9 \pm 0.5 \\ 91.5 \pm 0.6 \end{array}$ | $0.53 \pm .06$<br>$0.61 \pm .04$<br>$0.66 \pm .02$                          | $\begin{array}{c} 90.9 \pm 1.7 \\ 91.2 \pm 1.2 \\ 92.1 \pm 0.9 \end{array}$ | $\begin{array}{c} 0.79 \pm .03 \\ 0.83 \pm .01 \\ 0.87 \pm .01 \end{array}$ | $\begin{array}{c} 92.1 \pm 0.9 \\ 92.9 \pm 0.7 \\ 93.1 \pm 0.5 \end{array}$                                                       | $94.1 \pm 0.7$           |
+
+Table 3: The search time and test performance of the best architecture find by NAS methods on the condensed datasets. We consider two NAS algorithms: (1) the differentiable NAS algorithm DARTS-PT and (2) REINFORCE without parameter-sharing.
+
+<span id="page-7-0"></span>
+
+| NAS Algorithm         | Random      |                                  | DC          |                                  | HCDC       |           | Original   |           |
+|-----------------------|-------------|----------------------------------|-------------|----------------------------------|------------|-----------|------------|-----------|
+| NA3 Algoriumi         | Time (sec)  | Perf. (%)                        | Time (sec)  | Perf. (%)                        | Time (sec) | Perf. (%) | Time (sec) | Perf. (%) |
+| DARTS-PT<br>REINFORCE | 37.1<br>166 | $89.4 \pm 0.3$<br>$88.1 \pm 1.8$ | 39.2<br>105 | $85.2 \pm 1.9$<br>$80.1 \pm 6.5$ |            |           |            |           |
+
+Preserving architecture performance ranking on We follow the practice of (Cui et al., 2022) and construct the search space by sampling 100 networks from NAS-Bench-201 (Dong & Yang, 2020), which contains the ground-truth performance of 15,625 networks. All models are trained on CIFAR-10 or CIFAR-100 for 50 epochs under five random seeds and ranked according to their average accuracy on a held-out validation set of 10K images. As a common practice in NAS (Liu et al., 2018), we reduce the number of repeated blocks in all architecture from 15 to 3 during the search phase, as deep models are hard to train on the small condensed datasets. We consider three coreset baselines, including uniform random sampling, K-Center (Farahani & Hekmatfar, 2009), and Herding (Welling, 2009) coresets, as well as five standard condensation baselines, including dataset condensation (DC) (Zhao et al., 2020), differentiable siamese augmentation (DSA) (Zhao & Bilen, 2021a), distribution matching
+
+<span id="page-7-1"></span>![](figures/_page_7_Figure_6.jpeg)
+
+Figure 2: Visualization of the performance rankings of architectures (subsampled from the search space) evaluated on different condensed datasets. Colors indicate the performance ranking on the original dataset, while lighter shades refer to better performance. Spearman's rank correlations are shown on the right.
+
+(DM) (Zhao & Bilen, 2021b), Kernel Inducing Point (KIP) (Nguyen et al., 2020; 2021), and Training Trajectory Matching (TM) (Cazenavette et al., 2022). For the coreset and condensation baselines, we randomly split the condensed dataset to obtain the condensed validation data while keeping the train-validation split ratio. We subsample or compress the original dataset to 50 images per class for all baselines. As shown in Table 1, our HCDC is much better at preserving the performance ranking of architectures compared to all other coreset and condensation methods. At the same time, HCDC also consistently attains better-selected architectures' performance, which implies the HCDC condensed datasets are reliable proxies of the original datasets for architecture search.
+
+**Speeding up architecture search on images.** We then combine HCDC with some off-the-shelf NAS algorithms to demonstrate the efficiency gain when evaluated on the proxy condensed dataset. We consider two NAS algorithms: DARTS-PT (Wang et al., 2020), which is a parameter-sharing based differentiable NAS algorithm, and REINFORCE (Williams, 1992), which is a reinforcement learning algorithm without parameter sharing. In Table 3, we see all coreset/condensation baselines can bring significant speed-ups to the NAS algorithms since the models are trained on the small proxy datasets. Same as under the grid search setup, the test performance of the selected architecture on the HCDC condensed dataset is consistently higher. Here a small search space of 100 sampled architectures is used as in Table 3 and we expect even higher efficiency gain on larger search spaces.
