ICML 2026 Papers

When the color distribution of input images changes at inference, the performance of conventional neural network architectures drops considerably. A few researchers have begun to incorporate prior knowledge of color geometry in neural network design. These color equivariant architectures have modeled hue variation with 2D rotations, and saturation and luminance transformations as 1D translations. While this approach improves neural network robustness to color variations in a number of contexts, we find that approximating saturation and luminance (interval valued quantities) as 1D translations introduces appreciable artifacts. In this paper, we introduce a color equivariant architecture that is truly equivariant. Instead of approximating the interval with the real line, we lift values on the interval to values on the circle (a double-cover) and build equivariant representations there. Our approach resolves the approximation artifacts of previous methods, improves interpretability and generalizability, and achieves better predictive performance than conventional and equivariant baselines on tasks such as fine-grained classification and medical imaging tasks. Going beyond the context of color, we show that our proposed lifting can also extend to geometric transformations such as scale.

Mixed Integer Linear Programming (MILP) is a fundamental NP-hard problem that has garnered significant attention from both academia and industry. The Branch-and-Bound (B&B) algorithm is the dominant approach for solving MILPs, where branching decisions play a critical role and have recently been enhanced by neural methods. However, these methods still struggle with semantic variation across depths, the scarcity of upstream nodes, and the costly collection of strong branching samples. To address these issues, we propose SC-MILP, a Dynamic Stratified Contrastive Training Framework for MILP Branching. Our method groups B&B nodes based on their feature distributions and learns depth-aware, fine-grained node representations through dynamic stratified contrastive training. To address data scarcity and imbalance at upstream nodes, we introduce an upstream-augmented MILP derivation procedure that generates both theoretically equivalent and perturbed instances. Experiments on both synthetic and real-world MILP benchmarks, including large-scale instances, show that SC-MILP significantly improves branching accuracy, reduces solving time, with particularly strong gains at upstream nodes.

One-Shot Federated Learning (OSFL) addresses extreme communication regimes in which clients interact with the server only once, amplifying the impact of heterogeneous client data distributions. In particular, the interaction of domain shift and label shift across clients induces misaligned feature representations that cannot be corrected through iterative optimization. Existing OSFL methods rely on distillation, server-side generation or ensemble-based aggregation, but assume aligned representations or address domain and label shift separately. We introduce SLOT-Align (Single-round, Learning-free Optimal Transport Alignment), a geometry-aware feature harmonization framework for OSFL. SLOT-Align uses a shared frozen encoder to extract compact feature statistics, constructs a global reference via Bures–Wasserstein barycenters, and aligns local representations using closed-form geodesic optimal transport maps. The method is computationally efficient and can be combined with existing OSFL pipelines relying on frozen encoders without modifying their training procedures. Extensive experiments across multiple benchmarks, pretrained backbones, and OSFL methods show that SLOT-Align consistently improves accuracy and robustness under joint domain and label shift.

Speculative Decodin promises to accelerate Large Language Model inference, yet its efficacy often degrades in production-grade scenarios. Existing evaluations typically overlook the compute-bound nature of high-concurrency regimes, where verification compute becomes the dominant bottleneck. Consequently, prior methods face a dilemma: static trees incur massive verification waste, while dynamic trees suffer from cumulative misjudgments and kernel incompatibility. To bridge this gap, we introduce ECHO, a high concurrency-oriented framework integrated into SGLang that reformulates speculative execution as a budgeted scheduling problem. Crucially, ECHO employs sparse confidence gating to manage the batch as a unified super-tree, elastically pivoting budget between depth and width to co-optimize the trade-off between reducing global verification steps and maximizing per-step efficiency. Extensive evaluations across diverse model scales—particularly the industrial-grade Qwen3-235B—demonstrate that ECHO consistently outperforms state-of-the-art baselines in both low-load and high-load scenarios, achieving up to 5.35$\times$ walltime speedup and delivering over 20\% relative speedup gain against the strongest baselines.

Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification. In a Bayesian setting, targeting posterior distributions, errors may arise from the simulator, the noise or prior modelling. These model components are only approximations of reality, and severe mismatches can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by calibration observations. We rely on the later to guide the correction, without requiring explicit knowledge of the misspecification form or of which model components are affected. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty quantification compared to standard SBI baselines, while remaining computationally efficient.

