Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs

uncertainty quantification;uncertainty estimation;calibration;failure prediction;large language models;black-box language models;LLM evaluation

Summary: We propose a framework for eliciting confidence in black-box LLMs, revealing that while its calibration improves with model capacity, failure prediction remains a challenge.

Abstract: Empowering large language models (LLMs) to accurately express confidence in their answers is essential for reliable and trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks—confidence calibration and failure prediction—across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve, yet still far from ideal performance. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs. The code is publicly available at https://github.com/MiaoXiong2320/llm-uncertainty.


Efficient Subgraph GNNs by Learning Effective Selection Policies

Graph Neural Networks;Subgraphs;Expressive power;Sampling

Summary: We propose a novel framework that learns to select subgraphs sequentially in order to reduce the computational cost of Subgraph GNNs.

Abstract: Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

learning on graphs and other geometries & topologies


ZeRO++: Extremely Efficient Collective Communication for Large Model Training

low-precision LLM pretraining;2 bits;auto compression;low memory pretraining

Summary: Efficient collective communication design for large model training

Abstract: Zero Redundancy Optimizer (ZeRO) has been used to train a wide range of large language models on massive GPU clusters due to its ease of use, efficiency, and good scalability. However, when training on low-bandwidth clusters, and/or when small batch size per GPU is used, ZeRO’s effective throughput is limited due to communication overheads. To alleviate this limitation, this paper introduces ZeRO++ composing of three communication volume reduction techniques (lowprecision all-gather, data remapping, and low-precision gradient averaging) to significantly reduce the communication volume up to 4x that enables up to 2.16x better throughput at 384 GPU scale. Our results also show ZeRO++ can speedup the RLHF by 3.3x compared to vanilla ZeRO. To verify the convergence of ZeRO++, we test up to 13B model for pretraining with 8/6-bits all gather and up to 30B model for finetuning with 4/2-bits all gather, and demonstrate on-par accuracy as original ZeRO (aka standard training). As a byproduct, the model trained with ZeRO++ is naturally weight-quantized, which can be directly used for inference without post-training quantization or quantization-aware training.

infrastructure, software libraries, hardware, etc.


Understanding Certified Training with Interval Bound Propagation

Certified Robustness;Adversarial Robustness;Neural Network Verification;Certified Training

Summary: We theoretically investigate certified training with Interval Bound Propagation, using a novel metric measuring the tightness of the resulting bounds.

Abstract: As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case loss over a robustness specification. Curiously, training methods based on the imprecise interval bound propagation (IBP) consistently outperform those leveraging more precise bounds. Still, we lack a theoretical understanding of the mechanisms making IBP so successful. In this work, we investigate these mechanisms by leveraging a novel metric measuring the tightness of IBP bounds. We first show theoretically that, for deep linear models (DLNs), tightness decreases with width and depth at initialization, but improves with IBP training. We, then, derive sufficient and necessary conditions on weight matrices for IBP bounds to become exact and demonstrate that these impose strong regularization, providing an explanation for the observed robustness-accuracy trade-off. Finally, we show how these results on DLNs transfer to ReLU networks, before conducting an extensive empirical study, (i) confirming this transferability and yielding state-of-the-art certified accuracy, (ii) finding that while all IBP-based training methods lead to high tightness, this increase is dominated by the size of the propagated input regions rather than the robustness specification, and finally (iii) observing that non-IBP-based methods do not increase tightness. Together, these results help explain the success of recent certified training methods and may guide the development of new ones.

societal considerations including fairness, safety, privacy


Multi-Source Diffusion Models for Simultaneous Music Generation and Separation

source separation;probabilistic diffusion models;music generation

Summary: In this work, we define a diffusion-based generative model which is the first to be capable of both music generation and source separation. We also introduce the partial generation task, where we generate a subset of the sources given the others.

Abstract: In this work, we define a diffusion-based generative model capable of both music generation and source separation by learning the score of the joint probability density of sources sharing a context. Alongside the classic total inference tasks (i.e., generating a mixture, separating the sources), we also introduce and experiment on the partial generation task of source imputation, where we generate a subset of the sources given the others (e.g., play a piano track that goes well with the drums). Additionally, we introduce a novel inference method for the separation task based on Dirac likelihood functions. We train our model on Slakh2100, a standard dataset for musical source separation, provide qualitative results in the generation settings, and showcase competitive quantitative results in the source separation setting. Our method is the first example of a single model that can handle both generation and separation tasks, thus representing a step toward general audio models.


PhyloGFN: Phylogenetic inference with generative flow networks

Phylogenetic Inference;GFlowNets;Bayesian Inference;Deep Generative Modeling

Summary: We use generative flow networks as amortized samplers of phylogenetic trees, achieving strong results in both Bayesian and parsimony-based phylogenetic inference.

Abstract: Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains challenging: the high complexity of tree space poses a significant obstacle for the current combinatorial and probabilistic techniques. In this paper, we adopt the framework of generative flow networks (GFlowNets) to tackle two core problems in phylogenetics: parsimony-based and Bayesian phylogenetic inference. Because GFlowNets are well-suited for sampling complex combinatorial structures, they are a natural choice for exploring and sampling from the multimodal posterior distribution over tree topologies and evolutionary distances. We demonstrate that our amortized posterior sampler, PhyloGFN, produces diverse and high-quality evolutionary hypotheses on real benchmark datasets. PhyloGFN is competitive with prior works in marginal likelihood estimation and achieves a closer fit to the target distribution than state-of-the-art variational inference methods.

applications to physical sciences (physics, chemistry, biology, etc.)


True Knowledge Comes from Practice: Aligning Large Language Models with Embodied Environments via Reinforcement Learning

Reinforcement Learning;Large Language Models;Parameter-Efficient Fine-Tuning

Summary: Using reinforcement learning to train large language models to align their knowledge with embodied interactive environments.

Abstract: Despite the impressive performance across numerous tasks, large language models (LLMs) often fail in solving simple decision-making tasks due to the misalignment of the knowledge in LLMs with environments. On the contrary, reinforcement learning (RL) agents learn policies from scratch, which makes them always align with environments but difficult to incorporate prior knowledge for efficient explorations. To narrow the gap, we propose TWOSOME, a novel general online framework that deploys LLMs as decision-making agents to efficiently interact and align with embodied environments via RL without requiring any prepared datasets or prior knowledge of the environments. Firstly, we query the joint probabilities of each valid action with LLMs to form behavior policies. Then, to enhance the stability and robustness of the policies, we propose two normalization methods and summarize four prompt design principles. Finally, we design a novel parameter-efficient training architecture where the actor and critic share one frozen LLM equipped with low-rank adapters (LoRA) updated by PPO. We conduct extensive experiments to evaluate TWOSOME. i) TWOSOME exhibits significantly better sample efficiency and performance compared to the conventional RL method, PPO, and prompt tuning method, SayCan, in both classical decision-making environment, Overcooked, and simulated household environment, VirtualHome. ii) Benefiting from LLMs' open-vocabulary feature, TWOSOME shows superior generalization ability to unseen tasks. iii) Under our framework, there is no significant loss of the LLMs' original ability during online PPO finetuning.


Piecewise Linear Parametrization of Policies: Towards Interpretable Deep Reinforcement Learning

Summary: We propose a neural policy constrained to express a small number of linear behaviors, and show that it leads to improved interpretability while performing comparably to baselines in several control and navigation tasks.

Abstract: Learning inherently interpretable policies is a central challenge in the path to developing autonomous agents that humans can trust. Linear policies can justify their decisions while interacting in a dynamic environment, but their reduced expressivity prevents them from solving hard tasks. Instead, we argue for the use of piecewise-linear policies. We carefully study to what extent they can retain the interpretable properties of linear policies while reaching competitive performance with neural baselines. In particular, we propose the HyperCombinator (HC), a piecewise-linear neural architecture expressing a policy with a controllably small number of sub-policies. Each sub-policy is linear with respect to interpretable features, shedding light on the decision process of the agent without requiring an additional explanation model. We evaluate HC policies in control and navigation experiments, visualize the improved interpretability of the agent and highlight its trade-off with performance. Moreover, we validate that the restricted model class that the HyperCombinator belongs to is compatible with the algorithmic constraints of various reinforcement learning algorithms.


