ICLR 2024 Papers

International Conference on Learning Representations

Decision breakdown

2,260papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    863.8%
  • Spotlight
    36716.2%
  • Poster
    1,80780.0%

Browse all papers

InfoBatch: Lossless Training Speed Up by Unbiased Dynamic Data Pruning

Ziheng Qin, Kai Wang, Zangwei Zheng, Jianyang Gu, Xiangyu Peng, xu Zhao Pan, Daquan Zhou, Lei Shang, Baigui Sun, Xuansong Xie, Yang You

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Data pruning aims to obtain lossless performances with less overall cost. A common approach is to filter out samples that make less contribution to the training. This could lead to gradient expectation bias compared to the original data. To solve this problem, we propose InfoBatch, a novel framework aiming to achieve lossless training acceleration by unbiased dynamic data pruning. Specifically, InfoBatch randomly prunes a portion of less informative samples based on the loss distribution and rescales the gradients of the remaining samples to approximate the original gradient. As a plug-and-play and architecture-agnostic framework, InfoBatch consistently obtains lossless training results on classification, semantic segmentation, vision pertaining, and instruction fine-tuning tasks. On CIFAR10/100, ImageNet- 1K, and ADE20K, InfoBatch losslessly saves 40% overall cost. For pertaining MAE and diffusion model, InfoBatch can respectively save 24.8% and 27% cost. For LLaMA instruction fine-tuning, combining InfoBatch and the recent coreset selection method (DQ) can achieve 10 times acceleration. Our results encourage more exploration on the data efficiency aspect of large model training. Code is publicly available at NUS-HPC-AI-Lab/InfoBatch.

Oral
Jumanji: a Diverse Suite of Scalable Reinforcement Learning Environments in JAX

Clément Bonnet, Daniel Luo, Donal John Byrne, Shikha Surana, Sasha Abramowitz, Paul Duckworth, Vincent Coyette, Laurence Illing Midgley, Elshadai Tegegn, Tristan Kalloniatis, Omayma Mahjoub, Matthew Macfarlane, Andries Petrus Smit, Nathan Grinsztajn, Raphael Boige, Cemlyn Neil Waters, Mohamed Ali Ali Mimouni, Ulrich Armel Mbou Sob, Ruan John de Kock, Siddarth Singh, Daniel Furelos-Blanco, Victor Le, Arnu Pretorius, Alexandre Laterre

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Open-source reinforcement learning (RL) environments have played a crucial role in driving progress in the development of AI algorithms. In modern RL research, there is a need for simulated environments that are performant, scalable, and modular to enable their utilization in a wider range of potential real-world applications. Therefore, we present Jumanji, a suite of diverse RL environments specifically designed to be fast, flexible, and scalable. Jumanji provides a suite of environments focusing on combinatorial problems frequently encountered in industry, as well as challenging general decision-making tasks. By leveraging the efficiency of JAX and hardware accelerators like GPUs and TPUs, Jumanji enables rapid iteration of research ideas and large-scale experimentation, ultimately empowering more capable agents. Unlike existing RL environment suites, Jumanji is highly customizable, allowing users to tailor the initial state distribution and problem complexity to their needs. Furthermore, we provide actor-critic baselines for each environment, accompanied by preliminary findings on scaling and generalization scenarios. Jumanji aims to set a new standard for speed, adaptability, and scalability of RL environments.

Poster
Str2Str: A Score-based Framework for Zero-shot Protein Conformation Sampling

Jiarui Lu, Bozitao Zhong, Zuobai Zhang, Jian Tang

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The dynamic nature of proteins is crucial for determining their biological functions and properties, for which Monte Carlo (MC) and molecular dynamics (MD) simulations stand as predominant tools to study such phenomena. By utilizing empirically derived force fields, MC or MD simulations explore the conformational space through numerically evolving the system via Markov chain or Newtonian mechanics. However, the high-energy barrier of the force fields can hamper the exploration of both methods by the rare event, resulting in inadequately sampled ensemble without exhaustive running. Existing learning-based approaches perform direct sampling yet heavily rely on target-specific simulation data for training, which suffers from high data acquisition cost and poor generalizability. Inspired by simulated annealing, we propose Str2Str, a novel structure-to-structure translation framework capable of zero-shot conformation sampling with roto-translation equivariant property. Our method leverages an amortized denoising score matching objective trained on general crystal structures and has no reliance on simulation data during both training and inference. Experimental results across several benchmarking protein systems demonstrate that Str2Str outperforms previous state-of-the-art generative structure prediction models and can be orders of magnitude faster compared with long MD simulations.

