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

Image Background Serves as Good Proxy for Out-of-distribution Data

Sen Pei

Expand abstract

Out-of-distribution (OOD) detection empowers the model trained on the closed image set to identify unknown data in the open world. Though many prior techniques have yielded considerable improvements in this research direction, two crucial obstacles still remain. Firstly, a unified perspective has yet to be presented to view the developed arts with individual designs, which is vital for providing insights into future work. Secondly, we expect sufficient natural OOD supervision to promote the generation of compact boundaries between the in-distribution (ID) and OOD data without collecting explicit OOD samples. To tackle these issues, we propose a general probabilistic framework to interpret many existing methods and an OOD-data-free model, namely $\textbf{S}$elf-supervised $\textbf{S}$ampling for $\textbf{O}$OD $\textbf{D}$etection (SSOD). SSOD efficiently exploits natural OOD signals from the ID data based on the local property of convolution. With these supervisions, it jointly optimizes the OOD detection and conventional ID classification in an end-to-end manner. Extensive experiments reveal that SSOD establishes competitive state-of-the-art performance on many large-scale benchmarks, outperforming the best previous method by a large margin, e.g., reporting $\textbf{-6.28}$% FPR95 and $\textbf{+0.77}$% AUROC on ImageNet, $\textbf{-19.01}$% FPR95 and $\textbf{+3.04}$% AUROC on CIFAR-10, and top-ranked performance on hard OOD datasets, i.e., ImageNet-O and OpenImage-O.

Poster
Pre-Training and Fine-Tuning Generative Flow Networks

Ling Pan, Moksh Jain, Kanika Madan, Yoshua Bengio

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Generative Flow Networks (GFlowNets) are amortized samplers that learn stochastic policies to sequentially generate compositional objects from a given unnormalized reward distribution. They can generate diverse sets of high-reward objects, which is an important consideration in scientific discovery tasks. However, as they are typically trained from a given extrinsic reward function, it remains an important open challenge about how to leverage the power of pre-training and train GFlowNets in an unsupervised fashion for efficient adaptation to downstream tasks. Inspired by recent successes of unsupervised pre-training in various domains, we introduce a novel approach for reward-free pre-training of GFlowNets. By framing the training as a self-supervised problem, we propose an outcome-conditioned GFlowNet (OC-GFN) that learns to explore the candidate space. Specifically, OC-GFN learns to reach any targeted outcomes, akin to goal-conditioned policies in reinforcement learning. We show that the pre-trained OC-GFN model can allow for a direct extraction of a policy capable of sampling from any new reward functions in downstream tasks. Nonetheless, adapting OC-GFN on a downstream task-specific reward involves an intractable marginalization over possible outcomes. We propose a novel way to approximate this marginalization by learning an amortized predictor enabling efficient fine-tuning. Extensive experimental results validate the efficacy of our approach, demonstrating the effectiveness of pre-training the OC-GFN, and its ability to swiftly adapt to downstream tasks and discover modes more efficiently. This work may serve as a foundation for further exploration of pre-training strategies in the context of GFlowNets.

Spotlight
Incentivized Truthful Communication for Federated Bandits

Zhepei Wei, Chuanhao Li, Tianze Ren, Haifeng Xu, Hongning Wang

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To enhance the efficiency and practicality of federated bandit learning, recent advances have introduced incentives to motivate communication among clients, where a client participates only when the incentive offered by the server outweighs its participation cost. However, existing incentive mechanisms naively assume the clients are truthful: they all report their true cost and thus the higher cost one participating client claims, the more the server has to pay. Therefore, such mechanisms are vulnerable to strategic clients aiming to optimize their own utility by misreporting. To address this issue, we propose an incentive compatible (i.e., truthful) communication protocol, named Truth-FedBan, where the incentive for each participant is independent of its self-reported cost, and reporting the true cost is the only way to achieve the best utility. More importantly, Truth-FedBan still guarantees the sub-linear regret and communication cost without any overhead. In other words, the core conceptual contribution of this paper is, for the first time, demonstrating the possibility of simultaneously achieving incentive compatibility and nearly optimal regret in federated bandit learning. Extensive numerical studies further validate the effectiveness of our proposed solution.