Better Neural PDE Solvers Through Data-Free Mesh Movers

neural PDE solvers;adaptive moving mesh;neural operators;Monge-Ampère equation

Summary: This paper introduces a neural-network-based mesh adapter called Data-free Mesh Mover (DMM), which is trained in a physics-informed data-free way. The DMM can be embedded into the neural PDE solver through proper architectural design, called MM-PDE.

Abstract: Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Ampère equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git.


Information Bottleneck Analysis of Deep Neural Networks via Lossy Compression

deep learning;information bottleneck principle;stochastic neural networks;lossy compression

Summary: We propose and justify a lossy compression step to overcome the obstacles associated with high dimensionality in the information-theoretic approah to DNNs

Abstract: The Information Bottleneck (IB) principle offers an information-theoretic framework for analyzing the training process of deep neural networks (DNNs). Its essence lies in tracking the dynamics of two mutual information (MI) values: between the hidden layer output and the DNN input/target. According to the hypothesis put forth by Shwartz-Ziv & Tishby (2017), the training process consists of two distinct phases: fitting and compression. The latter phase is believed to account for the good generalization performance exhibited by DNNs. Due to the challenging nature of estimating MI between high-dimensional random vectors, this hypothesis was only partially verified for NNs of tiny sizes or specific types, such as quantized NNs. In this paper, we introduce a framework for conducting IB analysis of general NNs. Our approach leverages the stochastic NN method proposed by Goldfeld et al. (2019) and incorporates a compression step to overcome the obstacles associated with high dimensionality. In other words, we estimate the MI between the compressed representations of high-dimensional random vectors. The proposed method is supported by both theoretical and practical justifications. Notably, we demonstrate the accuracy of our estimator through synthetic experiments featuring predefined MI values and comparison with MINE (Belghazi et al., 2018). Finally, we perform IB analysis on a close-to-real-scale convolutional DNN, which reveals new features of the MI dynamics.


Feature emergence via margin maximization: case studies in algebraic tasks

inductive bias;margin maximization;feature learning;mechanistic interpretability

Summary: We prove that algebraic structure in training data leads to emergent Fourier/representation theoretic features in neural networks

Abstract: Understanding the internal representations learned by neural networks is a cornerstone challenge in the science of machine learning. While there have been significant recent strides in some cases towards understanding how neural networks implement specific target functions, this paper explores a complementary question -- why do networks arrive at particular computational strategies? Our inquiry focuses on the algebraic learning tasks of modular addition, sparse parities, and finite group operations. Our primary theoretical findings analytically characterize the features learned by stylized neural networks for these algebraic tasks. Notably, our main technique demonstrates how the principle of margin maximization alone can be used to fully specify the features learned by the network. Specifically, we prove that the trained networks utilize Fourier features to perform modular addition and employ features corresponding to irreducible group-theoretic representations to perform compositions in general groups, aligning closely with the empirical observations of Nanda et al. (2023) and Chughtai et al. (2023). More generally, we hope our techniques can help to foster a deeper understanding of why neural networks adopt specific computational strategies.


Negatively Correlated Ensemble Reinforcement Learning for Online Diverse Game Level Generation

Level Generation;Video Games;Deep Reinforcement Learning;Ensemble Learning;Regularisation

Summary: This paper proposes a regularised ensemble reinforcement learning approach with policy regularisation theorems to train generators that generates diverse and promising game levels in real-time.

Abstract: Deep reinforcement learning has recently been successfully applied to online procedural content generation in which a policy determines promising game-level segments. However, existing methods can hardly discover diverse level patterns, while the lack of diversity makes the gameplay boring. This paper proposes an ensemble reinforcement learning approach that uses multiple negatively correlated sub-policies to generate different alternative level segments, and stochastically selects one of them following a selector model. A novel policy regularisation technique is integrated into the approach to diversify the generated alternatives. In addition, we develop theorems to provide general methodologies for optimising policy regularisation in a Markov decision process. The proposed approach is compared with several state-of-the-art policy ensemble methods and classic methods on a well-known level generation benchmark, with two different reward functions expressing game-design goals from different perspectives. Results show that our approach boosts level diversity notably with competitive performance in terms of the reward. Furthermore, by varying the regularisation coefficient, the trained generators form a well-spread Pareto front, allowing explicit trade-offs between diversity and rewards of generated levels.


Poly-View Contrastive Learning

Contrastive learning;Self-Supervised Learning;SimCLR;Multi-View;Augmentations;Multiplicity;InfoMax;Sufficient Statistics

Summary: We look at contrastive learning with more than two related views per sample and find that for some objectives, performance can be improved compared to two views (e.g. SimCLR) at no computational cost.

Abstract: Contrastive learning typically matches pairs of related views among a number of unrelated negative views. Views can be generated (e.g. by augmentations) or be observed. We investigate matching when there are more than two related views which we call poly-view tasks, and derive new representation learning objectives using information maximization and sufficient statistics. We show that with unlimited computation, one should maximize the number of related views, and with a fixed compute budget, it is beneficial to decrease the number of unique samples whilst increasing the number of views of those samples. In particular, poly-view contrastive models trained for 128 epochs with batch size 256 outperform SimCLR trained for 1024 epochs at batch size 4096 on ImageNet1k, challenging the belief that contrastive models require large batch sizes and many training epochs.

unsupervised, self-supervised, semi-supervised, and supervised representation learning


Identifying Policy Gradient Subspaces

reinforcement learning;policy gradients;gradient subspaces

Summary: We investigate the potential of gradient subspaces in deep reinforcement learning.

Abstract: Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised learning can be accelerated by leveraging the fact that gradients lie in a low-dimensional and slowly-changing subspace. In this paper, we conduct a thorough evaluation of this phenomenon for two popular deep policy gradient methods on various simulated benchmark tasks. Our results demonstrate the existence of such gradient subspaces despite the continuously changing data distribution inherent to reinforcement learning. These findings reveal promising directions for future work on more efficient reinforcement learning, e.g., through improving parameter-space exploration or enabling second-order optimization.


Graph Metanetworks for Processing Diverse Neural Architectures

Summary: We develop metanetworks that allow expressive, permutation equivariant processing of diverse neural network architectures.

Abstract: Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks --- neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.


FreeNoise: Tuning-Free Longer Video Diffusion via Noise Rescheduling

Summary: A tuning-free and time-efficient paradigm for longer video generation based on pretrained video diffusion models

Abstract: With the availability of large-scale video datasets and the advances of diffusion models, text-driven video generation has achieved substantial progress. However, existing video generation models are typically trained on a limited number of frames, resulting in the inability to generate high-fidelity long videos during inference. Furthermore, these models only support single-text conditions, whereas real-life scenarios often require multi-text conditions as the video content changes over time. To tackle these challenges, this study explores the potential of extending the text-driven capability to generate longer videos conditioned on multiple texts. 1) We first analyze the impact of initial noise in video diffusion models. Then building upon the observation of noise, we propose FreeNoise, a tuning-free and time-efficient paradigm to enhance the generative capabilities of pretrained video diffusion models while preserving content consistency. Specifically, instead of initializing noises for all frames, we reschedule a sequence of noises for long-range correlation and perform temporal attention over them by window-based fusion. 2) Additionally, we design a novel motion injection method to support the generation of videos conditioned on multiple text prompts. Extensive experiments validate the superiority of our paradigm in extending the generative capabilities of video diffusion models. It is noteworthy that compared with the previous best-performing method which brought about 255% extra time cost, our method incurs only negligible time cost of approximately 17%. Generated video samples are available at our website: http://haonanqiu.com/projects/FreeNoise.html.


MAPE-PPI: Towards Effective and Efficient Protein-Protein Interaction Prediction via Microenvironment-Aware Protein Embedding

Bioinformatics;Protein-Protein Interaction;Protein Sequence-Structure Co-Modeling

Summary: In this paper, we propose Microenvironment-Aware Protein Embedding for PPI prediction (MPAE-PPI), which encodes microenvironments into chemically meaningful discrete codes via a sufficiently large microenvironment ``vocabulary" (i.e., codebook).

