Compositional Automata Embeddings for Goal-Conditioned Reinforcement Learning

reinforcement learning;goal-conditioned reinforcement learning;formal methods;graph embeddings;representation learning

Summary: We show how to produce rich neural embeddings of temporal tasks for use in goal-conditioned RL.

Abstract: Goal-conditioned reinforcement learning is a powerful way to control an AI agent's behavior at runtime. That said, popular goal representations, e.g., target states or natural language, are either limited to Markovian tasks or rely on ambiguous task semantics. We propose representing temporal goals using compositions of deterministic finite automata (cDFAs) and use cDFAs to guide RL agents. cDFAs balance the need for formal temporal semantics with ease of interpretation: if one can understand a flow chart, one can understand a cDFA. On the other hand, cDFAs form a countably infinite concept class with Boolean semantics, and subtle changes to the automaton can result in very different tasks, making them difficult to condition agent behavior on. To address this, we observe that all paths through a DFA correspond to a series of reach-avoid tasks and propose pre-training graph neural network embeddings on "reach-avoid derived" DFAs. Through empirical evaluation, we demonstrate that the proposed pre-training method enables zero-shot generalization to various cDFA task classes and accelerated policy specialization without the myopic suboptimality of hierarchical methods.


ROIDICE: Offline Return on Investment Maximization for Efficient Decision Making

Summary: Policy optimization that maximizes Return on Investment (ROI) of a policy

Abstract: In this paper, we propose a novel policy optimization framework that maximizes Return on Investment (ROI) of a policy using a fixed dataset within a Markov Decision Process (MDP) equipped with a cost function. ROI, defined as the ratio between the return and the accumulated cost of a policy, serves as a measure of efficiency of the policy. Despite the importance of maximizing ROI in various applications, it remains a challenging problem due to its nature as a ratio of two long-term values: return and accumulated cost. To address this, we formulate the ROI maximizing reinforcement learning problem as a linear fractional programming. We then incorporate the stationary distribution correction (DICE) framework to develop a practical offline ROI maximization algorithm. Our proposed algorithm, ROIDICE, yields an efficient policy that offers a superior trade-off between return and accumulated cost compared to policies trained using existing frameworks.


HYDRA-FL: Hybrid Knowledge Distillation for Robust and Accurate Federated Learning

Federated Learning;Knowledge Distillation;Poisoning Attacks

Summary: We show that Knowledge Distillation amplifies model poisoning attacks in FL, and design our algorithm HYDRA-FL to mitigate attack ampification.

Abstract: Data heterogeneity among Federated Learning (FL) users poses a significant challenge, resulting in reduced global model performance. The community has designed various techniques to tackle this issue, among which Knowledge Distillation (KD)-based techniques are common. While these techniques effectively improve performance under high heterogeneity, they inadvertently cause higher accuracy degradation under model poisoning attacks (known as \emph{attack amplification}). This paper presents a case study to reveal this critical vulnerability in KD-based FL systems. We show why KD causes this issue through empirical evidence and use it as motivation to design a hybrid distillation technique. We introduce a novel algorithm, Hybrid Knowledge Distillation for Robust and Accurate FL (HYDRA-FL), which reduces the impact of attacks in attack scenarios by offloading some of the KD loss to a shallow layer via an auxiliary classifier. We model HYDRA-FL as a generic framework and adapt it to two KD-based FL algorithms, FedNTD and MOON. Using these two as case studies, we demonstrate that our technique outperforms baselines in attack settings while maintaining comparable performance in benign settings.


Why Go Full? Elevating Federated Learning Through Partial Network Updates

Federated Learning;Partial Network Updates;Convergence Efficiency;Computational and Communicational Overhead Reduction

Summary: We observe the layer mismatch problem in federated learning and propose a partial network update method to address it, improving convergence speed, accuracy, and reducing computational and communication overhead.

Abstract: Federated learning is a distributed machine learning paradigm designed to protect user data privacy, which has been successfully implemented across various scenarios. In traditional federated learning, the entire parameter set of local models is updated and averaged in each training round. Although this full network update method maximizes knowledge acquisition and sharing for each model layer, it prevents the layers of the global model from cooperating effectively to complete the tasks of each client, a challenge we refer to as layer mismatch. This mismatch problem recurs after every parameter averaging, consequently slowing down model convergence and degrading overall performance. To address the layer mismatch issue, we introduce the FedPart method, which restricts model updates to either a single layer or a few layers during each communication round. Furthermore, to maintain the efficiency of knowledge acquisition and sharing, we develop several strategies to select trainable layers in each round, including sequential updating and multi-round cycle training. Through both theoretical analysis and experiments, our findings demonstrate that the FedPart method significantly surpasses conventional full network update strategies in terms of convergence speed and accuracy, while also reducing communication and computational overheads.


Improved Regret of Linear Ensemble Sampling

Summary:
We prove a
O
(
d
3
/
2
T
)
 frequentist regret bound for linear ensemble sampling.

Abstract:
In this work, we close the fundamental gap of theory and practice by providing an improved regret bound for linear ensemble sampling. We prove that with an ensemble size logarithmic in
T
, linear ensemble sampling can achieve a frequentist regret bound of
O
~
(
d
3
/
2
T
)
, matching state-of-the-art results for randomized linear bandit algorithms, where
d
and
T
are the dimension of the parameter and the time horizon respectively. Our approach introduces a general regret analysis framework for linear bandit algorithms. Additionally, we reveal a significant relationship between linear ensemble sampling and Linear Perturbed-History Exploration (LinPHE), showing that LinPHE is a special case of linear ensemble sampling when the ensemble size equals
T
. This insight allows us to derive a new regret bound of
O
~
(
d
3
/
2
T
)
for LinPHE, independent of the number of arms. Our contributions advance the theoretical foundation of ensemble sampling, bringing its regret bounds in line with the best known bounds for other randomized exploration algorithms.


Team-Fictitious Play for Reaching Team-Nash Equilibrium in Multi-team Games

Multi-agent reinforcement learning;fictitious play;multi-team games

Summary: A new variant of fictitious play provably converging to Team-Nash equilibrium in multi-team zero-sum games.

Abstract: Multi-team games, prevalent in robotics and resource management, involve team members striving for a joint best response against other teams. Team-Nash equilibrium (TNE) predicts the outcomes of such coordinated interactions. However, can teams of self-interested agents reach TNE? We introduce Team-Fictitious Play (Team-FP), a new variant of fictitious play where agents respond to the last actions of team members and the beliefs formed about other teams with some inertia in action updates. This design is essential in team coordination beyond the classical fictitious play dynamics. We focus on zero-sum potential team games (ZSPTGs) where teams can interact pairwise while the team members do not necessarily have identical payoffs. We show that Team-FP reaches near TNE in ZSPTGs with a quantifiable error bound. We extend Team-FP dynamics to multi-team Markov games for model-based and model-free cases. The convergence analysis tackles the challenge of non-stationarity induced by evolving opponent strategies based on the optimal coupling lemma and stochastic differential inclusion approximation methods. Our work strengthens the foundation for using TNE to predict the behavior of decentralized teams and offers a practical rule for team learning in multi-team environments. We provide extensive simulations of Team-FP dynamics and compare its performance with other widely studied dynamics such as smooth fictitious play and multiplicative weights update. We further explore how different parameters impact the speed of convergence.


PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models

Summary: PiSSA reinitializes LoRA's parameters by applying SVD to the base model, which enables faster convergence and ultimately superior performance. Additionally, it can reduce quantization error compared to QLoRA.

Abstract: To parameter-efficiently fine-tune (PEFT) large language models (LLMs), the low-rank adaptation (LoRA) method approximates the model changes $\Delta W \in \mathbb{R}^{m \times n}$ through the product of two matrices $A \in \mathbb{R}^{m \times r}$ and $B \in \mathbb{R}^{r \times n}$, where $r \ll \min(m, n)$, $A$ is initialized with Gaussian noise, and $B$ with zeros. LoRA freezes the original model $W$ and updates the "Noise & Zero" adapter, which may lead to slow convergence. To overcome this limitation, we introduce Principal Singular values and Singular vectors Adaptation (PiSSA). PiSSA shares the same architecture as LoRA, but initializes the adaptor matrices $A$ and $B$ with the principal components of the original matrix $W$, and put the remaining components into a residual matrix $W^{res} \in \mathbb{R}^{m \times n}$ which is frozen during fine-tuning. Compared to LoRA, PiSSA updates the principal components while freezing the "residual" parts, allowing faster convergence and enhanced performance. Comparative experiments of PiSSA and LoRA across 11 different models, ranging from 184M to 70B, encompassing 5 NLG and 8 NLU tasks, reveal that PiSSA consistently outperforms LoRA under identical experimental setups. On the GSM8K benchmark, Gemma-7B fine-tuned with PiSSA achieves an accuracy of 77.7%, surpassing LoRA's 74.53% by 3.25%. Due to the same architecture, PiSSA is also compatible with quantization to further reduce the memory requirement of fine-tuning. Compared to QLoRA, QPiSSA (PiSSA with 4-bit quantization) exhibits smaller quantization errors in the initial stages. Fine-tuning LLaMA-3-70B on GSM8K, QPiSSA attains an accuracy of 86.05%, exceeding the performances of QLoRA at 81.73%. Leveraging a fast SVD technique, PiSSA can be initialized in only a few seconds, presenting a negligible cost for transitioning from LoRA to PiSSA.


Universal Rates of Empirical Risk Minimization

Statistical learning theory;Universal learning;Empirical risk minimization;PAC learning

Summary: We consider the problem of universal learning by ERM in the realizable case and study the possible universal rates.