Poster
Chain of Log-Concave Markov Chains

Saeed Saremi, Ji Won Park, Francis Bach

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We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyvärinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

Poster
VDC: Versatile Data Cleanser based on Visual-Linguistic Inconsistency by Multimodal Large Language Models

Zihao Zhu, Mingda Zhang, Shaokui Wei, Bingzhe Wu, Baoyuan Wu

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The role of data in building AI systems has recently been emphasized by the emerging concept of data-centric AI. Unfortunately, in the real-world, datasets may contain dirty samples, such as poisoned samples from backdoor attack, noisy labels in crowdsourcing, and even hybrids of them. The presence of such dirty samples makes the DNNs vunerable and unreliable. Hence, it is critical to detect dirty samples to improve the quality and realiability of dataset. Existing detectors only focus on detecting poisoned samples or noisy labels, that are often prone to weak generalization when dealing with dirty samples from other fields. In this paper, we find a commonality of various dirty samples is visual-linguistic inconsistency between images and associated labels. To capture the semantic inconsistency between modalities, we propose versatile data cleanser (VDC) leveraging the surpassing capabilities of multimodal large language models (MLLM) in cross-modal alignment and reasoning. It consists of three consecutive modules: the visual question generation module to generate insightful questions about the image; the visual question answering module to acquire the semantics of the visual content by answering the questions with MLLM; followed by the visual answer evaluation module to evaluate the inconsistency. Extensive experiments demonstrate its superior performance and generalization to various categories and types of dirty samples. The code is available at [https://github.com/zihao-ai/vdc](https://github.com/zihao-ai/vdc).

Poster
Variance-enlarged Poisson Learning for Graph-based Semi-Supervised Learning with Extremely Sparse Labeled Data

Xiong Zhou, Xianming Liu, Hao Yu, Jialiang Wang, Zeke Xie, Junjun Jiang, Xiangyang Ji

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Graph-based semi-supervised learning, particularly in the context of extremely sparse labeled data, often suffers from degenerate solutions where label functions tend to be nearly constant across unlabeled data. In this paper, we introduce Variance-enlarged Poisson Learning (VPL), a simple yet powerful framework tailored to alleviate the issues arising from the presence of degenerate solutions. VPL incorporates a variance-enlarged regularization term, which induces a Poisson equation specifically for unlabeled data. This intuitive approach increases the dispersion of labels from their average mean, effectively reducing the likelihood of degenerate solutions characterized by nearly constant label functions. We subsequently introduce two streamlined algorithms, V-Laplace and V-Poisson, each intricately designed to enhance Laplace and Poisson learning, respectively. Furthermore, we broaden the scope of VPL to encompass graph neural networks, introducing Variance-enlarged Graph Poisson Networks (V-GPN) to facilitate improved label propagation. To achieve a deeper understanding of VPL's behavior, we conduct a comprehensive theoretical exploration in both discrete and variational cases. Our findings elucidate that VPL inherently amplifies the importance of connections within the same class while concurrently tempering those between different classes. We support our claims with extensive experiments, demonstrating the effectiveness of VPL and showcasing its superiority over existing methods. The code is available at https://github.com/hitcszx/VPL.

Poster
EmerNeRF: Emergent Spatial-Temporal Scene Decomposition via Self-Supervision

Jiawei Yang, Boris Ivanovic, Or Litany, Xinshuo Weng, Seung Wook Kim, Boyi Li, Tong Che, Danfei Xu, Sanja Fidler, Marco Pavone, Yue Wang

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We present EmerNeRF, a simple yet powerful approach for learning spatial-temporal representations of dynamic driving scenes. Grounded in neural fields, EmerNeRF simultaneously captures scene geometry, appearance, motion, and semantics via self-bootstrapping. EmerNeRF hinges upon two core components: First, it stratifies scenes into static and dynamic fields. This decomposition emerges purely from self-supervision, enabling our model to learn from general, in-the-wild data sources. Second, EmerNeRF parameterizes an induced flow field from the dynamic field and uses this flow field to further aggregate multi-frame features, amplifying the rendering precision of dynamic objects. Coupling these three fields (static, dynamic, and flow) enables EmerNeRF to represent highly-dynamic scenes self-sufficiently, without relying on ground truth object annotations or pre-trained models for dynamic object segmentation or optical flow estimation. Our method achieves state-of-the-art performance in sensor simulation, significantly outperforming previous methods when reconstructing static (+2.93 PSNR) and dynamic (+3.70 PSNR) scenes. In addition, to bolster EmerNeRF's semantic generalization, we lift 2D visual foundation model features into 4D space-time and address a general positional bias in modern Transformers, significantly boosting 3D perception performance (e.g., 37.50% relative improvement in occupancy prediction accuracy on average). Finally, we construct a diverse and challenging 120-sequence dataset to benchmark neural fields under extreme and highly-dynamic settings. See the project page for code, data, and request pre-trained models: https://emernerf.github.io

Poster
Towards Assessing and Benchmarking Risk-Return Tradeoff of Off-Policy Evaluation

