ICLR 2026 Papers

Forecasting how 3D medical scans evolve along time is important for disease progression, treatment planning, and developmental assessment. Yet existing models either rely on a single prior scan, fixed grid times, or target global labels, which limits voxel-level forecasting under irregular sampling. We present CRONOS, a unified framework for many-to-one prediction from multiple past scans that supports both discrete (grid-based) and continuous (real-valued) timestamps in one model, to the best of our knowledge the first to achieve continuous sequence-to-image forecasting for 3D medical data. CRONOS learns a spatio-temporal velocity field that transports context volumes toward a target volume at an arbitrary time, while operating directly in 3D voxel space. Across three public datasets spanning Cine-MRI, perfusion CT, and longitudinal MRI, CRONOS outperforms other baselines, while remaining computationally competitive. We will release code and evaluation protocols to enable reproducible, multi-dataset benchmarking of multi-context, continuous-time forecasting.

Large language models (LLMs) have demonstrated remarkable capability in function-level code generation tasks. Unlike isolated functions, real-world applications demand reasoning over the entire software system: developers must orchestrate how different components interact, maintain consistency across states over time, and ensure the application behaves correctly within the lifecycle and framework constraints. Yet, no existing benchmark adequately evaluates whether LLMs can bridge this gap and construct entire software systems from scratch. To address this gap, we propose \tool, a benchmark consisting of 101 software development problems drawn from real-world Android apps. Given a natural language specification detailing the app functionality, a language model is tasked with \textbf{implementing the functionality into an Android app from scratch}. Developing an Android app from scratch requires understanding and coordinating app states, lifecycle management, and asynchronous operations, calling for LLMs to generate context-aware, robust, and maintainable code. To construct \tool, we design a multi-agent system to automatically summarize the main functionalities from app documents and navigate the app to synthesize test cases validating the functional correctness of app implementation. Following rigorous manual verification by Android development experts, \tool incorporates the test cases within an automated evaluation framework that enables reproducible assessment without human intervention, making it easily adoptable for future research. Our evaluation on 12 flagship LLMs show that all evaluated models achieve low effectiveness, with the best-performing model (GPT-5) developing only 18.8\% functionally correct applications, highlighting fundamental limitations in current models' ability to handle complex, multi-component software engineering challenges.

Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that break rotational consistency. Existing spherical operators rely on rotational equivariance but often lack the flexibility for real-world complexity. We propose a generalized operator-design framework based on \textbf{designable Green’s function} and its harmonic expansion, establishing a solid operator-theoretic foundation for spherical learning. Based on this, we propose an absolute and relative position-dependent Green’s function that enables flexible balance of equivariance and invariance for real-world modeling. The resulting operator, \textit{Green's-function Spherical Neural Operator} (GSNO) with a novel spectral learning method, can adapt to non-equivariant systems while retaining spherical geometry, spectral efficiency and grid invariance. To exploit GSNO, we develop SHNet, a hierarchical architecture that combines multi-scale spectral modeling with spherical up-down sampling, enhancing global feature representation. Evaluations on diffusion MRI, shallow water dynamics, and global weather forecasting, GSNO and SHNet consistently outperform state-of-the-art methods. The theoretical and experimental results position GSNO as a principled and generalized framework for spherical operator learning, bridging rigorous theory with real-world complexity. The code is available at: \url{https://github.com/haot2025/GSNO}.

Coarse data arise when learners observe only partial information about samples; namely, a set containing the sample rather than its exact value. This occurs naturally through measurement rounding, sensor limitations, and lag in economic systems. We study Gaussian mean estimation from coarse data, where each true sample $x$ is drawn from a $d$-dimensional Gaussian distribution with identity covariance, but is revealed only through the set of a partition containing $x$. When the coarse samples, roughly speaking, have ``low'' information, the mean cannot be uniquely recovered from observed samples (i.e., the problem is not *identifiable*). Recent work by Fotakis et al. (2021) established that *sample*-efficient mean estimation is possible when the unknown mean is *identifiable* and the partition consists of only *convex* sets. Moreover, they showed that without convexity, mean estimation becomes NP-hard. However, two fundamental questions remained open: 1. When is the mean identifiable under convex partitions? 2. Is *computationally* efficient estimation possible under identifiability and convex partitions? This work resolves both questions. We provide a geometric characterization of when a convex partition is identifiable, showing it depends on whether the convex sets form ``slabs'' in a direction. Second, we give the first polynomial-time algorithm for finding $\varepsilon$-accurate estimates of the Gaussian mean given coarse samples from an unknown convex partition, matching the optimal $\widetilde{O}(d/\varepsilon^2)$ sample complexity. Our results have direct applications to robust machine learning, particularly robustness to observation rounding. As a concrete example, we derive a sample- and computationally- efficient algorithm for linear regression with market friction, a canonical problem in using ML in economics, where exact prices are unobserved and one only sees a range containing the price (Rosett, 1959).

