ICML 2026 论文列表

We develop a geometric theory of projection heads in self-supervised learning by modeling the head as a trainable Riemannian metric on the backbone representation manifold. We show that linear heads perform implicit subspace whitening, while nonlinear heads adapt local metrics to satisfy the specific topological constraints of the loss, with head depth empirically dictating this capacity. Analyzing dimensional collapse, we prove that smooth nonlinear heads natively induce negative eigenvalues in the Hessian at collapsed equilibria, making them unstable. We empirically validate this by continuously tracking the optimization geometry during training, which reveals that smooth activations like Swish can generate explicit negative curvature to escape collapse, whereas linear and ReLU heads under continuous-time gradient flow cannot, relying instead on discrete-time optimization dynamics and BatchNorm. Finally, we geometrically characterize how metric degeneracy governs the information-invariance trade-off, explaining why the head must be discarded. Evaluated across contrastive and decorrelation-based objectives on foundation models, our results demonstrate that the projection head acts as a universal geometric buffer, decoupling the semantic backbone from the rigid, destructive constraints of the pretraining objective.

Causal inference typically assumes centralized access to individual-level data. Yet, in practice, data are often decentralized across multiple sites, making centralization infeasible due to privacy, logistical, or legal constraints. We address this problem by estimating the Average Treatment Effect (ATE) from decentralized observational data via a Federated Learning (FL) approach, allowing inference through the exchange of aggregate statistics rather than individual-level data. We propose a novel method to estimate propensity scores via a federated weighted average of local scores using Membership Weights (MW), defined as probabilities of site membership conditional on covariates. MW can be flexibly estimated with parametric or non-parametric classification models using standard FL algorithms. The resulting propensity scores are used to construct Federated Inverse Propensity Weighting (Fed-IPW) and Augmented IPW (Fed-AIPW) estimators. In contrast to meta-analysis methods, which fail when any site violates positivity, our approach exploits heterogeneity in treatment assignment across sites to improve overlap. We show that Fed-IPW and Fed-AIPW perform well under site-level heterogeneity in sample sizes, treatment mechanisms, and covariate distributions. Theoretical analysis and experiments on simulated and real-world data demonstrate clear advantages over meta-analysis and related approaches.

Autonomous web agents are increasingly deployed for long-horizon tasks, yet their ability to adhere to real-world policies remains critically underexplored compared to standard safety objectives. To address this gap, we introduce PolicyGuardBench, a benchmark of 60k policy-trajectory pairs designed to evaluate compliance through both full-trajectory and novel prefix-based violation detection tasks. Using this dataset, we train PolicyGuard, a lightweight guardrail model that achieves strong detection accuracy while maintaining high inference efficiency. Notably, our model demonstrates robust generalization capabilities, preserving high performance even on unseen domains. These contributions establish a comprehensive framework for studying policy compliance, showing that accurate and generalizable guardrails are feasible at small scales.

We present SoftMatcha 2, an ultra-fast and flexible search algorithm that enables search over trillion-scale natural language corpora in under 0.3 seconds while allowing semantic variations in the form of substitution, insertion, and deletion. Our approach employs string matching based on suffix arrays that scales well with corpus size, and represents words as vectors, which underpin its semantic flexibility. To mitigate the combinatorial explosion induced by the semantic relaxation of queries, our method is built on two key algorithmic ideas: dynamic corpus-aware pruning and fast exact lookup enabled by a disk-aware design. We theoretically analyze the efficiency of the proposed method, indicating that it can mitigate exponential growth in the search space. Empirically, on FineWeb-Edu (Lozhkov et al., 2024) (1.4T tokens), it attains substantially lower search latency than existing methods: infini-gram (Liu et al., 2024), infini-gram mini (Xu et al., 2025), and SoftMatcha (Deguchi et al., 2025). As a practical application, our method uncovers benchmark contamination in training corpora that existing approaches miss, and it also benefits information retrieval and paraphrase detection. We also provide an online demo of fast, soft search across corpora in seven languages.

