ICML 2026 Papers

We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise in mixed-integer programming techniques such as strong branching and bound tightening. By leveraging matrix-matrix operations instead of repeated matrix-vector operations, we obtain significant computational advantages on GPU architectures. We demonstrate the effectiveness of our approach on various case studies and identify the problem sizes where first-order methods outperform traditional simplex-based solvers, depending on the computational environment. This is a significant step toward integer programming algorithms that tightly exploit GPU capabilities. We argue that some specific operations should be allocated to GPUs and performed in full, instead of relying on lightweight heuristic approaches on CPUs.

By sharing intermediate features, collaborative perception extends each agent's sensing beyond standalone limits, but real-world feature modality heterogeneity remains a key barrier to effective fusion. Most existing methods, including direct adaption and protocol-based transforma-tion, typically rely on training adapters for newly emerging feature modalities and often require additional retraining or fine-tuning. Such repeated training is costly and is often infeasible across manufacturers due to model and data privacy con-straints, limiting real-world scalability. To address this issue, we propose UniTrans, a universal any-to-any feature modality translation model that instantiates translators on the fly for arbitrary modalities. UniTrans pretrains a bank of translator expert parameters and learns their combination coefficients as a function of source-to-target modality mapping. The mapping is measured in a modality-intrinsic latent space, where an intrinsic encoder extracts modality-specific yet scene-invariant codes from single-frame intermediate features, enabling UniTrans to instantiate translators in a zero-shot manner. Experiments on OPV2V-H and DAIR-V2X demonstrate that UniTrans consistently outperforms state-of-the-art methods in both simulated and real-world set-tings, enabling efficient any-to-any translation through a universal model. Code will be made available.

Large Language Models (LLMs) have demonstrated remarkable capabilities in understanding and generation tasks. However, their massive parameter scale leads to significant resource consumption and latency during inference. Post-training weight-only quantization offers a promising solution by reducing model size and accelerating token generation through alleviating the memory-bound issue. Nevertheless, there are inherent systematic outliers in weights, and although some efforts have attempted to address them, such as scaling and rotation, the performance of low-bit quantization remains far from satisfactory. In this paper, we propose Outlier Self-Absorption Quantization (OSAQ), which performs second-order low-rank derived additive weight suppression for low-bit weight-only LLM quantization. Specifically, we observe that Hessian exhibits low-rank consistency across different inputs, with certain directions persistently lacking strength. Leveraging this property, we construct an additive weight transformation based on the Hessian’s null space, thereby suppressing weight outliers without affecting the task loss. This additive transformation can be absorbed into the weights offline, requiring no inter-layer transformations and introducing no inference overhead. Moreover, the construction is efficiently achieved by a closed-form solution, without resource-intensive training or iterative procedures. Extensive experiments across models of varying scales and tasks are conducted, and the results show that OSAQ effectively suppresses outliers and improves low-bit quantization performance.

A central insight in lossless data compression is the close connection between probabilistic next- symbol prediction and efficient sequence compression, whereby predictive models can be combined with classical coding techniques to achieve strong compression performance. Applying this approach with powerful modern learned models, such as LLMs, has been shown to achieve markedly better compression than traditional techniques across a wide range of domains. However, significant practical challenges remain, including model non-determinism, in which a model produces different predictions on different machines despite identical parameters and inputs; such mismatches between the encoder and decoder can lead to complete decoding failure. Probability Matching Interval Coding (PMATIC) was recently introduced as a drop-in framework for mismatch-robust coding and shown to enable reliable compression and decompression in the presence of bounded prediction mismatch (Adler & Tang, 2026). In this work, we present a generalization of PMATIC that allows the incorpo- ration of tight theoretical results into the design and more flexible parameter optimization, resulting in substantial improvements in compression efficiency and robustness.

We study query time bounds for the fundamental problem of estimating the kernel mean $\frac1{|X|}\sum_{x\in X}\mathbf{\mathrm{k}}(x,y)$ of a query $y$ in a finite dataset $X\subset\mathbb{R}^d$ up to a prescribed additive error $\varepsilon$. The best known bounds for the Gaussian kernel are $O(d/\varepsilon^2)$, $\widetilde O(d+1/\varepsilon^4)$, and $\widetilde O(d+\Delta^2/\varepsilon^2)$, where $\Delta$ is the diameter of a region containing the points. We prove the new bound $\tilde O(d+\varepsilon\Delta^2+1/\varepsilon^3)$, which improves over the previous ones in regimes with small error $\varepsilon$ and intermediate diameter $\Delta$. At the center of our proof is a new fast spherical embedding theorem in the sense introduced by Bartal, Recht and Schulman (2011), which limits the embedded data diameter while preserving local Euclidean distances and avoiding ``distance collapse'' at larger scales. This fast embedding theorem may be of independent interest.