Abstract: Protein-Protein Interactions (PPIs) are fundamental in various biological processes and play a key role in life activities. The growing demand and cost of experimental PPI assays require computational methods for efficient PPI prediction. While existing methods rely heavily on protein sequence for PPI prediction, it is the protein structure that is the key to determine the interactions. To take both protein modalities into account, we define the microenvironment of an amino acid residue by its sequence and structural contexts, which describe the surrounding chemical properties and geometric features. In addition, microenvironments defined in previous work are largely based on experimentally assayed physicochemical properties, for which the "vocabulary" is usually extremely small. This makes it difficult to cover the diversity and complexity of microenvironments. In this paper, we propose Microenvironment-Aware Protein Embedding for PPI prediction (MPAE-PPI), which encodes microenvironments into chemically meaningful discrete codes via a sufficiently large microenvironment "vocabulary" (i.e., codebook). Moreover, we propose a novel pre-training strategy, namely Masked Codebook Modeling (MCM), to capture the dependencies between different microenvironments by randomly masking the codebook and reconstructing the input. With the learned microenvironment codebook, we can reuse it as an off-the-shelf tool to efficiently and effectively encode proteins of different sizes and functions for large-scale PPI prediction. Extensive experiments show that MAPE-PPI can scale to PPI prediction with millions of PPIs with superior trade-offs between effectiveness and computational efficiency than the state-of-the-art competitors.


Learning Performance-Improving Code Edits

Large Language Models;Retrieval Augmented Generation;Program Synthesis;Program Optimization;Fine-Tuning;Goal-Conditioning;Data Augmentation;Self-Play;Synthetic Dataset;Performance Optimization;Machine Learning for Code Optimization;Dataset

Summary: We introduce a benchmark for reproducible research on neural program optimization, evaluate the capabilities of LLMs, and present three effective strategies for program optimization, achieving up to average 6.86X times speedup with our best model

Abstract:
With the decline of Moore's law, optimizing program performance has become a major focus of software research. However, high-level optimizations such as API and algorithm changes remain elusive due to the difficulty of understanding the semantics of code. Simultaneously, pretrained large language models (LLMs) have demonstrated strong capabilities at solving a wide range of programming tasks. To that end, we introduce a framework for adapting LLMs to high-level program optimization. First, we curate a dataset of performance-improving edits made by human programmers of over 77,000 competitive C++ programming submission pairs, accompanied by extensive unit tests. A major challenge is the significant variability of measuring performance on commodity hardware, which can lead to spurious "improvements." To isolate and reliably evaluate the impact of program optimizations, we design an environment based on the gem5 full system simulator, the de facto simulator used in academia and industry. Next, we propose a broad range of adaptation strategies for code optimization; for prompting, these include retrieval-based few-shot prompting and chain-of-thought, and for finetuning, these include performance-conditioned generation and synthetic data augmentation based on self-play. A combination of these techniques achieves a mean speedup of 6.86
×
with eight generations, higher than average optimizations from individual programmers (3.66
×
). Using our model's fastest generations, we set a new upper limit on the fastest speedup possible for our dataset at 9.64
×
compared to using the fastest human submissions available (9.56
×
).


Spoken Question Answering and Speech Continuation Using Spectrogram-Powered LLM

Speech Continuation;Spoken Question Answering

Summary: Spoken question answering and speech continuation leveraging pre-trained language model operating in the spectrogram domain

Abstract: We present Spectron, a novel approach to adapting pre-trained large language models (LLMs) to perform spoken question answering (QA) and speech continuation. By endowing the LLM with a pre-trained speech encoder, our model becomes able to take speech inputs and generate speech outputs. The entire system is trained end-to-end and operates directly on spectrograms, simplifying our architecture. Key to our approach is a training objective that jointly supervises speech recognition, text continuation, and speech synthesis using only paired speech-text pairs, enabling a `cross-modal' chain-of-thought within a single decoding pass. Our method surpasses existing spoken language models in speaker preservation and semantic coherence. Furthermore, the proposed model improves upon direct initialization in retaining the knowledge of the original LLM as demonstrated through spoken QA datasets. We release our audio samples and spoken QA dataset via our website.

general machine learning (i.e., none of the above)


Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency

Summary: We show how to effectively leverage latent (or stable) diffusion as generative priors for solving general inverse problems.

Abstract: Latent diffusion models have been demonstrated to generate high-quality images, while offering efficiency in model training compared to diffusion models operating in the pixel space. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.


Compressing Latent Space via Least Volume

Summary: This paper introduces a volume-based regularization that automatically reduces the dimensionality of latent space and order the latent dimensions..

Abstract: This paper introduces Least Volume---a simple yet effective regularization inspired by geometric intuition---that can reduce the necessary number of latent dimensions needed by an autoencoder without requiring any prior knowledge of the intrinsic dimensionality of the dataset. We show that the Lipschitz continuity of the decoder is the key to making it work, provide a proof that PCA is just a linear special case of it, and reveal that it has a similar PCA-like importance ordering effect when applied to nonlinear models. We demonstrate the intuition behind the regularization on some pedagogical toy problems, and its effectiveness on several benchmark problems, including MNIST, CIFAR-10 and CelebA.


Provably Efficient UCB-type Algorithms For Learning Predictive State Representations

Reinforcement learning;Sequential decision-making problem;Predictive state representation;POMDP;UCB;online and offline

Summary: We developed a provably efficient upper confidence bound algorithm for online and offline low rank decision-making problem, which is modeled by predictive state representation.

Abstract: The general sequential decision-making problem, which includes Markov decision processes (MDPs) and partially observable MDPs (POMDPs) as special cases, aims at maximizing a cumulative reward by making a sequence of decisions based on a history of observations and actions over time. Recent studies have shown that the sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs). Despite these advancements, existing approaches typically involve oracles or steps that are computationally intractable. On the other hand, the upper confidence bound (UCB) based approaches, which have served successfully as computationally efficient methods in bandits and MDPs, have not been investigated for more general PSRs, due to the difficulty of optimistic bonus design in these more challenging settings. This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. We further characterize the sample complexity bounds for our designed UCB-type algorithms for both online and offline PSRs. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational tractability, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.


Analyzing and Improving Optimal-Transport-based Adversarial Networks

Optimal Transport;Generative Adversarial Networks

Summary: We analyze and improve Optimal-Transport-based adversarial networks.

Abstract: Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a measure for assessing the distance between data and generated distributions. Recently, OT transport map between data and prior distributions has been utilized as a generative model. These OT-based generative models share a similar adversarial training objective. In this paper, we begin by unifying these OT-based adversarial methods within a single framework. Then, we elucidate the role of each component in training dynamics through a comprehensive analysis of this unified framework. Moreover, we suggest a simple but novel method that improves the previously best-performing OT-based model. Intuitively, our approach conducts a gradual refinement of the generated distribution, progressively aligning it with the data distribution. Our approach achieves a FID score of 2.51 on CIFAR-10 and 5.99 on CelebA-HQ-256, outperforming unified OT-based adversarial approaches.


Look, Remember and Reason: Grounded Reasoning in Videos with Language Models

Summary: We show the effectiveness of off-the-shelf language models for reasoning on videos, when grounded using surrogate tasks.

Abstract: Multi-modal language models (LM) have recently shown promising performance in high-level reasoning tasks on videos. However, existing methods still fall short in tasks like causal or compositional spatiotemporal reasoning over actions, in which model predictions need to be grounded in fine-grained low-level details, such as object motions and object interactions. In this work, we propose training an LM end-to-end on low-level surrogate tasks, including object detection, re-identification, and tracking, to endow the model with the required low-level visual capabilities. We show that a two-stream video encoder with spatiotemporal attention is effective at capturing the required static and motion-based cues in the video. By leveraging the LM's ability to perform the low-level surrogate tasks, we can cast reasoning in videos as the three-step process of Look, Remember, Reason, wherein visual information is extracted using low-level visual skills step-by-step and then integrated to arrive at a final answer. We demonstrate the effectiveness of our framework on diverse visual reasoning tasks from the ACRE, CATER, Something-Else and STAR datasets. Our approach is trainable end-to-end and surpasses state-of-the-art task-specific methods across these tasks by a large margin.

representation learning for computer vision, audio, language, and other modalities


Stochastic Controlled Averaging for Federated Learning with Communication Compression

federated learning;communication compression;data heterogeneity;controlled averaging

Summary: We propose SCALLION and SCAFCOM that are built on a new formulation of stochastic controlled averaging and reach the SOTA performance among compressed FL algorithms.