Transformers robustly exhibit the ability to perform in-context learning, whereby their predictive accuracy on a task can increase not by parameter updates but merely with the placement of training samples in their context windows. Recent works have shown that transformers achieve this by implementing gradient descent in their forward passes. Such results, however, are restricted to standard transformer architectures, which handle finite-dimensional inputs. In the space of PDE surrogate modeling, a generalization of transformers to handle infinite-dimensional function inputs, known as "continuum transformers," has been proposed and similarly observed to exhibit in-context learning. Despite impressive empirical performance, such in-context learning has yet to be theoretically characterized. We herein demonstrate that continuum transformers perform in-context operator learning by performing gradient descent in an operator RKHS. We demonstrate this using novel proof strategies that leverage a generalized representer theorem for Hilbert spaces and gradient flows over the space of functionals of a Hilbert space. We additionally show the operator learned in context is the Bayes Optimal Predictor in the infinite depth limit of the transformer. We then provide empirical validations of this optimality result and demonstrate that the parameters under which such gradient descent is performed are recovered through the continuum transformer training.

Protein language models (PLMs) have enabled advances in structure prediction and de novo protein design, yet they frequently collapse into pathological repetition during generation. Unlike in text, where repetition merely reduces readability, in proteins it undermines structural confidence and functional viability. To unify this problem, we present the first systematic study of repetition in PLMs. We first propose quantitative metrics to characterize motif-level and homopolymer repetition and then demonstrate their negative impact on folding reliability. To address this challenge, we propose UCCS (Utility-Controlled Contrastive Steering), which steers protein generation with a constrained dataset. Instead of naively contrasting high- vs. low-repetition sequences, we construct contrastive sets that maximize differences in repetition while tightly controlling for structural utility. This disentanglement yields steering vectors that specifically target repetition without degrading foldability. Injected at inference, these vectors consistently reduce repetition without retraining or heuristic decoding. Experiments with ESM-3 and ProtGPT2 in CATH, UniRef50, and SCOP show that our method outperforms decoding penalties and other baselines, substantially lowering repetition while preserving AlphaFold confidence scores. Our results establish repetition control as a central challenge for PLMs and highlight dataset-guided steering as a principled approach for reliable protein generation.

The integration of histology images and gene profiles has shown great promise for improving survival prediction in cancer. However, current approaches often struggle to model intra- and inter-modal interactions efficiently and effectively due to the high dimensionality and complexity of the inputs. A major challenge is capturing critical prognostic events that, though few, underlie the complexity of the observed inputs and largely determine patient outcomes. These events---manifested as high-level structural signals such as spatial histologic patterns or pathway co-activations---are typically sparse, patient-specific, and unannotated, making them inherently difficult to uncover. To address this, we propose SlotSPE, a slot-based framework for structural prognostic event modeling. Specifically, inspired by the principle of factorial coding, we compress each patient’s multimodal inputs into compact, modality-specific sets of mutually distinctive slots using slot attention. By leveraging these slot representations as encodings for prognostic events, our framework enables both efficient and effective modeling of complex intra- and inter-modal interactions, while also facilitating seamless incorporation of biological priors that enhance prognostic relevance. Extensive experiments on ten cancer benchmarks show that SlotSPE outperforms existing methods in 8 out of 10 cohorts, achieving an overall improvement of 2.9%. It remains robust under missing genomic data and delivers markedly improved interpretability through structured event decomposition.

