ICML 2026 Papers

Soil microorganisms control organic matter cycling and largely determine how soil systems can cope with and mitigate climate change and environmental threats. Representing microbial dynamics in process-based soil models is therefore critical to predict carbon cycling in soils, albeit highly challenging to inform from data. One promising approach to improve their parametrisation is the integration of genomic data, yet modelling the complex and unknown relationship between genomes and the processes the microbes are driving is an unsolved problem. In this work, we present the first hybrid modeling framework for deriving biokinetic parameter values of a process-based soil organic matter turnover model from metagenome-inferred functional traits based on DNA sequencing data. Our model predicts biokinetic parameters of the process-based model from genomic trait data with a neural network and integrates constraints from ecological theory and literature to ensure realistic behavior, even of non-observed state variables. We evaluate our method on synthetic genomic trait datasets of varying complexity and on real data, showing that our approach improves performance over multiple baselines and learns the dynamics of unmeasurable components of the process-based model effectively, even for small training datasets.

Source-Free Domain Adaptation (SFDA) enables model adaptation under distribution shifts without access to source data, providing a practical solution for privacy-sensitive applications and having shown substantial progress in classification. In contrast, regression involves ordered and continuous target variables, posing unique challenges for representation adaptation and pseudo-label refinement in the SFDA setting. To address this gap, we propose a novel algorithm for continuous label prediction in SFDA that leverages instance-dependent, discretized density–informed supervisory signals to refine pseudo-labels within an uncertainty-aware paradigm. By incorporating auxiliary discretized distribution learning, our method also promotes more compact and structured feature representations, mitigating the inherent difficulties of adapting regression models under distribution shift. We theoretically demonstrate that the resulting density structure is robust to potential perturbations, supporting reliable SFDA for regression. Extensive experiments across multiple benchmarks validate the effectiveness of the proposed approach.

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in scientific domains. In this work, we develop a computationally cheap, mathematically justified, and highly flexible distributional modification for combating known pitfalls in equality-constrained generative models. We propose perturbing the data distribution in a constraint-aware way such that the new distribution has support matching the ambient space dimension while still implicitly incorporating underlying manifold geometry. Through theoretical analyses and empirical evidence on several representative tasks, we illustrate that our approach consistently enables data distribution recovery and stable sampling with both diffusion models and normalizing flows.

Pruning at Initialisation methods discover sparse, trainable subnetworks before training, but their theoretical mechanisms remain elusive. Existing analyses are often limited to finite-width statistics, lacking a rigorous characterisation of the global sparsity patterns that emerge as networks grow large. In this work, we connect discrete pruning heuristics to graph limit theory via graphons, establishing the *graphon limit of PaI masks*. We introduce a *Factorised Saliency Model* that encompasses popular pruning criteria and prove that, under regularity conditions, the discrete masks generated by these algorithms converge to deterministic bipartite graphons. This limit framework establishes a novel topological taxonomy for sparse networks: while unstructured methods (e.g., Random, Magnitude) converge to homogeneous graphons representing uniform connectivity, data-driven methods (e.g., SNIP, GraSP) converge asymptotically to heterogeneous graphons that encode implicit feature selection. Leveraging this continuous characterisation, we derive two consequences. First, we prove a universal approximation theorem for sparse networks on active coordinate subspaces. Second, under the Graphon-NTK lazy-training regime, we connect the limiting graphon to NTK-style generalisation bounds and introduce a path-density interpretation of how sparse topology can modulate kernel alignment. Our results transform the study of sparse neural networks from combinatorial graph problems into a rigorous framework of continuous operators, offering a new mechanism for analysing expressivity and generalisation in sparse networks.