Abstract:
The well-known
empirical risk minimization
(ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is its so-called “learning curve”, that is, the decay of the expected error as a function of the input sample size. As the PAC model fails to explain the behavior of learning curves, recent research has explored an alternative universal learning model and has ultimately revealed a distinction between optimal universal and uniform learning rates (Bousquet et al., 2021). However, a basic understanding of such differences with a particular focus on the ERM principle has yet to be developed.
In this paper, we consider the problem of universal learning by ERM in the realizable case and study the possible universal rates. Our main result is a fundamental
tetrachotomy
: there are only four possible universal learning rates by ERM, namely, the learning curves of any concept class learnable by ERM decay either at
e
−
n
,
1
/
n
,
log

(
n
)
/
n
, or arbitrarily slow rates. Moreover, we provide a complete characterization of which concept classes fall into each of these categories, via new complexity structures. We also develop new combinatorial dimensions which supply sharp asymptotically-valid constant factors for these rates, whenever possible.


Understanding the Transferability of Representations via Task-Relatedness

Transfer Learning Analysis;Distribution Shift

Summary: We rigorously analyze transfer learning in terms of relatedness between tasks and show that task-relatedness accurately predicts transferability in various practical scenarios.

Abstract: The growing popularity of transfer learning due to the availability of models pre-trained on vast amounts of data, makes it imperative to understand when the knowledge of these pre-trained models can be transferred to obtain high-performing models on downstream target tasks. However, the exact conditions under which transfer learning succeeds in a cross-domain cross-task setting are still poorly understood. To bridge this gap, we propose a novel analysis that analyzes the transferability of the representations of pre-trained models to downstream tasks in terms of their relatedness to a given reference task. Our analysis leads to an upper bound on transferability in terms of task-relatedness, quantified using the difference between the class priors, label sets, and features of the two tasks.Our experiments using state-of-the-art pre-trained models show the effectiveness of task-relatedness in explaining transferability on various vision and language tasks. The efficient computability of task-relatedness even without labels of the target task and its high correlation with the model's accuracy after end-to-end fine-tuning on the target task makes it a useful metric for transferability estimation. Our empirical results of using task-relatedness on the problem of selecting the best pre-trained model from a model zoo for a target task highlight its utility for practical problems.


Classifier Clustering and Feature Alignment for Federated Learning under Distributed Concept Drift

federated learning;concept drift;data heterogeneity

Summary: We propose FedCCFA, a federated learning framework with classifier clustering and feature alignment.

Abstract:
Data heterogeneity is one of the key challenges in federated learning, and many efforts have been devoted to tackling this problem. However, distributed concept drift with data heterogeneity, where clients may additionally experience different concept drifts, is a largely unexplored area. In this work, we focus on real drift, where the conditional distribution
P
(
Y
|
X
)
changes. We first study how distributed concept drift affects the model training and find that local classifier plays a critical role in drift adaptation. Moreover, to address data heterogeneity, we study the feature alignment under distributed concept drift, and find two factors that are crucial for feature alignment: the conditional distribution
P
(
Y
|
X
)
and the degree of data heterogeneity. Motivated by the above findings, we propose FedCCFA, a federated learning framework with classifier clustering and feature alignment. To enhance collaboration under distributed concept drift, FedCCFA clusters local classifiers at class-level and generates clustered feature anchors according to the clustering results. Assisted by these anchors, FedCCFA adaptively aligns clients' feature spaces based on the entropy of label distribution
P
(
Y
)
, alleviating the inconsistency in feature space. Our results demonstrate that FedCCFA significantly outperforms existing methods under various concept drift settings. Code is available at https://github.com/Chen-Junbao/FedCCFA.


DreamClear: High-Capacity Real-World Image Restoration with Privacy-Safe Dataset Curation

Image restoration;Dataset Curation;Diffusion transformer

Summary: A high-capacity image restoration model trained on large-scale, privacy-safe high-quality image dataset

Abstract: Image restoration (IR) in real-world scenarios presents significant challenges due to the lack of high-capacity models and comprehensive datasets. To tackle these issues, we present a dual strategy: GenIR, an innovative data curation pipeline, and DreamClear, a cutting-edge Diffusion Transformer (DiT)-based image restoration model. GenIR, our pioneering contribution, is a dual-prompt learning pipeline that overcomes the limitations of existing datasets, which typically comprise only a few thousand images and thus offer limited generalizability for larger models. GenIR streamlines the process into three stages: image-text pair construction, dual-prompt based fine-tuning, and data generation & filtering. This approach circumvents the laborious data crawling process, ensuring copyright compliance and providing a cost-effective, privacy-safe solution for IR dataset construction. The result is a large-scale dataset of one million high-quality images. Our second contribution, DreamClear, is a DiT-based image restoration model. It utilizes the generative priors of text-to-image (T2I) diffusion models and the robust perceptual capabilities of multi-modal large language models (MLLMs) to achieve photorealistic restoration. To boost the model's adaptability to diverse real-world degradations, we introduce the Mixture of Adaptive Modulator (MoAM). It employs token-wise degradation priors to dynamically integrate various restoration experts, thereby expanding the range of degradations the model can address. Our exhaustive experiments confirm DreamClear's superior performance, underlining the efficacy of our dual strategy for real-world image restoration. Code and pre-trained models are available at: https://github.com/shallowdream204/DreamClear.


Scalable DP-SGD: Shuffling vs. Poisson Subsampling

Summary: Establishes new lower bounds on privacy analysis of DP-SGD with shuffling and provides a first comparative study of DP-SGD with Shuffling vs Poisson Subsampling in the light of the gaps in privacy analysis between the two approaches.

Abstract: We provide new lower bounds on the privacy guarantee of multi-epoch Adaptive Batch Linear Queries (ABLQ) mechanism with shuffled batch sampling, demonstrating substantial gaps when compared to Poisson subsampling; prior analysis was limited to a single epoch. Since the privacy analysis of Differentially Private Stochastic Gradient Descent (DP-SGD) is obtained by analyzing the ABLQ mechanism, this brings into serious question the common practice of implementing Shuffling based DP-SGD, but reporting privacy parameters as if Poisson subsampling was used. To understand the impact of this gap on the utility of trained machine learning models, we introduce a novel practical approach to implement Poisson subsampling at scale using massively parallel computation, and efficiently train models with the same. We provide a comparison between the utility of models trained with Poisson subsampling based DP-SGD, and the optimistic estimates of utility when using shuffling, via our new lower bounds on the privacy guarantee of ABLQ with shuffling.


MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models

Large Language Models;Pretraining;Data Curation

Summary: We introduce model-aware data selection with data influence models (MATES), where a data influence model continuously adapts to the evolving data preferences of the pretraining model and selects the data to optimize the efficacy of the pretraining.

Abstract: Pretraining data selection has the potential to improve language model pretraining efficiency by utilizing higher-quality data from massive web data corpora. Current data selection methods, which rely on either hand-crafted rules or larger reference models, are conducted statically and do not capture the evolving data preferences during pretraining. In this paper, we introduce model-aware data selection with data influence models (MATES), where a data influence model continuously adapts to the evolving data preferences of the pretraining model and then selects the data most effective for the current pretraining progress. Specifically, we collect oracle data influence by locally probing the pretraining model and fine-tune a small data influence model to approximate it accurately. The data influence model then predicts data influence over the whole pretraining corpus and selects the most influential data for the next pretraining stage. Experiments of pretraining 410M and 1B models on the C4 dataset demonstrate that MATES significantly outperforms random data selection on extensive downstream tasks. It doubles the gains achieved by the state-of-the-art data selection approach that leverages larger reference models and reduces the total FLOPs required to reach certain performances by half. Further analyses validate the effectiveness of the locally probed oracle data influence and the approximation with data influence models. Our code is open-sourced at https://github.com/cxcscmu/MATES.


Fisher Flow Matching for Generative Modeling over Discrete Data

Flow matching;Generative models;Riemannian manifolds;Discrete data

Summary: We propose a novel flow matching approach for discrete data by continuously reparameterising categorical distributions on the hypersphere.

Abstract:
Generative modeling over discrete data has recently seen numerous success stories, with applications spanning language modeling, biological sequence design, and graph-structured molecular data. The predominant generative modeling paradigm for discrete data is still autoregressive, with more recent alternatives based on diffusion or flow-matching falling short of their impressive performance in continuous data settings, such as image or video generation. In this work, we introduce Fisher-Flow, a novel flow-matching model for discrete data. Fisher-Flow takes a manifestly geometric perspective by considering categorical distributions over discrete data as points residing on a statistical manifold equipped with its natural Riemannian metric: the \emph{Fisher-Rao metric}. As a result, we demonstrate discrete data itself can be continuously reparameterised to points on the positive orthant of the
d
-hypersphere
S
+
d
, which allows us to define flows that map any source distribution to target in a principled manner by transporting mass along (closed-form) geodesics of
S
+
d
. Furthermore, the learned flows in Fisher-Flow can be further bootstrapped by leveraging Riemannian optimal transport leading to improved training dynamics. We prove that the gradient flow induced by Fisher-FLow is optimal in reducing the forward KL divergence. We evaluate Fisher-Flow on an array of synthetic and diverse real-world benchmarks, including designing DNA Promoter, and DNA Enhancer sequences. Empirically, we find that Fisher-Flow improves over prior diffusion and flow-matching models on these benchmarks.


Adaptive Visual Scene Understanding: Incremental Scene Graph Generation

Scene graph generation;Continual learning;In-context symbolic replay;Long tail distribution;Compositional scene graphs

Summary: We introduce a continual scene graph generation dataset and a model to tackle this problem.