Haruka Kiyohara, Ren Kishimoto, Kosuke Kawakami, Ken Kobayashi, Kazuhide Nakata, Yuta Saito

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**Off-Policy Evaluation (OPE)** aims to assess the effectiveness of counterfactual policies using offline logged data and is frequently utilized to identify the top-$k$ promising policies for deployment in online A/B tests. Existing evaluation metrics for OPE estimators primarily focus on the "accuracy" of OPE or that of downstream policy selection, neglecting risk-return tradeoff and *efficiency* in subsequent online policy deployment. To address this issue, we draw inspiration from portfolio evaluation in finance and develop a new metric, called **SharpeRatio@k**, which measures the risk-return tradeoff and efficiency of policy portfolios formed by an OPE estimator under varying online evaluation budgets ($k$). We first demonstrate, in two example scenarios, that our proposed metric can clearly distinguish between conservative and high-stakes OPE estimators and reliably identify the most *efficient* estimator capable of forming superior portfolios of candidate policies that maximize return with minimal risk during online deployment, while existing evaluation metrics produce only degenerate results. To facilitate a quick, accurate, and consistent evaluation of OPE via SharpeRatio@k, we have also implemented the proposed metric in an open-source software. Using SharpeRatio@k and the software, we conduct a benchmark experiment of various OPE estimators regarding their risk-return tradeoff, presenting several future directions for OPE research.

Poster
Safe Collaborative Filtering

Riku Togashi, Tatsushi Oka, Naoto Ohsaka, Tetsuro Morimura

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Excellent tail performance is crucial for modern machine learning tasks, such as algorithmic fairness, class imbalance, and risk-sensitive decision making, as it ensures the effective handling of challenging samples within a dataset. Tail performance is also a vital determinant of success for personalized recommender systems to reduce the risk of losing users with low satisfaction. This study introduces a "safe" collaborative filtering method that prioritizes recommendation quality for less-satisfied users rather than focusing on the average performance. Our approach minimizes the conditional value at risk (CVaR), which represents the average risk over the tails of users' loss. To overcome computational challenges for web-scale recommender systems, we develop a robust yet practical algorithm that extends the most scalable method, implicit alternating least squares (iALS). Empirical evaluation on real-world datasets demonstrates the excellent tail performance of our approach while maintaining competitive computational efficiency.

Poster
Hybrid Sharing for Multi-Label Image Classification

Zihao Yin, Chen Gan, Kelei He, Yang Gao, Junfeng Zhang

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Existing multi-label classification methods have long suffered from label heterogeneity, where learning a label obscures another. By modeling multi-label classification as a multi-task problem, this issue can be regarded as a negative transfer, which indicates challenges to achieve simultaneously satisfied performance across multiple tasks. In this work, we propose the Hybrid Sharing Query (HSQ), a transformer-based model that introduces the mixture-of-experts architecture to image multi-label classification. HSQ is designed to leverage label correlations while mitigating heterogeneity effectively. To this end, HSQ is incorporated with a fusion expert framework that enables it to optimally combine the strengths of task-specialized experts with shared experts, ultimately enhancing multi-label classification performance across most labels. Extensive experiments are conducted on two benchmark datasets, with the results demonstrating that the proposed method achieves state-of-the-art performance and yields simultaneous improvements across most labels. The code is available at https://github.com/zihao-yin/HSQ

Poster
Bayes Conditional Distribution Estimation for Knowledge Distillation Based on Conditional Mutual Information

Linfeng Ye, Shayan Mohajer Hamidi, Renhao Tan, EN-HUI YANG

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It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. In fact, maximizing the teacher's CMI value ensures that the teacher can effectively capture the contextual information within the images, and for visualizing this information, we deploy Eigen-CAM. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot).

Poster
ValUES: A Framework for Systematic Validation of Uncertainty Estimation in Semantic Segmentation

Kim-Celine Kahl, Carsten T. Lüth, Maximilian Zenk, Klaus Maier-Hein, Paul F Jaeger