Steering intermediate representations has emerged as a powerful strategy for controlling generative models. However, despite its empirical success, it currently lacks a comprehensive theoretical framework. In this paper, we bridge this gap by formalizing the theory of concept steering. First, we establish a link between steering and affine concept erasure, proving that the standard approach for removing unwanted behaviors is a special case of LEACE (a closed-form method for affine erasure). Next, we formulate a principled theoretical framework for concept switching, LEACE-Switch, and characterize the assumptions under which it provides an optimal affine solution. Building on this analysis, we then introduce MidSteer (Minimal Disturbance concept Steering), a more general affine framework for concept manipulation that relaxes these assumptions and enables directed, minimal-disturbance transformations. We empirically demonstrate that MidSteer performs favorably across a range of tasks, modalities, and architectures, including vision diffusion models and large language models.

Probabilistic models are typically trained using task-agnostic objectives like log-loss, which can lead to significant errors in downstream estimation. This disconnect is especially critical in Inverse Probability Weighting (IPW) for causal inference, where propensity score errors near $0$ and $1$ often lead to high bias and variance. We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric. We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping that can be readily integrated with any model like a neural network or a gradient boosting algorithm. Extensive evaluations on causal inference benchmarks demonstrate that our tailored objective consistently outperforms standard likelihood-based and covariate-balancing approaches.

While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision. Existing equivariant methods often sacrifice the efficiency and flexibility that make Transformers so effective through complex, computationally intensive designs. We introduce the Platonic Transformer to resolve this trade-off. By defining attention relative to reference frames from the Platonic solid symmetry groups, our method induces a principled weight-sharing scheme. This enables combined equivariance to continuous translations and Platonic symmetries, while preserving the exact architecture and computational cost of a standard Transformer. Furthermore, we show that this attention is formally equivalent to a dynamic group convolution, which reveals that the model learns adaptive geometric filters and enables a *highly scalable, linear-time convolutional variant*. Across diverse benchmarks in computer vision (CIFAR-10), 3D point clouds (ScanObjectNN), and molecular dynamics, property prediction and generation (OMol25, ProteinMD, QM9), the Platonic Transformer achieves competitive performance by leveraging these geometric constraints at no additional cost.

To overcome the computational burden of traditional computational fluid dynamics (CFD), graph neural network-based (GNN) learned simulators have attracted growing interest because they naturally operate on CFD meshes. However, classical GNNs only exchange information between neighbouring nodes, limiting flow prediction accuracy. While graph rewiring can improve information propagation, existing methods are mostly designed for generic graphs, and PIORF relies on long-range connections for fluid simulation. In this work, we show that simply connecting all 2-hop nodes can already achieve competitive performance with PIORF, raising questions about the necessity of distant rewiring. Motivated by fluid transport principles, we propose Flow Alignment Rewiring (FLARE), a simple and efficient local rewiring method that connects 2-hop nodes only when their relative direction aligns with the input flow direction. Hence, FLARE is a physics-informed local rewiring method, different from PIORF and well-aligned with fluid physics. Extensive numerical experiments on flows over a cylinder, single-, and tandem-airfoil under different flow conditions and deep network architectures demonstrate that FLARE outperforms PIORF and various 2-hop rewiring approaches by a significant margin.

Robust aerial target detection for autonomous UAV-on-UAV pursuit is severely hindered by continuous scale drift, long-tailed scale imbalance, and flight-induced visual noise, rendering standard empirical risk minimization strategies poorly aligned with real-world deployment. To address these challenges, we propose a scale-aware robust optimization framework that performs group-wise minimax optimization over scale-partitioned data, ensuring balanced robustness across long-, mid-, and close-range engagement regimes. We further introduce an uncertainty-rectified regression loss to suppress noise-driven errors without discarding informative hard examples, complemented by a control-aligned center accuracy penalty that prioritizes the localization precision required for stable flight control. Extensive experiments demonstrate that our method yields substantially improved robustness under visual degradation, with significantly slower decay in detection mAP and center-point accuracy compared to baselines. Validated through both photorealistic simulations and real-world flight tests, our system achieves **real-time performance of 120 FPS** on an embedded NVIDIA Orin NX platform, confirming its practical efficacy for high-speed interception.

Reinforcement Learning with Verifiable Reward (RLVR) has proven effective in improving Large Language Model's (LLM) reasoning ability. However, the learning dynamics of RLVR remain underexplored. In this paper, we reveal a counterintuitive phenomenon: among hard examples that the model initially struggles with, a substantial subset remains unlearnable even when correct rollouts are present. To understand the phenomenon, we first demonstrate that existing optimization and sampling techniques fail to resolve unlearnability. With cross-example gradient analysis, we show that unlearnable examples have fundamental representation issue, characterized by low gradient similarity with the rest of the examples and ungeneralizable reasoning patterns. We further show that representation flaws are difficult to mitigate in RL, as data augmentation does not improve gradient similarity. Our study provides the first systematic characterization of unlearnable data in RLVR training and reveals fundamental limitations in current RL approaches for reasoning tasks.

