ICLR 2025 论文列表

International Conference on Learning Representations

录用类型

3,703篇论文

按官方录用论文列表统计,可能与会议公布的数字略有出入。

  • Oral
    2135.8%
  • Spotlight
    38010.3%
  • Poster
    3,11084.0%

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Fair Clustering in the Sliding Window Model

Vincent Cohen-Addad, Shaofeng H.-C. Jiang, Qiaoyuan Yang, Yubo Zhang, Samson Zhou

展开摘要

We study streaming algorithms for proportionally fair clustering, a notion originally suggested by Chierichetti et al. (2017), in the sliding window model. We show that although there exist efficient streaming algorithms in the insertion-only model, surprisingly no algorithm can achieve finite ratio without violating the fairness constraint in sliding window. Hence, the problem of fair clustering is a rare separation between the insertion-only streaming model and the sliding window model. On the other hand, we show that if the fairness constraint is relaxed by a multiplicative $(1+\varepsilon)$ factor, there exists a $(1 + \varepsilon)$-approximate sliding window algorithm that uses $\text{poly}(k\varepsilon^{-1}\log n)$ space. This achieves essentially the best parameters (up to degree in the polynomial) provided the aforementioned lower bound. We also implement a number of empirical evaluations on real datasets to complement our theoretical results.

Spotlight
Language Model Alignment in Multilingual Trolley Problems

Zhijing Jin, Max Kleiman-Weiner, Giorgio Piatti, Sydney Levine, Jiarui Liu, Fernando Gonzalez Adauto, Francesco Ortu, András Strausz, Mrinmaya Sachan, Rada Mihalcea, Yejin Choi, Bernhard Schölkopf

展开摘要

We evaluate the moral alignment of large language models (LLMs) with human preferences in multilingual trolley problems. Building on the Moral Machine experiment, which captures over 40 million human judgments across 200+ countries, we develop a cross-lingual corpus of moral dilemma vignettes in over 100 languages called MultiTP. This dataset enables the assessment of LLMs' decision-making processes in diverse linguistic contexts. Our analysis explores the alignment of 19 different LLMs with human judgments, capturing preferences across six moral dimensions: species, gender, fitness, status, age, and the number of lives involved. By correlating these preferences with the demographic distribution of language speakers and examining the consistency of LLM responses to various prompt paraphrasings, our findings provide insights into cross-lingual and ethical biases of LLMs and their intersection. We discover significant variance in alignment across languages, challenging the assumption of uniform moral reasoning in AI systems and highlighting the importance of incorporating diverse perspectives in AI ethics. The results underscore the need for further research on the integration of multilingual dimensions in responsible AI research to ensure fair and equitable AI interactions worldwide.

Spotlight
Neural Dueling Bandits: Preference-Based Optimization with Human Feedback

Arun Verma, Zhongxiang Dai, Xiaoqiang Lin, Patrick Jaillet, Bryan Kian Hsiang Low

展开摘要

Contextual dueling bandit is used to model the bandit problems, where a learner's goal is to find the best arm for a given context using observed noisy human preference feedback over the selected arms for the past contexts. However, existing algorithms assume the reward function is linear, which can be complex and non-linear in many real-life applications like online recommendations or ranking web search results. To overcome this challenge, we use a neural network to estimate the reward function using preference feedback for the previously selected arms. We propose upper confidence bound- and Thompson sampling-based algorithms with sub-linear regret guarantees that efficiently select arms in each round. We also extend our theoretical results to contextual bandit problems with binary feedback, which is in itself a non-trivial contribution. Experimental results on the problem instances derived from synthetic datasets corroborate our theoretical results.

Poster
Divergence of Neural Tangent Kernel in Classification Problems

Zixiong Yu, Songtao Tian, Guhan Chen

展开摘要

This paper primarily investigates the convergence of the Neural Tangent Kernel (NTK) in classification problems. This study firstly show the strictly positive definiteness of NTK of multi-layer fully connected neural networks and residual neural networks. Then, through a contradiction argument, it indicates that, during training with the cross-entropy loss function, the neural network parameters diverge due to the strictly positive definiteness of the NTK. Consequently, the empirical NTK does not consistently converge but instead diverges as time approaches infinity. This finding implies that NTK theory is not applicable in this context, highlighting significant theoretical implications for the study of neural networks in classification problems. These results can also be easily generalized to other network structures, provided that the NTK is strictly positive definite.