Poster
The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing

Blaise Delattre, Alexandre Araujo, Quentin Barthélemy, Alexandre Allauzen

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Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However how to design an efficient classifier with an associated certified radius? Randomized smoothing provides a promising framework by relying on noise injection into the inputs to obtain a smoothed and robust classifier. In this paper, we first show that the variance introduced by the Monte-Carlo sampling in the randomized smoothing procedure estimate closely interacts with two other important properties of the classifier, \textit{i.e.} its Lipschitz constant and margin. More precisely, our work emphasizes the dual impact of the Lipschitz constant of the base classifier, on both the smoothed classifier and the empirical variance. To increase the certified robust radius, we introduce a different way to convert logits to probability vectors for the base classifier to leverage the variance-margin trade-off. We leverage the use of Bernstein's concentration inequality along with enhanced Lipschitz bounds for randomized smoothing. Experimental results show a significant improvement in certified accuracy compared to current state-of-the-art methods. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.

Poster
Mitigating the Curse of Dimensionality for Certified Robustness via Dual Randomized Smoothing

Song Xia, Yi Yu, Xudong Jiang, Henghui Ding

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Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of ${\ell_2}$ certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension $d$, proportionally decreasing at a rate of $1/\sqrt{d}$. This paper explores the feasibility of providing ${\ell_2}$ certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight ${\ell_2}$ certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the ${\ell_2}$ robustness radius, which decreases proportionally at a rate of $(1/\sqrt m + 1/\sqrt n )$ with $m+n=d$. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and ${\ell_2}$ certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

Poster
PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedback

Souradip Chakraborty, Amrit Bedi, Alec Koppel, Huazheng Wang, Dinesh Manocha, Mengdi Wang, Furong Huang

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We present a novel unified bilevel optimization-based framework, \textsf{PARL}, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning using utility or preference-based feedback. We identify a major gap within current algorithmic designs for solving policy alignment due to a lack of precise characterization of the dependence of the alignment objective on the data generated by policy trajectories. This shortfall contributes to the sub-optimal performance observed in contemporary algorithms. Our framework addressed these concerns by explicitly parameterizing the distribution of the upper alignment objective (reward design) by the lower optimal variable (optimal policy for the designed reward). Interestingly, from an optimization perspective, our formulation leads to a new class of stochastic bilevel problems where the stochasticity at the upper objective depends upon the lower-level variable. {True to our best knowledge, this work presents the first formulation of the RLHF as a bilevel optimization problem which generalizes the existing RLHF formulations and addresses the existing distribution shift issues in RLHF formulations.} To demonstrate the efficacy of our formulation in resolving alignment issues in RL, we devised an algorithm named \textsf{A-PARL} to solve PARL problem, establishing sample complexity bounds of order $\mathcal{O}(1/T)$. Our empirical results substantiate that the proposed \textsf{PARL} can address the alignment concerns in RL by showing significant improvements (up to 63\% in terms of required samples) for policy alignment in large-scale environments of the Deepmind control suite and Meta world tasks.

Poster
Benign Overfitting and Grokking in ReLU Networks for XOR Cluster Data

Zhiwei Xu, Yutong Wang, Spencer Frei, Gal Vardi, Wei Hu

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Neural networks trained by gradient descent (GD) have exhibited a number of surprising generalization behaviors. First, they can achieve a perfect fit to noisy training data and still generalize near-optimally, showing that overfitting can sometimes be benign. Second, they can undergo a period of classical, harmful overfitting---achieving a perfect fit to training data with near-random performance on test data---before transitioning (''grokking'') to near-optimal generalization later in training. In this work, we show that both of these phenomena provably occur in two-layer ReLU networks trained by GD on XOR cluster data where a constant fraction of the training labels are flipped. In this setting, we show that after the first step of GD, the network achieves 100\% training accuracy, perfectly fitting the noisy labels in the training data, but achieves near-random test accuracy. At a later training step, the network achieves near-optimal test accuracy while still fitting the random labels in the training data, exhibiting a ''grokking'' phenomenon. This provides the first theoretical result of benign overfitting in neural network classification when the data distribution is not linearly separable. Our proofs rely on analyzing the feature learning process under GD, which reveals that the network implements a non-generalizable linear classifier after one step and gradually learns generalizable features in later steps.