Abstract: Scene graph generation (SGG) analyzes images to extract meaningful information about objects and their relationships. In the dynamic visual world, it is crucial for AI systems to continuously detect new objects and establish their relationships with existing ones. Recently, numerous studies have focused on continual learning within the domains of object detection and image recognition. However, a limited amount of research focuses on a more challenging continual learning problem in SGG. This increased difficulty arises from the intricate interactions and dynamic relationships among objects, and their associated contexts. Thus, in continual learning, SGG models are often required to expand, modify, retain, and reason scene graphs within the process of adaptive visual scene understanding. To systematically explore Continual Scene Graph Generation (CSEGG), we present a comprehensive benchmark comprising three learning regimes: relationship incremental, scene incremental, and relationship generalization. Moreover, we introduce a ``Replays via Analysis by Synthesis" method named RAS. This approach leverages the scene graphs, decomposes and re-composes them to represent different scenes, and replays the synthesized scenes based on these compositional scene graphs. The replayed synthesized scenes act as a means to practice and refine proficiency in SGG in known and unknown environments. Our experimental results not only highlight the challenges of directly combining existing continual learning methods with SGG backbones but also demonstrate the effectiveness of our proposed approach, enhancing CSEGG efficiency while simultaneously preserving privacy and memory usage. All data and source code will be made public.


Block Transformer: Global-to-Local Language Modeling for Fast Inference

language model;model architecture;efficient inference

Summary: We propose the Block Transformer architecture that adopts global-to-local modeling to autoregressive transformers to mitigate the bottlenecks of global self-attention and significantly improve inference throughput compared to vanilla transformers.

Abstract: We introduce the Block Transformer which adopts hierarchical global-to-local modeling to autoregressive transformers to mitigate the inference bottlenecks associated with self-attention. Self-attention requires the key-value (KV) cache of all previous sequences to be retrieved from memory at every decoding step to retrieve context information, leading to two primary bottlenecks during batch inference. First, there is a significant delay in obtaining the first token, as the information of the entire prompt must first be processed to prefill the KV cache. Second, computation of subsequent tokens is bottlenecked by the high memory I/O demand of fetching the entire KV cache, which grows linearly with sequence length, incurring quadratic memory reads overall. We design the Block Transformer to strategically mitigate these costs, by incorporating coarsity and locality into an integrated global-to-local architecture. At the lower layers, we aggregate tokens into fixed size blocks to apply attention across the entire sequence at coarse-grained detail, to capture the global context while minimizing KV cache overhead. At upper layers, we apply attention within each block to decode individual tokens, to model fine-grained details with a lightweight local KV cache. We pretrain vanilla and Block Transformers from scratch and demonstrate that Block Transformers reach 10--20x inference throughput compared to vanilla transformers with equivalent perplexity and zero-shot task performance.


Memorize What Matters: Emergent Scene Decomposition from Multitraverse

Autonomous Driving;Self-Supervised Learning;3D Gaussian Splatting

Summary: Self-supervised 2D ephemerality segmentation and 3D environmental mapping in urban scenes

Abstract: Humans naturally retain memories of permanent elements, while ephemeral moments often slip through the cracks of memory. This selective retention is crucial for robotic perception, localization, and mapping. To endow robots with this capability, we introduce 3D Gaussian Mapping (3DGM), a self-supervised, camera-only offline mapping framework grounded in 3D Gaussian Splatting. 3DGM converts multitraverse RGB videos from the same region into a Gaussian-based environmental map while concurrently performing 2D ephemeral object segmentation. Our key observation is that the environment remains consistent across traversals, while objects frequently change. This allows us to exploit self-supervision from repeated traversals to achieve environment-object decomposition. More specifically, 3DGM formulates multitraverse environmental mapping as a robust 3D representation learning problem, treating pixels of the environment and objects as inliers and outliers, respectively. Using robust feature distillation, feature residual mining, and robust optimization, 3DGM simultaneously performs 2D segmentation and 3D mapping without human intervention. We build the Mapverse benchmark, sourced from the Ithaca365 and nuPlan datasets, to evaluate our method in unsupervised 2D segmentation, 3D reconstruction, and neural rendering. Extensive results verify the effectiveness and potential of our method for self-driving and robotics.


Towards Next-Level Post-Training Quantization of Hyper-Scale Transformers

Summary: We have proposed a next-level post-training quantization scheme for Hyper-scale Transformer models

Abstract: With the increasing complexity of generative AI models, post-training quantization (PTQ) has emerged as a promising solution for deploying hyper-scale models on edge devices such as mobile and TVs. Existing PTQ schemes, however, consume considerable time and resources, which could be a bottleneck in real situations where frequent model updates and multiple hyperparameter tunings are required. As a cost-effective alternative, learning-free PTQ schemes have been proposed. However, the performance is somewhat limited because they cannot consider the inter-layer dependency within the attention module, which is a significant feature of Transformers. In this paper, we thus propose a novel PTQ algorithm that balances accuracy and efficiency. The key idea of the proposed algorithm called aespa is to perform quantization layer-wise for efficiency while targeting attention-wise reconstruction to consider the cross-layer dependency. Through extensive experiments on various language models and complexity analysis, we demonstrate that aespa is accurate and efficient in quantizing Transformer models. The code will be available at https: //github.com/SamsungLabs/aespa.


Fast Rates for Bandit PAC Multiclass Classification

Summary: We establish optimal sample complexity bounds for agnostic PAC in bandit multiclass classification with finite hypothesis classes and Natarajan classes

Abstract:
We study multiclass PAC learning with bandit feedback, where inputs are classified into one of
K
possible labels and feedback is limited to whether or not the predicted labels are correct. Our main contribution is in designing a novel learning algorithm for the agnostic
(
ε
,
δ
)
-PAC version of the problem, with sample complexity of
O
(
(
poly
(
K
)
+
1
/
ε
2
)
log

(
|
H
|
/
δ
)
)
for any finite hypothesis class
H
. In terms of the leading dependence on
ε
, this improves upon existing bounds for the problem, that are of the form
O
(
K
/
ε
2
)
. We also provide an extension of this result to general classes and establish similar sample complexity bounds in which
log

|
H
|
is replaced by the Natarajan dimension. This matches the optimal rate in the full-information version of the problem and resolves an open question studied by Daniely, Sabato, Ben-David, and Shalev-Shwartz (2011) who demonstrated that the multiplicative price of bandit feedback in realizable PAC learning is
Θ
(
K
)
. We complement this by revealing a stark contrast with the agnostic case, where the price of bandit feedback is only
O
(
1
)
as
ε
→
0
. Our algorithm utilizes a stochastic optimization technique to minimize a log-barrier potential based on Frank-Wolfe updates for computing a low-variance exploration distribution over the hypotheses, and is made computationally efficient provided access to an ERM oracle over
H
.


Sample-Efficient Private Learning of Mixtures of Gaussians

Differential Privacy;Density Estimation;Mixtures of Gaussians;Sample Complexity

Summary: We provide improved sample complexity bounds for learning mixtures of Gaussians with differential privacy, which are optimal for sufficiently large dimension or for one-dimensional Gaussian Mixtures..

Abstract:
We study the problem of learning mixtures of Gaussians with approximate differential privacy. We prove that roughly
k
d
2
+
k
1.5
d
1.75
+
k
2
d
samples suffice to learn a mixture of
k
arbitrary
d
-dimensional Gaussians up to low total variation distance, with differential privacy. Our work improves over the previous best result (which required roughly
k
2
d
4
samples) and is provably optimal when
d
is much larger than
k
2
. Moreover, we give the first optimal bound for privately learning mixtures of
k
univariate (i.e.,
1
-dimensional) Gaussians. Importantly, we show that the sample complexity for learning mixtures of univariate Gaussians is linear in the number of components
k
, whereas the previous best sample complexity was quadratic in
k
. Our algorithms utilize various techniques, including the inverse sensitivity mechanism, sample compression for distributions, and methods for bounding volumes of sumsets.


CLIPAway: Harmonizing focused embeddings for removing objects via diffusion models

Summary: A training-free, plug-and-play method that uses CLIP embeddings to focus on background areas for seamless object removal in diffusion models without requiring specialized datasets.

Abstract: Advanced image editing techniques, particularly inpainting, are essential for seamlessly removing unwanted elements while preserving visual integrity. Traditional GAN-based methods have achieved notable success, but recent advancements in diffusion models have produced superior results due to their training on large-scale datasets, enabling the generation of remarkably realistic inpainted images. Despite their strengths, diffusion models often struggle with object removal tasks without explicit guidance, leading to unintended hallucinations of the removed object. To address this issue, we introduce CLIPAway, a novel approach leveraging CLIP embeddings to focus on background regions while excluding foreground elements. CLIPAway enhances inpainting accuracy and quality by identifying embeddings that prioritize the background, thus achieving seamless object removal. Unlike other methods that rely on specialized training datasets or costly manual annotations, CLIPAway provides a flexible, plug-and-play solution compatible with various diffusion-based inpainting techniques.


Language Models as Zero-shot Lossless Gradient Compressors: Towards General Neural Parameter Prior Models

large-scale language models;lossless gradient compression

Summary: We show that LLMs can compress gradients in a zero-shot setting, demonstrating a promising direction toward general parameter priors.

Abstract: Despite the widespread use of statistical prior models in various fields, such models for neural network gradients have long been overlooked. The inherent challenge stems from their high-dimensional structures and complex interdependencies, which complicate effective modeling. In this work, we demonstrate the potential of large language models (LLMs) to act as gradient priors in a zero-shot setting. We examine the property by considering lossless gradient compression -- a critical application in distributed learning -- that depends heavily on precise probability modeling. To achieve this, we introduce LM-GC, a novel method that integrates LLMs with arithmetic coding. Our technique converts plain gradients into text-like formats, enhancing token efficiency by up to 38 times compared to their plain representations. We ensure that this data conversion maintains a close alignment with the structure of plain gradients and the symbols commonly recognized by LLMs. Our experiments indicate that LM-GC surpasses existing state-of-the-art lossless compression methods, improving compression rates by 10% up to 17.2% across various datasets and architectures. Additionally, our approach shows promising compatibility with lossy compression techniques such as quantization and sparsification. These findings highlight the significant potential of LLMs as a model for effectively handling gradients. Code is available at https://github.com/hui-po-wang/LM-GC.