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Uncertainty estimation is an essential and heavily-studied component for the reliable application of semantic segmentation methods. While various studies exist claiming methodological advances on the one hand, and successful application on the other hand, the field is currently hampered by a gap between theory and practice leaving fundamental questions unanswered: Can data-related and model-related uncertainty really be separated in practice? Which components of an uncertainty method are essential for real-world performance? Which uncertainty method works well for which application? In this work, we link this research gap to a lack of systematic and comprehensive evaluation of uncertainty methods. Specifically, we identify three key pitfalls in current literature and present an evaluation framework that bridges the research gap by providing 1) a controlled environment for studying data ambiguities as well as distribution shifts, 2) systematic ablations of relevant method components, and 3) test-beds for the five predominant uncertainty applications: OoD-detection, active learning, failure detection, calibration, and ambiguity modeling. Empirical results on simulated as well as real-world data demonstrate how the proposed framework is able to answer the predominant questions in the field revealing for instance that 1) separation of uncertainty types works on simulated data but does not necessarily translate to real-world data, 2) aggregation of scores is a crucial but currently neglected component of uncertainty methods, 3) While ensembles are performing most robustly across the different downstream tasks and settings, test-time augmentation often constitutes a light-weight alternative. Code is at: https://github.com/IML-DKFZ/values

Oral
Provable Reward-Agnostic Preference-Based Reinforcement Learning

Wenhao Zhan, Masatoshi Uehara, Wen Sun, Jason D. Lee

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Preference-based Reinforcement Learning (PbRL) is a paradigm in which an RL agent learns to optimize a task using pair-wise preference-based feedback over trajectories, rather than explicit reward signals. While PbRL has demonstrated practical success in fine-tuning language models, existing theoretical work focuses on regret minimization and fails to capture most of the practical frameworks. In this study, we fill in such a gap between theoretical PbRL and practical algorithms by proposing a theoretical reward-agnostic PbRL framework where exploratory trajectories that enable accurate learning of hidden reward functions are acquired before collecting any human feedback. Theoretical analysis demonstrates that our algorithm requires less human feedback for learning the optimal policy under preference-based models with linear parameterization and unknown transitions, compared to the existing theoretical literature. Specifically, our framework can incorporate linear and low-rank MDPs with efficient sample complexity. Additionally, we investigate reward-agnostic RL with action-based comparison feedback and introduce an efficient querying algorithm tailored to this scenario.

Spotlight
Sparse MoE with Language Guided Routing for Multilingual Machine Translation

Xinyu Zhao, Xuxi Chen, Yu Cheng, Tianlong Chen

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Sparse Mixture-of-Experts (SMoE) has gained increasing popularity as a promising framework for scaling up multilingual machine translation (MMT) models with negligible extra computational overheads. However, current SMoE solutions neglect the intrinsic structures of the MMT problem: ($a$) $\textit{Linguistics Hierarchy.}$ Languages are naturally grouped according to their lingual properties like genetic families, phonological characteristics, etc; ($b$) $\textit{Language Complexity.}$ The learning difficulties are varied for diverse languages due to their grammar complexity, available resources, etc. Therefore, routing a fixed number of experts (e.g., $1$ or $2$ experts in usual) only at the word level leads to inferior performance. To fill in the missing puzzle, we propose $\textbf{\texttt{Lingual-SMoE}}$ by equipping the SMoE with adaptive and linguistic-guided routing policies. Specifically, it ($1$) extracts language representations to incorporate linguistic knowledge and uses them to allocate experts into different groups; ($2$) determines the number of activated experts for each target language in an adaptive and automatic manner, according to their translation difficulties, which aims to mitigate the potential over-/under-fitting issues of learning simple/challenges translations. Sufficient experimental studies on MMT benchmarks with {$16$, $50$, $100$} language pairs and various network architectures, consistently validate the superior performance of our proposals. For instance, $\texttt{Lingual-SMoE}$ outperforms its dense counterpart by over $5\%$ BLEU scores on $\texttt{OPUS-100}$ dataset.

Poster
Conversational Drug Editing Using Retrieval and Domain Feedback

Shengchao Liu, Jiongxiao Wang, Yijin Yang, Chengpeng Wang, Ling Liu, Hongyu Guo, Chaowei Xiao

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Recent advancements in conversational large language models (LLMs), such as ChatGPT, have demonstrated remarkable promise in various domains, including drug discovery. However, existing works mainly focus on investigating the capabilities of conversational LLMs on chemical reactions and retrosynthesis. While drug editing, a critical task in the drug discovery pipeline, remains largely unexplored. To bridge this gap, we propose ChatDrug, a framework to facilitate the systematic investigation of drug editing using LLMs. ChatDrug jointly leverages a prompt module, a retrieval and domain feedback module, and a conversation module to streamline effective drug editing. We empirically show that ChatDrug reaches the best performance on all 39 drug editing tasks, encompassing small molecules, peptides, and proteins. We further demonstrate, through 10 case studies, that ChatDrug can successfully identify the key substructures for manipulation, generating diverse and valid suggestions for drug editing. Promisingly, we also show that ChatDrug can offer insightful explanations from a domain-specific perspective, enhancing interpretability and enabling informed decision-making.