Deep learning has demonstrated remarkable capabilities in simulating complex dynamic systems. However, existing methods require known physical properties as supervision or inputs, limiting their applicability under unknown conditions. To explore this challenge, we introduce Cloth Dynamics Grounding (CDG), a novel scenario for unsupervised learning of cloth dynamics from multi-view visual observations. We further propose Cloth Dynamics Splatting (CloDS), an unsupervised dynamic learning framework designed for CDG. CloDS adopts a three-stage pipeline that first performs video-to-geometry grounding and then trains a dynamics model on the grounded meshes. To cope with large non-linear deformations and severe self-occlusions during grounding, we introduce a dual-position opacity modulation that supports bidirectional mapping between 2D observations and 3D geometry via mesh-based Gaussian splatting in video-to-geometry grounding stage. It jointly considers the absolute and relative position of Gaussian components. Comprehensive experimental evaluations demonstrate that CloDS effectively learns cloth dynamics from visual data while maintaining strong generalization capabilities for unseen configurations. Our code is available at https://github.com/whynot-zyl/CloDS. Visualization results are available at https://github.com/whynot-zyl/CloDS_video.

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications, including optimal transport (OT) and generative models. Despite their broad applicability, solving high-dimensional MFGs remains a significant challenge due to fundamental computational and analytical obstacles. In this work, we propose a particle-based deep Flow-Matching (FM) method to tackle high-dimensional deterministic MFG computation. In each iteration of our proximal best response scheme, particles are updated using first-order information, and a flow neural network is trained to match the velocity of the sample trajectories in a simulation-free manner. Theoretically, in the optimal control setting, we prove that our scheme converges to a stationary point sublinearly, and upgrade to linear (exponential) convergence under additional convexity assumptions. Our proof uses FM to induce an Eulerian coordinate (density-based) from a Lagrangian one (particle-based), and this also leads to certain equivalence results between the two formulations for MFGs when the Eulerian solution is sufficiently regular. Our method demonstrates promising performance on non-potential MFGs and high-dimensional OT problems cast as MFGs through a relaxed terminal-cost formulation.

Evaluating progress in large language models (LLMs) is often constrained by the challenge of verifying responses, limiting assessments to tasks like mathematics, programming, and short-form question-answering. However, many real-world applications require evaluating LLMs in processing professional documents, synthesizing information, and generating comprehensive reports in response to user queries. We introduce ProfBench: a set of over 7000 response-criterion pairs as evaluated by human-experts with professional knowledge across Physics PhD, Chemistry PhD, Finance MBA and Consulting MBA. We build robust and affordable LLM-Judges to evaluate ProfBench rubrics, by mitigating self-enhancement bias and reducing the cost of evaluation by 2-3 orders of magnitude, to make it fair and accessible to the broader community. Our findings reveal that ProfBench poses significant challenges even for state-of-the-art LLMs, with top-performing models like GPT-5-high achieving only 65.9\% overall performance. Furthermore, we identify notable performance disparities between proprietary and open-weight models and provide insights into the role that extended thinking plays in addressing complex, professional-domain tasks.

Integrating multimodal screening data is challenging because biological signals only partially overlap and cell-level pairing is frequently unavailable. Existing approaches either require pairing or fail to capture both shared and modality-specific information in an end-to-end manner. We present PETRI, an early-fusion transformer that learns a unified cell embedding from unpaired cellular images and gene expression profiles. PETRI groups cells by shared experimental context into multimodal “documents” and performs masked joint reconstruction with cross-modal attention, permitting information sharing while preserving modality-specific capacity. The resulting latent space supports construction of perturbation-level profiles by simple averaging across modalities. Applying sparse autoencoders to the embeddings reveals learned concepts that are biologically meaningful, multimodal, and retain perturbation-specific effects. To support further machine learning research, we release a blinded, matched optical pooled screen (OPS) and Perturb-seq dataset in HepG2 cells.

