ICML 2026 Papers

Conformal prediction (CP) is a distribution-free method to construct reliable prediction intervals that has gained significant attention in recent years. Despite its success and various proposed extensions, a significant practical feature which has been overlooked in previous research is the potential skewed nature of the noise, or of the residuals when the predictive model exhibits bias. In this work, we leverage recent developments in CP to propose a new asymmetric procedure that bridges the gap between skewed and non-skewed noise distributions, while still maintaining adaptivity of the prediction intervals. We introduce a new statistical learning problem to construct adaptive and asymmetric prediction bands, with a unique feature based on a penalty which promotes symmetry: when the penalty intensity varies, the intervals smoothly change from symmetric to asymmetric ones. This statistical learning problem is based on reproducing kernel Hilbert spaces and the recently introduced kernel sum-of-squares framework. First, we establish representer theorems to make our problem tractable in practice, and derive dual formulations which are essential for scalability to larger datasets. Second, the intensity of the penalty is chosen using a novel data-driven method which automatically identifies the symmetric nature of the noise. We show that consenting to some asymmetry can let the learned prediction bands better adapt to small sample regimes, outliers or biased predictive models. Finally, our experiments illustrate the efficiency of such penalized kernel sum-of-squares to construct adaptive prediction bands.

In Mixture-of-Experts (MoE) training, sparse routing, i.e., activating only the top-$K$ experts per token, is essential for balancing convergence speed and computational cost. However, existing works typically choose $K$ empirically, without theoretical guidance. To address this gap, we characterize the convergence behavior of MoE training using stochastic optimization theory. Specifically, we derive a convergence upper bound of $\mathcal{O}\left(\frac{1+M/K}{\sqrt{T}}\right)$, where $T$ is the number of training iterations and $M$ is the total number of experts per MoE layer. This result guarantees convergence and shows that increasing $K$ can accelerate training. By further fixing the total computational budget $R$ (in FLOPs), we obtain a refined bound of $\mathcal{O}\left(\sqrt{\frac{K}{R}} + \frac{M}{\sqrt{K R}}\right)$, which is convex in $K$ and implies the existence of an optimal $K^{*}\in[1,M]$ that achieves the best convergence performance. Extensive experiments validate our theoretical analysis under diverse settings.

3D visual grounding requires robust cross-modal representation to achieve fine-grained semantic alignment and precise geometric reasoning. However, most methods employ unimodal pre-trained encoders that transfer visual and linguistic knowledge independently, inducing domain shift and poor cross-modal alignment. Meanwhile, spatial modeling with handcrafted priors limits cross-modal geometric representation, struggling to capture complex object relations due to spectral bias. To address these challenges, we propose Text-Aware Feature Tuning (TFT) and Decomposed Spectral Geometry (DSG) to enhance cross-modal semantic representation. Specifically, TFT injects linguistic context into the visual hierarchy to mitigate domain shift and facilitate early cross-modal alignment. DSG employs a learnable Fourier basis and explicitly decomposes pairwise relations into symmetric and antisymmetric spectral components, allowing the model to capture high-frequency geometric details and direction-aware relations for precise spatial reasoning. Extensive experiments on ScanRefer, Nr3D and Sr3D validate the effectiveness of our method, demonstrating state-of-the-art performance with improvements of 2.05\% Acc@0.25 for 3DREC and 1.09\% mIoU for 3DRES on ScanRefer.

The persistent storage requirements for high-resolution, spatiotemporally evolving fields governed by large-scale and high-dimensional partial differential equations (PDEs) have reached the petabyte-to-exabyte scale. Transient simulations modeling Navier-Stokes equations, magnetohydrodynamics, plasma physics, or binary black hole mergers generate data volumes that are prohibitive for modern high-performance computing (HPC) infrastructures. To address this bottleneck, we introduce ANTIC (Adaptive Neural Temporal in situ Compressor), an end-to-end in situ compression pipeline. ANTIC consists of an adaptive temporal selector tailored to high-dimensional physics that identifies and filters informative snapshots at simulation time, combined with a spatial neural compression module based on continual fine-tuning that learns residual updates between adjacent snapshots using neural fields. By operating in a single streaming pass, ANTIC enables a combined compression of temporal and spatial components and effectively alleviates the need for explicit on-disk storage of entire time-evolved trajectories. Experimental results demonstrate that ANTIC achieves storage reductions of approximately $\sim 400\times$ for 2D Kolmogorov flow simulations and $\sim 7000\times$ for large-scale physics simulations such as binary black hole mergers.