Token merging accelerates Transformer inference by clustering similar tokens to reduce sequence length (retention ratio $r$), but distorts attention outputs, inducing covariate shift in residual streams and performance collapse under high compression. Existing heuristics, such as proportional attention, mitigate mild compression effectively but degrade sharply at aggressive ratios due to unaddressed energy drift and biased attention distributions. We reframe token merging as a statistical reconstruction problem in high dimensions and introduce an asymptotic radial-angular decomposition of the reconstruction error, an analytical framework decoupling magnitude and distributional distortions. Minimizing this decomposed risk under minimal assumptions of finite second moments and variance stationarity yields closed-form optimal corrections governed by a single scaling factor $\sqrt{r}$: scaling merged values and shrinking merged logits toward the cluster-size prior. This calibrates both energy balance and distributional fidelity. Extensive experiments on vision Transformers demonstrate superior accuracy and robustness across compression levels.

Optimal Transport (OT) traditionally relies on a fixed ground cost to produce a single deterministic transport plan—a practice that overlooks the inherent variability and noise in real-world data. While recent sampling based approaches of OT offer a principled way to quantify this uncertainty, these are computationally prohibitive and struggle to scale. In this paper, we introduce Sinkhorn-parameterized Variational Inference, a first scalable variational framework for performing posterior inference over transport plans. Our key insight is that the Sinkhorn map can be treated as a differentiable reparameterization of the set of entropic plans. This enables the use of flexible generative models like normalizing flows to approximate distributions over transport plans while enforcing marginal constraints. We experimentally demonstrate that our method matches the quality of intensive sampling techniques at a fraction of the computational cost, scaling effectively to large-scale problems.

Imbalanced Unreliable Partial Label Learning (I-UPLL) is a challenging weakly supervised learning setting in which severe class imbalance and unreliable candidate labels jointly degrade model performance. By revisiting existing approaches for imbalanced learning, we observe that most of them fundamentally rely on estimating the class prior to guide balancing operations, such as re-sampling, pseudo-label generation, or logit adjustment. However, under I-UPLL, obtaining stable and accurate prior estimates at the early stage of training is often unrealistic due to the ambiguity and unreliability of partial labels, thereby leading the model to rapidly converge to a suboptimal solution. To address this issue, we propose CLAPOR, a novel CLAss-PriOr perturbation-Robust regularization framework that fundamentally avoids dependence on accurate prior estimation. Specifically, the proposed regularization trains the model under deliberately perturbed class priors, sampled from a Dirichlet distribution that deviates from the current estimated prior. This design encourages consistent performance under prior uncertainty and naturally preserves attention to minority classes. Extensive experiments on benchmark datasets demonstrate the effectiveness of CLAPOR across various settings of I-UPLL.

Deep learning models for supervised learning on tabular data are rapidly improving. Notably, ensembles (mixtures of multiple models) often play an important role in achieving top performance, which motivates designing _ensemble-first_ systems rather than treating ensembling as an ad hoc trick. In this work, we present TabPack — a new ensembling approach that packs many base model–optimizer pairs with different hyperparameters into a single neural network and a single optimizer. The base model and optimizer hyperparameters are sampled randomly, after which all base models are trained in parallel, and the final ensemble is built on the fly during training. As a result, TabPack produces powerful ensembles in a single run, with substantial efficiency gains over traditional approaches. With its remarkable efficiency, strong performance on medium-to-large datasets, and reduced reliance on traditional hyperparameter tuning, TabPack is an appealing solution for practitioners and researchers that makes tabular DL more accessible on consumer-grade hardware and suggests a new avenue for designing better tabular deep learning systems.

Data mixing---determining the ratios of data from different domains---is a first-order concern for training language models (LMs), but existing mixing methods have poorly understood design choices and assume that the set of domains remain fixed throughout development. We present Olmix, a framework that addresses two challenges encountered during LM development. First, the configuration space for developing a mixing method is not well understood---design choices across existing methods lack justification or consensus and overlook practical issues like data constraints. We conduct a comprehensive empirical study of this space, identifying which design choices lead to a strong mixing method. Second, the domain set evolves throughout LM development as datasets are revised and expanded---a problem setting largely unaddressed by existing works. We study how to efficiently recompute the mixture after the domain set is updated, given an existing mix from before the update. We introduce mixture reuse, a mechanism that reuses existing relative ratios and recomputes ratios only for domains affected by an update. Over a sequence of five domain-set updates mirroring real-world LM development, mixture reuse matches the performance of fully recomputing the mix after each update with 74% less compute and improves over training without mixing by 11.6% on downstream tasks.