Poster
Regret Bounds for Episodic Risk-Sensitive Linear Quadratic Regulator

Wenhao XU, Xuefeng Gao, Xuedong He

展开摘要

Risk-sensitive linear quadratic regulator is one of the most fundamental problems in risk-sensitive optimal control. In this paper, we study online adaptive control of risk-sensitive linear quadratic regulator in the finite horizon episodic setting. We propose a simple least-squares greedy algorithm and show that it achieves $\widetilde{\mathcal{O}}(\log N)$ regret under a specific identifiability assumption, where $N$ is the total number of episodes. If the identifiability assumption is not satisfied, we propose incorporating exploration noise into the least-squares-based algorithm, resulting in an algorithm with $\widetilde{\mathcal{O}}(\sqrt{N})$ regret. To our best knowledge, this is the first set of regret bounds for episodic risk-sensitive linear quadratic regulator. Our proof relies on perturbation analysis of less-standard Riccati equations for risk-sensitive linear quadratic control, and a delicate analysis of the loss in the risk-sensitive performance criterion due to applying the suboptimal controller in the online learning process.

Poster
Joint Reward and Policy Learning with Demonstrations and Human Feedback Improves Alignment

Chenliang Li, Siliang Zeng, Zeyi Liao, Jiaxiang Li, Dongyeop Kang, Alfredo Garcia, Mingyi Hong

展开摘要

Aligning to human preferences and/or intentions is an important requirement for contemporary foundation models. To ensure alignment, popular approaches such as reinforcement learning with human feedback (RLHF) break down the task into three stages: (i) a model is computed with supervised fine-tuning (SFT) based upon large demonstrations data, (ii) a reward model (RM) is estimated based upon human feedback data, and (iii) reinforcement learning (RL) is used to further refine the SFT model by optimizing the estimated reward model. Demonstrations and human feedback data reflect human user preferences in different ways. As a result, the reward model estimate obtained from only human feedback data is likely not as accurate as a reward model estimate obtained from both demonstration and human feedback data. A policy model that optimizes the reward model estimate obtained from both demonstration and human feedback data will likely exhibit better alignment performance. We introduce a tractable algorithm for finding the reward and policy models and provide a finite-time performance guarantee. Additionally, we demonstrate the efficiency of the proposed solution with extensive experiments including alignment problems in LLMs and robotic control problems in MuJoCo. We observe that the proposed solutions outperform the existing alignment algorithm by large margins, especially when the amounts of demonstration and preference data are unbalanced.

Spotlight
How Low Can You Go? Searching for the Intrinsic Dimensionality of Complex Networks using Metric Node Embeddings

Nikolaos Nakis, Niels Raunkjær Holm, Andreas Lyhne Fiehn, Morten Mørup

展开摘要

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified exact low-dimensional embeddings, the limits of the required embedding dimensions remain unclear. We presently prove that lower dimensional embeddings are possible when using Euclidean metric embeddings as opposed to vector-based Logistic PCA (LPCA) embeddings. In particular, we provide an efficient logarithmic search procedure for identifying the exact embedding dimension and demonstrate how metric embeddings enable inference of the exact embedding dimensions of large-scale networks by exploiting that the metric properties can be used to provide linearithmic scaling. Empirically, we show that our approach extracts substantially lower dimensional representations of networks than previously reported for small-sized networks. For the first time, we demonstrate that even large-scale networks can be effectively embedded in very low-dimensional spaces, and provide examples of scalable, exact reconstruction for graphs with up to a million nodes. Our approach highlights that the intrinsic dimensionality of networks is substantially lower than previously reported and provides a computationally efficient assessment of the exact embedding dimension also of large-scale networks. The surprisingly low dimensional representations achieved demonstrate that networks in general can be losslessly represented using very low dimensional feature spaces, which can be used to guide existing network analysis tasks from community detection and node classification to structure revealing exact network visualizations.