Poster
Bidirectional Temporal Diffusion Model for Temporally Consistent Human Animation

Tserendorj Adiya, Jae Shin Yoon, JUNGEUN LEE, Sanghun Kim, Hwasup Lim

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We introduce a method to generate temporally coherent human animation from a single image, a video, or a random noise. This problem has been formulated as modeling of an auto-regressive generation, i.e., to regress past frames to decode future frames. However, such unidirectional generation is highly prone to motion drifting over time, generating unrealistic human animation with significant artifacts such as appearance distortion. We claim that bidirectional temporal modeling enforces temporal coherence on a generative network by largely suppressing the appearance ambiguity. To prove our claim, we design a novel human animation framework using a denoising diffusion model: a neural network learns to generate the image of a person by denoising temporal Gaussian noises whose intermediate results are cross-conditioned bidirectionally between consecutive frames. In the experiments, our method demonstrates strong performance compared to existing unidirectional approaches with realistic temporal coherence.

Poster
Transformers as Decision Makers: Provable In-Context Reinforcement Learning via Supervised Pretraining

Licong Lin, Yu Bai, Song Mei

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Large transformer models pretrained on offline reinforcement learning datasets have demonstrated remarkable in-context reinforcement learning (ICRL) capabilities, where they can make good decisions when prompted with interaction trajectories from unseen environments. However, when and how transformers can be trained to perform ICRL have not been theoretically well-understood. In particular, it is unclear which reinforcement-learning algorithms transformers can perform in context, and how distribution mismatch in offline training data affects the learned algorithms. This paper provides a theoretical framework that analyzes supervised pretraining for ICRL. This includes two recently proposed training methods --- algorithm distillation and decision-pretrained transformers. First, assuming model realizability, we prove the supervised-pretrained transformer will imitate the conditional expectation of the expert algorithm given the observed trajectory. The generalization error will scale with model capacity and a distribution divergence factor between the expert and offline algorithms. Second, we show transformers with ReLU attention can efficiently approximate near-optimal online reinforcement learning algorithms like LinUCB and Thompson sampling for stochastic linear bandits, and UCB-VI for tabular Markov decision processes. This provides the first quantitative analysis of the ICRL capabilities of transformers pretrained from offline trajectories.

Poster
MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning

Xiang Yue, Xingwei Qu, Ge Zhang, Yao Fu, Wenhao Huang, Huan Sun, Yu Su, Wenhu Chen

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We introduce MAmmoTH, a series of open-source large language models (LLMs) specifically tailored for general math problem-solving. The MAmmoTH models are trained on MathInstruct, our meticulously curated instruction tuning dataset. MathInstruct is compiled from 13 math datasets with intermediate rationales, six of which have rationales newly curated by us. It presents a unique hybrid of chain-of-thought (CoT) and program-of-thought (PoT) rationales, and also ensures extensive coverage of diverse fields in math. The hybrid of CoT and PoT not only unleashes the potential of tool use but also allows different thought processes for different math problems. As a result, the MAmmoTH series substantially outperform existing open-source models on nine mathematical reasoning datasets across all scales with an average accuracy gain between 16% and 32%. Remarkably, our MAmmoTH-7B model reaches 33% on MATH (a competition-level dataset), which exceeds the best open-source 7B model (WizardMath) by 23%, and the MAmmoTH-34B model achieves 44% accuracy on MATH, even surpassing GPT-4’s CoT result. Our work underscores the importance of diverse problem coverage and the use of hybrid rationales in developing superior math generalist models.

Spotlight
Faithful and Efficient Explanations for Neural Networks via Neural Tangent Kernel Surrogate Models

Andrew William Engel, Zhichao Wang, Natalie Frank, Ioana Dumitriu, Sutanay Choudhury, Anand Sarwate, Tony Chiang

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A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer.

Spotlight
Inverse Approximation Theory for Nonlinear Recurrent Neural Networks

Shida Wang, Zhong Li, Qianxiao Li

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We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs). This is a so-called Bernstein-type result in approximation theory, which deduces properties of a target function under the assumption that it can be effectively approximated by a hypothesis space. In particular, we show that nonlinear sequence relationships that can be stably approximated by nonlinear RNNs must have an exponential decaying memory structure - a notion that can be made precise. This extends the previously identified curse of memory in linear RNNs into the general nonlinear setting, and quantifies the essential limitations of the RNN architecture for learning sequential relationships with long-term memory. Based on the analysis, we propose a principled reparameterization method to overcome the limitations. Our theoretical results are confirmed by numerical experiments.

Spotlight