Poster
Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equations

Yujee Song, Donghyun Lee, Rui Meng, Won Hwa Kim

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A Marked Temporal Point Process (MTPP) is a stochastic process whose realization is a set of event-time data. MTPP is often used to understand complex dynamics of asynchronous temporal events such as money transaction, social media, healthcare, etc. Recent studies have utilized deep neural networks to capture complex temporal dependencies of events and generate embedding that aptly represent the observed events. While most previous studies focus on the inter-event dependencies and their representations, how individual events influence the overall dynamics over time has been under-explored. In this regime, we propose a Decoupled MTPP framework that disentangles characterization of a stochastic process into a set of evolving influences from different events. Our approach employs Neural Ordinary Differential Equations (Neural ODEs) to learn flexible continuous dynamics of these influences while simultaneously addressing multiple inference problems, such as density estimation and survival rate computation. We emphasize the significance of disentangling the influences by comparing our framework with state-of-the-art methods on real-life datasets, and provide analysis on the model behavior for potential applications.

Poster
Inducing High Energy-Latency of Large Vision-Language Models with Verbose Images

Kuofeng Gao, Yang Bai, Jindong Gu, Shu-Tao Xia, Philip Torr, Zhifeng Li, Wei Liu

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Large vision-language models (VLMs) such as GPT-4 have achieved exceptional performance across various multi-modal tasks. However, the deployment of VLMs necessitates substantial energy consumption and computational resources. Once attackers maliciously induce high energy consumption and latency time (energy-latency cost) during inference of VLMs, it will exhaust computational resources. In this paper, we explore this attack surface about availability of VLMs and aim to induce high energy-latency cost during inference of VLMs. We find that high energy-latency cost during inference of VLMs can be manipulated by maximizing the length of generated sequences. To this end, we propose verbose images, with the goal of crafting an imperceptible perturbation to induce VLMs to generate long sentences during inference. Concretely, we design three loss objectives. First, a loss is proposed to delay the occurrence of end-of-sequence (EOS) token, where EOS token is a signal for VLMs to stop generating further tokens. Moreover, an uncertainty loss and a token diversity loss are proposed to increase the uncertainty over each generated token and the diversity among all tokens of the whole generated sequence, respectively, which can break output dependency at token-level and sequence-level. Furthermore, a temporal weight adjustment algorithm is proposed, which can effectively balance these losses. Extensive experiments demonstrate that our verbose images can increase the length of generated sequences by 7.87× and 8.56× compared to original images on MS-COCO and ImageNet datasets, which presents potential challenges for various applications.

Poster
Causal-StoNet: Causal Inference for High-Dimensional Complex Data

Yaxin Fang, Faming Liang

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With the advancement of data science, the collection of increasingly complex datasets has become commonplace. In such datasets, the data dimension can be extremely high, and the underlying data generation process can be unknown and highly nonlinear. As a result, the task of making causal inference with high-dimensional complex data has become a fundamental problem in many disciplines, such as medicine, econometrics, and social science. However, the existing methods for causal inference are frequently developed under the assumption that the data dimension is low or that the underlying data generation process is linear or approximately linear. To address these challenges, this paper proposes a novel stochastic deep learning approach for conducting causal inference with high-dimensional complex data. The proposed approach is based on some deep learning techniques, including sparse deep learning theory and stochastic neural networks, that have been developed in recent literature. By using these techniques, the proposed approach can address both the high dimensionality and unknown data generation process in a coherent way. Furthermore, the proposed approach can also be used when missing values are present in the datasets. Extensive numerical studies indicate that the proposed approach outperforms existing ones.

Poster
Solving Diffusion ODEs with Optimal Boundary Conditions for Better Image Super-Resolution

Yiyang Ma, Huan Yang, Wenhan Yang, Jianlong Fu, Jiaying Liu

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Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method ''boosts'' current diffusion-based SR models without any additional training.

Poster
Multimodal Learning Without Labeled Multimodal Data: Guarantees and Applications

Paul Pu Liang, Chun Kai Ling, Yun Cheng, Alexander Obolenskiy, Yudong Liu, Rohan Pandey, Alex Wilf, Louis-Philippe Morency, Russ Salakhutdinov

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In many machine learning systems that jointly learn from multiple modalities, a core research question is to understand the nature of multimodal interactions: how modalities combine to provide new task-relevant information that was not present in either alone. We study this challenge of interaction quantification in a semi-supervised setting with only labeled unimodal data and naturally co-occurring multimodal data (e.g., unlabeled images and captions, video and corresponding audio) but when labeling them is time-consuming. Using a precise information-theoretic definition of interactions, our key contribution is the derivation of lower and upper bounds to quantify the amount of multimodal interactions in this semi-supervised setting. We propose two lower bounds: one based on the shared information between modalities and the other based on disagreement between separately trained unimodal classifiers, and derive an upper bound through connections to approximate algorithms for min-entropy couplings. We validate these estimated bounds and show how they accurately track true interactions. Finally, we show how these theoretical results can be used to estimate multimodal model performance, guide data collection, and select appropriate multimodal models for various tasks.