Multimodal alignment can fail under deployment shift because standard objectives entangle cross-modal dependence with marginal-sensitive geometry. Stable Spectral Copula Alignment (SSCA) provides a deployment protocol for copula-stable dependence under approximately coordinate-wise monotone marginal distortions, together with auditable, label-free diagnostics for monitoring and mitigation. SSCA combines (i) clipped soft-rank Gaussianization that suppresses marginal effects while tracking tie and approximation errors, (ii) dependence-weighted sliced Wasserstein hub coupling for globally coherent multiway alignment with cycle auditing, and (iii) diagonal-stabilized block-spectral learning with eigengap-normalized Davis-Kahan diagnostics, yielding an actionable subspace-risk inequality. A calibrated gate maps diagnostic proxies to a reliability signal with a measurable false-alarm/miss trade-off, enabling stability-mode updates, budgeted remediation, and conservative no-update fallback for out-of-scope drift. Evaluations on MOSEI/MELD, MSCOCO, and CC3M-500K show improved performance under perturbation and substantially reduced degradation under controlled monotone distortions, raw-pipeline drifts, and frozen-feature retrieval stress tests.

Physics-based motion imitation is central to humanoid control, yet current evaluation metrics(e.g., MPJPE) only quantify imitation outcomes, not their underlying causes. This conflation obscures a critical diagnostic question: when imitation error occurs, does it stem from policy limitations or the intrinsic learning difficulty of the target motion? To resolve this ambiguity, we propose the Torque Variation Score (TVS), a physics-grounded metric that quantifies the inherent learning difficulty of a motion independently of any policy's performance. TVS measures the magnitude of torque variation required to correct small pose perturbations, directly capturing how dynamical properties shape the reinforcement learning landscape. We establish that high-TV motions induce flat reward landscapes and vanishing policy gradients, explaining persistent imitation failures. Extensive experiments with state-of-the-art methods (UHC, PHC+) confirm TVS strongly correlates with imitation error and enables principled error attribution: high error on low-TV motions indicates policy deficiency, while high error on high-TV motions reflects fundamental learning constraints. Beyond error diagnosis, TVS facilitates three practical applications: Maximum Imitable Difficulty (MID) for policy capability assessment, Difficulty-Stratified Joint Error (DSJE) for granular performance profiling, and Flawed Motion Detection for identifying segments with abnormally high learning difficulty to support mocap data curation and quality control. TVS provides a rigorous lens to distinguish policy-induced errors from motion-inherent challenges and enhances motion dataset reliability.

Spurious correlations that lead models to correct predictions for the wrong reasons pose a critical challenge for robust real-world generalization. Existing research attributes this issue to group imbalance and addresses it by maximizing group-balanced or worst-group accuracy, which heavily relies on expensive bias annotations. A compromise approach involves predicting bias information using extensively pretrained foundation models, which requires large-scale data and is limited to physically interpretable biases. To address these challenges, we offer a novel perspective by reframing the spurious correlations as imbalances/mismatches in class-conditional distributions caused by general biases, whether interpretable or not, and propose a simple yet effective robust learning method that mitigates the need for bias annotations or predictions. With the goal of maximizing the conditional entropy (uncertainty) of the label given spurious factors, our method leverages a sample reweighting strategy to achieve class-conditional distribution balancing, which automatically highlights minority groups and classes, effectively mitigating spurious correlations and producing a debiased data distribution for classification. Extensive experiments and analysis demonstrate that our approach consistently delivers strong overall performance, and is competitive with methods that rely on bias supervision.

Recent advanced diffusion methods typically derive strong generative priors by scaling diffusion transformers. However, scaling fails to generalize when adapted for real-time compression scenarios that demand lightweight models. In this paper, we explore the design of real-time and lightweight diffusion codecs by addressing two pivotal questions. First, does diffusion pre-training benefit lightweight diffusion codecs? Through systematic analysis, we find that generation-oriented pre-training is less effective at small model scales whereas compression-oriented pre-training yields consistently better performance. Second, are transformers essential? We find that while global attention is crucial for standard generation, lightweight convolutions suffice for compression-oriented diffusion when paired with distillation. Guided by these findings, we establish a one-step lightweight convolution diffusion codec that achieves real-time 60 FPS encoding and 42 FPS decoding at 1080p. Further enhanced by distillation and adversarial learning, the proposed codec reduces bitrate by 85% at a comparable FID to MS-ILLM, bridging the gap between generative compression and practical real-time deployment. Codes are released at https://github.com/microsoft/GenCodec/tree/main/CoD_Lite.

