ICLR 2026 论文列表

Permutation equivariant neural networks employing parameter-sharing schemes have emerged as powerful models for leveraging a wide range of data symmetries, significantly enhancing the generalization and computational efficiency of the resulting models. Recently, Kolmogorov-Arnold Networks (KANs) have demonstrated promise through their improved interpretability and expressivity compared to traditional architectures based on MLPs. While equivariant KANs have been explored in recent literature for a few specific data types, a principled framework for applying them to data with permutation symmetries in a general context remains absent. This paper introduces Function Sharing KAN (FS-KAN), a principled approach to constructing equivariant and invariant KA layers for arbitrary permutation symmetry groups, unifying and significantly extending previous work in this domain. We derive the basic construction of these FS-KAN layers by generalizing parameter-sharing schemes to the Kolmogorov-Arnold setup and provide a theoretical analysis demonstrating that FS-KANs have the same expressive power as networks that use standard parameter-sharing layers, allowing us to transfer well-known and important expressivity results from parameter-sharing networks to FS-KANs. Empirical evaluations on multiple data types and symmetry groups show that FS-KANs exhibit superior data efficiency compared to standard parameter-sharing layers, by a wide margin in certain cases, while preserving the interpretability and adaptability of KANs, making them an excellent architecture choice in low-data regimes.

Sample efficiency is one of the main bottlenecks for optimal decision making via reinforcement learning. Pretraining a policy to maximize the entropy of the state visitation can substantially speedup reinforcement learning of downstream tasks. It is still an open question how to maximize the state entropy in POMDPs, where the true states of the environment, or their entropy, are not observed. In this work, we propose to maximize the entropy of a sufficient statistic of the history, which is called an information state. First, we show that a recursive latent model that predicts future observations is an information state in this setting. Then, we provide a practical algorithm, called LatEnt, to simultaneously learn the latent model and a latent-based policy maximizing the corresponding entropy objective from reward-free interactions with the POMDP. We empirically show that our approach induces higher state entropy than existing methods, which translates to better performance on downstream tasks. As a byproduct, we open-source PROBE, the first benchmark to test reward-free pretraining in POMDPs.

Work in psychology has highlighted that the geometric model of similarity standard in deep learning is not psychologically plausible because its metric properties such as symmetry do not align with human perception of similarity. In contrast, (Tversky,1977) proposed an axiomatic theory of similarity with psychological plausibility based on a representation of objects as sets of features, and their similarity as a function of their common and distinctive features. This model of similarity has not been used in deep learning before, in part because of the challenge of incorporating discrete set operations. In this paper, we develop a differentiable parameterization of Tversky's similarity that is learnable through gradient descent, and derive basic neural network building blocks such as the \emph{Tversky projection layer}, which unlike the linear projection layer can model non-linear functions such as {\sc xor}. Through experiments with image recognition and language modeling neural networks, we show that the Tversky projection layer is a beneficial replacement for the linear projection layer. For instance, on the NABirds image classification task, a frozen ResNet-50 adapted with a Tversky projection layer achieves a 24.7\% relative accuracy improvement over the linear layer adapter baseline. With Tversky projection layers, GPT-2's perplexity on PTB decreases by 7.8\%, and its parameter count by 34.8\%. Finally, we propose a unified interpretation of both types of projection layers as computing similarities of input stimuli to learned prototypes for which we also propose a novel visualization technique highlighting the interpretability of Tversky projection layers. Our work offers a new paradigm for thinking about the similarity model implicit in modern deep learning, and designing neural networks that are interpretable under an established theory of psychological similarity.

While Vision–language models (VLMs) have demonstrated remarkable performance across multi-modal tasks, their choice of vision encoders presents a fundamental weakness: their low-level features lack the robust structural and spatial information essential for document understanding and web agents. To bridge this gap, we introduce DAVE, a vision encoder purpose-built for VLMs and tailored for these tasks. Our training pipeline is designed to leverage abundant unlabeled data to bypass the need for costly large-scale annotations for document and web images. We begin with a self-supervised pretraining stage on unlabeled images, followed by a supervised autoregressive pretraining stage, where the model learns tasks like parsing and localization from limited, high-quality data. Within the supervised stage, we adopt two strategies to improve our encoder’s alignment with both general visual knowledge and diverse document and web agentic tasks: (i) We introduce a novel model-merging scheme, combining encoders trained with different text decoders to ensure broad compatibility with different web agentic architectures. (ii) We use ensemble training to fuse features from pretrained generalist encoders (e.g., SigLIP2) with our own document and web-specific representations. Extensive experiments on classic document tasks, VQAs, web localization, and agent-based benchmarks validate the effectiveness of our approach, establishing DAVE as a strong vision encoder for document and web applications.