DataStealing: Steal Data from Diffusion Models in Federated Learning with Multiple Trojans

Federated Learning;Diffusion Models;DataStealing;Multiple Trojans;Adaptive Scale

Summary: This paper presents a new privacy vulnerability in training diffusion models with Federated Learning and proposes an adaptive Trojan attack to bypass advanced defenses and achieve DataStealing.

Abstract:
Federated Learning (FL) is commonly used to collaboratively train models with privacy preservation. In this paper, we found out that the popular diffusion models have introduced a new vulnerability to FL, which brings serious privacy threats. Despite stringent data management measures, attackers can steal massive private data from local clients through multiple Trojans, which control generative behaviors with multiple triggers. We refer to the new task as
DataStealing
and demonstrate that the attacker can achieve the purpose based on our proposed Combinatorial Triggers (ComboTs) in a vanilla FL system. However, advanced distance-based FL defenses are still effective in filtering the malicious update according to the distances between each local update. Hence, we propose an Adaptive Scale Critical Parameters (AdaSCP) attack to circumvent the defenses and seamlessly incorporate malicious updates into the global model. Specifically, AdaSCP evaluates the importance of parameters with the gradients in dominant timesteps of the diffusion model. Subsequently, it adaptively seeks the optimal scale factor and magnifies critical parameter updates before uploading to the server. As a result, the malicious update becomes similar to the benign update, making it difficult for distance-based defenses to identify. Extensive experiments reveal the risk of leaking thousands of images in training diffusion models with FL. Moreover, these experiments demonstrate the effectiveness of AdaSCP in defeating advanced distance-based defenses. We hope this work will attract more attention from the FL community to the critical privacy security issues of Diffusion Models. Code: https://github.com/yuangan/DataStealing.


Zero-Shot Reinforcement Learning from Low Quality Data

reinforcement learning;offline reinforcement learning;unsupervised reinforcement learning;zero-shot reinforcement learning

Summary: We propose methods for improving the performance of zero-shot RL methods when trained on low quality offline datasets.

Abstract: Zero-shot reinforcement learning (RL) promises to provide agents that can perform any task in an environment after an offline, reward-free pre-training phase. Methods leveraging successor measures and successor features have shown strong performance in this setting, but require access to large heterogenous datasets for pre-training which cannot be expected for most real problems. Here, we explore how the performance of zero-shot RL methods degrades when trained on small homogeneous datasets, and propose fixes inspired by conservatism, a well-established feature of performant single-task offline RL algorithms. We evaluate our proposals across various datasets, domains and tasks, and show that conservative zero-shot RL algorithms outperform their non-conservative counterparts on low quality datasets, and perform no worse on high quality datasets. Somewhat surprisingly, our proposals also outperform baselines that get to see the task during training. Our code is available via the project page https://enjeeneer.io/projects/zero-shot-rl/.


Is Your LiDAR Placement Optimized for 3D Scene Understanding?

Autonomous Driving;LiDAR Semantic Segmentation;Sensor Placement

Summary: Place3D is a full-cycle pipeline that encompasses LiDAR placement optimization, data generation, and downstream evaluations.

Abstract: The reliability of driving perception systems under unprecedented conditions is crucial for practical usage. Latest advancements have prompted increasing interest in multi-LiDAR perception. However, prevailing driving datasets predominantly utilize single-LiDAR systems and collect data devoid of adverse conditions, failing to capture the complexities of real-world environments accurately. Addressing these gaps, we proposed Place3D, a full-cycle pipeline that encompasses LiDAR placement optimization, data generation, and downstream evaluations. Our framework makes three appealing contributions. 1) To identify the most effective configurations for multi-LiDAR systems, we introduce the Surrogate Metric of the Semantic Occupancy Grids (M-SOG) to evaluate LiDAR placement quality. 2) Leveraging the M-SOG metric, we propose a novel optimization strategy to refine multi-LiDAR placements. 3) Centered around the theme of multi-condition multi-LiDAR perception, we collect a 280,000-frame dataset from both clean and adverse conditions. Extensive experiments demonstrate that LiDAR placements optimized using our approach outperform various baselines. We showcase exceptional results in both LiDAR semantic segmentation and 3D object detection tasks, under diverse weather and sensor failure conditions.


Right this way: Can VLMs Guide Us to See More to Answer Questions?

visual accessibility;self-knowledge;vision language models

Summary: Our study explores VLMs capabilities in assessing answerability and guiding information acquisition, introducing a novel task with  a benchmark dataset and a data-efficient training framework to improve the model's performance.

Abstract: In question-answering scenarios, humans can assess whether the available information is sufficient and seek additional information if necessary, rather than providing a forced answer. In contrast, Vision Language Models (VLMs) typically generate direct, one-shot responses without evaluating the sufficiency of the information. To investigate this gap, we identify a critical and challenging task in the Visual Question Answering (VQA) scenario: can VLMs indicate how to adjust an image when the visual information is insufficient to answer a question? This capability is especially valuable for assisting visually impaired individuals who often need guidance to capture images correctly. To evaluate this capability of current VLMs, we introduce a human-labeled dataset as a benchmark for this task. Additionally, we present an automated framework that generates synthetic training data by simulating ``where to know'' scenarios. Our empirical results show significant performance improvements in mainstream VLMs when fine-tuned with this synthetic data. This study demonstrates the potential to narrow the gap between information assessment and acquisition in VLMs, bringing their performance closer to humans.


Learning with Fitzpatrick Losses

loss functions;convex analysis;monotone operators

Summary: A new family of loss functions based on monotone operator theory that lower bound Fenchel-Young losses, such as the the logistic loss.

Abstract: Fenchel-Young losses are a family of loss functions, encompassing the squared, logistic and sparsemax losses, among others. They are convex w.r.t. the model output and the target, separately. Each Fenchel-Young loss is implicitly associated with a link function, that maps model outputs to predictions. For instance, the logistic loss is associated with the soft argmax link function. Can we build new loss functions associated with the same link function as Fenchel-Young losses? In this paper, we introduce Fitzpatrick losses, a new family of separately convex loss functions based on the Fitzpatrick function. A well-known theoretical tool in maximal monotone operator theory, the Fitzpatrick function naturally leads to a refined Fenchel-Young inequality, making Fitzpatrick losses tighter than Fenchel- Young losses, while maintaining the same link function for prediction. As an example, we introduce the Fitzpatrick logistic loss and the Fitzpatrick sparsemax loss, counterparts of the logistic and the sparsemax losses. This yields two new tighter losses associated with the soft argmax and the sparse argmax, two of the most ubiquitous output layers used in machine learning. We study in details the properties of Fitzpatrick losses and, in particular, we show that they can be seen as Fenchel-Young losses using a modified, target-dependent generating function. We demonstrate the effectiveness of Fitzpatrick losses for label proportion estimation.


Learning Place Cell Representations and Context-Dependent Remapping

Summary: We train neural networks to minimize a similarity-based objective function to learn joint encodings of space and context, and observe place cell-like representations and remapping in network responses

Abstract: Hippocampal place cells are known for their spatially selective firing patterns, which has led to the suggestion that they encode an animal's location. However, place cells also respond to contextual cues, such as smell. Furthermore, they have the ability to remap, wherein the firing fields and rates of cells change in response to changes in the environment. How place cell responses emerge, and how these representations remap is not fully understood. In this work, we propose a similarity-based objective function that translates proximity in space, to proximity in representation. We show that a neural network trained to minimize the proposed objective learns place-like representations. We also show that the proposed objective is easily extended to include other sources of information, such as context information, in the same way. When trained to encode multiple contexts, networks learn distinct representations, exhibiting remapping behaviors between contexts. The proposed objective is invariant to orthogonal transformations. Such transformations of the original trained representation (e.g. rotations), therefore yield new representations distinct from the original, without explicit relearning, akin to remapping. Our findings shed new light on the formation and encoding properties of place cells, and also demonstrate an interesting case of representational reuse.


Harnessing Multiple Correlated Networks for Exact Community Recovery

Stochastic block model;community recovery;graph matching;correlated random graphs;information-theoretic limits

Summary: We derive the precise information-theoretic threshold for exact community recovery from any constant number of correlated stochastic block models, showcasing the power of integrative data analysis and quantifying the value of each additional graph.

Abstract:
We study the problem of learning latent community structure from multiple correlated networks, focusing on edge-correlated stochastic block models with two balanced communities. Recent work of Gaudio, Rácz, and Sridhar (COLT 2022) determined the precise information-theoretic threshold for exact community recovery using two correlated graphs; in particular, this showcased the subtle interplay between community recovery and graph matching. Here we study the natural setting of more than two graphs. The main challenge lies in understanding how to aggregate information across several graphs when none of the pairwise latent vertex correspondences can be exactly recovered. Our main result derives the precise information-theoretic threshold for exact community recovery using any constant number of correlated graphs, answering a question of Gaudio, Rácz, and Sridhar (COLT 2022). In particular, for every
K
≥
3
we uncover and characterize a region of the parameter space where exact community recovery is possible using
K
correlated graphs, even though (1) this is information-theoretically impossible using any
K
−
1
of them and (2) none of the latent matchings can be exactly recovered.


COLD: Causal reasOning in cLosed Daily activities

Causal Common Sense;Causal NLP;LLMs;Commonsense Reasoning

Summary: We present a new perspective on causal reasoning in NLP by using a closed system (defined by real-world commonsense activities) and propose a framework with underlying causal graphs. The causal queries help validate causal reasoning in LLMs.