Poster
LLM-CXR: Instruction-Finetuned LLM for CXR Image Understanding and Generation

Suhyeon Lee, Won Jun Kim, Jinho Chang, Jong Chul Ye

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Following the impressive development of LLMs, vision-language alignment in LLMs is actively being researched to enable multimodal reasoning and visual input/output. This direction of research is particularly relevant to medical imaging because accurate medical image analysis and generation consist of a combination of reasoning based on visual features and prior knowledge. Many recent works have focused on training adapter networks that serve as an information bridge between image processing (encoding or generating) networks and LLMs; but presumably, in order to achieve maximum reasoning potential of LLMs on visual information as well, visual and language features should be allowed to interact more freely. This is especially important in the medical domain because understanding and generating medical images such as chest X-rays (CXR) require not only accurate visual and language-based reasoning but also a more intimate mapping between the two modalities. Thus, taking inspiration from previous work on the transformer and VQ-GAN combination for bidirectional image and text generation, we build upon this approach and develop a method for instruction-tuning an LLM pre-trained only on text to gain vision-language capabilities for medical images. Specifically, we leverage a pretrained LLM’s existing question-answering and instruction-following abilities to teach it to understand visual inputs by instructing it to answer questions about image inputs and, symmetrically, output both text and image responses appropriate to a given query by tuning the LLM with diverse tasks that encompass image-based text-generation and text-based image-generation. We show that our LLM-CXR trained in this approach shows better image-text alignment in both CXR understanding and generation tasks while being smaller in size compared to previously developed models that perform a narrower range of tasks.

Poster
Enhancing Human Experience in Human-Agent Collaboration: A Human-Centered Modeling Approach Based on Positive Human Gain

Yiming Gao, Feiyu Liu, Liang Wang, Dehua Zheng, Zhenjie Lian, Weixuan Wang, Wenjin Yang, Siqin Li, Xianliang Wang, Wenhui Chen, Jing Dai, Qiang Fu, Yang Wei, Lanxiao Huang, Wei Liu

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Existing game AI research mainly focuses on enhancing agents' abilities to win games, but this does not inherently make humans have a better experience when collaborating with these agents. For example, agents may dominate the collaboration and exhibit unintended or detrimental behaviors, leading to poor experiences for their human partners. In other words, most game AI agents are modeled in a "self-centered" manner. In this paper, we propose a "human-centered" modeling scheme for collaborative agents that aims to enhance the experience of humans. Specifically, we model the experience of humans as the goals they expect to achieve during the task. We expect that agents should learn to enhance the extent to which humans achieve these goals while maintaining agents' original abilities (e.g., winning games). To achieve this, we propose the Reinforcement Learning from Human Gain (RLHG) approach. The RLHG approach introduces a "baseline", which corresponds to the extent to which humans primitively achieve their goals, and encourages agents to learn behaviors that can effectively enhance humans in achieving their goals better. We evaluate the RLHG agent in the popular Multi-player Online Battle Arena (MOBA) game, Honor of Kings, by conducting real-world human-agent tests. Both objective performance and subjective preference results show that the RLHG agent provides participants better gaming experience.

Poster
Stochastic Modified Equations and Dynamics of Dropout Algorithm

Zhongwang Zhang, Yuqing Li, Tao Luo, Zhi-Qin John Xu

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Dropout is a widely utilized regularization technique in the training of neural networks, nevertheless, its underlying mechanism and impact on achieving good generalization abilities remain to be further understood. In this work, we start by undertaking a rigorous theoretical derivation of the stochastic modified equations, with the primary aim of providing an effective approximation for the discrete iterative process of dropout. Meanwhile, we experimentally verify SDE's ability to approximate dropout under a wider range of settings. Subsequently, we empirically delve into the intricate mechanisms by which dropout facilitates the identification of flatter minima. This exploration is conducted through intuitive approximations, exploiting the structural analogies inherent in the Hessian of loss landscape and the covariance of dropout. Our empirical findings substantiate the ubiquitous presence of the Hessian-variance alignment relation throughout the training process of dropout.