Abstract: Communication compression has been an important topic in Federated Learning (FL) for alleviating the communication overhead. However, communication compression brings forth new challenges in FL due to the interplay of compression-incurred information distortion and inherent characteristics of FL such as partial participation and data heterogeneity. Despite the recent development, the existing approaches either cannot accommodate arbitrary data heterogeneity or partial participation, or require stringent conditions on compression. In this paper, we revisit the seminal stochastic controlled averaging method by proposing an equivalent but more efficient/simplified formulation with halved uplink communication costs, building upon which we propose two compressed FL algorithms, SCALLION and SCAFCOM, to support unbiased and biased compression, respectively. Both the proposed methods outperform the existing compressed FL methods in terms of communication and computation complexities. Moreover,SCALLION and SCAFCOM attain fast convergence rates under arbitrary data heterogeneity without any additional assumptions on compression errors. Experiments show that \scallion and \scafcom outperform recent compressed FL methods under the same communication budget.


C-TPT: Calibrated Test-Time Prompt Tuning for Vision-Language Models via Text Feature Dispersion

Summary: We address the critical yet under-explored challenge of achieving calibrated zero-shot inference during test-time prompt tuning in large-scale vision-language models.

Abstract: In deep learning, test-time adaptation has gained attention as a method for model fine-tuning without the need for labeled data. A prime exemplification is the recently proposed test-time prompt tuning for large-scale vision-language models such as CLIP. Unfortunately, these prompts have been mainly developed to improve accuracy, overlooking the importance of calibration, which is a crucial aspect for quantifying prediction uncertainty. However, traditional calibration methods rely on substantial amounts of labeled data, making them impractical for test-time scenarios. To this end, this paper explores calibration during test-time prompt tuning by leveraging the inherent properties of CLIP. Through a series of observations, we find that the prompt choice significantly affects the calibration in CLIP, where the prompts leading to higher text feature dispersion result in better-calibrated predictions. Introducing the Average Text Feature Dispersion (ATFD), we establish its relationship with calibration error and present a novel method, Calibrated Test-time Prompt Tuning (C-TPT), for optimizing prompts during test-time with enhanced calibration. Through extensive experiments on different CLIP architectures and datasets, we show that C-TPT can effectively improve the calibration of test-time prompt tuning without needing labeled data. The code is publicly accessible at https://github.com/hee-suk-yoon/C-TPT.


Test-Time Adaptation with CLIP Reward for Zero-Shot Generalization in Vision-Language Models

Vision-Language Models;Zero-Shot Generalization;Test-Time Adaptation;CLIP reward

Summary: We propose to improve the zero-shot generalization capacity  of vision-language models on the fly with CLIP as the feedback source.

Abstract: One fascinating aspect of pre-trained vision-language models (VLMs) learning under language supervision is their impressive zero-shot generalization capability. However, this ability is hindered by distribution shifts between the training and testing data. Previous test time adaptation (TTA) methods for VLMs in zero-shot classification rely on minimizing the entropy of model outputs, tending to be stuck in incorrect model predictions. In this work, we propose TTA with feedback to rectify the model output and prevent the model from becoming blindly confident. Specifically, a CLIP model is adopted as the reward model during TTA and provides feedback for the VLM. Given a single test sample, the VLM is forced to maximize the CLIP reward between the input and sampled results from the VLM output distribution. The proposed \textit{reinforcement learning with CLIP feedback~(RLCF)} framework is highly flexible and universal. Beyond the classification task, with task-specific sampling strategies and a proper reward baseline choice, RLCF can be easily extended to not only discrimination tasks like retrieval but also generalization tasks like image captioning, improving the zero-shot generalization capacity of VLMs. According to the characteristics of these VL tasks, we build different fully TTA pipelines with RLCF to improve the zero-shot generalization ability of various VLMs. Extensive experiments along with promising empirical results demonstrate the effectiveness of RLCF. The code is available at https://github.com/mzhaoshuai/RLCF.


Towards Aligned Layout Generation via Diffusion Model with Aesthetic Constraints

Diffusion model;Layout generation;Constrained Optimization

Summary: Unified model for layout generation using constrained diffusion.

Abstract: Controllable layout generation refers to the process of creating a plausible visual arrangement of elements within a graphic design (e.g., document and web designs) with constraints representing design intentions. Although recent diffusion-based models have achieved state-of-the-art FID scores, they tend to exhibit more pronounced misalignment compared to earlier transformer-based models. In this work, we propose the LAyout Constraint diffusion modEl (LACE), a unified model to handle a broad range of layout generation tasks, such as arranging elements with specified attributes and refining or completing a coarse layout design. The model is based on continuous diffusion models. Compared with existing methods that use discrete diffusion models, continuous state-space design can enable the incorporation of continuous aesthetic constraint functions in training more naturally. For conditional generation, we propose injecting layout conditions in the form of masks or gradient guidance during inference. Empirical results show that LACE produces high-quality layouts and outperforms existing state-of-the-art baselines. We will release our source code and model checkpoints.


SF(DA)$^2$: Source-free Domain Adaptation Through the Lens of Data Augmentation

Source-free domain adaptation;Data augmentation

Summary: We propose a novel source-free domain adaptation method that leverages intuitions derived from data augmentation

Abstract:
In the face of the deep learning model's vulnerability to domain shift, source-free domain adaptation (SFDA) methods have been proposed to adapt models to new, unseen target domains without requiring access to source domain data. Although the potential benefits of applying data augmentation to SFDA are attractive, several challenges arise such as the dependence on prior knowledge of class-preserving transformations and the increase in memory and computational requirements. In this paper, we propose Source-free Domain Adaptation Through the Lens of Data Augmentation (SF(DA)
2
), a novel approach that leverages the benefits of data augmentation without suffering from these challenges. We construct an augmentation graph in the feature space of the pretrained model using the neighbor relationships between target features and propose spectral neighborhood clustering to identify partitions in the prediction space. Furthermore, we propose implicit feature augmentation and feature disentanglement as regularization loss functions that effectively utilize class semantic information within the feature space. These regularizers simulate the inclusion of an unlimited number of augmented target features into the augmentation graph while minimizing computational and memory demands. Our method shows superior adaptation performance in SFDA scenarios, including 2D image and 3D point cloud datasets and a highly imbalanced dataset.


Multi-resolution HuBERT: Multi-resolution Speech Self-Supervised Learning with Masked Unit Prediction

Speech Representation Learning;Self-supervised Learning;Multi-resolution

Summary: We propose a multi-resolution framework for speech representation learning, which demonstrate significant gain in performance and efficiency.

Abstract: Existing Self-Supervised Learning (SSL) models for speech typically process speech signals at a fixed resolution of 20 milliseconds. This approach overlooks the varying informational content present at different resolutions in speech signals. In contrast, this paper aims to incorporate multi-resolution information into speech self-supervised representation learning. We introduce an SSL model that leverages a hierarchical Transformer architecture, complemented by HuBERT-style masked prediction objectives, to process speech at multiple resolutions. Experimental results indicate that the proposed model not only achieves more efficient inference but also exhibits superior or comparable performance to the original HuBERT model over various tasks. Specifically, significant performance improvements over the original HuBERT have been observed in fine-tuning experiments on the LibriSpeech speech recognition benchmark as well as in evaluations using the Speech Universal PERformance Benchmark (SUPERB) and Multilingual SUPERB (ML-SUPERB).


Beyond Memorization: Violating Privacy via Inference with Large Language Models

Summary: We present the first comprehensive study on the capabilities of pretrained LLMs to infer personal attributes from texts given at inference.