Binary Neural Networks (BNNs), which constrain both weights and activations to binary values, offer substantial reductions in computational complexity, memory footprint, and energy consumption. These advantages make them particularly well suited for deployment on resource-constrained devices. However, training BNNs via gradient-based optimization remains challenging due to the discrete nature of their variables. The dominant approach, quantization-aware training, circumvents this issue by employing surrogate gradients. Yet, this method requires maintaining latent full-precision parameters and performing the backward pass with floating-point arithmetic, thereby forfeiting the efficiency of binary operations during training. While alternative approaches based on local learning rules exist, they are unsuitable for global credit assignment and for back-propagating errors in multi-layer architectures. This paper introduces Binary Error Propagation (BEP), the first learning algorithm to establish a principled, discrete analog of the backpropagation chain rule. This mechanism enables error signals, represented as binary vectors, to be propagated backward through multiple layers of a neural network. BEP operates entirely on binary variables, with all forward and backward computations performed using only bitwise operations. Crucially, this makes BEP the first solution to enable end-to-end binary training for recurrent neural network architectures. We validate the effectiveness of BEP on both multi-layer perceptrons and recurrent neural networks, demonstrating gains of up to $+6.89$% and $+10.57$% in test accuracy, respectively. The proposed algorithm is released as an open-source repository.

Practical classification requires both high predictive accuracy and reliable confidence for human-AI collaboration. Given that a high-quality dataset is expensive and sometimes impossible, learning with noisy labels (LNL) is of great importance. The state-of-the-art works propose many denoising approaches by categorically correcting the label noise, i.e., change a label from one class to another. While effective in improving accuracy, they are less effective for learning reliable confidence. This happens especially when the number of classes grows, giving rise to more ambiguous samples. In addition, traditional approaches usually curate the training dataset (e.g., reweighting samples or correcting data labels) by intrinsically learning normalities from the noisy dataset. The curation performance can suffer when the noisy ratio is high enough to form a polluting normality. In this work, we propose a training-time data-curation framework, TrainRef, to uniformly address predictive accuracy and confidence calibration by (1) an extrinsic small set of reference samples $D_{{ref}}$ to avoid normality pollution and (2) curate labels into a class distribution instead of a categorical class to handle sample ambiguity. Our insights lie in that the extrinsic information allows us to select more precise clean samples even when $|D_{{ref}}|$ equals to the number of classes (i.e., one sample per class). Technically, we design (1) a reference augmentation technique to select clean samples from the dataset based on $D_{{ref}}$; and (2) a model-dataset co-evolving technique for a near-perfect embedding space, which is used to vote on the class-distribution for the label of a noisy sample. Extensive experiments on CIFAR-100, Animal10N, and WebVision demonstrate that TrainRef outperform the state-of-the-art denoising techniques (DISC, L2B, and DivideMix) and model calibration techniques (label smoothing, Mixup, and temperature scaling). Furthermore, our user study shows that the model confidence trained by TrainRef well aligns with human intuition. More demonstration, proof, and experimental details are available at https://sites.google.com/view/train-ref.

Evaluating the quality of a clustering result without access to ground truth labels is fundamental for research in data mining. However, most cluster validation indices (CVIs) do not consider the noise assignments by density-based clustering methods like DBSCAN or HDBSCAN, even though the ability to correctly determine noise is paramount to successful clustering. In this paper, we propose DISCO, a **D**ensity-based **I**nternal **S**core for **C**lusterings with n**O**ise, the first CVI to explicitly assess the *quality* of noise assignments rather than merely counting them. DISCO is based on the Silhouette Coefficient, but adopts density-connectivity to evaluate clusters of arbitrary shapes, and proposes explicit noise evaluation: it rewards correctly assigned noise labels and penalizes noise labels where a cluster label would have been more appropriate. The pointwise definition of DISCO allows for the seamless integration of noise evaluation into the final clustering evaluation, while also enabling explainable evaluations of the clustered data. In contrast to most state-of-the-art, DISCO is well-defined and also covers edge cases that regularly appear as output from clustering algorithms, such as singleton clusters or a single cluster plus noise.