Compressing long chains of thought (CoT) into compact latent tokens is crucial for efficient reasoning with large language models (LLMs). Recent studies employ autoencoders to achieve this by reconstructing textual CoT from latent tokens, thus encoding CoT semantics. However, treating textual CoT as the reconstruction target forces latent tokens to preserve surface-level linguistic features (e.g., word choice and syntax), introducing a strong linguistic inductive bias that prioritizes linguistic form over reasoning structure and limits logical abstraction. Thus, we propose ImgCoT that replaces the reconstruction target from textual CoT to the visual CoT obtained by rendering CoT into images. This substitutes linguistic bias with spatial inductive bias, i.e., a tendency to model spatial layouts of the reasoning steps in visual CoT, enabling latent tokens to better capture global reasoning structure. Moreover, although visual latent tokens encode abstract reasoning structure, they may blur reasoning details. We thus propose a loose ImgCoT, a hybrid reasoning that augments visual latent tokens with a few key textual reasoning steps, selected based on low token log-likelihood. This design allows LLMs to retain both global reasoning structure and fine-grained reasoning details with fewer tokens than the complete CoT. Extensive experiments across multiple datasets and LLMs demonstrate the effectiveness of the two versions of ImgCoT.

Spatial proteomics enables single-cell-resolution characterization of protein expression within tissue architecture, playing a critical role in understanding tumor microenvironments and guiding precision medicine. However, current analysis workflows remain fragmented, requiring expert manual orchestration of heterogeneous tools and limiting research scalability and reproducibility. We present SP-Mind, the first autonomous AI agent designed to unify the spatial proteomics analysis pipeline, from raw multiplexed tissue imaging to downstream phenotype discovery. Equipped with expert-curated biological analysis skills and specialized computational tools, SP-Mind converts natural-language queries into end-to-end analytical workflows without task-specific fine-tuning. To rigorously evaluate its capabilities, we introduce SP-Bench, a comprehensive benchmark spanning diverse tissue types, comprising 102 tasks across 18 distinct categories. Through extensive evaluation on SP-Bench and established downstream tasks, SP-Mind achieves state-of-the-art performance compared to existing open-source biomedical agent baselines.

Continual Learning (CL) requires models to sequentially adapt to new tasks without forgetting old knowledge. Recently, Low-Rank Adaptation (LoRA), a representative Parameter-Efficient Fine-Tuning (PEFT) method, has gained increasing attention in CL. Several LoRA-based CL methods reduce interference across tasks by separating their update spaces, typically building the new space from the estimated null space of past tasks. However, they (i) overlook task-shared directions, which suppresses knowledge transfer, and (ii) fail to capture truly effective task-specific directions since these ``null bases" of old tasks can remain nearly inactive for new task under correlated tasks. To address this, we study LoRA learning capability from a projection energy perspective, and propose Low-rank Decomposition and Adaptation (LoDA). It performs a task-driven decomposition to build general and truly task-specific LoRA subspaces by solving two energy-based objectives, decoupling directions for knowledge sharing and isolation. LoDA fixes LoRA down-projections on two subspaces and learns robust up-projections via a Gradient-Aligned Optimization (GAO) approach. After each task, before integrating the LoRA updates into the backbone, LoDA derives a closed-form recalibration for the general update, approximating a feature-level joint optimum along this task-shared direction. Experiments indicate that LoDA outperforms existing CL methods.

We derive algorithms for smooth nonconvex nonconcave minimax optimization and establish linear convergence rates for problems that satisfy the two-sided Polyak-Lojasiewicz (PL) inequality. At the core of our approach is the observation that Lyapunov functions can be used not only to certify convergence a posteriori, but also to design algorithms. By replacing an idealized, intractable Lyapunov function with a computable surrogate based on gradient information, we derive TALDA (Tri-Action Lyapunov Descent Ascent), a single-loop algorithm that enforces Lyapunov descent by construction. TALDA guarantees linear convergence under the two-sided PL condition, with a rate that depends explicitly on the cross-smoothness constant. This recovers existing worst-case guarantees while yielding sharper convergence rates in weakly coupled min–max problems.