Adapting large language models (LLMs) to low-resource domains remains challenging due to the scarcity of domain-specific data. While in-domain data is limited, there exists a vast amount of general-domain data that shares similar question–answer formats and reasoning patterns with domain tasks. This observation raises an important question: can useful general-domain data be mined to improve low-resource domain adaptation? Our initial findings show that general-domain chain-of-thought data contains useful auxiliary signals for domain adaptation, even without careful selection. This observation motivates a new paradigm for domain adaptation beyond exclusive reliance on domain-specific data. To systematically identify the most beneficial general-domain samples, we propose NTK-Selector, motivated by the Neural Tangent Kernel’s ability to capture alignment in training dynamics. Since directly applying NTK to pretrained LLMs is impractical, we introduce a Jacobian-free NTK approximation and empirically demonstrate stable NTK-like behavior during fine-tuning. Extensive experiments across medical, financial, legal, and psychological domains demonstrate that NTK-Selector consistently outperforms domain-only fine-tuning and existing data selection baselines. In particular, NTK-Selector achieves gains of +8.7 and +5.1 points on Llama3-8B-Instruct and Qwen3-8B, respectively, compared to only +0.8 and +0.9 points from domain-only fine-tuning.

High-precision robotic manipulation requires fine-grained spatial reasoning that is often difficult to achieve with RGB-only policies due to depth ambiguity and perspective scale issues. Policies that leverage 3D information directly, such as those based on point clouds, offer a stronger geometric prior over purely image-based ones, yet their performance remains highly task-dependent. We hypothesize that this discrepancy may be due to the spectral bias of neural networks towards learning low frequency functions, which especially affects architectures conditioned on slow-moving Cartesian features. We thus propose to map point clouds from Cartesian space into high-dimensional Fourier space, effectively equipping the point cloud encoder with direct access to high-frequency features. We experimentally validate the use of Fourier features on challenging manipulation tasks from the RoboCasa and ManiSkill3 benchmarks and on a real robot setup. Despite their simplicity, we find that Fourier features provide significant benefits across diverse encoder architectures and benchmarks and are robust across hyperparameters. Our results indicate that Fourier features let policies leverage geometric details more effectively than Cartesian features, showing their potential as a general-purpose tool for point cloud-based imitation learning. We provide source code and videos on our project page: https://fourier-il.github.io/fourier-il.

Large Language Models (LLMs) have catalyzed vibe coding, where users leverage LLMs to generate and iteratively refine code through natural language interactions until it passes their *vibe check*. *Vibe check* reflects human preference and goes beyond functionality: the solution should feel right, read cleanly, preserve intent, and remain correct. However, current code evaluation remains anchored to pass@k and captures only functional correctness, overlooking non-functional instructions that users routinely apply. In this paper, we hypothesize that instruction following is the missing piece underlying *vibe check* besides functional correctness. To quantify models' code instruction-following capabilities with measurable signals, we present VeriCode, a taxonomy of 30 verifiable code instructions together with deterministic verifiers. We use the taxonomy to augment established evaluation suites, resulting in **SWE-IF**, a testbed to assess both instruction following and functional correctness. Evaluating 31 LLMs, we show that even the strongest models struggle to comply with multiple instructions and exhibit functional regression. Most importantly, a composite score of functional correctness and instruction following correlates best with human preference, with instruction following emerging as the primary differentiator among LLMs. Our code, data, and taxonomy are available at https://github.com/maszhongming/SWE-IF.

In open-world settings, thermal infrared (TIR) image degradations continuously emerge and evolve, while most existing all-in-one restoration methods are built on a closed-set assumption and struggle to continually adapt to novel degradations. To address this, we propose ECMRNet, an Expandable, Compressible, and Mineable Restoration Network for open-world TIR restoration from a continual learning perspective. Conceptually, ECMRNet unifies continual degradation learning as an "expand–compress–mine" closed-loop process, enabling sustained adaptation to new degradations with controllable evolution. Structurally, ECMRNet decomposes intermediate representations into group-isolated subspaces, and achieves strict parameter isolation and fast adaptation to new degradations by freezing historical groups and isomorphically expanding new ones. To curb model growth as tasks accumulate, we present Structural Entropy Pruning, which identifies and removes redundant channel groups via two-dimensional structural entropy minimization, achieving information contribution–driven adaptive compression. Moreover, we design a Sub-degradation Knowledge Mining Module that dynamically retrieves and recombines transferable components from historical representations to improve restoration under compound degradations. Experimental results demonstrate that ECMRNet achieves superior overall performance across diverse single and compound degradations while using fewer parameters and lower computational cost.