Predictive coding networks (PCNs) offer a local-learning alternative to backpropagation in which layers communicate residual errors, aligning well with biological computation and neuromorphic hardware. In this work we introduce Difference Predictive Coding (DiffPC), a spike-native PC formulation for spiking neural networks. DiffPC replaces dense floating-point messages with sparse ternary spikes, provides spike-compatible target and error updates, and employs adaptive threshold schedules for event-driven operation. We validate DiffPC on fully connected and convolutional architectures, demonstrating competitive performance on MNIST (99.3\%) and Fashion-MNIST (89.6\%), and outperforming a backpropagation baseline on CIFAR-10. Crucially, this performance is achieved with high communication sparsity, reducing data movement by over two orders of magnitude compared to standard predictive coding. DiffPC thus establishes a faithful, hardware-aligned framework for communication-efficient training on neuromorphic platforms.

Given the wide range of deployment targets, flexible model selection is essential for optimizing performance within a given compute budget. Recent work demonstrates that stitching pretrained models within a model family enables cost-effective interpolation of the accuracy-efficiency tradeoff space. Stitching transforms intermediate activations from one pretrained model into another, producing a new interpolated stitched network. Such networks provide a pool of deployment options along the accuracy-efficiency spectrum. However, existing stitching approaches often yield suboptimal tradeoffs and lack generalizability, as they primarily rely on heuristics to select stitch configurations. We argue that constructing improved accuracy-efficiency tradeoffs requires explicitly capturing and leveraging the _similarity_ between pretrained models being stitched. To this end, we introduce KLAS, a novel stitch selection framework that automates and generalizes stitch selection across model families by leveraging KL divergence between intermediate representations. KLAS identifies the most promising stitches from the $\mathcal{O}(n^k)$ possibilities for $k$ pretrained models of depth $n$. Through comprehensive experiments, we demonstrate that KLAS produces improved accuracy-efficiency curve of stitched models at the same cost as baselines. KLAS achieves up to $1.21\%$ higher ImageNet-1K top-1 accuracy at the same computational cost, or maintains accuracy with a $1.33\times$ reduction in FLOPs.

We investigate the mechanisms underlying a range of list-processing tasks in LLMs, and we find that they have learned to encode a compact, causal representation of a general filtering operation that mirrors the generic ``filter'' function of functional programming. Using causal mediation analysis on a diverse set of list-processing tasks, we find that a small number of attention heads, which we dub *filter heads*, encode a compact representation of the filtering predicate in their query states at certain tokens. We demonstrate that this predicate representation is general and portable: it can be extracted and reapplied to execute the same filtering operation on different collections, presented in different formats, languages, or even in tasks. However, we also identify situations where LMs can exploit a different strategy for filtering: eagerly evaluating if an item satisfies the predicate and storing this intermediate result as a flag directly in the item representations. Our results reveal that transformer LMs can develop human-interpretable implementations of abstract computational operations that generalize in ways that are surprisingly similar to strategies used in traditional functional programming patterns.

Effectively processing long contexts is a critical challenge for language models. While standard Transformers are limited by quadratic complexity and poor length extrapolation, alternative architectures like sliding window attention and state space models sacrifice the ability to effectively utilize the full context due to their fixed-size memory. Chunk-based sparse attention has emerged as a promising paradigm for extreme length generalization, yet the key architectural principles underpinning its success are not yet fully understood. In this work, we present a systematic dissection of these models to identify the core components driving their performance. Through a unified framework and comprehensive ablation studies, we demonstrate that a combination of three design principles is critical: (1) an expressive, non-linear Chunk Encoder with a dedicated CLS token to produce representations for retrieval; (2) a Bypassing Residual Path to stably integrate retrieved global information without it being overridden by the local residual stream; and (3) enforced selection sparsity during pre-training to bridge the train-test distribution gap. We provide a theoretical motivation for intra-chunk information processing and landmark generation. By combining these principles, we establish a new state-of-the-art for training-free length extrapolation, successfully generalizing models trained on a 4K context to 32 million tokens on RULER and BABILong. Our findings provide a clear and empirically-grounded set of design principles for developing future, highly-capable long-context language models.