While Vision Transformers (ViTs) offer strong global modeling, their quadratic computational cost limits utility in latency-sensitive applications like person re-identification (ReID). Existing compression strategies, such as token pruning or generic merging, typically rely on coarse-grained criteria tailored for image classification. In fine-grained retrieval, these approaches often discard or smooth out subtle but discriminative local details. To resolve this, we propose SRE-Merge, a training-free framework designed for discriminative token compression. SRE-Merge injects spatial priors into the merging process through three mechanisms: (i) Spatial-Entropy Saliency Assessment (SES-Assess), which quantifies token importance as Spatial-Entropic Mass (SE-Mass) by coupling spatial structure with local attention entropy; (ii) Hybrid Context-Affinity Matching (HCA-Match), which guides precise pair selection by combining feature similarity with mass-derived context; and (iii) Energy-Preserving Weighted Fusion (EPW-Fuse), which incorporates SE-Mass weighting to counteract feature variance reduction. Extensive experiments on standard benchmarks show that SRE-Merge reduces GFLOPs of the base ViT model by about 24\% while retaining competitive retrieval accuracy, establishing a superior accuracy-efficiency trade-off.

Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods treat mass as a continuous fluid, performing inference at the population level. However, this macroscopic view often fails to capture the discrete, jump-like nature of birth-death events at single-cell resolution, which is essential for understanding lineage branching and fate decisions. We present **Unbalanced Schrödinger Bridge (USB)**, a simulation-free framework for learning underlying dynamics that effectively integrates both stochastic and unbalanced effects which also models the discrete, jump-like birth–death dynamics at single-cell resolution. Theoretically, USB provides a tractable solution to the Branching Schrödinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps. Technically, the method implements an efficient solver by introducing a simulation-free training objective that effectively scales to high-dimensional omics data. Empirically, we demonstrate on both simulated and real-world datasets that USB not only achieves trajectory reconstruction performance better than or comparable to deterministic baselines but also uniquely enables realistic discrete simulation of birth-death dynamics at single-cell resolution.

We propose **GradPower**, a lightweight gradient-transformation technique for accelerating language model pre-training. Given a gradient vector $\boldsymbol{g}=(g_ {i})_ {i}$, GradPower first applies the elementwise `sign-power` transformation: $ \varphi_ p(\boldsymbol{g}) = \left({\rm sign}(g_ i)|g_ i|^p\right)_ {i} $ for a fixed $p>0$, and then feeds the transformed gradient into a base optimizer. Notably, GradPower requires only a **single-line code change** and no modifications to the base optimizer’s internal logic, including the hyperparameters. When applied to AdamW (termed **AdamWPower**), GradPower consistently achieves lower terminal loss across diverse architectures (LLaMA, Qwen2MoE), parameter scales (66M to 2B), datasets (C4, OpenWebText), and learning-rate schedules (cosine, warmup-stable-decay). The most pronounced gains are observed when training modern mixture-of-experts models with warmup-stable-decay schedules. GradPower also integrates seamlessly with other state-of-the-art optimizers, such as Muon, yielding further improvements. Finally, we provide theoretical analyses that reveal the underlying mechanism of GradPower and highlight the influence of gradient noise.

We study bandit learning in matching markets, where players and arms constitute the two market sides, and the players' utilities are linear in the arm contexts. In each round, new arms arrive with observable contexts. Then, the algorithm matches them to players, aiming to minimize each player's regret against a *stable matching benchmark*. This contextual structure creates significant complexity: subtle context shifts can slightly alter one player's utility while completely reconfiguring the underlying benchmark, causing large regret spikes for others. We address this in two settings: *stochastic* contexts, drawn from a latent distribution, and *adversarial* contexts, which may be arbitrary. For the stochastic case, we introduce a novel minimum preference gap to capture learning difficulty and provide a fully adaptive algorithm with an instance-dependent poly-logarithmic regret upper bound. We also establish matching instance-independent regret upper and lower bounds under a mild distributional assumption. For the adversarial setting, we propose a tractable regret notion that remains valid under arbitrary contexts and achieves an instance-independent sublinear regret bound via an adaptive algorithm.