Large language models (LLMs) can be influenced by harmful or irrelevant context, which can significantly harm model performance on downstream tasks. This motivates principled designs in which LLM systems include built-in mechanisms to guard against such "garbage in, garbage out" scenarios. We propose a novel approach to limit the degree to which harmful context can degrade model performance. First, we define a baseline "safe" behavior for the model -- the model's performance given no context at all (zero-shot). Next, we apply distribution-free risk control (DFRC) to control the extent to which the user-provided context can decay performance below this safe zero-shot baseline. We achieve this by leveraging dynamic early exit prediction, ignoring later attention heads that attend the most to the unsafe inputs. Finally, we propose modifications to DFRC that allow it to both control risk for harmful inputs *and* leverage performance and efficiency gains on helpful inputs. We present both theoretical and empirical results across 9 tasks spanning in-context learning and open-ended question answering, showing that our approach can effectively control risk for harmful context and simultaneously achieve substantial computational efficiency gains with helpful context.

Tail-end risk measures such as static conditional value-at-risk (CVaR) are used in safety-critical applications to prevent rare, yet catastrophic events. Unlike risk-neutral objectives, the static CVaR of the return depends on entire trajectories without admitting a recursive Bellman decomposition in the underlying Markov decision process. A classical resolution relies on state augmentation with a continuous variable. However, unless restricted to a specialized class of admissible value functions, this formulation induces sparse rewards and degenerate fixed points. In this work, we propose a novel formulation of the static CVaR objective based on augmentation. Our alternative approach leads to a Bellman operator with: (1) dense per-step rewards; (2) contracting properties on the full space of bounded value functions. Building on this theoretical foundation, we develop risk-averse value iteration and model-free Q-learning algorithms that rely on discretized augmented states. We further provide convergence guarantees and approximation error bounds due to discretization. Empirical results demonstrate that our algorithms successfully learn CVaR-sensitive policies and achieve effective performance-safety trade-offs.

Hybrid sequence models—combining Transformer and state-space model layers—seek to gain the expressive versatility of attention as well as the computational efficiency of state-space model layers. Despite burgeoning interest in hybrid models, we lack a basic understanding of the settings where—and underlying mechanisms through which—they offer benefits over their constituent models. In this paper, we study this question, focusing on a broad family of core synthetic tasks. For this family of tasks, we prove the existence of fundamental limitations for non-hybrid models. Specifically, any Transformer or state-space model that solves the underlying task requires either a large number of parameters or a large working memory. On the other hand, for two prototypical tasks within this family—namely selective copying and associative recall—we construct hybrid models of small size and working memory that provably solve these tasks, thus achieving the best of both worlds. Our experimental evaluation empirically validates our theoretical findings. Importantly, going beyond the settings in our theoretical analysis, we empirically show that learned—rather than constructed—hybrids outperform non-hybrid models with up to $6 \times$ as many parameters. We additionally demonstrate that hybrid models exhibit stronger length generalization and out-of-distribution robustness than non-hybrids.

We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on Unbalanced Optimal Transport, called ***Unbalanced Optimal Transport Map for Inverse Problems (UOTIP)***. Our method formulates the reconstruction task—predicting clean target signals from noisy measurements—as learning a UOT Map from noisy measurement distribution to clean signal distribution by incorporating a likelihood-based cost function. By relaxing the exact marginal constraint, the UOT framework provides key advantages to our model: robustness to multi-level observation noise, adaptability to class imbalance between noisy and clean datasets, and generalizability to diverse noise-type scenarios. Furthermore, we theoretically demonstrate that incorporating a quadratic cost term ensures the existence and uniqueness of the transport map by satisfying the twist condition, even for ill-posed inverse problems. Our experiments demonstrate that UOTIP achieves state-of-the-art performance on unpaired image inverse problem benchmarks, across linear and nonlinear inverse problems.