Abstract: Current privacy research on large language models (LLMs) primarily focuses on the issue of extracting memorized training data. At the same time, models’ inference capabilities have increased drastically. This raises the key question of whether current LLMs could violate individuals’ privacy by inferring personal attributes from text given at inference time. In this work, we present the first comprehensive study on the capabilities of pretrained LLMs to infer personal attributes from text. We construct a dataset consisting of real Reddit profiles, and show that current LLMs can infer a wide range of personal attributes (e.g., location, income, sex), achieving up to 85% top-1 and 95% top-3 accuracy at a fraction of the cost (100x) and time (240x) required by humans. As people increasingly interact with LLM-powered chatbots across all aspects of life, we also explore the emerging threat of privacy-invasive chatbots trying to extract personal information through seemingly benign questions. Finally, we show that common mitigations, i.e., text anonymization and model alignment, are currently ineffective at protecting user privacy against LLM inference. Our findings highlight that current LLMs can infer personal data at a previously unattainable scale. In the absence of working defenses, we advocate for a broader discussion around LLM privacy implications beyond memorization, striving for stronger and wider privacy protection.


Hiding in Plain Sight: Disguising Data Stealing Attacks in Federated Learning

Summary: We study detectability of malicious server attacks in federated learning, show that prior attacks are detectable, and propose SEER, a novel attack framework that reconstructs data from large batch sizes and is by design harder to detect.

Abstract: Malicious server (MS) attacks have enabled the scaling of data stealing in federated learning to large batch sizes and secure aggregation, settings previously considered private. However, many concerns regarding the client-side detectability of MS attacks were raised, questioning their practicality. In this work, for the first time, we thoroughly study client-side detectability. We first demonstrate that all prior MS attacks are detectable by principled checks, and formulate a necessary set of requirements that a practical MS attack must satisfy. Next, we propose SEER, a novel attack framework that satisfies these requirements. The key insight of SEER is the use of a secret decoder, jointly trained with the shared model. We show that SEER can steal user data from gradients of realistic networks, even for large batch sizes of up to 512 and under secure aggregation. Our work is a promising step towards assessing the true vulnerability of federated learning in real-world settings.


Estimating Shape Distances on Neural Representations with Limited Samples

representational geometry;shape metrics;dissimilarity metrics

Summary: Novel estimator of geometric similarity with tunable bias-variance tradeoff, outperforms standard estimators in high-dimensional settings.

Abstract: Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distance—a measure of representational dissimilarity proposed by Williams et al. (2021). These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a novel method-of-moments estimator with a tunable bias-variance tradeoff parameterized by an upper bound on bias. We show that this estimator achieves superior performance to standard estimators in simulation and on neural data, particularly in high-dimensional settings. Our theoretical work and estimator thus respectively define and dramatically expand the scope of neural data for which geometric similarity can be accurately measured.

applications to neuroscience & cognitive science


A Poincaré Inequality and Consistency Results for Signal Sampling on Large Graphs

Summary: We formulate sampling problems in the graphon limit to discover intrinsic structures of large graph, with both theoretical guarantees and empirical evidence.

Abstract: Large-scale graph machine learning is challenging as the complexity of learning models scales with the graph size. Subsampling the graph is a viable alternative, but sampling on graphs is nontrivial as graphs are non-Euclidean. Existing graph sampling techniques require not only computing the spectra of large matrices but also repeating these computations when the graph changes, e.g., grows. In this paper, we introduce a signal sampling theory for a type of graph limit---the graphon. We prove a Poincaré inequality for graphon signals and show that complements of node subsets satisfying this inequality are unique sampling sets for Paley-Wiener spaces of graphon signals. Exploiting connections with spectral clustering and Gaussian elimination, we prove that such sampling sets are consistent in the sense that unique sampling sets on a convergent graph sequence converge to unique sampling sets on the graphon. We then propose a related graphon signal sampling algorithm for large graphs, and demonstrate its good empirical performance on graph machine learning tasks.


Demonstration-Regularized RL

reinforcement learning;regularization in reinforcement leaning;learning with demonstrations;reinforcemenet learning with human feedback

Summary: We showed a theoretically efficient way to inject expert demonstrations into RL agent and, moreover, into RLHF.

Abstract:
Incorporating expert demonstrations has empirically helped to improve the sample efficiency of reinforcement learning (RL). This paper quantifies theoretically to what extent this extra information reduces RL's sample complexity. In particular, we study the demonstration-regularized reinforcement learning framework that leverages the expert demonstrations by
KL
-regularization for a policy learned by behavior cloning. Our findings reveal that using
N
E
expert demonstrations enables the identification of an optimal policy at a sample complexity of order
O
~
(
Poly
(
S
,
A
,
H
)
/
(
ε
2
N
E
)
)
in finite and
O
~
(
Poly
(
d
,
H
)
/
(
ε
2
N
E
)
)
in linear Markov decision processes, where
ε
is the target precision,
H
the horizon,
A
the number of action,
S
the number of states in the finite case and
d
the dimension of the feature space in the linear case. As a by-product, we provide tight convergence guarantees for the behavior cloning procedure under general assumptions on the policy classes. Additionally, we establish that demonstration-regularized methods are provably efficient for reinforcement learning from human feedback (RLHF). In this respect, we provide theoretical evidence showing the benefits of KL-regularization for RLHF in tabular and linear MDPs. Interestingly, we avoid pessimism injection by employing computationally feasible regularization to handle reward estimation uncertainty, thus setting our approach apart from the prior works.


On Diffusion Modeling for Anomaly Detection

Diffusion based models;Anomaly detection;Probabilistic Inference

Summary: Identify anomalies in a dataset by estimating the diffusion time, anomalies have higher diffusion times

Abstract: Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detection. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)


The Cost of Scaling Down Large Language Models: Reducing Model Size Affects Memory before In-context Learning

large language model;scaling;in-context learning;pruning

Summary: Moderate down-scaling harms fact recall, and yet the ability to learn from a few input-output examples from context withstands aggressive down-scaling.

Abstract: We study how down-scaling large language model (LLM) size impacts LLM capabilities. We begin by measuring the effects of weight pruning – a popular technique for reducing model size – on the two abilities of LLMs: (a) recalling facts presented during pre-training and (b) processing information presented in context. Surprisingly, we find that existing pruning techniques affect these two abilities of LLMs differently. For example, pruning more than 30% of weights significantly decreases an LLM’s ability to recall facts presented during pre-training. Yet pruning 60-70% of weights largely preserves an LLM’s ability to process information in-context, ranging from retrieving answers based on information presented in context to learning parameterized functions such as a linear classifier based on a few examples. Moderate pruning impairs LLM’s ability to recall facts learnt from pre-training. However, its effect on model’s ability to process information presented in context is much less pronounced. The said disparate effects similarly arise when replacing the original model with a smaller dense one with reduced width and depth. This similarity suggests that model size reduction in general underpins the said disparity.


The Expressive Power of Low-Rank Adaptation

LoRA;expressive power;parameter-efficient fine-tuning;adaptation;neural networks;transformer

Summary: This paper takes the first step to theoretically analyzing the expressive power of Low-Rank Adaptation (LoRA).

Abstract:
Low-Rank Adaptation (LoRA), a parameter-efficient fine-tuning method that leverages low-rank adaptation of weight matrices, has emerged as a prevalent technique for fine-tuning pre-trained models such as large language models and diffusion models. Despite its huge success in practice, the theoretical underpinnings of LoRA have largely remained unexplored. This paper takes the first step to bridge this gap by theoretically analyzing the expressive power of LoRA. We prove that, for fully connected neural networks, LoRA can adapt any model
f
to accurately represent any smaller target model
f
¯
if LoRA-rank
≥
(
width of
f
)
×
depth of
f
¯
depth of
f
, under a mild assumption. We also quantify the approximation error when the LoRA-rank is lower than the threshold. For Transformer networks, we show any model can be adapted to a target model of the same size with rank-
(
embedding size
2
)
LoRA adapters. All our theoretical insights are validated by numerical experiments.


Submodular Reinforcement Learning

Reinforcement learning;Non-Markovian rewards;Submodular optimization;Policy gradient;Complex objectives in RL

Summary: The paper introduces SubRL, a paradigm for policy optimization under submodular reward functions. It discusses the difficulty of approximating SubRL and proposes SubPO, a simple PG-based algorithm inspired by submodular optimization's greedy strategy

Abstract: In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are independent of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose Submodular RL (subRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions, which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose subPO, a simple policy gradient-based algorithm for subRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), subPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing subRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying subPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.