Poster
Advancing Prompt-Based Methods for Replay-Independent General Continual Learning

Zhiqi KANG, Liyuan Wang, Xingxing Zhang, Karteek Alahari

展开摘要

General continual learning (GCL) is a broad concept to describe real-world continual learning (CL) problems, which are often characterized by online data streams without distinct transitions between tasks, i.e., blurry task boundaries. Such requirements result in poor initial performance, limited generalizability, and severe catastrophic forgetting, heavily impacting the effectiveness of mainstream GCL models trained from scratch. While the use of a frozen pretrained backbone with appropriate prompt tuning can partially address these challenges, such prompt-based methods remain suboptimal for CL of remaining tunable parameters on the fly. In this regard, we propose an innovative approach named MISA (Mask and Initial Session Adaption) to advance prompt-based methods in GCL. It includes a forgetting-aware initial session adaption that employs pretraining data to initialize prompt parameters and improve generalizability, as well as a non-parametric logit mask of the output layers to mitigate catastrophic forgetting. Empirical results demonstrate substantial performance gains of our approach compared to recent competitors, especially without a replay buffer (e.g., up to 18.39, 22.06, and 11.96% points performance lead on CIFAR-100, Tiny-ImageNet, and ImageNet-R, respectively). Moreover, our approach features the plug-in nature for prompt-based methods, independence of replay, ease of implementation, and avoidance of CL-relevant hyperparameters, serving as a strong baseline for GCL research. Our source code is publicly available at https://github.com/kangzhiq/MISA

Poster
Robustness Auditing for Linear Regression: To Singularity and Beyond

Ittai Rubinstein, Samuel B. Hopkins

展开摘要

It has recently been discovered that the conclusions of many highly influential econometrics studies can be overturned by removing a very small fraction of their samples (often less than $0.5\%$). These conclusions are typically based on the results of one or more Ordinary Least Squares (OLS) regressions, raising the question: given a dataset, can we certify the robustness of an OLS fit on this dataset to the removal of a given number of samples? Brute-force techniques quickly break down even on small datasets. Existing approaches which go beyond brute force either can only find candidate small subsets to remove (but cannot certify their non-existence) [BGM20, KZC21], are computationally intractable beyond low dimensional settings [MR22], or require very strong assumptions on the data distribution and too many samples to give reasonable bounds in practice [BP21, FH23]. We present an efficient algorithm for certifying the robustness of linear regressions to removals of samples. We implement our algorithm and run it on several landmark econometrics datasets with hundreds of dimensions and tens of thousands of samples, giving the first non-trivial certificates of robustness to sample removal for datasets of dimension $4$ or greater. We prove that under distributional assumptions on a dataset, the bounds produced by our algorithm are tight up to a $1 + o(1)$ multiplicative factor.

Poster
Agent Security Bench (ASB): Formalizing and Benchmarking Attacks and Defenses in LLM-based Agents

Hanrong Zhang, Jingyuan Huang, Kai Mei, Yifei Yao, Zhenting Wang, Chenlu Zhan, Hongwei Wang, Yongfeng Zhang

展开摘要

Although LLM-based agents, powered by Large Language Models (LLMs), can use external tools and memory mechanisms to solve complex real-world tasks, they may also introduce critical security vulnerabilities. However, the existing literature does not comprehensively evaluate attacks and defenses against LLM-based agents. To address this, we introduce Agent Security Bench (ASB), a comprehensive framework designed to formalize, benchmark, and evaluate the attacks and defenses of LLM-based agents, including 10 scenarios (e.g., e-commerce, autonomous driving, finance), 10 agents targeting the scenarios, over 400 tools, 27 different types of attack/defense methods, and 7 evaluation metrics. Based on ASB, we benchmark 10 prompt injection attacks, a memory poisoning attack, a novel Plan-of-Thought backdoor attack, 4 mixed attacks, and 11 corresponding defenses across 13 LLM backbones. Our benchmark results reveal critical vulnerabilities in different stages of agent operation, including system prompt, user prompt handling, tool usage, and memory retrieval, with the highest average attack success rate of 84.30\%, but limited effectiveness shown in current defenses, unveiling important works to be done in terms of agent security for the community. We also introduce a new metric to evaluate the agents' capability to balance utility and security. Our code can be found at https://github.com/agiresearch/ASB.