Large Language Models (LLMs) are increasingly used to simulate how specific users respond to any context, enabling more user-centric applications that rely on user feedback. However, existing user simulators mostly imitate surface-level patterns and language styles, which fails to reflect the underlying state of real users (e.g., beliefs, emotions). To address these limitations, we propose a novel training framework, HumanLM, which builds user simulators that accurately reflect real users. Our key insight is, in addition to generating responses, we generate natural-language latent states that align with the ground truth responses through reinforcement learning. These latent states correspond to a set of state dimensions which psychologically lead to how real users respond. HumanLM further synthesizes these aligned latent states into responses that accurately represent real users. For extensive evaluation, we develop Humanual, a comprehensive benchmark on simulating real users based on public data. Humanual consists of six large-scale datasets with 26k users and 216k responses in total. It spans diverse tasks such as generating user responses to daily life issues, political blogs, and chat sessions with LLM assistants. Across the datasets, HumanLM significantly outperforms the best alternative approaches by an average relative improvement of 16.3% on alignment score from an LLM judge. In a real-time simulation study with 37 participants, HumanLM achieves the highest scores on similarity with real user responses and human-likeness.

The inherent sparsity, lack of structure, and rotation sensitivity of point clouds often lead to high computational and parameter cost in robust feature learning. To address these problems, we present QPoint, a lightweight framework that leverages robust quaternion feature learning. QPoint incorporates a Quaternion-Enhanced local perception module that uses learnable rotations to stabilize local features against geometric transformations, and a Quaternion global attention mechanism that employs quaternion similarity to capture global geometric context with inherent rotation invariance. Extensive experiments show that QPoint achieves top performance across multiple tasks. It achieves excellent 95.0%, 93.9%, and 92.1% on the challenging ScanObjectNN variants (OBJ_BG, OBJ_ONLY, PB_T50_RS), 94.7% overall accuracy on ModelNet40, and 87.0% instance mIoU on ShapeNetParts. Furthermore, QPoint exhibits superior generalization in few-shot learning scenarios. Crucially, it accomplishes this with extremely minimal parameter and computational requirements, establishing a strong and efficient baseline for point cloud processing. Our source code is in the supplementary material and will be released to the public.

Processing long sequence data such as speech requires models to maintain long-term dependencies, which is challenging for recurrent spiking neural networks due to high temporal dynamics in neuron models that leak stored information in their membrane potentials, and due to vanishing gradients during backpropagation through time. These issues can be mitigated by employing more complex neuron designs, such as ALIF and TC-LIF, but these neuron-level solutions often incur high computational costs and complicate hardware implementation, undermining the efficiency advantages of spiking neural networks. Here we propose an architectural-level solution that leverages the dynamical interactions of a few leaky integrate-and-fire (LIF) neurons to enhance long-term information storage. The memory capability of this LIF-based micro-circuit is adaptively modulated by global recurrent connections of the recurrent spiking neural network, contributing to selective enhancement of temporal information retention, and promoting stable gradient propagation through time. The proposed model outperforms baselines including LSTM, ALIF, and TC-LIF in long sequence tasks, achieving 96.52\% accuracy on the PS-MNIST dataset. Furthermore, our method also provides a compelling efficiency advantage, yielding up to 277$\times$ computational efficiency improvement compared to conventional models such as LSTM. This work paves the way for building cost-effective, hardware-friendly, and interpretable spiking neural networks for long sequence modeling.

