ICML 2026 Papers

We propose *refined GRFs* (GRFs++), a new class of *Graph Random Features* (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel *walk-stitching* technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase our claims and complement our results with theoretical analysis.

The application of generative models for experimental drug discovery campaigns is severely limited by the difficulty of designing molecules de novo that can be synthesized in practice. Previous works have leveraged Generative Flow Networks (GFlowNets) to impose hard synthesizability constraints through the design of state and action spaces based on predefined reaction templates and building blocks. Despite the promising prospects of this approach, it currently lacks flexibility and scalability. As an alternative, we propose S3-GFN, which generates synthesizable SMILES molecules via simple soft regularization of a sequence-based GFlowNet. Our approach leverages rich molecular priors learned from large-scale SMILES corpora to steer molecular generation towards high-reward, synthesizable chemical spaces. The model induces constraints through off-policy replay training with a contrastive learning signal based on separate buffers of synthesizable and unsynthesizable samples. Our experiments show that S3-GFN learns to generate synthesizable molecules ($\geq 95$%) with higher rewards in diverse tasks.

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce **D**irichlet-**a**pproximated **p**ossibilistic **p**osterior p**r**edictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency.

Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from Riemannian geometry, to integrate multiple models into a unified transfer learning framework. By aligning the Ricci curvature of latent space of individual models, we construct an interrelated architecture, namely Geometric Embedding Alignment via cuRvature matching in transfer learning (GEAR), which ensures comprehensive geometric representation across datapoints. This framework enables the effective aggregation of knowledge from diverse sources, thereby improving performance on target tasks. We evaluate our model on 23 molecular task pairs and demonstrate significant performance gains over existing benchmark models—achieving improvements of at least 14.4% under random splits and 8.3% under scaffold splits.

The Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) is a Bayesian nonparametric extension of the classical Hidden Markov Model, well-suited for learning from (spatio-)temporal data. To relax the restrictive geometric assumption on state durations, the HDP Hidden Semi-Markov Model was introduced. However, both models assume stationary state durations, which limits their expressive power. In this work, we extend the HDP-HMM framework by incorporating recurrent explicit duration modeling, resulting in a more general and flexible model: the Recurrent Explicit Duration HDP-HMM (RED-HDP-HMM). We propose a Gibbs sampling method for efficient inference in this model. Empirical results on both synthetic and real-world segmentation tasks demonstrate that RED-HDP-HMM consistently outperforms the disentangled sticky HDP-HMM and the standard sticky HDP-HMM.

Offline goal-conditioned RL (GCRL) learns goal-reaching policies from static datasets, but real-world environments are often partially observable, so the collected trajectories are only partly consistent with the Markov assumption while other segments remain history-dependent. History-aware sequence models such as Decision Transformer (DT) are a natural fit for long-term dependency modeling, yet pure attention is inefficient and brittle when handling local Markovian structure and long-range context simultaneously. Although recent hybrid architectures (e.g., LSDT) introduce local extractors, their fixed-window extraction cannot adapt the effective memory to varying dependency lengths, often truncating long-range context instead of compressing it. Moreover, under sparse rewards, return-to-go (RTG) becomes non-discriminative across sub-trajectories, offering little guidance for stitching goal-reaching behaviors from diverse demonstrations. To address these limitations, we propose QHyer (Q-conditioned Hybrid Attention-Mamba Transformer), which replaces RTG with a Normalizing Flows (NFs) parameterized goal-reaching Q-estimator used directly as conditioning tokens, and a gated Hybrid Attention-Mamba backbone whose selective state-space dynamics enable content-adaptive history compression while attention captures global goal-directed dependencies. Extensive experiments on OGBench and D4RL demonstrate that QHyer achieves state-of-the-art performance on both non-Markovian and Markovian datasets, validating its effectiveness for diverse scenarios.

Despite the recent success of Multimodal Large Language Models (MLLMs), existing approaches predominantly assume the availability of multiple modalities during training and inference. In practice, multimodal data is often incomplete because modalities may be missing, collected asynchronously, or available only for a subset of examples. In this work, we propose PRIMO, a supervised latent-variable imputation model that quantifies the predictive impact of any missing modality within the multimodal learning setting. PRIMO enables the use of all available training examples, whether modalities are complete or partial. Specifically, it models the missing modality through a latent variable that captures its relationship with the observed modality in the context of prediction. During inference, we draw many samples from the learned distribution over the missing modality to both obtain the marginal predictive distribution (for the purpose of prediction) and analyze the impact of the missing modalities on the prediction for each instance. We evaluate PRIMO on a synthetic XOR dataset, Audio-Vision MNIST, and MIMIC-III for mortality and ICD-9 prediction. Across all datasets, PRIMO obtains performance comparable to unimodal baselines when a modality is fully missing and to multimodal baselines when all modalities are available. PRIMO quantifies the predictive impact of a modality at the instance level using a variance-based metric computed from predictions across latent completions. We visually demonstrate how varying completions of the missing modality result in a set of plausible labels.

Recovering radiometric fidelity from unknown dynamic range compression (UDRC), such as low-light enhancement and HDR reconstruction, is a challenging blind inverse problem, due to the unknown forward model and irreversible information loss introduced by compression. To address this challenge, we first identify monotonicity as the fundamental physical invariant shared across UDRC tasks. Leveraging this insight, we introduce the cascaded monotonic Bernstein (CaMB) operator to parameterize the unknown forward model. CaMB enforces monotonicity as a hard architectural inductive bias, constraining optimization to physically consistent mappings and enabling robust and stable operator estimation. We further integrate CaMB with a plug-and-play diffusion framework, proposing CaMB-Diff. Within this framework, the diffusion model serves as a powerful geometric prior for structural and semantic recovery, while CaMB explicitly models and corrects radiometric distortions through a physically grounded forward operator. Extensive experiments on a variety of zero-shot UDRC tasks, including low-light enhancement, low-field MRI enhancement, and HDR reconstruction, demonstrate that CaMB-Diff significantly outperforms state-of-the-art zero-shot baselines in terms of both signal fidelity and physical consistency. Moreover, we empirically validate the effectiveness of the proposed CaMB parameterization in accurately modeling the unknown forward operator.