Poster
Attention as a Hypernetwork

Simon Schug, Seijin Kobayashi, Yassir Akram, Joao Sacramento, Razvan Pascanu

展开摘要

Transformers can under some circumstances generalize to novel problem instances whose constituent parts might have been encountered during training, but whose compositions have not. What mechanisms underlie this ability for compositional generalization? By reformulating multi-head attention as a hypernetwork, we reveal that a composable, low-dimensional latent code specifies key-query specific operations. We find empirically that this latent code is predictive of the subtasks the network performs on unseen task compositions, revealing that latent codes acquired during training are reused to solve unseen problem instances. To further examine the hypothesis that the intrinsic hypernetwork of multi-head attention supports compositional generalization, we ablate whether making the hypernetwork-generated linear value network nonlinear strengthens compositionality. We find that this modification improves compositional generalization on abstract reasoning tasks. In particular, we introduce a symbolic version of the Raven's Progressive Matrices human intelligence test, which gives us precise control over the problem compositions encountered during training and evaluation. We demonstrate on this task how scaling model size and data enables compositional generalization in transformers and gives rise to a functionally structured latent space.

Oral
RA-TTA: Retrieval-Augmented Test-Time Adaptation for Vision-Language Models

Youngjun Lee, Doyoung Kim, Junhyeok Kang, Jihwan Bang, Hwanjun Song, Jae-Gil Lee

展开摘要

Vision-language models (VLMs) are known to be susceptible to distribution shifts between pre-training data and test data, and test-time adaptation (TTA) methods for VLMs have been proposed to mitigate the detrimental impact of the distribution shifts. However, the existing methods solely rely on the internal knowledge encoded within the model parameters, which are constrained to pre-training data. To complement the limitation of the internal knowledge, we propose **Retrieval-Augmented-TTA (RA-TTA)** for adapting VLMs to test distribution using **external** knowledge obtained from a web-scale image database. By fully exploiting the bi-modality of VLMs, RA-TTA **adaptively** retrieves proper external images for each test image to refine VLMs' predictions using the retrieved external images, where fine-grained **text descriptions** are leveraged to extend the granularity of external knowledge. Extensive experiments on 17 datasets demonstrate that the proposed RA-TTA outperforms the state-of-the-art methods by 3.01-9.63\% on average.

Poster
Decision Tree Induction Through LLMs via Semantically-Aware Evolution

Tennison Liu, Nicolas Huynh, Mihaela van der Schaar

展开摘要

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce $\texttt{LLEGO}$, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce $\textit{fitness-guided}$ crossover to exploit high-performing regions, and $\textit{diversity-guided}$ mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that $\texttt{LLEGO}$ evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Poster
Fictitious Synthetic Data Can Improve LLM Factuality via Prerequisite Learning

Yujian Liu, Shiyu Chang, Tommi Jaakkola, Yang Zhang

展开摘要

Recent studies have identified one aggravating factor of LLM hallucinations as the knowledge inconsistency between pre-training and fine-tuning, where unfamiliar fine-tuning data mislead the LLM to fabricate plausible but wrong outputs. In this paper, we propose a novel fine-tuning strategy called Prereq-Tune to address this knowledge inconsistency and reduce hallucinations. Fundamentally, Prereq-Tune disentangles the learning of skills and knowledge, so the model learns only the task skills without being impacted by the knowledge inconsistency. To achieve this, Prereq-Tune introduces an additional prerequisite learning stage to learn the necessary knowledge for SFT, allowing subsequent SFT to focus only on task skills. Prereq-Tune can also be combined with fictitious synthetic data to enhance the grounding of LLM outputs to their internal knowledge. Experiments show that Prereq-Tune outperforms existing baselines in improving LLM's factuality across short QA and long-form generation tasks. It also opens new possibilities for knowledge-controlled generation in LLMs. Our code is available at https://github.com/UCSB-NLP-Chang/Prereq_tune.git.