+
+<span id="page-8-1"></span>In Fig. [2,](#page-7-1) we directly visualize the performance rankings of architectures on different condensed datasets. Each color slice indicates one architecture and and are re-ordered with the ranking from the condensation algorithm. rows that are more similar to the 'optimal' gradient indicate that the algorithm is ranking the architectures similarly to the optimial ranking. The best architectures with the HCDC algorithm are among the best in the original dataset.
+
+![](figures/_page_8_Picture_2.jpeg)
+
+Figure 3: Visualization of some example condensed validation set images using our HCDC algorithm on CIFAR-10.
+
+Finding the best convolution filter on graphs. We now consider the search space of graph neural networks' (GNN) convolution filters, which is intrinsically continuous (i.e., defined by a few continuous hyperparameters which parameterize the convolution filter, see Section [5](#page-4-0) for details). Our goal is to speed up the selection of the best-suited convolution filter design on large graphs. We consider 2-layer message-passing GNNs whose convolution matrix is a truncated sum of powers of the graph Laplacian; see Appendix [J.](#page--1-7) Four node classification graph benchmarks are used, including two small graphs (Cora and Citeseer) and two large graphs (Ogbn-arxiv and Reddit) with more than 100K nodes. To compute the Spearman's rank correlations, we sample 80 hyperparameter setups from the search space and compare their performance rankings. We test HCDC against three baselines: (1) Random: random uniform sampling of nodes and find their induced subgraph, (2) GCond-X: graph condensation [\(Jin et al.,](#page-10-6) [2021\)](#page-10-6) but fix the synthetic adjacency to the identity matrix, (3) GCond: graph condensation which also learns the adjacency. The whole graph performance is oracle and shows the best possible test performance when the convolution filter is optimized on the original datasets using hypergradient-based method [\(Lorraine et al.,](#page-11-0) [2020\)](#page-11-0). In Table [2,](#page-7-2) we see HCDC consistently outperforms the other approaches, and the test performance of selected architecture is close to the ground-truth optimal.
+
+Speeding up off-the-shelf graph architecture search algorithms. Finally, we demonstrate HCDC can speed up off-the-shelf graph architecture search methods. We use graph NAS [\(Gao et al.,](#page-10-7) [2019\)](#page-10-7) on Ogbn-arxiv with a compression ratio of ctrain/n = 0.5%, where n is the size of the original graph, and ctrain is the number of training nodes in the condensed graph. The search space of GNN architectures is the same as in [\(Gao et al.,](#page-10-7) [2019\)](#page-10-7), where various attention and aggregation functions are incorporated. We plot the best test performance of searched architecture versus the search time in Fig. [4.](#page-8-0) We see that when evaluated on the dataset condensed by HCDC, the search algorithm finds the better architectures
+
+<span id="page-8-0"></span>![](figures/_page_8_Figure_6.jpeg)
+
+Figure 4: Speed-up of graph NAS's search process, when evaluated on the small proxy dataset condensed by HCDC.
+
+much faster. This efficiency gain provided by the small proxy dataset is orthogonal to the design of search strategies and should be applied to any type of data, including graph and images.
+
+## 8 CONCLUSION
+
+We propose a hyperparameter calibration formulation for dataset condensation to preserve the outcome of hyperparameter optimization, which is then solved by aligning the hyperparameter gradients. We demonstrate both theoretically and experimentally that HCDC can effectively preserve the validation performance rankings of architectures and accelerate the hyperparameter/architecture search on images and graphs. The overall performance of HCDC can be affected by (1) how the differentiable NAS model used for condensation generalizes to unseen architectures, (2) where we align hypergradients in the search space, (3) how we learn the synthetic training set, (4) how we parameterize the synthetic dataset, and we leave the exploration of these design choices to future work. We hope our work opens up a promising avenue for speeding up hyperparameter/architecture search by dataset compression.
+
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