Real-world federated systems seldom operate on static data: input distributions drift while privacy rules forbid raw data sharing. We study Federated Domain-Incremental Learning (FDIL), where (i) clients are heterogeneous, (ii) tasks arrive sequentially with shifting domains, and (iii) the label space remains fixed. Two theoretical pillars remain missing for FDIL under partial participation: a guarantee of backward knowledge transfer (BKT) and a convergence rate that holds *uniformly across the task sequence*. We introduce SPECIAL (Server-Proximal Efficient Continual Aggregation for Learning), a simple, replay-free FDIL algorithm that adds a single server-side ``anchor'' to FedAvg: in each round, the server aggregates updates from a uniformly sampled subset of clients and then blends the result with the previous global model via a lightweight proximal step. This anchor curbs cumulative drift without replay buffers, synthetic data, or task-specific heads, leaving communication cost and model size unchanged. Our theory shows that SPECIAL (i) *preserves earlier tasks*: a BKT bound caps any increase in earlier-task loss by a drift-controlled term that shrinks with more rounds, local epochs, and participating clients; and (ii) *achieves task-uniform, communication-efficient convergence* for non-convex FDIL with partial participation: $\mathcal{O}\big(\sqrt{E/(NT)}\big)$ in expected gradient norm, with $E$ local epochs, $T$ rounds, and $N$ participating clients, while explicitly separating optimization variance from inter-task drift. Experiments on standard FDIL benchmarks corroborate the theory.

We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min–Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min–max characterization of key statistics, enabling approximation of the mean $\mu_{\hat{\theta}}$ and covariance $C_{\hat{\theta}}$ of the ERM estimator $\hat{\theta}$. Specifically, under a concentration assumption on the data matrix and standard regularity conditions on the loss and regularizer, we show that for a test covariate $x$ independent of the training data, the projection $\hat{\theta}^\top x$ approximately follows the convolution of the (generally non-Gaussian) distribution of $\mu_{\hat{\theta}}^\top x$ with an independent centered Gaussian variable of variance $\mathrm{tr}\!\big(C_{\hat{\theta}}\,\mathbb{E}[xx^\top]\big)$. This result clarifies the scope and limits of Gaussian universality for ERMs. Additionally, we prove that any $\mathcal{C}^2$ regularizer is asymptotically equivalent to a quadratic form determined solely by its Hessian at zero and gradient at $\mu_{\hat{\theta}}$. Numerical simulations across diverse losses and models are provided to validate our theoretical predictions and qualitative insights.

High-fidelity 3D generation depends on 3D VAEs that can compress and reconstruct complex geometry at high resolution. Recent methods often convert raw meshes into signed distance fields (SDFs), but this preprocessing can be lossy, especially for open or non-watertight assets. Render-supervised VAEs such as TripoSF avoid this conversion by matching rendered depth and normal maps, yet render losses supervise only the visible geometry for each view, leaving many latent voxels weakly constrained while still incurring unnecessary decoding and attention costs. We introduce Focusing, a view-consistent sparse-voxel training scheme for efficient 3D VAEs. Given a training view, Focusing performs depth-driven voxel carving directly in the structured latent space: voxels inconsistent with the rendered depth are removed before decoding, allowing the decoder and attention layers to operate only on locally relevant geometry. This view-dependent sparsity reduces memory and computation while concentrating learning on surface regions that contribute to the render. To stabilize training across shapes and viewpoints, we further propose adaptive zooming, which adjusts camera intrinsics to keep the number of active voxels within a target range and strengths supervision for fine details. The VAE is trained with render-based depth, normal, mask, and perceptual losses, together with sparse-voxel total variation and a brief TSDF warm-up to improve convergence and suppress holes. Across standard reconstruction benchmarks, Focusing improves Chamfer Distance and F-score over strong baselines while substantially reducing video random access memory (VRAM) consumption, enabling $1024^3$-resolution VAE training with as little as 50 GB of VRAM. These results demonstrate that local, view-consistent sparsity is an effective path toward higher-resolution and more efficient 3D VAE training.