Conventional dynamic SLAM approaches typically treat dynamic objects as outliers based on pre-defined categories, creating perceptual blind spots that limit the comprehensive environmental perception required for embodied agents. Although integrating Gaussian Splatting into SLAM enables holistic scene representation, it introduces an optimization paradox: without categorical priors, flexible dynamic primitives rapidly overfit static residuals. This phenomenon undermines the self-supervised error signals necessary for distinguishing motion. In response, we present De4D-SLAM, a novel framework designed for decoupled 4D reconstruction from monocular video. Our approach features a Gradient-Isolated Decoupling strategy, which leverages static reconstruction residuals to supervise a Spatially-Aware Kolmogorov-Arnold Network (SA-KAN), ensuring robust, category-agnostic motion segmentation. Additionally, we propose a Flow-Induced Initialization prior to stabilize the non-convex optimization of 4D Gaussian primitives using dense optical flow. Extensive evaluations on the TUM and Bonn benchmarks demonstrate that De4D-SLAM achieves competitive performance in both tracking and dynamic reconstruction, successfully reconciling the tension between robust localization and high-fidelity 4D mapping.

The rapid adoption of large language models (LLMs) has created significant challenges for efficient inference at scale. Unlike traditional workloads, LLM inference is constrained by both computation and the memory overhead of key–value (KV) caching, which accelerates decoding but quickly exhausts GPU memory. In this paper, we introduce the first queueing-theoretic framework that explicitly incorporates both computation and GPU memory constraints into the analysis of LLM inference. Based on this framework, we derive rigorous stability and instability conditions that determine whether an LLM inference service can sustain incoming demand without unbounded queue growth. This result offers a powerful tool for system deployment, potentially addressing the core challenge of GPU provisioning. By combining an estimated request arrival rate with our derived stable service rate, operators can calculate the necessary cluster size to avoid both costly over-purchasing and performance-violating under-provisioning. We further validate our theoretical predictions through extensive experiments in real GPU production environments. Our results show that the predicted stability conditions are highly accurate, with deviations typically within 10%.

This paper studies the Minimal Embeddable Dimension (MED): the least dimension in which there exists a configuration of $m$ object vectors so that every subset of size at most $k$ is exactly retrieved by score comparison. Our result shows MED is $\Theta(k)$, independent of $m$, for inner product, Euclidean distance, and cosine similarity. We then consider Robust MED (RMED), where all vectors are unit normed and an $\epsilon$ gap of scores is required. We derive the $m$-dependent feasibility ceiling $\epsilon_\star(m,k)=m/\sqrt{k(m-1)(m-k)}$, which approaches $1/\sqrt{k}$ when $m\gg k$, and a Gaussian centroid construction gives a robust witness upper bound in the feasible margin regime. Numerical simulation on synthetic top-$2$ retrieval with cyclic polytope and centroid query optimization confirmed our theoretical claims. Experiments on LIMIT and LIMIT-small datasets also show that simple embedding-based retrieval baselines can overfit and outperform the reported single-vector LLM embedding baseline. Both theoretical and empirical findings rule out the lack of exact geometric capacity as the obstruction.

We consider a linear contextual bandit model where contexts and rewards are governed by a finite hidden Markov chain. We first revisit the simplified model by Nelson et al. (2022), in which rewards are linear functions of the posterior probabilities over the hidden states given the observed contexts (called beliefs), rather than functions of the hidden states themselves. This simplified model may be handled through a direct reduction to standard linear contextual bandits. We extend the theoretical analysis of this reduction to take into account the estimation of the parameters of the hidden Markov model [HMM] in the regret bound and to provide high-probability bounds not depending anymore on the reward functions and only depending on the model through the estimation of the HMM parameters. Second, and most importantly, we instead study the more natural and more complex model incorporating direct dependencies in the hidden states (on top of dependencies on the observed contexts, as is natural for contextual bandits). Under a classic HMM forgetting condition, the main algorithmic tool introduced to cope with the various statistical dependencies that the reward structure introduces is to only periodically update reward-model parameters.

Multi-modal remote sensing imagery provides complementary observations of the same geographic scene, yet such observations are frequently incomplete in practice. Existing cross-modal translation methods treat each modality pair as an independent task, resulting in quadratic complexity and limited generalization to unseen modality combinations. We formulate Any-to-Any translation as inference over a shared latent representation of the scene, where different modalities correspond to partial observations of the same underlying semantics. Based on this formulation, we propose Any2Any, a unified latent diffusion framework that projects heterogeneous inputs into a geometrically aligned latent space. Such structure performs anchored latent regression with a shared backbone, decoupling modality-specific representation learning from semantic mapping. Moreover, lightweight target-specific residual adapters are used to correct systematic latent mismatches without increasing inference complexity. To support learning under sparse but connected supervision, we introduce RST-1M, the first million-scale remote sensing dataset with paired observations across five sensing modalities, providing supervision anchors for any-to-any translation. Experiments across 14 translation tasks show that Any2Any consistently outperforms pairwise translation methods and exhibits strong zero-shot generalization to unseen modality pairs. Code and models are available at https://github.com/MiliLab/Any2Any.