Accurate detection of all pathological findings in 3D medical images remains a significant challenge, as supervised models are limited to detecting only the few pathology classes annotated in existing datasets. To address this, we frame pathology detection as an unsupervised visual anomaly segmentation (UVAS) problem, leveraging the inherent rarity of pathological patterns compared to healthy ones. We enhance the existing density-based UVAS framework with two key innovations: (1) dense self-supervised learning for feature extraction, eliminating the need for supervised pretraining, and (2) learned, masking-invariant dense features as conditioning variables, replacing hand-crafted positional encodings. Trained on over 30,000 unlabeled 3D CT volumes, our fully self-supervised model, Screener, outperforms existing UVAS methods on four large-scale test datasets comprising 1,820 scans with diverse pathologies. Furthermore, in a low-shot supervised fine-tuning setting, Screener surpasses existing self-supervised pretraining methods, establishing it as a state-of-the-art foundation for pathology segmentation. The code and pretrained models will be made publicly available.

Optimistic exploration is central to improving sample efficiency in reinforcement learning with human feedback, yet existing exploratory bonus methods often fail to realize true optimism. We provide a theoretical analysis showing that current formulations, under KL or $\alpha$-divergence regularization, unintentionally bias exploration toward high-probability regions of the reference model, thereby reinforcing conservative behavior instead of promoting discovery of uncertain regions. To address this pitfall, we introduce the General Exploratory Bonus (GEB), a novel theoretical framework that provably satisfies the optimism principle. GEB counteracts divergence-induced bias via reference-dependent reward regulation and unifies prior heuristic bonuses as special cases, while extending naturally across the full $\alpha$-divergence family. Empirically, GEB consistently outperforms baselines on alignment tasks across multiple divergence settings and large language model backbones. These results demonstrate that GEB offers both a principled and practical solution for optimistic exploration in RLHF.

Active perception is a fundamental skill that enables us humans to deal with uncertainty in our inherently partially observable environment. For senses such as touch, where the information is sparse and local, active perception becomes crucial. In recent years, active perception has emerged as an important research domain in robotics. However, current methods are often bound to specific tasks or make strong assumptions, which limit their generality. To address this gap, this work introduces APPLE (Active Perception Policy Learning) - a novel framework that leverages reinforcement learning (RL) to address a range of different active perception problems. APPLE jointly trains a transformer-based perception module and decision-making policy with a unified optimization objective, learning how to actively gather information. By design, APPLE is not limited to a specific task and can, in principle, be applied to a wide range of active perception problems. We evaluate two variants of APPLE across different tasks, including tactile exploration problems from the Tactile MNIST benchmark. Experiments demonstrate the efficacy of APPLE, achieving high accuracies on both regression and classification tasks. These findings underscore the potential of APPLE as a versatile and general framework for advancing active perception in robotics.

A prior represents a set of beliefs or assumptions about a system, aiding inference and decision-making. In this paper, we introduce the challenge of unsupervised categorical prior learning in pose estimation, where AI models learn a general pose prior for an object category from images in a self-supervised manner. Although priors are effective in estimating pose, acquiring them can be difficult. We propose a novel method, named Pose Prior Learner (PPL), to learn a general pose prior for any object category. PPL uses a hierarchical memory to store compositional parts of prototypical poses, from which we distill a general pose prior. This prior improves pose estimation accuracy through template transformation and image reconstruction. PPL learns meaningful pose priors without any additional human annotations or interventions, outperforming competitive baselines on both human and animal pose estimation datasets. Notably, our experimental results reveal the effectiveness of PPL using learned prototypical poses for pose estimation on occluded images. Through iterative inference, PPL leverages the pose prior to refine estimated poses, regressing them to any prototypical poses stored in memory. Our code, model, and data will be publicly available.