Abstract: Large Language Models (LLMs) have shown state-of-the-art performance in a variety of tasks, including arithmetic and reasoning; however, to gauge the intellectual capabilities of LLMs, causal reasoning has become a reliable proxy for validating a general understanding of the mechanics and intricacies of the world similar to humans. Previous works in natural language processing (NLP) have either focused on open-ended causal reasoning via causal commonsense reasoning (CCR) or framed a symbolic representation-based question answering for theoretically backed-up analysis via a causal inference engine. The former adds an advantage of real-world grounding but lacks theoretically backed-up analysis/validation, whereas the latter is far from real-world grounding. In this work, we bridge this gap by proposing the COLD (Causal reasOning in cLosed Daily activities) framework, which is built upon human understanding of daily real-world activities to reason about the causal nature of events. We show that the proposed framework facilitates the creation of enormous causal queries (∼ 9 million) and comes close to the mini-turing test, simulating causal reasoning to evaluate the understanding of a daily real-world task. We evaluate multiple LLMs on the created causal queries and find that causal reasoning is challenging even for activities trivial to humans. We further explore (the causal reasoning abilities of LLMs) using the backdoor criterion to determine the causal strength between events.


Learning Social Welfare Functions

Social Choice Learning;Power Mean Functions;PAC Learning;Preference Learning;Statistical Learning Theory;Social Welfare Functions

Summary: We show how to learn a policy maker's implicit social welfare function from their past decisions by fitting power mean functions, with provable sample complexity guarantees even under noisy observations.

Abstract: Is it possible to understand or imitate a policy maker's rationale by looking at past decisions they made? We formalize this question as the problem of learning social welfare functions belonging to the well-studied family of power mean functions. We focus on two learning tasks; in the first, the input is vectors of utilities of an action (decision or policy) for individuals in a group and their associated social welfare as judged by a policy maker, whereas in the second, the input is pairwise comparisons between the welfares associated with a given pair of utility vectors. We show that power mean functions are learnable with polynomial sample complexity in both cases, even if the social welfare information is noisy. Finally, we design practical algorithms for these tasks and evaluate their performance.


Great Minds Think Alike: The Universal Convergence Trend of Input Salience

explainable artificial intelligence;saliency maps;model distributions

Summary: Leveraging input saliency maps, we discover that with increasing capacities, the distributions of models converge to the almost-shared population mean, and thus the limiting of model can be estimated through the population mean of small models.

Abstract: Uncertainty is introduced in optimized DNNs through stochastic algorithms, forming specific distributions. Training models can be seen as random sampling from this distribution of optimized models. In this work, we study the distribution of optimized DNNs as a family of functions by leveraging a pointwise approach. We focus on the input saliency maps, as the input gradient field is decisive to the models' mathematical essence. Our investigation of saliency maps reveals a counter-intuitive trend: two stochastically optimized models tend to resemble each other more as either of their capacities increases. Therefore, we hypothesize several properties of these distributions, suggesting that (1) Within the same model architecture (e.g., CNNs, ResNets), different family variants (e.g., varying capacities) tend to align in terms of their population mean directions of the input salience. And (2) the distributions of optimized models follow a convergence trend to their shared population mean as the capacity increases. Furthermore, we also propose semi-parametric distributions based on the Saw distribution to model the convergence trend, satisfying all the counter-intuitive observations. Our experiments shed light on the significant implications of our hypotheses in various application domains, including black-box attacks, deep ensembles, etc. These findings not only enhance our understanding of DNN behaviors but also offer valuable insights for their practical application in diverse areas of deep learning.


Doubly Mild Generalization for Offline Reinforcement Learning

Summary: This work proposes Doubly Mild Generalization, comprising mild action generalization and mild generalization propagation, to appropriately exploit generalization in offline RL.

Abstract: Offline Reinforcement Learning (RL) suffers from the extrapolation error and value overestimation. From a generalization perspective, this issue can be attributed to the over-generalization of value functions or policies towards out-of-distribution (OOD) actions. Significant efforts have been devoted to mitigating such generalization, and recent in-sample learning approaches have further succeeded in entirely eschewing it. Nevertheless, we show that mild generalization beyond the dataset can be trusted and leveraged to improve performance under certain conditions. To appropriately exploit generalization in offline RL, we propose Doubly Mild Generalization (DMG), comprising (i) mild action generalization and (ii) mild generalization propagation. The former refers to selecting actions in a close neighborhood of the dataset to maximize the Q values. Even so, the potential erroneous generalization can still be propagated, accumulated, and exacerbated by bootstrapping. In light of this, the latter concept is introduced to mitigate the generalization propagation without impeding the propagation of RL learning signals. Theoretically, DMG guarantees better performance than the in-sample optimal policy in the oracle generalization scenario. Even under worst-case generalization, DMG can still control value overestimation at a certain level and lower bound the performance. Empirically, DMG achieves state-of-the-art performance across Gym-MuJoCo locomotion tasks and challenging AntMaze tasks. Moreover, benefiting from its flexibility in both generalization aspects, DMG enjoys a seamless transition from offline to online learning and attains strong online fine-tuning performance.


Randomized Exploration in Cooperative Multi-Agent Reinforcement Learning

Multi-Agent Reinforcement Learning;Randomized Exploration;Deep Reinforcement Learning

Summary: This paper presents the first study on provably efficient randomized exploration in cooperative multi-agent reinforcement learning.

Abstract:
We present the first study on provably efficient randomized exploration in cooperative multi-agent reinforcement learning (MARL). We propose a unified algorithm framework for randomized exploration in parallel Markov Decision Processes (MDPs), and two Thompson Sampling (TS)-type algorithms, CoopTS-PHE and CoopTS-LMC, incorporating the perturbed-history exploration (PHE) strategy and the Langevin Monte Carlo exploration (LMC) strategy respectively, which are flexible in design and easy to implement in practice. For a special class of parallel MDPs where the transition is (approximately) linear, we theoretically prove that both CoopTS-PHE and CoopTS-LMC achieve a
O
~
(
d
3
/
2
H
2
M
K
)
regret bound with communication complexity
O
~
(
d
H
M
2
)
, where
d
is the feature dimension,
H
is the horizon length,
M
is the number of agents, and
K
is the number of episodes. This is the first theoretical result for randomized exploration in cooperative MARL. We evaluate our proposed method on multiple parallel RL environments, including a deep exploration problem (i.e.,
N
-chain), a video game, and a real-world problem in energy systems. Our experimental results support that our framework can achieve better performance, even under conditions of misspecified transition models. Additionally, we establish a connection between our unified framework and the practical application of federated learning.


Towards Harmless Rawlsian Fairness Regardless of Demographic Prior

Harmless fairness;demographics-free;reducing variance of losses

Summary: Harmless Rawlsian Fairness Regardless of Demographics via decreasing Variance of Losses

Abstract: Due to privacy and security concerns, recent advancements in group fairness advocate for model training regardless of demographic information. However, most methods still require prior knowledge of demographics. In this study, we explore the potential for achieving fairness without compromising its utility when no prior demographics are provided to the training set, namely harmless Rawlsian fairness. We ascertain that such a fairness requirement with no prior demographic information essential promotes training losses to exhibit a Dirac delta distribution. To this end, we propose a simple but effective method named VFair to minimize the variance of training losses inside the optimal set of empirical losses. This problem is then optimized by a tailored dynamic update approach that operates in both loss and gradient dimensions, directing the model towards relatively fairer solutions while preserving its intact utility. Our experimental findings indicate that regression tasks, which are relatively unexplored from literature, can achieve significant fairness improvement through VFair regardless of any prior, whereas classification tasks usually do not because of their quantized utility measurements. The implementation of our method is publicly available at https://github.com/wxqpxw/VFair.


Interpreting CLIP with Sparse Linear Concept Embeddings (SpLiCE)

Interpretable Machine Learning;Dictionary Learning;Representation Learning;Multimodal Models;Interpretability;CLIP

Summary: We use dictionary learning to interpret CLIP embeddings by representing them as sparse combinations of semantic concepts, resulting in interpretability while maintaining high performance and unlocking novel use cases.

Abstract: CLIP embeddings have demonstrated remarkable performance across a wide range of multimodal applications. However, these high-dimensional, dense vector representations are not easily interpretable, limiting our understanding of the rich structure of CLIP and its use in downstream applications that require transparency. In this work, we show that the semantic structure of CLIP's latent space can be leveraged to provide interpretability, allowing for the decomposition of representations into semantic concepts. We formulate this problem as one of sparse recovery and propose a novel method, Sparse Linear Concept Embeddings (SpLiCE), for transforming CLIP representations into sparse linear combinations of human-interpretable concepts. Distinct from previous work, \method is task-agnostic and can be used, without training, to explain and even replace traditional dense CLIP representations, maintaining high downstream performance while significantly improving their interpretability. We also demonstrate significant use cases of \method representations including detecting spurious correlations and model editing. Code is provided at https://github.com/AI4LIFE-GROUP/SpLiCE.


Human-3Diffusion: Realistic Avatar Creation via Explicit 3D Consistent Diffusion Models

3D Reconstruction;3D Human Reconstruction;Diffusion Models;3D Generative Models;2D Foundation Models

Summary: A novel 3D consistent diffusion framework that utilize pretrained 2D diffusion prior for 3D reconstruction and use reconstructed 3D to guide 2D sampling process

Abstract: Creating realistic avatars from a single RGB image is an attractive yet challenging problem. To deal with challenging loose clothing or occlusion by interaction objects, we leverage powerful shape prior from 2D diffusion models pretrained on large datasets. Although 2D diffusion models demonstrate strong generalization capability, they cannot provide multi-view shape priors with guaranteed 3D consistency. We propose Human-3Diffusion: Realistic Avatar Creation via Explicit 3D Consistent Diffusion. Our key insight is that 2D multi-view diffusion and 3D reconstruction models provide complementary information for each other. By coupling them in a tight manner, we can fully leverage the potential of both models. We introduce a novel image-conditioned generative 3D Gaussian Splats reconstruction model that leverages the prior from 2D multi-view diffusion models, and provides an explicit 3D representation, which further guides the 2D reverse sampling process to have better 3D consistency. Experiments show that our proposed framework outperforms state-of-the-art methods and enables the creation of realistic avatars from a single RGB image, achieving high-fidelity in both geometry and appearance. Extensive ablations also validate the efficacy of our design, (1) multi-view 2D priors conditioning in generative 3D reconstruction and (2) consistency refinement of sampling trajectory via the explicit 3D representation. Our code and models are released at https://yuxuan-xue.com/human-3diffusion/.