To the Cutoff... and Beyond? A Longitudinal Perspective on LLM Data Contamination

Summary: We present the first thorough study of LLM data contamination on datasets released over time, showing that LLMs’ ability to solve coding problems changes dramatically as a function of metrics such as release date and GitHub popularity.

Abstract: Recent claims about the impressive abilities of large language models (LLMs) are often supported by evaluating publicly available benchmarks. Since LLMs train on wide swaths of the internet, this practice raises concerns of data contamination, i.e., evaluating on examples that are explicitly or implicitly included in the training data. Data contamination remains notoriously challenging to measure and mitigate, even with partial attempts like controlled experimentation of training data, canary strings, or embedding similarities. In this work, we conduct the first thorough longitudinal analysis of data contamination in LLMs by using the natural experiment of training cutoffs in GPT models to look at benchmarks released over time. Specifically, we consider two code/mathematical problem-solving datasets, Codeforces and Project Euler, and find statistically significant trends among LLM pass rate vs. GitHub popularity and release date that provide strong evidence of contamination. By open-sourcing our dataset, raw results, and evaluation framework, our work paves the way for rigorous analyses of data contamination in modern models. We conclude with a discussion of best practices and future steps for publicly releasing benchmark in the age of LLMs which train on webscale data.


Rethinking the Benefits of Steerable Features in 3D Equivariant Graph Neural Networks

Steerable features;Equivariant graph neural networks;Message passing

Summary: We discuss the benefits of steerable features of different types for 3D equivariant graph neural networks

Abstract:
Theoretical and empirical comparisons have been made to assess the expressive power and performance of invariant and equivariant GNNs. However, there is currently no theoretical result comparing the expressive power of
k
-hop invariant GNNs and equivariant GNNs. Additionally, little is understood about whether the performance of equivariant GNNs, employing steerable features up to type-
L
, increases as
L
grows -- especially when the feature dimension is held constant. In this study, we introduce a key lemma that allows us to analyze steerable features by examining their corresponding invariant features. The lemma facilitates us in understanding the limitations of
k
-hop invariant GNNs, which fail to capture the global geometric structure due to the loss of geometric information between local structures. Furthermore, we investigate the invariant features associated with different types of steerable features and demonstrate that the expressiveness of steerable features is primarily determined by their dimension -- independent of their irreducible decomposition. This suggests that when the feature dimension is constant, increasing
L
does not lead to essentially improved performance in equivariant GNNs employing steerable features up to type-
L
. We substantiate our theoretical insights with numerical evidence.


A Hierarchical Bayesian Model for Few-Shot Meta Learning

Bayesian models;Meta learning;Few-shot learning

Summary: A novel hierarchical Bayesian model for the few-shot meta learning problem, with the efficient one-time episodic learning algorithm that can scale up to modern architectures (eg, ViT).

Abstract: We propose a novel hierarchical Bayesian model for the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific generative processes, where these local random variables are governed by a higher-level global random variable. The global variable captures information shared across episodes, while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our framework, prediction on a novel episode/task can be seen as a Bayesian inference problem. For tractable training, we need to be able to relate each local episode-specific solution to the global higher-level parameters. We propose a Normal-Inverse-Wishart model, for which establishing this local-global relationship becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it does not maintain a costly computational graph for the sequence of gradient descent steps in an episode. Our approach is also different from existing Bayesian meta learning methods in that rather than modeling a single random variable for all episodes, it leverages a hierarchical structure that exploits the local-global relationships desirable for principled Bayesian learning with many related tasks.


Analyzing Feed-Forward Blocks in Transformers through the Lens of Attention Maps

Transformer;Attention map;Feed-forward;Contextualization;Interpretation;Analysis;Pre-trained models;Masked language models;Causal language models

Summary: We analyze the input contextualization effects of Feed-Forward blocks in Transformer-based models by rendering them in the attention maps.

Abstract: Transformers are ubiquitous in wide tasks. Interpreting their internals is a pivotal goal. Nevertheless, their particular components, feed-forward (FF) blocks, have typically been less analyzed despite their substantial parameter amounts. We analyze the input contextualization effects of FF blocks by rendering them in the attention maps as a human-friendly visualization scheme. Our experiments with both masked- and causal-language models reveal that FF networks modify the input contextualization to emphasize specific types of linguistic compositions. In addition, FF and its surrounding components tend to cancel out each other's effects, suggesting potential redundancy in the processing of the Transformer layer.

visualization or interpretation of learned representations


Skeleton-of-Thought: Prompting LLMs for Efficient Parallel Generation

large language model;efficient inference;data-centric optimization;parallel generation;prompt engineering;planning

Summary: As a data-centric efficiency technique, SoT decreases the generation latency by guiding the LLM itself to organize the output data and generate multiple segments in parallel.

Abstract: This work aims at decreasing the end-to-end generation latency of large language models (LLMs). One of the major causes of the high generation latency is the sequential decoding approach adopted by almost all state-of-the-art LLMs. In this work, motivated by the thinking and writing process of humans, we propose Skeleton-of-Thought (SoT), which first guides LLMs to generate the skeleton of the answer, and then conducts parallel API calls or batched decoding to complete the contents of each skeleton point in parallel. Not only does SoT provide considerable speed-ups across 12 LLMs, but it can also potentially improve the answer quality on several question categories. SoT is an initial attempt at data-centric optimization for inference efficiency, and showcases the potential of eliciting high-quality answers by explicitly planning the answer structure in language.


Bridging State and History Representations: Understanding Self-Predictive RL

Reinforcement Learning;Representation Learning;POMDPs;Information States;Self-supervised Learning

Summary: We offer theoretical insights into learning self-predictive representations in POMDPs and validate our theories with our simplified algorithm across several benchmarks.

Abstract: Representations are at the core of all deep reinforcement learning (RL) methods for both Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs). Many representation learning methods and theoretical frameworks have been developed to understand what constitutes an effective representation. However, the relationships between these methods and the shared properties among them remain unclear. In this paper, we show that many of these seemingly distinct methods and frameworks for state and history abstractions are, in fact, based on a common idea of self-predictive abstraction. Furthermore, we provide theoretical insights into the widely adopted objectives and optimization, such as the stop-gradient technique, in learning self-predictive representations. These findings together yield a minimalist algorithm to learn self-predictive representations for states and histories. We validate our theories by applying our algorithm to standard MDPs, MDPs with distractors, and POMDPs with sparse rewards. These findings culminate in a set of preliminary guidelines for RL practitioners.


FedCompass: Efficient Cross-Silo Federated Learning on Heterogeneous Client Devices Using a Computing Power-Aware Scheduler

Federated Learning;Device Heterogeneity;Cross-silo Federated Learning

Summary: We propose FedCompass, a semi-asynchronous federated learning algorithm for faster convergence on heterogeneous clients and data.

Abstract: Cross-silo federated learning offers a promising solution to collaboratively train robust and generalized AI models without compromising the privacy of local datasets, e.g., healthcare, financial, as well as scientific projects that lack a centralized data facility. Nonetheless, because of the disparity of computing resources among different clients (i.e., device heterogeneity), synchronous federated learning algorithms suffer from degraded efficiency when waiting for straggler clients. Similarly, asynchronous federated learning algorithms experience degradation in the convergence rate and final model accuracy on non-identically and independently distributed (non-IID) heterogeneous datasets due to stale local models and client drift. To address these limitations in cross-silo federated learning with heterogeneous clients and data, we propose FedCompass, an innovative semi-asynchronous federated learning algorithm with a computing power-aware scheduler on the server side, which adaptively assigns varying amounts of training tasks to different clients using the knowledge of the computing power of individual clients. FedCompass ensures that multiple locally trained models from clients are received almost simultaneously as a group for aggregation, effectively reducing the staleness of local models. At the same time, the overall training process remains asynchronous, eliminating prolonged waiting periods from straggler clients. Using diverse non-IID heterogeneous distributed datasets, we demonstrate that FedCompass achieves faster convergence and higher accuracy than other asynchronous algorithms while remaining more efficient than synchronous algorithms when performing federated learning on heterogeneous clients. The source code for FedCompass is available at https://github.com/APPFL/FedCompass.