Within the context of representation learning for Earth observation, geographic Implicit Neural Representations (INRs) embed low-dimensional location inputs (longitude, latitude) into high-dimensional embeddings, through models trained on geo-referenced satellite, image or text data. Despite the common aim of geographic INRs to distill Earth's data into compact, learning-friendly representations, we lack an understanding of how much information is contained in these Earth representations, and where that information is concentrated. The intrinsic dimension of a dataset measures the number of degrees of freedom required to capture its local variability, regardless of the ambient high-dimensional space in which it is embedded. This work provides the first study of the intrinsic dimensionality of geographic INRs. Analyzing INRs with ambient dimension between 256 and 512, we find that their intrinsic dimensions fall roughly between 2 and 10 and are sensitive to changing spatial resolution and input modalities during INR pre-training. Furthermore, we show that the intrinsic dimension of a geographic INR correlates with downstream task performance and can capture spatial artifacts, facilitating model evaluation and diagnostics. More broadly, our work offers an architecture-agnostic, label-free metric of information content that can enable unsupervised evaluation, model selection, and pre-training design across INRs.

The Tsetlin Machine (TM) is an innovative machine learning algorithm grounded in propositional logic, achieving state-of-the-art performance across a variety of pattern recognition tasks. Prior theoretical work has established convergence results for the 1-bit operator under both noisy and noise-free conditions, and for the 2-bit XOR operator under noise-free conditions. This paper first extends the analysis to the 2-bit AND and OR operators. We show that the TM converges almost surely to the correct 2-bit AND and OR operators under noise-free training, and we identify a distinctive property of the 2-bit OR case, where a single clause can jointly represent two sub-patterns, in contrast to the XOR operator. We further investigate noisy training scenarios, demonstrating that mislabelled samples prevent exact convergence but still permit efficient learning, whereas irrelevant variables do not impede almost-sure convergence. Building on the 2-bit analysis, we then generalize the results to the $k$-bit setting ($k>2$), providing a unified treatment applicable to general scenarios. Together, these findings provide a robust and comprehensive theoretical foundation for analysing TM convergence.

Prototypical self-supervised learning methods consistently suffer from partial prototype collapse, where multiple prototypes converge to nearly identical representations. This undermines their central purpose—providing diverse and informative targets to guide encoders toward rich representations—and has led practitioners to over-parameterize prototype sets or add ad-hoc regularizers, which mitigate symptoms rather than address the root cause. We empirically trace the collapse to the joint optimization of encoders and prototypes, which encourages a type of shortcut learning: early in training prototypes drift toward redundant representations that minimize loss without necessarily enhancing representation diversity. To break the joint optimization, we introduce a fully decoupled training strategy that learns prototypes and encoders under separate objectives. Concretely, we model prototypes as a Gaussian mixture updated with an online EM-style procedure, independent of the encoder's loss. This simple yet principled decoupling eliminates prototype collapse without explicit regularization and yields consistently diverse prototypes, which in several settings translate to improved downstream performance.

Unsupervised domain adaptive hashing transfers knowledge from labeled source domains to unlabeled target domains, addressing domain shift challenges in real-world retrieval tasks. Existing methods face two critical limitations: target domain noise severely misleads model training, and indiscriminate domain alignment strategies treat all target samples equally, potentially distorting essential feature structures. We propose an uncertainty-aware adaptive hashing approach that addresses these challenges through a hierarchical conformal calibration framework. At the semantic level, we employ conformal inference to generate confidence prediction sets, replacing single pseudo-labels with set-based predictions whose sizes directly quantify sample reliability for weighted pseudo-label learning and domain alignment. This enables the model to focus on reliable samples while suppressing noise. At the representation level, we predict the stability of individual hash bits, where bit-level confidence guides a robust weighted quantization loss and enables dynamic weighted Hamming distance during retrieval, fundamentally enhancing hash code quality and retrieval robustness. Through this hierarchical calibration mechanism, our method achieves more adaptive and robust cross-domain knowledge transfer. Extensive experiments on multiple benchmark datasets demonstrate significant improvements over existing approaches, validating the effectiveness and superiority of our method.