Progressive Entropic Optimal Transport Solvers

Summary: We propose a progressive algorithm for estimation of OT maps and plans. We prove its statistically consistency and demonstrate its performance on synthetic and single-cell data.

Abstract:
Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds of sizes
n
and
m
in
R
d
, entropic OT (EOT) solvers have emerged as the most reliable tool to either solve the Kantorovich problem and output a
n
×
m
coupling matrix, or to solve the Monge problem and learn a vector-valued push-forward map. While the robustness of EOT couplings/maps makes them a go-to choice in practical applications, EOT solvers remain difficult to tune because of a small but influential set of hyperparameters, notably the omnipresent entropic regularization strength
ε
. Setting
ε
can be difficult, as it simultaneously impacts various performance metrics, such as compute speed, statistical performance, generalization, and bias. In this work, we propose a new class of EOT solvers (ProgOT), that can estimate both plans and transport maps. We take advantage of several opportunities to optimize the computation of EOT solutions by dividing mass displacement using a time discretization, borrowing inspiration from dynamic OT formulations, and conquering each of these steps using EOT with properly scheduled parameters. We provide experimental evidence demonstrating that ProgOT is a faster and more robust alternative to standard solvers when computing couplings at large scales, even outperforming neural network-based approaches. We also prove statistical consistency of our approach for estimating OT maps.


Asynchronous Perception Machine for Efficient Test Time Training

MORTAL COMPUTATION;GLOM;test time training;neural fields;implicit representation;distillation

Summary: APM introduces asynchronous patch-processing for test-time-training instead of parallel perception. APM leverages GLOM's islands of agreement. We present the scientific evidence towards validating GLOM's insight:  if input percept is really a field.

Abstract:
In this work, we propose Asynchronous Perception Machine (APM), a computationally-efficient architecture for test-time-training (TTT). APM can process patches of an image one at a time in any order asymmetrically and still encode semantic-awareness in the net. We demonstrate APM's ability to recognize out-of-distribution images without dataset-specific pre-training, augmentation or any-pretext task. APM offers competitive performance over existing TTT approaches. To perform TTT, APM just distills test sample's representation once. APM possesses a unique property: it can learn using just this single representation and starts predicting semantically-aware features. APM demostrates potential applications beyond test-time-training: APM can scale up to a dataset of 2D images and yield semantic-clusterings in a single forward pass. APM also provides first empirical evidence towards validating GLOM's insight, i.e. input percept is a field. Therefore, APM helps us converge towards an implementation which can do both interpolation and perception on a shared-connectionist hardware. Our code is publicly available at https://rajatmodi62.github.io/apm_project_page/
It now appears that some of the ideas in GLOM could be made to work.
https://www.technologyreview.com/2021/04/16/1021871/geoffrey-hinton-glom-godfather-ai-neural-networks/
GLOM = Geoff's Latest Original Model.
   .-""""""-.
 .'          '.
/   O      O   \
|      O       |
 \  '------'  /
  '.        .'
    '-....-'
Silent men in deep-contemplation.
Silent men emerges only sometimes.
Silent men love all.
Silent men practice slow science.


Ensemble Learning for Heterogeneous Large Language Models with Deep Parallel Collaboration

Ensemble Learning;Large Language Model;Relative Representation

Summary: Enable the probability distribution averaging between heterogeneous large language models

Abstract: Large language models (LLMs) exhibit complementary strengths in various tasks, motivating the research of LLM ensembling. However, existing work focuses on training an extra reward model or fusion model to select or combine all candidate answers, posing a great challenge to the generalization on unseen data distributions. Besides, prior methods use textual responses as communication media, ignoring the valuable information in the internal representations. In this work, we propose a training-free ensemble framework \textsc{DeePEn}, fusing the informative probability distributions yielded by different LLMs at each decoding step. Unfortunately, the vocabulary discrepancy between heterogeneous LLMs directly makes averaging the distributions unfeasible due to the token misalignment. To address this challenge, \textsc{DeePEn} maps the probability distribution of each model from its own probability space to a universal \textit{relative space} based on the relative representation theory, and performs aggregation. Next, we devise a search-based inverse transformation to transform the aggregated result back to the probability space of one of the ensembling LLMs (main model), in order to determine the next token. We conduct extensive experiments on ensembles of different number of LLMs, ensembles of LLMs with different architectures, and ensembles between the LLM and the specialist model. Experimental results show that (i) \textsc{DeePEn} achieves consistent improvements across six benchmarks covering subject examination, reasoning, and knowledge, (ii) a well-performing specialist model can benefit from a less effective LLM through distribution fusion, and (iii) \textsc{DeePEn} has complementary strengths with other ensemble methods such as voting.


Vidu4D: Single Generated Video to High-Fidelity 4D Reconstruction with Dynamic Gaussian Surfels

generative models;4D reconstruction;Gaussian splatting

Summary: Vidu4D, a reconstruction model that excels in accurately reconstructing dynamic gaussian surfels from single generated videos.

Abstract: Video generative models are receiving particular attention given their ability to generate realistic and imaginative frames. Besides, these models are also observed to exhibit strong 3D consistency, significantly enhancing their potential to act as world simulators. In this work, we present Vidu4D, a novel reconstruction model that excels in accurately reconstructing 4D (i.e., sequential 3D) representations from single generated videos, addressing challenges associated with non-rigidity and frame distortion. This capability is pivotal for creating high-fidelity virtual contents that maintain both spatial and temporal coherence. At the core of Vidu4D is our proposed Dynamic Gaussian Surfels (DGS) technique. DGS optimizes time-varying warping functions to transform Gaussian surfels (surface elements) from a static state to a dynamically warped state. This transformation enables a precise depiction of motion and deformation over time. To preserve the structural integrity of surface-aligned Gaussian surfels, we design the warped-state geometric regularization based on continuous warping fields for estimating normals. Additionally, we learn refinements on rotation and scaling parameters of Gaussian surfels, which greatly alleviates texture flickering during the warping process and enhances the capture of fine-grained appearance details. Vidu4D also contains a novel initialization state that provides a proper start for the warping fields in DGS. Equipping Vidu4D with an existing video generative model, the overall framework demonstrates high-fidelity text-to-4D generation in both appearance and geometry.


DistillNeRF: Perceiving 3D Scenes from Single-Glance Images by Distilling Neural Fields and Foundation Model Features

Autonomous Driving; Generalizable NeRF; Scene Representation Learning; Distillation

Summary: DistillNeRF, perceiving/reconstructing the 3D driving world without any labels or per-scene training!

Abstract: We propose DistillNeRF, a self-supervised learning framework addressing the challenge of understanding 3D environments from limited 2D observations in outdoor autonomous driving scenes. Our method is a generalizable feedforward model that predicts a rich neural scene representation from sparse, single-frame multi-view camera inputs with limited view overlap, and is trained self-supervised with differentiable rendering to reconstruct RGB, depth, or feature images. Our first insight is to exploit per-scene optimized Neural Radiance Fields (NeRFs) by generating dense depth and virtual camera targets from them, which helps our model to learn enhanced 3D geometry from sparse non-overlapping image inputs. Second, to learn a semantically rich 3D representation, we propose distilling features from pre-trained 2D foundation models, such as CLIP or DINOv2, thereby enabling various downstream tasks without the need for costly 3D human annotations. To leverage these two insights, we introduce a novel model architecture with a two-stage lift-splat-shoot encoder and a parameterized sparse hierarchical voxel representation. Experimental results on the NuScenes and Waymo NOTR datasets demonstrate that DistillNeRF significantly outperforms existing comparable state-of-the-art self-supervised methods for scene reconstruction, novel view synthesis, and depth estimation; and it allows for competitive zero-shot 3D semantic occupancy prediction, as well as open-world scene understanding through distilled foundation model features. Demos and code will be available at https://distillnerf.github.io/.


Navigable Graphs for High-Dimensional Nearest Neighbor Search: Constructions and Limits

vector databases;navigable graphs;near-neighbor search

Summary: We prove tight upper and lower bounds for the average degree of navigable graphs for high-dimensional point sets.

Abstract:
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of (approximately) "navigable" graphs over high-dimensional point sets. A graph is navigable if we can successfully move from any starting node to any target node using a greedy routing strategy where we always move to the neighbor that is closest to the destination according to the given distance function. The complete graph is obviously navigable for any point set, but the important question for applications is if sparser graphs can be constructed. While this question is fairly well understood in low-dimensions, we establish some of the first upper and lower bounds for high-dimensional point sets. First, we give a simple and efficient way to construct a navigable graph with average degree
O
(
n
log

n
)
for any set of
n
points, in any dimension, for any distance function. We compliment this result with a nearly matching lower bound: even under the Euclidean metric in
O
(
log

n
)
dimensions, a random point set has no navigable graph with average degree
O
(
n
α
)
for any
α
<
1
/
2
. Our lower bound relies on sharp anti-concentration bounds for binomial random variables, which we use to show that the {near-neighborhoods} of a set of random points do not overlap significantly, forcing any navigable graph to have many edges.