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph comparison without ground-truth correspondences. However, these methods suffer from two critical limitations: the degradation of node distinctiveness due to oversmoothing in GNN-based embeddings, and the misalignment of latent spaces across graphs caused by structural noise, feature heterogeneity, and training instability, ultimately leading to unreliable node correspondences. We propose a novel framework employing a dual-pass encoder to inject high-frequency discriminability into node features, paired with a geometry-aware functional map module that learns bijective and isometric transformations to align latent spaces while acting as a low-pass filter on correspondences, enforcing smoothness and robustness as a structural prior in map space. Extensive experiments on graph benchmarks demonstrate that our method consistently outperforms existing unsupervised alignment baselines, exhibiting superior robustness to structural inconsistencies and challenging alignment scenarios. The implementation is available at https://github.com/maysambehmanesh/GADL.

Low-discrepancy points are designed to efficiently fill the space in a uniform manner. This uniformity is highly advantageous in many problems in science and engineering, including in numerical integration, computer vision, machine perception, computer graphics, machine learning, and simulation. Whereas most previous low-discrepancy constructions rely on abstract algebra and number theory, Message-Passing Monte Carlo (MPMC) was recently introduced to exploit machine learning methods for generating point sets with lower discrepancy than previously possible. However, MPMC is limited to generating point sets and cannot be extended to low-discrepancy sequences (LDS), i.e., sequences of points in which every prefix has low discrepancy, a property essential for many applications. To address this limitation, we introduce Neural Low-Discrepancy Sequences (*NeuroLDS*), the first machine learning-based framework for generating finite LDS. Drawing inspiration from classical LDS, we train a neural network to map indices to points such that the resulting sequences exhibit minimal discrepancy across all prefixes. To this end, we deploy a two-stage learning process: supervised approximation of classical constructions followed by unsupervised fine-tuning to minimize prefix discrepancies. We demonstrate that *NeuroLDS* outperforms all previous LDS constructions by a significant margin with respect to discrepancy measures. Moreover, we demonstrate the effectiveness of *NeuroLDS* across diverse applications, including numerical integration, robot motion planning, and scientific machine learning. These results highlight the promise and broad significance of Neural Low-Discrepancy Sequences.

Bridging the gap between visual realism and physical understanding is a core challenge for video-based world models. We study the structural identifiability of continuous-time physical laws from raw pixels, focusing on whether an encoder-only pipeline can uniquely recover the parameters of second-order linear ODEs. We prove that a level-set slope-coverage condition ensures the learned latent space is locally affine to the true physical state, enabling exact parameter recovery. Our theory provides the first characterization of minimal data requirements across damping regimes, establishing that underdamped systems are identifiable from a single video clip, whereas other regimes require three diverse trajectories. We further introduce a variance-floor regularizer to stabilize the decoder-free objective and prevent latent collapse. Validated on synthetic and real-world data, our approach demonstrates that interpretable physical constants can be reliably estimated from video without the need for compute-intensive pixel reconstruction, ensuring both physical correctness and transparency. Code is available at https://github.com/wenjiewang3/PhysicsFromVideo.

Standard generative models struggle with heavy-tailed data: Lipschitz architectures cannot produce power-law tails from Gaussian noise, and interpolating between heavy-tailed data and Gaussians is ill-posed. We propose a simple fix: apply the soft-log transform $\phi(x) = \mathrm{sign}(x) \cdot \log(1 + |x|)$ coordinate-wise to data before training, then exponentiate samples after generation. A Hill diagnostic decides per-coordinate whether to transform, leaving light-tailed margins untouched at no added complexity. This compresses heavy tails into a range where standard flow matching succeeds, without heavy-tailed base distributions or architectural modifications. We provide theoretical intuition for why this works: the log-transform maps Pareto tails to exponentials, and the induced dynamics implement a form of tail annealing via power transformations. On a 144-configuration multivariate benchmark (3 copulas, $d$ up to 100, 4 tail indices), Log-FM dominates specialized baselines on $W_1$, CVaR$_{99}$, and extreme-quantile metrics, and is the only method with zero severe divergences across 2{,}880 runs.