The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting particle systems such as infinite-width two-layer neural networks. However, many problems of interest have constrained domains, which are not solved by existing mean-field algorithms due to the global diffusion term. We study the optimization of probability measures constrained to a convex subset of $\mathbb{R}^d$ by proposing the \emph{mirror mean-field Langevin dynamics} (MMFLD), an extension of MFLD to the mirror Langevin framework. We obtain linear convergence guarantees for the continuous MMFLD via a uniform log-Sobolev inequality, and uniform-in-time propagation of chaos results for its time- and particle-discretized counterpart.

While recent Text-to-Image (T2I) models show impressive capabilities in synthesizing images from brief descriptions, they struggle with the long, detailed prompts required for professional applications. We present DetailMaster, a comprehensive benchmark for evaluating T2I capabilities on long prompts with complex compositional requirements, accompanied by an automated data construction pipeline and an evaluation workflow. Comprising expert-validated prompts averaging 284.89 tokens, our benchmark introduces four critical evaluation dimensions: Character Attributes, Structured Character Locations, Multi-Dimensional Scene Attributes, and Spatial/Interactive Relationships. Evaluations on various general-purpose and long-prompt-optimized models reveal critical performance limitations, showing that weak encoders struggle to preserve syntactic dependencies within prompts and diffusion models suffer from attribute leakage under detail-intensive conditions. Through a controlled ablation study under varying constraints, we further show that high-fidelity generation requires a synergistic combination of expanded prompt limits and long-prompt training. We open-source our dataset and code to foster progress in long-prompt-driven T2I generation.

We study online configuration selection with admission control problem, which arises in LLM serving, GPU scheduling, and revenue management. In a planning horizon with $T$ periods, we consider a two-layer framework for the decisions made within each time period. In the first layer, the decision maker selects one of the $K$ configurations (ex. quantization, parallelism, fare class) which induces distribution over the reward-resource pair of the incoming request. In the second layer, the decision maker observes the request and then decides whether to accept it or not. Benchmarking this framework requires care. We introduce a **switching-aware fluid oracle** that accounts for the value of mixing configurations over time, provably upper-bounding any online policy. We derive a max-min formulation for evaluating the benchmark, and we characterize saddle points of the max-min problem via primal-dual optimality conditions linking equilibrium, feasibility, and complementarity. This guides the design of **SP-UCB–OLP** algorithm, which solves an optimistic saddle point problem and achieves $\tilde{O}(\sqrt{KT})$ regret.

Autoregressive language models frequently degrade during long-horizon generation, producing repetitive text, losing instruction adherence, and exhibiting unstable entropy. Despite the prevalence of these failures, practitioners lack online diagnostics to detect them in real-time as they occur. We formalize this degradation as cognitive fatigue, a measurable generation-time state characterized by decay in attention to the original prompt, representational drift, and entropy miscalibration. We introduce the Fatigue Index (FI), a lightweight, model-agnostic diagnostic that aggregates these three signals under explicit axioms (monotonicity, boundedness, interpretability) enabling reliable runtime monitoring. Across nine models (1B–13B parameters), FI trajectories exhibit structured temporal dynamics, predict task degradation (AUROC = 0.95) and repetition ($\rho = 0.94$), and reveal non-monotonic scaling behavior: instruction-tuned models below 3B exhibit faster collapse than base models, with this trend reversing at 7B. Stress analyses further show that FI onset accelerates under longer contexts, middle-positioned evidence, and reduced numerical precision. These results establish cognitive fatigue as a coherent and measurable phenomenon, and position FI as a principled tool for runtime reliability monitoring in production LLM systems.

Deep learning in de novo protein design has achieved atomic-level fidelity. However, existing models remain largely non-deliberative: they directly synthesize molecular geometries without explicitly reasoning about which residues or interactions are functionally essential. As a result, design decisions are entangled with continuous sampling dynamics, limiting interpretability, controllability, and systematic reuse of biochemical knowledge. We introduce Proteo-R1, a reasoning-guided protein design framework that explicitly decouples molecular understanding from geometric generation. Proteo-R1 adopts a dual-expert architecture, where a multimodal large language model (LLM) serves as an understanding expert, analyzes protein sequences, structures, and textual context to identify key functional residues that govern binding and specificity. These residue-level decisions are then passed to a separate diffusion-based generation expert, which performs conditional co-design while respecting the fixed interaction anchors. This factorization mirrors how human experts approach molecular engineering: first, reasoning about critical interactions, then optimizing geometry subject to those constraints. By operationalizing reasoning as explicit residue-level commitments rather than latent textual guidance, Proteo-R1 achieves stable, interpretable, and modular integration of LLM reasoning with advanced geometric generative models. Code and demos are at https://proteor1.github.io.