Retrieval-Retro: Retrieval-based Inorganic Retrosynthesis with Expert Knowledge

Inogranic Synthesis;Inorganic Retrosynthesis;Material Science

Summary: Inorganic Retrosynthesis

Abstract: While inorganic retrosynthesis planning is essential in the field of chemical science, the application of machine learning in this area has been notably less explored compared to organic retrosynthesis planning. In this paper, we propose Retrieval-Retro for inorganic retrosynthesis planning, which implicitly extracts the precursor information of reference materials that are retrieved from the knowledge base regarding domain expertise in the field. Specifically, instead of directly employing the precursor information of reference materials, we propose implicitly extracting it with various attention layers, which enables the model to learn novel synthesis recipes more effectively. Moreover, during retrieval, we consider the thermodynamic relationship between target material and precursors, which is essential domain expertise in identifying the most probable precursor set among various options. Extensive experiments demonstrate the superiority of Retrieval-Retro in retrosynthesis planning, especially in discovering novel synthesis recipes, which is crucial for materials discovery. The source code for Retrieval-Retro is available at https://github.com/HeewoongNoh/Retrieval-Retro.


QTIP: Quantization with Trellises and Incoherence Processing

quantization;llms;trellises;fast inference;post training quantization;trellis coded quantization;model compression;computed codes

Summary: We present the first tractable ultra-high dimensional quantizer for LLM PTQ that supports fast inference, enabling in state of the art quantization quality and inference speed.

Abstract:
Post-training quantization (PTQ) reduces the memory footprint of LLMs by quantizing weights to low-precision datatypes. Since LLM inference is usually memory-bound, PTQ methods can improve inference throughput. Recent state-of-the-art PTQ approaches use vector quantization (VQ) to quantize multiple weights at once, which improves information utilization through better shaping. However, VQ requires a codebook with size exponential in the dimension. This limits current VQ-based PTQ works to low VQ dimensions (
≤
8
) that in turn limit quantization quality. Here, we introduce QTIP, which instead uses trellis coded quantization (TCQ) to achieve ultra-high-dimensional quantization. TCQ uses a stateful decoder that separates the codebook size from the bitrate and effective dimension. QTIP introduces a spectrum of lookup-only to computed lookup-free trellis codes designed for a hardware-efficient "bitshift" trellis structure; these codes achieve state-of-the-art results in both quantization quality and inference speed.


Flipping-based Policy for Chance-Constrained Markov Decision Processes

Reinforcement learning;Chance constraints;Stochastic policy

Summary: We present a flipping-based policy for safe reinforcement learning and provide theoretical foundations for its optimality and practical implementation.

Abstract: Safe reinforcement learning (RL) is a promising approach for many real-world decision-making problems where ensuring safety is a critical necessity. In safe RL research, while expected cumulative safety constraints (ECSCs) are typically the first choices, chance constraints are often more pragmatic for incorporating safety under uncertainties. This paper proposes a \textit{flipping-based policy} for Chance-Constrained Markov Decision Processes (CCMDPs). The flipping-based policy selects the next action by tossing a potentially distorted coin between two action candidates. The probability of the flip and the two action candidates vary depending on the state. We establish a Bellman equation for CCMDPs and further prove the existence of a flipping-based policy within the optimal solution sets. Since solving the problem with joint chance constraints is challenging in practice, we then prove that joint chance constraints can be approximated into Expected Cumulative Safety Constraints (ECSCs) and that there exists a flipping-based policy in the optimal solution sets for constrained MDPs with ECSCs. As a specific instance of practical implementations, we present a framework for adapting constrained policy optimization to train a flipping-based policy. This framework can be applied to other safe RL algorithms. We demonstrate that the flipping-based policy can improve the performance of the existing safe RL algorithms under the same limits of safety constraints on Safety Gym benchmarks.


Randomized Exploration for Reinforcement Learning with Multinomial Logistic Function Approximation

Reinforcement learning;Function approximation;Multinomial logistic regression;Regret analysis

Summary: We propose randomized exploration model-based RL algorithms with multinomial logistic function approximation.

Abstract:
We study reinforcement learning with multinomial logistic (MNL) function approximation where the underlying transition probability kernel of the Markov decision processes (MDPs) is parametrized by an unknown transition core with features of state and action. For the finite horizon episodic setting with inhomogeneous state transitions, we propose provably efficient algorithms with randomized exploration having frequentist regret guarantees. For our first algorithm,
RRL-MNL
, we adapt optimistic sampling to ensure the optimism of the estimated value function with sufficient frequency and establish that
RRL-MNL
is both statistically and computationally efficient, achieving a
O
~
(
κ
−
1
d
3
2
H
3
2
T
)
frequentist regret bound with constant-time computational cost per episode. Here,
d
is the dimension of the transition core,
H
is the horizon length,
T
is the total number of steps, and
κ
is a problem-dependent constant. Despite the simplicity and practicality of
RRL-MNL
, its regret bound scales with
κ
−
1
, which is potentially large in the worst case. To improve the dependence on
κ
−
1
, we propose
ORRL-MNL
, which estimates the value function using local gradient information of the MNL transition model. We show that its frequentist regret bound is
O
~
(
d
3
2
H
3
2
T
+
κ
−
1
d
2
H
2
)
. To the best of our knowledge, these are the first randomized RL algorithms for the MNL transition model that achieve both computational and statistical efficiency. Numerical experiments demonstrate the superior performance of the proposed algorithms.


Identifying Functionally Important Features with End-to-End Sparse Dictionary Learning

Mechnastic Interpretability;Interpretability;Explainability;Transparency;Sparse Coding;Causal mediation analysis;High dimensional data analysis

Summary: We introduce end-to-end sparse autoencoders, which aim to learn functionally relevant features from network activations. They are a pareto improvement over standard sparse autoencoders.

Abstract: Identifying the features learned by neural networks is a core challenge in mechanistic interpretability. Sparse autoencoders (SAEs), which learn a sparse, overcomplete dictionary that reconstructs a network's internal activations, have been used to identify these features. However, SAEs may learn more about the structure of the datatset than the computational structure of the network. There is therefore only indirect reason to believe that the directions found in these dictionaries are functionally important to the network. We propose end-to-end (e2e) sparse dictionary learning, a method for training SAEs that ensures the features learned are functionally important by minimizing the KL divergence between the output distributions of the original model and the model with SAE activations inserted. Compared to standard SAEs, e2e SAEs offer a Pareto improvement: They explain more network performance, require fewer total features, and require fewer simultaneously active features per datapoint, all with no cost to interpretability. We explore geometric and qualitative differences between e2e SAE features and standard SAE features. E2e dictionary learning brings us closer to methods that can explain network behavior concisely and accurately. We release our library for training e2e SAEs and reproducing our analysis at https://github.com/ApolloResearch/e2e_sae.


Not All Diffusion Model Activations Have Been Evaluated as Discriminative Features

Diffusion Models;Representation Learning;Model Property Study

Summary: We evaluate and exploit previously-ignored activations from diffusion backbones based on our new discoveries of their properties, thus resulting in better features for discrimination.

Abstract: Diffusion models are initially designed for image generation. Recent research shows that the internal signals within their backbones, named activations, can also serve as dense features for various discriminative tasks such as semantic segmentation. Given numerous activations, selecting a small yet effective subset poses a fundamental problem. To this end, the early study of this field performs a large-scale quantitative comparison of the discriminative ability of the activations. However, we find that many potential activations have not been evaluated, such as the queries and keys used to compute attention scores. Moreover, recent advancements in diffusion architectures bring many new activations, such as those within embedded ViT modules. Both combined, activation selection remains unresolved but overlooked. To tackle this issue, this paper takes a further step with a much broader range of activations evaluated. Considering the significant increase in activations, a full-scale quantitative comparison is no longer operational. Instead, we seek to understand the properties of these activations, such that the activations that are clearly inferior can be filtered out in advance via simple qualitative evaluation. After careful analysis, we discover three properties universal among diffusion models, enabling this study to go beyond specific models. On top of this, we present effective feature selection solutions for several popular diffusion models. Finally, the experiments across multiple discriminative tasks validate the superiority of our method over the SOTA competitors. Our code is available at https://github.com/Darkbblue/generic-diffusion-feature.


Online Posterior Sampling with a Diffusion Prior

posterior sampling;diffusion models;online learning;contextual bandits

Summary: We propose Laplace posterior sampling approximations for linear models and GLMs with a diffusion model prior, and apply them to contextual bandits.

Abstract: Posterior sampling in contextual bandits with a Gaussian prior can be implemented exactly or approximately using the Laplace approximation. The Gaussian prior is computationally efficient but it cannot describe complex distributions. In this work, we propose approximate posterior sampling algorithms for contextual bandits with a diffusion model prior. The key idea is to sample from a chain of approximate conditional posteriors, one for each stage of the reverse diffusion process, which are obtained by the Laplace approximation. Our approximations are motivated by posterior sampling with a Gaussian prior, and inherit its simplicity and efficiency. They are asymptotically consistent and perform well empirically on a variety of contextual bandit problems.


Sub-optimal Experts mitigate Ambiguity in Inverse Reinforcement Learning

Inverse Reinforcement Learning;Sub-optimal Experts;Sample Complexity

Summary: We study how the presence of multiple and sub-optimal experts can mitigate the ambuigity that affects Inverse Reinforcement Learning.

Abstract: Inverse Reinforcement Learning (IRL) deals with the problem of deducing a reward function that explains the behavior of an expert agent who is assumed to act optimally in an underlying unknown task. Recent works have studied the IRL problem from the perspective of recovering the feasible reward set, i.e., the class of reward functions that are compatible with a unique optimal expert. However, in several problems of interest it is possible to observe the behavior of multiple experts with different degree of optimality (e.g., racing drivers whose skills ranges from amateurs to professionals). For this reason, in this work, we focus on the reconstruction of the feasible reward set when, in addition to demonstrations from the optimal expert, we observe the behavior of multiple sub-optimal experts. Given this problem, we first study the theoretical properties showing that the presence of multiple sub-optimal experts, in addition to the optimal one, can significantly shrink the set of compatible rewards, ultimately mitigating the inherent ambiguity of IRL. Furthermore, we study the statistical complexity of estimating the feasible reward set with a generative model and analyze a uniform sampling algorithm that turns out to be minimax optimal whenever the sub-optimal experts' performance level is sufficiently close to that of the optimal expert.