Poster
Think Then React: Towards Unconstrained Action-to-Reaction Motion Generation

Wenhui Tan, Boyuan Li, Chuhao Jin, Wenbing Huang, Xiting Wang, Ruihua Song

展开摘要

Modeling human-like action-to-reaction generation has significant real-world applications, like human-robot interaction and games. Despite recent advancements in single-person motion generation, it is still challenging to well handle action-to-reaction generation, due to the difficulty of directly predicting reaction from action sequence without prompts, and the absence of a unified representation that effectively encodes multi-person motion. To address these challenges, we introduce Think-Then-React (TTR), a large language-model-based framework designed to generate human-like reactions. First, with our fine-grained multimodal training strategy, TTR is capable to unify two processes during inference: a thinking process that explicitly infers action intentions and reasons corresponding reaction description, which serve as semantic prompts, and a reacting process that predicts reactions based on input action and the inferred semantic prompts. Second, to effectively represent multi-person motion in language models, we propose a unified motion tokenizer by decoupling egocentric pose and absolute space features, which effectively represents action and reaction motion with same encoding. Extensive experiments demonstrate that TTR outperforms existing baselines, achieving significant improvements in evaluation metrics, such as reducing FID from 3.988 to 1.942.

Poster
Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspective

Zeyu Gan, Yong Liu

展开摘要

Synthetic data has become a pivotal resource in post-training tasks for large language models (LLMs) due to the scarcity of high-quality, specific data. While various methods have been developed to generate synthetic data, there remains a discernible gap between the practical effects of synthetic data and our theoretical comprehension. To address this challenge, we commence by presenting a detailed modeling of the prevalent synthetic data generation process. Building upon this modeling, we demonstrate that the generalization capability of the post-trained model is critically determined by the information gain derived from the generative model, as analyzed from a novel reverse-bottleneck perspective. Moreover, we introduce the concept of Generalization Gain via Mutual Information (GGMI) and elucidate the relationship between generalization gain and information gain. This analysis serves as a theoretical foundation for synthetic data generation and further highlights its connection with the generalization capability of post-trained models, offering an understanding about the design of synthetic data generation techniques and the optimization of the post-training process. We open-source our code at https://github.com/ZyGan1999/Towards-a-Theoretical-Understanding-of-Synthetic-Data-in-LLM-Post-Training.

Poster
Triples as the Key: Structuring Makes Decomposition and Verification Easier in LLM-based TableQA

Zhen Yang, Ziwei Du, Minghan Zhang, Wei Du, Jie Chen, Zhen Duan, Shu Zhao

展开摘要

As the mainstream approach, LLMs have been widely applied and researched in TableQA tasks. Currently, the core of LLM-based TableQA methods typically include three phases: question decomposition, sub-question TableQA reasoning, and answer verification. However, several challenges remain in this process: i) Sub-questions generated by these methods often exhibit significant gaps with the original question due to critical information overlooked during the LLM's direct decomposition; ii) Verification of answers is typically challenging because LLMs tend to generate optimal responses during self-correct. To address these challenges, we propose a Triple-Inspired Decomposition and vErification (TIDE) strategy, which leverages the structural properties of triples to assist in decomposition and verification in TableQA. The inherent structure of triples (head entity, relation, tail entity) requires the LLM to extract as many entities and relations from the question as possible. Unlike direct decomposition methods that may overlook key information, our transformed sub-questions using triples encompass more critical details. Additionally, this explicit structure facilitates verification. By comparing the triples derived from the answers with those from the question decomposition, we can achieve easier and more straightforward validation than when relying on the LLM's self-correct tendencies. By employing triples alongside established LLM modes, Direct Prompting and Agent modes, TIDE achieves state-of-the-art performance across multiple TableQA datasets, demonstrating the effectiveness of our method.