Conventional patchified Transformers operate on uniform spatial partitions, distributing computational effort evenly across the domain irrespective of local features. This inflexible tokenization scheme is inherently limited in its ability to efficiently represent and process solutions to complex PDEs. To address this, we propose MeshTok, an adaptive mesh refinement (AMR)-inspired tokenization and sequence modeling framework. This method selectively refines spatial regions exhibiting sharp gradients, transient features, or multiscale structures, generating a heterogeneous set of multiscale tokens defined on a fixed simulation grid. These tokens are processed within a unified Transformer sequence, enabling the model to simultaneously capture coarse-grained global context and fine-grained local details without requiring specialized architectural components. Although adaptive refinement moderately increases token count, it promotes a more targeted allocation of computational resources to physically informative regions, which we view as a practical inductive bias rather than a formal optimality guarantee. Experimental evaluations across multiple PDE families and benchmark datasets demonstrate that MeshTok consistently improves the efficiency-accuracy trade-off compared to uniform-grid baselines. This suggests adaptive multiscale tokenization as a scalable and generalizable design principle for neural PDE modeling. Code is available at https://github.com/SCAILab-USTC/MeshTok.

The deployment of Large Language Models (LLMs) with extended context windows is increasingly constrained by the linear growth of Key-Value (KV) cache memory. Vector Quantization (VQ), particularly Residual Quantization (RQ), is a promising approach for pushing KV cache storage toward the sub-1-bit regime by progressively encoding residuals with small codebooks. However, most VQ methods still rely on standard $\ell_2$ $K$-means as the core codebook-learning primitive. We identify a subtle high-dimensional issue of this primitive: Euclidean centroid averaging can induce centroid shrinkage, which weakens the angular alignment term in the $\ell_2$ distortion and makes directional preservation harder. To address this issue, we propose Gain-Shape $K$-means (GSKM), a drop-in replacement for $K$-means that improves directional fidelity while matching, and in some regimes improving, $\ell_2$ distortion. We then build Gain-Shape Residual Quantization (GSRQ) by incorporating a weighted extension of GSKM into an RQ pipeline. On LLaMA-3-8B, GSRQ substantially improves over strong KV cache quantization baselines across bit rates. At 1-bit, it improves the average accuracy across LongBench tasks from 11.34 to 33.54, a gain of 22.20 percentage points over VQLLM.

Standard practice across domains from robotics to language is to first pretrain a policy on a large-scale demonstration dataset, and then finetune this policy, typically with reinforcement learning (RL), in order to improve performance on deployment domains. This finetuning step has proved critical in achieving human or super-human performance, yet while much attention has been given to developing more effective finetuning algorithms, little attention has been given to ensuring the pretrained policy is an effective initialization for RL finetuning. In this work we seek to understand how the pretrained policy affects finetuning performance, and how to pretrain policies in order to ensure they are effective initializations for finetuning. We first show theoretically that standard behavioral cloning (BC) can fail to ensure coverage over the demonstrator's actions, a minimal condition necessary for effective RL finetuning. We then show that if, instead of exactly fitting the observed demonstrations, we train a policy to model the posterior distribution of the demonstrator's behavior given the demonstration dataset, we do obtain a policy that ensures coverage over the demonstrator's actions, enabling more effective finetuning. Furthermore, this policy achieves this while ensuring pretrained performance is no worse than that of the BC policy. We then show this approach is practically implementable with modern generative models and leads to significantly improved RL finetuning performance on both realistic robotic control benchmarks and real-world robotic manipulation tasks, as compared to standard behavioral cloning.

The two-sample testing problem, a fundamental task in statistics and machine learning, seeks to determine whether two sets of samples, drawn from underlying distributions $p$ and $q$, are in fact identically distributed (i.e.~whether $p=q$). A popular and intuitive approach is the classifier two-sample test (C2ST), where a classifier is trained to distinguish between samples from $p$ and $q$. Yet despite simplicity of the C2ST, its reliability hinges on access to a near-Bayes-optimal classifier, a requirement that is rarely met and difficult to verify. This raises a major open question: can a weak classifier still be useful for two-sample testing? We show that the answer is a definitive yes. Building on the work of Hu & Lei (2024), we analyze two conformal variants of the C2ST that convert the scores from any trained classifier---even if weak, biased, or overfit---into exact, finite-sample p-values. We establish two key theoretical properties of the conformal C2ST: (i) finite-sample Type-I error control, and (ii) non-trivial power that degrades gently in tandem with the error of the trained classifier. The upshot is that even poorly performing classifiers can yield powerful and reliable two-sample tests. This general framework finds a powerful application in Bayesian inference, particularly for validating Neural Posterior Estimation (NPE) models, where the task of comparing a learned posterior approximation $q(\theta \mid y)$ to the true posterior $p(\theta \mid y)$ can be framed as a two-sample test. Empirically, the Conformal C2ST outperforms classical discriminative tests across a wide range of benchmarks for this task. Our results establish the conformal C2ST as a practical, theoretically grounded diagnostic tool.