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such as sampling from the Bayesian posterior for tall datasets and the `doubly-intractable' distributions. In this paper, we begin by observing that seemingly different Markov chain Monte Carlo (MCMC) algorithms, such as the exchange algorithm, PoissonMH, and TunaMH, can be unified under a simple common procedure. We then extend this procedure into a novel framework that allows the use of auxiliary variables in both the proposal and the acceptance--rejection step. Several new MCMC algorithms emerge from this framework that uses estimated gradients to guide the proposal moves. They have demonstrated significantly better performance than existing methods on both synthetic and real datasets. We also develop theory for the new framework and use it to simplify and extend results for existing algorithms. The code to reproduce the experimental results can be found at https://github.com/ywwes26/Auxiliary-MCMC.

Large language models are powerful generalists, yet solving deep and complex problems such as those of the Humanity’s Last Exam (HLE) remains both conceptually challenging and computationally expensive. We show that small orchestrators managing other models and a variety of tools are able to both push the upper bound of intelligence and improve efficiency in solving difficult agentic tasks. We introduce ToolOrchestra, a method for training small orchestrators that coordinate the use of intelligent tools. ToolOrchestra makes explicit use of reinforcement learning with outcome-, efficiency-, and user-preference-aware rewards. Using ToolOrchestra, we produce Orchestrator, an 8B model that achieves higher accuracy at lower cost than previous tool-use agents while aligning with user preferences on which tools are to be used for a given query. On HLE, Orchestrator achieves a score of 37.1%, outperforming GPT-5 (35.1%) while being 2.5x more efficient. On $\tau ^2$-Bench and FRAMES, Orchestrator surpasses GPT-5 by a wide margin while using only about 30% of the cost. Extensive analysis shows that Orchestrator achieves the best trade-off between performance and cost under multiple metrics, and generalizes robustly to previously unseen tools. These results demonstrate that composing diverse tools with a lightweight orchestration model is both more efficient and more effective than existing methods, paving the way for practical and scalable tool-augmented reasoning systems. These results demonstrate that orchestrating diverse tools with lightweight agents is not only more efficient, but also more effective, paving the way for practical and scalable tool-augmented reasoning systems.

Spiking neural networks have attracted increasing attention for their energy efficiency, multiplication-free computation, and sparse event-based processing. In parallel, state space models have emerged as a scalable alternative to transformers for long-range sequence modelling by avoiding quadratic dependence on sequence length. We propose here a spiking heterogeneous harmonic resonate-and-fire state space model (S$H^2$RFSSM), a second-order spiking SSM for classification and regression on ultra-long sequences. S$H^2$RFSSM outperforms transformers and first-order SSMs on average while eliminating matrix multiplications, making it highly suitable for resource-constrained applications. Furthermore, we introduce a kernel-based spiking regressor that enables accurate modelling of dependencies in sequences of up to 50k steps. We also observe a reduction in spiking operations and improved performance with heterogeneity and discretisation in harmonic resonate-and-fire neuronal layers. Overall, we evaluate Harmonic Resonate-and Fire layers across 17 diverse datasets, spanning sensors, time series, and classification to long-term forecasting. Our results demonstrate that S$H^2$RFSSM achieves superior long-range modelling capability with energy efficiency, positioning it as a strong candidate for signal processing on resource-constrained devices for human activity recognition, time series classification, and regression.

Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a *mechanistic explanation* for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose *head-wise RMSNorm*, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence. The code is available at [https://github.com/Siquan-Li/Head-wise-RMSNorm](https://github.com/Siquan-Li/Head-wise-RMSNorm).

Multi-view classifiers typically fuse all observed views into a single representation, which becomes fragile when some views are missing or corrupted.We propose a prototype-anchored fusion module based on an entropically regularized unbalanced optimal transport (UOT) barycenter.Each view is summarized into a small set of learned atoms and is matched to a shared prototype support; fusion outputs a probability measure over prototypes with fixed dimension.By relaxing marginal constraints with a generalized KL penalty, the UOT objective can leave a fraction of view mass unmatched when matching is geometrically costly, yielding a simple differentiable trimming mechanism without hand-tuned thresholds.We provide a basic theoretical result showing that discarding an arbitrary subset of atom mass incurs a penalty bounded by its total mass, independent of transport distances.Experiments on multi-view action recognition benchmarks under simulated missing views, missing-rate shift, and feature-space corruption demonstrate consistently improved stability under severe missingness with modest overhead on top of strong backbones.

Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to incorporate geometric structure directly into the sum nodes of a PC. However, naïvely introducing such structure breaks tractability. We formalize this incompatibility and develop two complementary solutions: (1) an approximate inference framework that provides guaranteed lower and upper bounds for inference, and (2) a structural condition for VT under which exact tractable inference is recovered. Finally, we introduce a differentiable relaxation for VT that enables gradient-based learning and empirically validate the resulting approach on standard density estimation tasks.

We investigate decentralized online convex optimization with compressed communication, where $n$ learners connected by a network collaboratively minimize a sequence of global loss functions using only local information and compressed data from their neighbors. Prior work has established regret bounds of $O(\max\\{\omega^{-2}\rho^{-4}n^{1/2},\omega^{-4}\rho^{-8}\\}n\sqrt{T})$ and $O(\max\\{\omega^{-2}\rho^{-4}n^{1/2},\omega^{-4}\rho^{-8}\\}n\ln{T})$ for convex and strongly convex functions, respectively, where $\omega\in(0,1]$ is the compression quality factor and $\rho<1$ is the spectral gap of the communication matrix. However, these regret bounds suffer from a prohibitively high quadratic or even quartic dependence on $\omega^{-1}$. Moreover, the super-linear dependence on $n$ is also undesirable. To overcome these shortcomings, we propose a novel algorithm that achieves improved regret bounds of $\tilde{O}(\omega^{-1/2}\rho^{-1}n\sqrt{T})$ and $\tilde{O}(\omega^{-1}\rho^{-2}n\ln{T})$ for convex and strongly convex functions, respectively. The primary idea is to design a two-level blocking update framework incorporating two novel ingredients: an online gossip strategy and an error compensation scheme, which work together to promote better consensus among learners. Furthermore, we establish the first lower bounds for this problem, justifying the optimality of our results with respect to both $\omega$ and $T$. Additionally, we consider the bandit feedback scenario and extend our method with classical gradient estimators to enhance existing regret bounds.

Flow map matching (FMM) enables one- and few-step sampling for diffusion-style generation, yet its performance is often hindered by the mismatch between ground-truth training transitions and model-induced flow maps. We propose **Contrastive Flow Map Matching (CFMM)**, a principled framework that explicitly aligns FMM training with practical sampling. Our approach is motivated by a joint-KL decomposition on the reverse KL divergence, which decomposes the distributional gap into a marginal mismatch over intermediate states and a conditional mismatch in endpoint reconstruction. This analysis motivates two complementary objectives: average-velocity regression for marginal alignment and a sampling-aligned InfoNCE contrastive loss for conditional refinement. CFMM is a training-only plug-in for pre-trained FMMs, incurs no inference-time overhead, and supports training FMMs from scratch. Experiments on CIFAR-10, ImageNet, and LSUN across multiple FMM baselines demonstrate consistent improvements in fidelity and perceptual quality with only modest additional training cost.

Text-to-image generation models have advanced rapidly, yet achieving fine-grained control over generated images remains difficult, largely due to limited understanding of how semantic information is encoded. We develop an interpretation of the color representation in the Variational Autoencoder latent space of FLUX.1 [Dev], revealing a structure reflecting Hue, Saturation, and Lightness. We verify our Latent Color Subspace (LCS) interpretation by demonstrating that it can both predict and explicitly control color, introducing a fully training-free method in FLUX based solely on closed-form latent-space manipulation. Code is available at https://github.com/ExplainableML/LCS.

In open-ended domains, natural language instructions are often \textit{underspecified}, mapping to multiple valid yet functionally distinct latent intents. Although Large Language Models (LLMs) excel at generation, their interactive disambiguation remains limited by *semantic blindness*: they may spend clarification turns distinguishing superficial syntactic variants rather than resolving substantive intent differences. We propose *Topological Active Inference* (TAI), a geometric framework that recasts task disambiguation as *intent-manifold contraction*. TAI uses *Persistent Homology* to recover persistent intent clusters from sampled solutions, filtering short-lived syntactic variations while preserving robust semantic structure under mild separability assumptions. It then synthesizes clarifying questions as semantic separators and selects them with *Topological Expected Information Gain* (TEIG), which optimizes uncertainty reduction over intent clusters rather than individual candidates. This reduces the effective hypothesis space from $N$ sampled solutions to $K$ latent intents and yields logarithmic interaction complexity $\mathcal{O}(\log K)$ under balanced-split conditions. Experiments across code, visualization, and navigation tasks show that TAI resolves user intent with fewer turns and remains robust to noisy feedback, and smaller model scales.