Poster
Fast-DetectGPT: Efficient Zero-Shot Detection of Machine-Generated Text via Conditional Probability Curvature

Guangsheng Bao, Yanbin Zhao, Zhiyang Teng, Linyi Yang, Yue Zhang

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Large language models (LLMs) have shown the ability to produce fluent and cogent content, presenting both productivity opportunities and societal risks. To build trustworthy AI systems, it is imperative to distinguish between machine-generated and human-authored content. The leading zero-shot detector, DetectGPT, showcases commendable performance but is marred by its intensive computational costs. In this paper, we introduce the concept of **conditional probability curvature** to elucidate discrepancies in word choices between LLMs and humans within a given context. Utilizing this curvature as a foundational metric, we present **Fast-DetectGPT**, an optimized zero-shot detector, which substitutes DetectGPT's perturbation step with a more efficient sampling step. Our evaluations on various datasets, source models, and test conditions indicate that Fast-DetectGPT not only surpasses DetectGPT by a relative around 75\% in both the white-box and black-box settings but also accelerates the detection process by a factor of 340, as detailed in Table 1.

Poster
Out-Of-Domain Unlabeled Data Improves Generalization

seyed amir hossein saberi, Amir Najafi, Alireza Heidari, Mohammad Hosein Movasaghinia, Abolfazl Motahari, Babak Khalaj

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We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered. Notably, we allow the unlabeled samples to deviate slightly (in total variation sense) from the in-domain distribution. The core idea behind our framework is to combine Distributionally Robust Optimization (DRO) with self-supervised training. As a result, we also leverage efficient polynomial-time algorithms for the training stage. From a theoretical standpoint, we apply our framework on the classification problem of a mixture of two Gaussians in $\mathbb{R}^d$, where in addition to the $m$ independent and labeled samples from the true distribution, a set of $n$ (usually with $n\gg m$) out of domain and unlabeled samples are gievn as well. Using only the labeled data, it is known that the generalization error can be bounded by $\propto\left(d/m\right)^{1/2}$. However, using our method on both isotropic and non-isotropic Gaussian mixture models, one can derive a new set of analytically explicit and non-asymptotic bounds which show substantial improvement on the generalization error compared ERM. Our results underscore two significant insights: 1) out-of-domain samples, even when unlabeled, can be harnessed to narrow the generalization gap, provided that the true data distribution adheres to a form of the "cluster assumption", and 2) the semi-supervised learning paradigm can be regarded as a special case of our framework when there are no distributional shifts. We validate our claims through experiments conducted on a variety of synthetic and real-world datasets.

Spotlight
Complete and Efficient Graph Transformers for Crystal Material Property Prediction

Keqiang Yan, Cong Fu, Xiaofeng Qian, Xiaoning Qian, Shuiwang Ji

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Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph representation learning. Specifically, constructing graphs that effectively capture the complete geometric information of crystals and handle chiral crystals remains an unsolved and challenging problem. In this paper, we introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom, enabling efficient and expressive graph representations of crystals. Furthermore, we propose ComFormer, a SE(3) transformer designed specifically for crystalline materials. ComFormer includes two variants; namely, iComFormer that employs invariant geometric descriptors of Euclidean distances and angles, and eComFormer that utilizes equivariant vector representations. Experimental results demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks across three widely-used crystal benchmarks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Poster
Continual Momentum Filtering on Parameter Space for Online Test-time Adaptation

Jae-Hong Lee, Joon-Hyuk Chang

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Deep neural networks (DNNs) have revolutionized tasks such as image classification and speech recognition but often falter when training and test data diverge in distribution. External factors, from weather effects on images to varied speech environments, can cause this discrepancy, compromising DNN performance. Online test-time adaptation (OTTA) methods present a promising solution, recalibrating models in real-time during the test stage without requiring historical data. However, the OTTA paradigm is imperfect, often falling prey to issues such as catastrophic forgetting due to its reliance on noisy, self-trained predictions. Although some contemporary strategies mitigate this by tying adaptations to the static source model, this restricts model flexibility. This paper introduces a continual momentum filtering (CMF) framework, leveraging the Kalman filter (KF) to strike a balance between model adaptability and information retention. The CMF intertwines optimization via stochastic gradient descent with a KF-based inference process. This methodology not only aids in averting catastrophic forgetting but also provides high adaptability to shifting data distributions. We validate our framework on various OTTA scenarios and real-world situations regarding covariate and label shifts, and the CMF consistently shows superior performance compared to state-of-the-art methods.

Poster
A Fast and Provable Algorithm for Sparse Phase Retrieval

Jian-Feng CAI, Yu Long, Ruixue WEN, Jiaxi Ying

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We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the $s$-sparse ground truth signal $\boldsymbol{x}^{\natural} \in \mathbb{R}^n$ (up to a global sign) at a quadratic convergence rate after at most $O(\log (\Vert\boldsymbol{x}^{\natural} \Vert /x_{\min}^{\natural}))$ iterations, using $\Omega(s^2\log n)$ Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

Poster