Poster
How DNNs break the Curse of Dimensionality: Compositionality and Symmetry Learning

Arthur Jacot, Seok Hoan Choi, Yuxiao Wen

展开摘要

We show that deep neural networks (DNNs) can efficiently learn any composition of functions with bounded $F_{1}$-norm, which allows DNNs to break the curse of dimensionality in ways that shallow networks cannot. More specifically, we derive a generalization bound that combines a covering number argument for compositionality, and the $F_{1}$-norm (or the related Barron norm) for large width adaptivity. We show that the global minimizer of the regularized loss of DNNs can fit for example the composition of two functions $f^{\*}=h\circ g$ from a small number of observations, assuming $g$ is smooth/regular and reduces the dimensionality (e.g. $g$ could be the quotient map of the symmetries of $f^{*}$), so that $h$ can be learned in spite of its low regularity. The measures of regularity we consider is the Sobolev norm with different levels of differentiability, which is well adapted to the $F_{1}$ norm. We compute scaling laws empirically and observe phase transitions depending on whether $g$ or $h$ is harder to learn, as predicted by our theory.

Poster
Biologically Constrained Barrel Cortex Model Integrates Whisker Inputs and Replicates Key Brain Network Dynamics

Tianfang Zhu, Dongli Hu, Jiandong Zhou, Kai Du, Anan LI

展开摘要

The brain's ability to transform sensory inputs into motor functions is central to neuroscience and crucial for the development of embodied intelligence. Sensory-motor integration involves complex neural circuits, diverse neuronal types, and intricate intercellular connections. Bridging the gap between biological realism and behavioral functionality presents a formidable challenge. In this study, we focus on the columnar structure of the superficial layers of mouse barrel cortex as a model system. We constructed a model comprising 4,218 neurons across 13 neuronal subtypes, with neural distribution and connection strengths constrained by anatomical experimental findings. A key innovation of our work is the development of an effective construction and training pipeline tailored for this biologically constrained model. Additionally, we converted an existing simulated whisker sweep dataset into a spiking-based format, enabling our network to be trained and tested on neural signals that more closely mimic those observed in biological systems. The results of object discrimination utilizing whisker signals demonstrate that our barrel cortex model, grounded in biological constraints, achieves a classification accuracy exceeds classical convolutional neural networks (CNNs), recurrent neural networks (RNNs), and long short-term memory networks (LSTMs), by an average of 8.6%, and is on par with recent spiking neural networks (SNNs) in performance. Interestingly, a whisker deprivation experiment, designed in accordance with neuroscience practices, further validates the perceptual capabilities of our model in behavioral tasks. Critically, it offers significant biological interpretability: post-training analysis reveals that neurons within our model exhibit firing characteristics and distribution patterns similar to those observed in the actual neuronal systems of the barrel cortex. This study advances our understanding of neural processing in the barrel cortex and exemplifies how integrating detailed biological structures into neural network models can enhance both scientific inquiry and artificial intelligence applications. The code is available at https://github.com/fun0515/RSNN_bfd.

Spotlight
Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues

Riccardo Grazzi, Julien Siems, Arber Zela, Jörg K.H. Franke, Frank Hutter, Massimiliano Pontil

展开摘要

Linear Recurrent Neural Networks (LRNNs) such as Mamba, RWKV, GLA, mLSTM, and DeltaNet have emerged as efficient alternatives to Transformers for long sequences. However, both Transformers and LRNNs struggle to perform state-tracking, which may impair performance in tasks such as code evaluation. In one forward pass, current architectures are unable to solve even parity, the simplest state-tracking task, which non-linear RNNs can handle effectively. Recently, Sarrof et al. (2024) demonstrated that the failure of LRNNs like Mamba to solve parity stems from restricting the value range of their diagonal state-transition matrices to $[0, 1]$ and that incorporating negative values can resolve this issue. We extend this result to non-diagonal LRNNs such as DeltaNet. We prove that finite precision LRNNs with state-transition matrices having only positive eigenvalues cannot solve parity, while non-triangular matrices are needed to count modulo $3$. Notably, we also prove that LRNNs can learn any regular language when their state-transition matrices are products of identity minus vector outer product matrices, each with eigenvalues in the range $[-1, 1]$. Our experiments confirm that extending the eigenvalue range of Mamba and DeltaNet to include negative values not only enables them to solve parity but consistently improves their performance on state-tracking tasks. We also show that state-tracking enabled LRNNs can be pretrained stably and efficiently at scale (1.3B parameters), achieving competitive performance on language modeling and showing promise on code and math tasks.

Oral