OctoPack: Instruction Tuning Code Large Language Models

large language models;large code models;instruction tuning

Summary: Data, models and evaluation for instruction tuning code large language models

Abstract: Finetuning large language models (LLMs) on instructions leads to vast performance improvements on natural language tasks. We apply instruction tuning using code, leveraging the natural structure of Git commits, which pair code changes with human instructions. We compile CommitPack: 4 terabytes of Git commits across 350 programming languages. We benchmark CommitPack against other natural and synthetic code instructions (xP3x, Self-Instruct, OASST) on the 16B parameter StarCoder model, and achieve state-of-the-art performance among models not trained on OpenAI outputs, on the HumanEval Python benchmark (46.2% pass@1). We further introduce HumanEvalPack, expanding the HumanEval benchmark to a total of 3 coding tasks (Code Repair, Code Explanation, Code Synthesis) across 6 languages (Python, JavaScript, Java, Go, C++, Rust). Our models, OctoCoder and OctoGeeX, achieve the best performance across HumanEvalPack among all permissive models, demonstrating CommitPack's benefits in generalizing to a wider set of languages and natural coding tasks. Code, models and data are freely available at https://github.com/bigcode-project/octopack.


Communication-Efficient Federated Non-Linear Bandit Optimization

federated optimization;communication cost;non-linear bandit;bandit optimization;cumulative regret

Summary: federated bandit optimization of generic non-linear objective function

Abstract: Federated optimization studies the problem of collaborative function optimization among multiple clients (e.g. mobile devices or organizations) under the coordination of a central server. Since the data is collected separately by each client and always remains decentralized, federated optimization preserves data privacy and allows for large-scale computing, which makes it a promising decentralized machine learning paradigm. Though it is often deployed for tasks that are online in nature, e.g., next-word prediction on keyboard apps, most works formulate it as an offline problem. The few exceptions that consider federated bandit optimization are limited to very simplistic function classes, e.g., linear, generalized linear, or non-parametric function class with bounded RKHS norm, which severely hinders its practical usage. In this paper, we propose a new algorithm, named Fed-GO-UCB, for federated bandit optimization with generic non-linear objective function. Under some mild conditions, we rigorously prove that Fed-GO-UCB is able to achieve sub-linear rate for both cumulative regret and communication cost. At the heart of our theoretical analysis are distributed regression oracle and individual confidence set construction, which can be of independent interests. Empirical evaluations also demonstrate the effectiveness of the proposed algorithm.


Are Transformers with One Layer Self-Attention Using Low-Rank Weight Matrices Universal Approximators?

Transformer;Self-Attention;Memorization;Universal Approximation Theorem;Contextual Mapping

Summary: One-layer and single-head self-attention with low-rank weight matrices is expressive enough to be a contextual mapping.

Abstract: Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous functions on a compact domain.


Input-gradient space particle inference for neural network ensembles

deep ensembles;diversity;input gradient;robustness;covariate shift;particle variational inference

Summary: We learn an ensemble of neural networks that is diverse with respect to their input gradients.

Abstract: Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets and transfer learning tasks show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.


A Simple and Scalable Representation for Graph Generation

Graph generative models;graph neural networks;graph representation

Summary: We propose a simple and scalable edge list-based graph representation, gap encoded edge list (GEEL).

Abstract: Recently, there has been a surge of interest in employing neural networks for graph generation, a fundamental statistical learning problem with critical applications like molecule design and community analysis. However, most approaches encounter significant limitations when generating large-scale graphs. This is due to their requirement to output the full adjacency matrices whose size grows quadratically with the number of nodes. In response to this challenge, we introduce a new, simple, and scalable graph representation named gap encoded edge list (GEEL) that has a small representation size that aligns with the number of edges. In addition, GEEL significantly reduces the vocabulary size by incorporating the gap encoding and bandwidth restriction schemes. GEEL can be autoregressively generated with the incorporation of node positional encoding, and we further extend GEEL to deal with attributed graphs by designing a new grammar. Our findings reveal that the adoption of this compact representation not only enhances scalability but also bolsters performance by simplifying the graph generation process. We conduct a comprehensive evaluation across ten non-attributed and two molecular graph generation tasks, demonstrating the effectiveness of GEEL.


Interpretable Meta-Learning of Physical Systems

meta-learning;physical systems;multi-task learning;interpretable deep learning;identifiability;electrostatics;robotics;control;reinforcement learning;scientific discovery

Summary: We propose a new multi-environment meta-learning architecture for physical systems called CAMEL, that learns and generalizes at minimal cost and with interpretable weights.

Abstract: Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. We introduce CAMEL, a new meta-learning architecture capable of learning efficiently from multiple environments, with an affine structure with respect to the learning task. We prove that CAMEL can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to parameter identification and to adaptive control and system identification.


Leveraging Uncertainty Estimates To Improve Classifier Performance

Uncertainty estimation;binary classification;imbalanced classification;score recalibration;uncertainty based decision making;classification decision boundary;bin packing;estimation bias;posterior networks

Summary: 2D decision boundary on model score & uncertainty space boosts binary classification performance

Abstract: Binary classification typically involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound). However, model scores are often not aligned with true positivity rate. This is especially true when the training involves a differential sampling of classes or there is distributional drift between train and test settings. In this paper, we provide theoretical analysis and empirical evidence of the dependence of estimation bias on both uncertainty and model score. Further, we formulate the decision boundary selection using both model score and uncertainty, prove that it is NP-hard, and present algorithms based on dynamic programming and isotonic regression. Evaluation of the proposed algorithms on three real-world datasets yield 25%-40% improvement in recall at high precision bounds over the traditional approach of using model score alone, highlighting the benefits of leveraging uncertainty.


Sampling Multimodal Distributions with the Vanilla Score: Benefits of Data-Based Initialization

sampling;score matching;contrastive divergence;langevin dynamics

Summary: We show that sampling multimodal distributions with the vanilla score is provably fixed by data-based initialization.

Abstract: There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on \emph{score functions} --- derivatives of the log-likelihood of a distribution. In seminal works, Hyv"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered --- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).


LMUFormer: Low Complexity Yet Powerful Spiking Model With Legendre Memory Units

Legendre Memory Unit;Spiking Neural Network;Recurrent Neural Network

Summary: In this paper, we propose a novel model named LMUFormer, which enhances the LMU with patch embedding, channel mixer and SNN, and is low-computational, and powerful in the STC and NLP fields.

Abstract:
Transformer models have demonstrated high accuracy in numerous applications but have high complexity and lack sequential processing capability making them ill-suited for many streaming applications at the edge where devices are heavily resource-constrained. Thus motivated, many researchers have proposed reformulating the transformer models as RNN modules which modify the self-attention computation with explicit states. However, these approaches often incur significant performance degradation. The ultimate goal is to develop a model that has the following properties: parallel training, streaming and low-cost inference, and state-of-the-art (SOTA) performance. In this paper, we propose a new direction to achieve this goal. We show how architectural modifications to a fully-sequential recurrent model can help push its performance toward Transformer models while retaining its sequential processing capability. Specifically, inspired by the recent success of Legendre Memory Units (LMU) in sequence learning tasks, we propose LMUFormer, which augments the LMU with convolutional patch embedding and convolutional channel mixer. Moreover, we present a spiking version of this architecture, which introduces the benefit of states within the patch embedding and channel mixer modules while simultaneously reducing the computing complexity. We evaluated our architectures on multiple sequence datasets. Of particular note is our performance on the Speech Commands V2 dataset (35 classes). In comparison to SOTA transformer-based models within the ANN domain, our LMUFormer demonstrates comparable performance while necessitating a remarkable
70
×
reduction in parameters and a substantial
140
×
decrement in FLOPs. Furthermore, when benchmarked against extant low-complexity SNN variants, our model establishes a new SOTA with an accuracy of 96.12%. Additionally, owing to our model's proficiency in real-time data processing, we are able to achieve a 32.03% reduction in sequence length, all while incurring an inconsequential decline in performance.


Entropy-MCMC: Sampling from Flat Basins with Ease

MCMC;Bayesian Deep Learning;Flatness-aware Learning

Summary: We propose a practical MCMC algorithm to sample from the flat basins of deep neural network posteriors.