Robotic systems can require multimodal reasoning under stringent constraints of latency, memory, and energy. Standard instruction tuning and token-level distillation fail to deliver decision quality, reliability, and interpretability under these constraints. We introduce BOLT, a decision-aligned distillation and budget-aware routing framework that treats multi-choice prediction as a decision surface to be aligned during training and selectively refined at inference. During training, BOLT introduces Option-level Decision Distillation to align student models directly on the decision surface of multi-choice answers, thereby eliminating prompt artifacts, improving calibration, and optimizing the exact output space. At inference, BOLT activates Budget-aware Test-time Augmentation, a calibrated router that uses low-cost signals such as confidence, margin, entropy, retrieval affinity, and agreement across short question decompositions to trigger high-resolution reevaluation, type-matched retrieval exemplars, or question decomposition only when their expected benefit outweighs cost. On Robo2VLM-1, a 2B BOLT student distilled from LLaVA-1.5-13B improves accuracy from 28.66 in zero-shot to 42.89 with decision distillation and to 50.50 with budgeted routing, surpassing the 13B teacher at 36.74. It lowers expected calibration error, strengthens the risk-coverage frontier, and slashes GPU memory from 26,878 MB for the teacher to 3,035 MB for the distilled student, and 3,817 MB with all augmentations enabled. By constraining outputs to valid options while exposing retrieved evidence and decomposition traces, BOLT reduces hallucination and provides transparent decision-making, enabling large-model quality on edge robots.

Multimodal spatiotemporal learning on real-world experimental data is constrained by two challenges: within-modality measurements are sparse, irregular, and noisy (QA/QC artifacts) but cross-modally correlated; the set of available modalities varies across space and time, shrinking the usable record unless models can adapt to arbitrary subsets at train and test time. We propose OmniField, a continuity-aware framework that learns a continuous neural field conditioned on available modalities and iteratively fuses cross-modal context. A multimodal crosstalk block architecture paired with iterative cross-modal refinement aligns signals prior to the decoder, enabling unified reconstruction, interpolation, forecasting, and cross-modal prediction without gridding or surrogate preprocessing. Extensive evaluations show that OmniField consistently outperforms eight strong multimodal spatiotemporal baselines. Under heavy simulated sensor noise, performance remains close to clean-input levels, highlighting robustness to corrupted measurements.

Local non-stationarity is pivotal to solving partial differential equations (PDEs). However, in operator learning, the spatially local information inherent in the data is often overlooked. Even when explicitly modeled, it is usually collapsed into local superpositions within the model architecture, preventing full exploitation of local features in physical phenomena. To address this limitation, our paper proposes a novel Riesz Neural Operator (RNO) based on the spectral derivative representation. Since PDEs are fundamentally governed by local derivatives, RNO leverages the Riesz transform, a natural spectral representation of derivatives, to mix global spectral information with local directional variations. This approach allows the RNO to outperform existing operators in complex scenarios that require sensitivity to local detail. Our design bridges the gap between physical interpretability and local dynamics. Experimental results demonstrate that the RNO consistently achieves superior prediction accuracy and generalization performance compared to existing approaches across various benchmark PDE problems and complex real-world datasets, presenting superior non-linear reconstruction capability in model analysis.

Determining the binding pose of a ligand to a protein, known as molecular docking, is a fundamental task in drug discovery. Generative approaches promise faster, improved, and more diverse pose sampling than physics-based methods, but are often hindered by chemically implausible outputs, poor generalisability, and high computational cost. To address these challenges, we introduce a novel fragmentation scheme, leveraging inductive biases from structural chemistry, to decompose ligands into rigid-body fragments. Building on this decomposition, we present SigmaDock, an SE(3) Riemannian diffusion model that generates poses by learning to reassemble these rigid bodies within the binding pocket. By operating at the level of fragments in SE(3), SigmaDock exploits well-established geometric priors while avoiding overly complex diffusion processes and unstable training dynamics. Experimentally, we show SigmaDock achieves state-of-the-art performance, reaching Top-1 success rates (RMSD <2 & PB-valid) above 79.9% on the PoseBusters set, compared to 12.7-32.8% reported by recent deep learning approaches, whilst demonstrating consistent generalisation to unseen proteins. SigmaDock is the first deep learning approach to surpass classical physics-based docking under the PB train-test split, marking a significant leap forward in the reliability and feasibility of deep learning for molecular modelling.