AI-assisted task delegation is increasingly common, yet human effort in such systems is costly and typically unobserved. Recent work by Bastani & Cachon (2025); Sambasivan et al. (2021) shows that accuracy-based payment schemes suffer from incentive collapse: as AI accuracy improves, sustaining positive human effort requires unbounded payments. We study this phenomenon in a budget-constrained principal-agent framework with strategic human agents whose output accuracy depends on unobserved effort. Our first contribution is a general impossibility result showing that incentive collapse is not merely a limitation of simple linear payments, but arises for any payment rule based only on observed task accuracy. To overcome this barrier, we propose a sentinel-auditing payment mechanism that enforces a strictly positive and controllable level of human effort at finite cost, independent of AI accuracy. Building on this incentive-robust foundation, we develop an incentive-aware active statistical inference framework that jointly optimizes (i) the auditing rate and (ii) active sampling and budget allocation across tasks of varying difficulty to minimize the final statistical loss under a single budget. Experiments demonstrate improved cost-error tradeoffs relative to standard active learning and auditing-only baselines.

We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework is based on a Galerkin discretization of the underlying variational forms, and its high efficiency stems from a novel highly-optimized and GPU-compliant TensorGalerkin framework for linear system assembly (stiffness matrices and load vectors). TensorGalerkin operates by tensorizing element-wise operations within a Python-level Map stage and then performs global reduction with a sparse matrix multiplication that performs message passing on the mesh-induced sparsity graph. The Map and Reduce stages are co-designed inside PyTorch's autograd so that the assembly graph contains $O(1)$ nodes regardless of how the number of elements and local DoFs scale. We validate this $O(1)$-graph property by deploying TensorGalerkin downstream as i) a highly-efficient numerical PDEs solver, ii) an end-to-end differentiable framework for PDE-constrained optimization, and iii) a physics-informed operator learning algorithm for PDEs. With multiple benchmarks, including 2D and 3D elliptic, parabolic, and hyperbolic PDEs on unstructured meshes, we demonstrate that the proposed framework provides significant computational efficiency and accuracy gains over a variety of baselines in all the targeted downstream applications.

Training large language models for code generation often involves selecting data from verifiable multi-solution pools, where each problem admits multiple correct implementations. Conventional studies on data selection suggest that complex selection strategies, such as diversity maximization or difficulty ranking, should outperform naive random sampling. In this work, we systematically evaluate within-problem solution selection strategies across different representation spaces, including continuous embeddings, discrete tokens, and syntactic structures, using various base language models. Instead, simple random sampling achieves consistently competitive performance across all models, exhibiting greater cross-model stability than complex methods. We interpret these results through the lens of *implicit knowledge consensus*: verified solution pools may contain representative algorithmic patterns that random sampling can preserve. Our findings suggest that practitioners should treat random sampling as a low-cost default for verifiable code-generation fine-tuning and move to complex selectors when hard-tail or constraint-focused coverage is the target.

We study the active learning problem of fixed-confidence top-$k$ identification from noisy pairwise comparisons. In this problem, an algorithm sequentially chooses pairs of items to compare, observes the outcomes, and stops when it can return the set of top-$k$ items with error probability at most $\delta$. The objective is to design such a *$\delta$-correct* procedure that minimizes the expected number of comparisons (the sample complexity). This problem falls within the broader literature on fixed-confidence pure exploration in bandit models, where a common target is asymptotic optimality: the algorithm's expected sample complexity matches the information theoretic lower bound as $\delta \to 0$. Asymptotically optimal procedures have been developed for a range of fixed-confidence pure-exploration problems, however to the best of our knowledge, for top-$1$, or more generally top-$k$ identification from pairwise comparisons under latent utility models an asymptotically optimal algorithm has not been established. In this setting, we develop such an algorithm. We characterize the structure of the lower bound and formulate it as a saddle-point problem. This structure enables a computationally efficient primal--dual procedure that learns the asymptotically optimal comparison allocation online. We then construct an adaptive comparison-allocation algorithm that tracks the allocation learned by the primal--dual procedure and prove it is asymptotically optimal.