Generative Recommendation (GR) has emerged as a promising paradigm by formulating item recommendation as a sequence-to-sequence generation task over item identifiers. Recent studies have incorporated multimodal signals to provide richer token-level evidence for generation. However, existing approaches largely rely on alignment-centric fusion and underexplore synergistic information across modalities. In practice, synergistic information plays a critical role in capturing emergent item properties that cannot be inferred from any single modality alone. Such properties encode intrinsic item semantics and guide user preferences, enabling models to move beyond surface-level feature matching. To address this limitation, we propose \textbf{SynGR}, a synergistic generative recommendation framework that explicitly encourages the exploitation of cross-modal dependencies during generation. By constraining overreliance on dominant modalities, SynGR enables the model to capture emergent item semantics beyond shared or modality-specific signals. Extensive experiments across three benchmark datasets demonstrate that SynGR achieves superior performance.

Logit-based watermarking is a widely used mechanism for identifying LLM generated content, yet its effectiveness is governed by a fundamental trade-off between detectability and semantic distortion. Existing analyses provide limited guidance for principled hyperparameter selection, leaving practical deployments reliant on heuristic tuning. In this work, we develop a power-calibrated statistical framework that establishes explicit quantitative relationships between watermark hyperparameters, detection power, and distortion. This characterization transforms watermark design into a guided optimization problem. Building on these results, we derive practical parameter selection procedures that achieve optimal trade-offs under constraints. Extensive experiments across multiple language models and datasets validate the theory and demonstrate that the proposed framework consistently identifies Pareto-optimal points.

The pursuit of spatial intelligence fundamentally relies on access to large-scale, fine-grained 3D data. However, existing approaches predominantly construct spatial understanding benchmarks by generating question–answer (QA) pairs from a limited number of manually annotated datasets, rather than systematically annotating new large-scale 3D scenes from raw web data. As a result, their scalability is severely constrained, and model performance is further hindered by domain gaps inherent in these narrowly curated datasets. In this work, we propose \textbf{Holi-Spatial}, the first fully automated, large-scale, spatially-aware multimodal dataset, constructed from raw video inputs without human intervention, using the proposed data curation pipeline. Holi-Spatial supports multi-level spatial supervision, ranging from geometrically accurate 3D Gaussian Splatting (3DGS) reconstructions with rendered depth maps to object-level and relational semantic annotations, together with corresponding spatial Question–Answer (QA) pairs. Following a principled and systematic pipeline, we further construct \textbf{Holi-Spatial-4M}, the first large-scale, high-quality 3D semantic dataset, containing 12K optimized 3DGS scenes, 1.3M 2D masks, 320K 3D bounding boxes, 320K instance captions, 1.2M 3D grounding instances, and 1.2M spatial QA pairs spanning diverse geometric, relational, and semantic reasoning tasks. Holi-Spatial demonstrates exceptional performance in data curation quality, significantly outperforming existing feed-forward and per-scene optimized methods on datasets such as ScanNet, ScanNet++, and DL3DV. Furthermore, fine-tuning Vision-Language Models (VLMs) on spatial reasoning tasks using this dataset has also led to substantial improvements in model performance.

Tokenization is a promising path to multi-modal models capable of jointly understanding protein sequences, structure, and function. Existing protein structure tokenizers create tokens by pooling information from local neighborhoods, an approach that limits their performance on generative and representation tasks. In this work, we present a method for global tokenization of protein structures in which successive tokens contribute increasing levels of detail to a global representation. This change resolves several issues with generative models based on local protein tokenization: it mitigates error accumulation, provides embeddings without sequence-reduction operations, and allows task-specific adaptation of a tokenized sequence's information content. We validate our method on reconstruction, generative, and representation tasks and demonstrate that it matches or outperforms existing models based on local protein structure tokenizers. We show that our adaptive approach enables inference criteria based on the information content of the generated proteins. We validate representations generated from our tokenizer on CATH classification tasks and demonstrate that non-linear probing on our tokenized sequences outperforms equivalent probing on representations from other tokenizers. Finally, we demonstrate how our method supports zero-shot protein shrinking and affinity maturation.