Chain-of-Thought (CoT) training has markedly advanced the reasoning capabilities of large language models (LLMs), yet the mechanisms by which CoT training enhances generalization remain inadequately understood. In this work, we demonstrate that compositional generalization is fundamental: models systematically combine simpler learned skills during CoT training to address novel and more complex problems. Through a theoretical and structural analysis, we formalize this process: 1) Theoretically, the information-theoretic generalization bounds through distributional divergence can be decomposed into in-distribution (ID) and out-of-distribution (OOD) components. Specifically, the non-CoT models fail on OOD tasks due to unseen compositional patterns, whereas CoT-trained models achieve strong generalization by composing previously learned skills. In addition, controlled experiments and real-world validation confirm that CoT training accelerates convergence and enhances generalization from ID to both ID and OOD scenarios while maintaining robust performance even with tolerable noise. 2) Structurally, CoT training internalizes reasoning into a two-stage compositional circuit, where the number of stages corresponds to the explicit reasoning steps during training. Notably, CoT-trained models resolve intermediate results at shallower layers compared to non-CoT counterparts, freeing up deeper layers to specialize in subsequent reasoning steps. A key insight is that CoT training teaches models how to think—by fostering compositional reasoning—rather than merely what to think, through the provision of correct answers alone. This paper offers valuable insights for designing CoT strategies to enhance LLMs' reasoning robustness.

Single‑molecule localization microscopy (SMLM) allows reconstructing cellular organelles and biology-relevant structures far beyond the limited spatial resolution imposed by optics constrains, using tagged biomolecule positions. Currently, efficient SMLM requires non‑overlapping emitting fluorophores, to ensure proper image deconvolution leading to long acquisition times that hinders live‑cell imaging. Recent deep‑learning approaches can handle denser emissions, but they rely on variants of non‑maximum suppression (NMS) layers, which are unfortunately non‑differentiable and may discard true positives with their local fusion strategy. In this presentation, we reformulate the SMLM training objective as a set‑matching problem, deriving an optimal‑transport loss that eliminates the need for NMS during inference and enables end‑to‑end training. Additionally, we propose an iterative neural network that integrates knowledge of the microscope’s optical system inside our model. Experiments on synthetic benchmarks and real biological data show that both our new loss function and architecture surpass the state of the art at moderate and high emitter densities. Code is available at \url{anonymized_url}.

Predicting molecule-protein interactions (MPIs) is a fundamental task in computational biology, with crucial applications in drug discovery and molecular function annotation. However, existing MPI models face two major challenges. First, the scarcity of labeled molecule-protein pairs significantly limits model performance, as available datasets capture only a small fraction of biological relevant interactions. Second, most methods rely solely on molecular and protein features, ignoring broader biological context—such as genes, metabolic pathways, and functional annotations—that could provide essential complementary information. To address these limitations, our framework first aggregates diverse biological datasets, including molecular, protein, genes and pathway-level interactions, and then develop an optimal transport-based approach to generate high-quality pseudo-labels for unlabeled molecule-protein pairs, leveraging the underlying distribution of known interactions to guide label assignment. By treating pseudo-labeling as a mechanism for bridging disparate biological modalities, our approach enables the effective use of heterogeneous data to enhance MPI prediction. We evaluate our framework on multiple MPI datasets including virtual screening tasks and protein retrieval tasks, demonstrating substantial improvements over state-of-the-art methods in prediction accuracies and zero shot ability across unseen interactions. Beyond MPI prediction, our approach provides a new paradigm for leveraging diverse biological data sources to tackle problems traditionally constrained by single or bi-modal learning, paving the way for future advances in computational biology and drug discovery.

Independence testing involves determining whether two variables are independent based on observed samples, which is a fundamental problem in statistics and machine learning. Existing testing methods, such as HSIC, can theoretically detect broad forms of dependence, but may sacrifice statistical power when applied to limited samples with background knowledge of the distribution. In this paper, we focus on the linear non-Gaussian data, a widely supported model in scientific data analysis and causal discovery, where variables are linked linearly with noise terms that are non-Gaussian distributed. We provide a new theoretical characterization of independence in this case, showing that constancy of the conditional mean and variance is sufficient to guarantee independence under linear non-Gaussian models. Building on this result, we develop a kernel-based testing framework with provable asymptotic guarantees. Extensive experiments on synthetic and real-world datasets demonstrate that our method achieves higher power than existing approaches and significantly improves downstream causal discovery performance.