Adversarially Trained Weighted Actor-Critic for Safe Offline Reinforcement Learning

Summary: We propose a novel algorithm for Safe Offline RL under functional approximation; our algorithm achieves robust safe policy improvement (first such result) using only single policy concentrability assumption.

Abstract:
We propose WSAC (Weighted Safe Actor-Critic), a novel algorithm for Safe Offline Reinforcement Learning (RL) under functional approximation, which can robustly optimize policies to improve upon an arbitrary reference policy with limited data coverage. WSAC is designed as a two-player Stackelberg game to optimize a refined objective function. The actor optimizes the policy against two adversarially trained value critics with small importance-weighted Bellman errors, which focus on scenarios where the actor's performance is inferior to the reference policy. In theory, we demonstrate that when the actor employs a no-regret optimization oracle, WSAC achieves a number of guarantees:
(
i
)
For the first time in the safe offline RL setting, we establish that WSAC can produce a policy that outperforms {\bf any} reference policy while maintaining the same level of safety, which is critical to designing a safe algorithm for offline RL.
(
i
i
)
WSAC achieves the optimal statistical convergence rate of
1
/
N
to the reference policy, where
N
is the size of the offline dataset.
(
i
i
i
)
We theoretically show that WSAC guarantees a safe policy improvement across a broad range of hyperparameters that control the degree of pessimism, indicating its practical robustness. Additionally, we offer a practical version of WSAC and compare it with existing state-of-the-art safe offline RL algorithms in several continuous control environments. WSAC outperforms all baselines across a range of tasks, supporting the theoretical results.


Offline Oracle-Efficient Learning for Contextual MDPs via Layerwise Exploration-Exploitation Tradeoff

reinforcement learning;contextual MDP;offline density estimation;computational efficiency

Summary: This paper presents a statistical and computational reduction from CMDPs to offline density estimation with little overhead.

Abstract:
Motivated by the recent discovery of a statistical and computational reduction from contextual bandits to offline regression \citep{simchi2020bypassing}, we address the general (stochastic) Contextual Markov Decision Process (CMDP) problem with horizon
H
(as known as CMDP with
H
layers). In this paper, we introduce a reduction from CMDPs to offline density estimation under the realizability assumption, i.e., a model class
M
containing the true underlying CMDP is provided in advance. We develop an efficient, statistically near-optimal algorithm requiring only
O
(
H
log

T
)
calls to an offline density estimation algorithm (or oracle) across all
T
rounds. This number can be further reduced to
O
(
H
log

log

T
)
if
T
is known in advance. Our results mark the first efficient and near-optimal reduction from CMDPs to offline density estimation without imposing any structural assumptions on the model class. A notable feature of our algorithm is the design of a layerwise exploration-exploitation tradeoff tailored to address the layerwise structure of CMDPs. Additionally, our algorithm is versatile and applicable to pure exploration tasks in reward-free reinforcement learning.


Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models

Summary: We uncover an inherent limitation of generative image restoration: higher perceptual quality comes at the expense of greater uncertainty.

Abstract: The pursuit of high perceptual quality in image restoration has driven the development of revolutionary generative models, capable of producing results often visually indistinguishable from real data. However, as their perceptual quality continues to improve, these models also exhibit a growing tendency to generate hallucinations – realistic-looking details that do not exist in the ground truth images. Hallucinations in these models create uncertainty about their reliability, raising major concerns about their practical application. This paper investigates this phenomenon through the lens of information theory, revealing a fundamental tradeoff between uncertainty and perception. We rigorously analyze the relationship between these two factors, proving that the global minimal uncertainty in generative models grows in tandem with perception. In particular, we define the inherent uncertainty of the restoration problem and show that attaining perfect perceptual quality entails at least twice this uncertainty. Additionally, we establish a relation between distortion, uncertainty and perception, through which we prove the aforementioned uncertainly-perception tradeoff induces the well-known perception-distortion tradeoff. We demonstrate our theoretical findings through experiments with super-resolution and inpainting algorithms. This work uncovers fundamental limitations of generative models in achieving both high perceptual quality and reliable predictions for image restoration. Thus, we aim to raise awareness among practitioners about this inherent tradeoff, empowering them to make informed decisions and potentially prioritize safety over perceptual performance.


Self-supervised Transformation Learning for Equivariant Representations

Equivariant Learning;Transformation Representation;Self-supervised Transformation Learning

Summary: Self-Supervised Transformation Learning (STL) uses transformation representations from image pairs instead of labels to learn equivariant transformations, enhancing performance efficiently.

Abstract: Unsupervised representation learning has significantly advanced various machine learning tasks. In the computer vision domain, state-of-the-art approaches utilize transformations like random crop and color jitter to achieve invariant representations, embedding semantically the same inputs despite transformations. However, this can degrade performance in tasks requiring precise features, such as localization or flower classification. To address this, recent research incorporates equivariant representation learning, which captures transformation-sensitive information. However, current methods depend on transformation labels and thus struggle with interdependency and complex transformations. We propose Self-supervised Transformation Learning (STL), replacing transformation labels with transformation representations derived from image pairs. The proposed method ensures transformation representation is image-invariant and learns corresponding equivariant transformations, enhancing performance without increased batch complexity. We demonstrate the approach’s effectiveness across diverse classification and detection tasks, outperforming existing methods in 7 out of 11 benchmarks and excelling in detection. By integrating complex transformations like AugMix, unusable by prior equivariant methods, this approach enhances performance across tasks, underscoring its adaptability and resilience. Additionally, its compatibility with various base models highlights its flexibility and broad applicability. The code is available at https://github.com/jaemyung-u/stl.


Benign overfitting in leaky ReLU networks with moderate input dimension

benign overfitting;leaky relu;optimization;generalization;hinge loss;margin;overparameterization

Summary: We investigate the conditions under which leaky ReLU networks generalize well beyond the regime of near-orthogonal training data.

Abstract:
The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two-layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data which can be decomposed into the sum of a common signal and a random noise component, which lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign, or harmful, overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non-benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property. In contrast to prior work we do not require the training data to be nearly orthogonal. Notably, for input dimension
d
and training sample size
n
, while results in prior work require
d
=
Ω
(
n
2
log

n
)
, here we require only
d
=
Ω
(
n
)
.


On the Expressivity and Sample Complexity of Node-Individualized Graph Neural Networks

Graph neural networks;graph learning;Weisfeiler-Leman;VC dimension

Summary: A theoretical analysis of the sample complexity of GNNs with node individualization schemes.

Abstract: Graph neural networks (GNNs) employing message passing for graph classification are inherently limited by the expressive power of the Weisfeiler-Leman (WL) test for graph isomorphism. Node individualization schemes, which assign unique identifiers to nodes (e.g., by adding random noise to features), are a common approach for achieving universal expressiveness. However, the ability of GNNs endowed with individualization schemes to generalize beyond the training data is still an open question. To address this question, this paper presents a theoretical analysis of the sample complexity of such GNNs from a statistical learning perspective, employing Vapnik–Chervonenkis (VC) dimension and covering number bounds. We demonstrate that node individualization schemes that are permutation-equivariant result in lower sample complexity, and design novel individualization schemes that exploit these results. As an application of this analysis, we also develop a novel architecture that can perform substructure identification (i.e., subgraph isomorphism) while having a lower VC dimension compared to competing methods. Finally, our theoretical findings are validated experimentally on both synthetic and real-world datasets.


Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization

Bayesian Nonparametrics;Distributionally Robust Optimization;Dirichlet Process;Decision Theory;Ambiguity Aversion;Machine Learning

Summary: We introduce and study a novel distributionally robust optimization procedure, combining insights from Bayesian nonparametric (Dirichlet process) theory and a popular decision-theoretic model of smooth ambiguity-averse preferences.

Abstract: Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample performance due to distributional uncertainty. In the spirit of distributionally robust optimization, we propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet process) theory and a recent decision-theoretic model of smooth ambiguity-averse preferences. First, we highlight novel connections with standard regularized empirical risk minimization techniques, among which Ridge and LASSO regressions. Then, we theoretically demonstrate the existence of favorable finite-sample and asymptotic statistical guarantees on the performance of the robust optimization procedure. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet process representations. We also show that the smoothness of the criterion naturally leads to standard gradient-based numerical optimization. Finally, we provide insights into the workings of our method by applying it to a variety of tasks based on simulated and real datasets.


Adjust Pearson's $r$ to Measure Arbitrary Monotone Dependence

Pearson's r;correlation coefficient;rearrangement inequality;nonlinear monotone dependence

Summary: The most used Pearson's r, typically regarded as a measure only for linear dependence, has been enhanced to accurately measure nonlinear monotone dependence,  with the aid of an inequality tighter than Cauchy-Schwartz Inequality.

Abstract: Pearson's $r$, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research challenges this notion, suggesting that Pearson's $r$ should not be ruled out a priori for measuring nonlinear monotone relationships. Pearson's $r$ is essentially a scaled covariance, rooted in the renowned Cauchy-Schwarz Inequality. Our findings reveal that different scaling bounds yield coefficients with different capture ranges, and interestingly, tighter bounds actually expand these ranges. We derive a tighter inequality than Cauchy-Schwarz Inequality, leverage it to refine Pearson's $r$, and propose a new correlation coefficient, i.e., rearrangement correlation. This coefficient is able to capture arbitrary monotone relationships, both linear and nonlinear ones. It reverts to Pearson's $r$ in linear scenarios. Simulation experiments and real-life investigations show that the rearrangement correlation is more accurate in measuring nonlinear monotone dependence than the three classical correlation coefficients, and other recently proposed dependence measures.