Abstract: Bayesian deep learning counts on the quality of posterior distribution estimation. However, the posterior of deep neural networks is highly multi-modal in nature, with local modes exhibiting varying generalization performance. Given a practical budget, targeting at the original posterior can lead to suboptimal performance, as some samples may become trapped in "bad" modes and suffer from overfitting. Leveraging the observation that "good" modes with low generalization error often reside in flat basins of the energy landscape, we propose to bias sampling on the posterior toward these flat regions. Specifically, we introduce an auxiliary guiding variable, the stationary distribution of which resembles a smoothed posterior free from sharp modes, to lead the MCMC sampler to flat basins. By integrating this guiding variable with the model parameter, we create a simple joint distribution that enables efficient sampling with minimal computational overhead. We prove the convergence of our method and further show that it converges faster than several existing flatness-aware methods in the strongly convex setting. Empirical results demonstrate that our method can successfully sample from flat basins of the posterior, and outperforms all compared baselines on multiple benchmarks including classification, calibration, and out-of-distribution detection.


DNABERT-2: Efficient Foundation Model and Benchmark For Multi-Species Genomes

Summary: An efficient and effective foundation model for multi-species genomes.

Abstract:
Decoding the linguistic intricacies of the genome is a crucial problem in biology, and pre-trained foundational models such as DNABERT and Nucleotide Transformer have made significant strides in this area. Existing works have largely hinged on k-mer, fixed-length permutations of A, T, C, and G, as the token of the genome language due to its simplicity. However, we argue that the computation and sample inefficiencies introduced by k-mer tokenization are primary obstacles in developing large genome foundational models. We provide conceptual and empirical insights into genome tokenization, building on which we propose to replace k-mer tokenization with Byte Pair Encoding (BPE), a statistics-based data compression algorithm that constructs tokens by iteratively merging the most frequent co-occurring genome segment in the corpus. We demonstrate that BPE not only overcomes the limitations of k-mer tokenization but also benefits from the computational efficiency of non-overlapping tokenization. Based on these insights, we introduce DNABERT-2, a refined genome foundation model that adapts an efficient tokenizer and employs multiple strategies to overcome input length constraints, reduce time and memory expenditure, and enhance model capability. Furthermore, we identify the absence of a comprehensive and standardized benchmark for genome understanding as another significant impediment to fair comparative analysis. In response, we propose the Genome Understanding Evaluation (GUE), a comprehensive multi-species genome classification dataset that amalgamates
36
distinct datasets across
9
tasks, with input lengths ranging from
70
to
10000
. Through comprehensive experiments on the GUE benchmark, we demonstrate that DNABERT-2 achieves comparable performance to the state-of-the-art model with
21
×
fewer parameters and approximately
92
×
less GPU time in pre-training. Compared to DNABERT, while being
3
×
more efficient, DNABERT-2 outperforms it on
23
out of
28
datasets, with an average improvement of
6
absolute scores on GUE. The code, data, and pre-trained model are available at \url{https://github.com/MAGICS-LAB/DNABERT_2}.


A Unified Framework for Bayesian Optimization under Contextual Uncertainty

Summary: Generalization of distributionally robust BO to other notions of risk such as value-at-risk, mean-variance tradeoff etc., along with a general algorithm with a regret bound.

Abstract: Bayesian optimization under contextual uncertainty (BOCU) is a family of BO problems in which the learner makes a decision prior to observing the context and must manage the risks involved. Distributionally robust BO (DRBO) is a subset of BOCU that affords robustness against context distribution shift, and includes the optimization of expected values and worst-case values as special cases. By considering the first derivatives of the DRBO objective, we generalize DRBO to one that includes several other uncertainty objectives studied in the BOCU literature such as worst-case sensitivity (and thus notions of risk such as variance, range, and conditional value-at-risk) and mean-risk tradeoffs. We develop a general Thompson sampling algorithm that is able to optimize any objective within the BOCU framework, analyze its theoretical properties, and compare it to suitable baselines across different experimental settings and uncertainty objectives.


Graph Neural Networks for Learning Equivariant Representations of Neural Networks

Deep weight space;Graph neural networks;Transformers;Permutation equivariance;Implicit neural representations;Networks for networks;Neural graphs

Summary: We propose graph neural networks that learn permutation equivariant representations of other neural networks

Abstract: Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However, existing approaches either overlook the inherent permutation symmetry in the neural network or rely on intricate weight-sharing patterns to achieve equivariance, while ignoring the impact of the network architecture itself. In this work, we propose to represent neural networks as computational graphs of parameters, which allows us to harness powerful graph neural networks and transformers that preserve permutation symmetry. Consequently, our approach enables a single model to encode neural computational graphs with diverse architectures. We showcase the effectiveness of our method on a wide range of tasks, including classification and editing of implicit neural representations, predicting generalization performance, and learning to optimize, while consistently outperforming state-of-the-art methods. The source code is open-sourced at https://github.com/mkofinas/neural-graphs.


Towards Cheaper Inference in Deep Networks with Lower Bit-Width Accumulators

Deep Neural Networks;Quantized Neural Networks;Network Quantization;Accumulators;Accelerators;Inference;Computer Vision;Language Models

Summary: We show that model can be fine tuned for inference with 12 bit accumulators, and develop methods for training with even smaller accumulators.

Abstract:
The majority of the research on the quantization of Deep Neural Networks (DNNs) is focused on reducing the precision of tensors visible by high-level frameworks (e.g., weights, activations, and gradients). However, current hardware still relies on high-accuracy core operations. Most significant is the operation of accumulating products. This high-precision accumulation operation is gradually becoming the main computational bottleneck. This is because, so far, the usage of low-precision accumulators led to a significant degradation in performance. In this work, we present a simple method to train and fine-tune DNNs, to allow, for the first time, utilization of cheaper,
12
-bits accumulators, with no significant degradation in accuracy. Lastly, we show that as we decrease the accumulation precision further, using fine-grained gradient approximations can improve the DNN accuracy.


ExeDec: Execution Decomposition for Compositional Generalization in Neural Program Synthesis

Program Synthesis;Programming By Example;Generalization;Compositional Generalization

Summary: We describe different forms of compositional generalization that are desirable in program synthesis, and present a decomposition-based approach to synthesis achieving higher compositional generalization on two domains compared to prior approaches.

Abstract: When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, we can measure whether they compositionally generalize, that is, whether a model that has been trained on the simpler subtasks is subsequently able to solve more complex tasks. In this paper, we characterize several different forms of compositional generalization that are desirable in program synthesis, forming a meta-benchmark which we use to create generalization tasks for two popular datasets, RobustFill and DeepCoder. We then propose ExeDec, a novel decomposition-based synthesis strategy that predicts execution subgoals to solve problems step-by-step informed by program execution at each step. When used with Transformer models trained from scratch, ExeDec has better synthesis performance and greatly improved compositional generalization ability compared to baselines. Finally, we use our benchmarks to demonstrate that LLMs struggle to compositionally generalize when asked to do programming-by-example in a few-shot setting, but an ExeDec-style prompting approach can improve the generalization ability and overall performance.


Magnushammer: A Transformer-Based Approach to Premise Selection

transformers;interactive theorem proving;automated reasoning;contrastive learning;premise selection

Summary: Contrastively trained transformers outperform state-of-the-art symbolic methods for premise selection, a challenging reasoning task of selecting relevant facts for proving new theorems in formal mathematics.

Abstract:
This paper presents a novel approach to premise selection, a crucial reasoning task in automated theorem proving. Traditionally, symbolic methods that rely on extensive domain knowledge and engineering effort are applied to this task. In contrast, this work demonstrates that contrastive training with the transformer architecture can achieve higher-quality retrieval of relevant premises, without the knowledge or feature engineering overhead. Our method, Magnushammer, outperforms the most advanced and widely used automation tool in interactive theorem proving called Sledgehammer. On the PISA and miniF2f benchmarks Magnushammer achieves
59.5
(against
38.3
) and
34.0
(against
20.9
) success rates, respectively. By combining Magnushammer with a language-model-based automated theorem prover, we further improve the state-of-the-art proof success rate from
57.0
to
71.0
on the PISA benchmark using
4
x fewer parameters. Moreover, we develop and open source a novel dataset for premise selection, containing textual representations of (proof state, relevant premise) pairs. To the best of our knowledge, this is the largest available premise selection dataset, and the first dataset of this kind for the Isabelle proof assistant.

neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)