We introduce Conditional Clifford-Steerable CNNs (C-CSCNNs), a unified framework that incorporates equivariance to arbitrary pseudo-Euclidean groups and significantly improves the expressivity of standard CSCNNs. We show that the kernel basis of the standard formulation is incomplete, limiting model capacity. To address this, we augment the kernels with equivariant representations of the input feature field. We derive the equivariance constraint for these input-dependent kernels and show how it can be solved efficiently via implicit parameterization. We empirically validate on multiple PDE forecasting tasks, including fluid dynamics and relativistic electrodynamics, where our method consistently outperforms standard CSCNNs and performs on par with state-of-the-art baselines.

Sequence models typically operate at a fixed temporal or spatial scale and struggle to generalize to substantially longer horizons or higher resolutions without retraining. Existing hierarchical architectures expand receptive fields but rely on scale-specific parameters and lack mechanisms to enforce consistent dynamics across scales. We propose Dynamic Fractal Mamba (DF-Mamba), a recursive state-space model that applies a single shared operator across multiple scales. By sharing parameters across recursion depths and exponentially scaling the effective time step, DF-Mamba achieves an exponentially expanding receptive field while preserving linear computational complexity. A learned content-aware coarse-graining module aggregates representations across scales. Auxiliary reconstruction and cross-scale consistency objectives stabilize recursive training. We evaluate DF-Mamba on long-range time-series forecasting, spatial transcriptomics, and computational pathology. Across all tasks, DF-Mamba consistently outperforms Transformers and flat Mamba baselines while using fewer parameters and maintaining linear-time scalability. Importantly, models trained on short sequences or low-resolution inputs generalize in a zero-shot manner to substantially larger temporal and spatial scales unseen during training. These results demonstrate that recursive parameter sharing provides an effective inductive bias for learning scale-consistent and efficient sequence representations.

Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However, existing works often struggle to verify the correctness of the generated optimization models, without checking the rationality of the constraints and variables or the validity of solutions to the generated models. This hampers the subsequent verification and correction steps, and thus it severely hurts the modeling accuracy. To address this challenge, we propose a novel LLM-based framework with Dual-side Verification (OptiVer) from both structure and solution perspectives, thereby improving the modeling accuracy. The structure-side verification ensures that the modeling structure of the generated optimization models aligns with the original problem description, accurately capturing the problem's constraints and requirements. Meanwhile, the solution-side verification interprets and evaluates the validity of the solutions, confirming that the optimization models are logically and mathematically sound. Extensive experiments on several popular benchmarks demonstrate that our approach significantly outperforms the state-of-the-art, achieving over 20\% improvement in accuracy.

Estimating free energy differences quantifies thermodynamic preferences in molecular interactions, which is central to chemistry and drug discovery. Despite fruitful progress, existing methods still face key limitations: classical computational approaches remain prohibitively expensive due to their reliance on extensive molecular dynamics simulations, while deep learning-based methods are constrained by either less-expressive generative models or input dimensions tied to a specific system, resulting in negligible generalization. To address these challenges, we propose CARD, a generative framework that employs a novel radix-based decomposition to bijectively convert 3D coordinates into mixed discrete-continuous sequences, enabling coarse-to-fine autoregressive modeling with enhanced expressiveness. Notably, the model corresponds to a distribution with zero free energy, serving as a proposal for absolute free energy computation of arbitrary systems without relying on alchemical pathways. Experiments across diverse tasks demonstrate that CARD matches the accuracy of classical computational methods on unseen systems with diverse topologies, while achieving an approximately 40-fold speedup in inference.

High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension. We propose **Riemannian metric matching**: a denoising probabilistic framework for learning the Riemannian geometry of data using neural networks. Specifically, we learn the *carré du champ* operator, which, using diffusion geometry, gives us access to the Riemannian geometry toolkit for downstream machine learning and statistical tasks. Our key observation is that the carré du champ operator can be formulated as a conditional expectation over random perturbations of the data, which can be exploited for sample-wise training and constant cost, amortized inference without explicit kernel construction. Empirically, metric matching rivals or improves the accuracy of $k$-NN-based diffusion geometry estimators, while enabling amortized inference that is up to $400\times$ faster, and supports graph-free geometric analysis on high-dimensional images where nearest neighbors break down.

Unlike most static material properties widely studied in the machine learning literature, ionic transport properties are inherently dynamic, making their fast and accurate prediction from static atomic structures challenging. The current standard approach, molecular dynamics (MD) simulations, suffers from prohibitively high computational cost. Recent autoregressive learning-based MD acceleration methods requiring sequential inference remain slow and prone to error accumulation; in contrast, existing non-autoregressive material property prediction models are less accurate because they fail to exploit dynamics. Moreover, existing methods typically benefit from datasets either with or without atomic trajectories, but not both. To overcome these limitations, we propose a non-autoregressive learning framework based on auxiliary modality learning, which treats atomic trajectories as an auxiliary modality during training but does not require them at inference. This enables the predictor to learn dynamics without sequential inference while benefiting from both types of datasets. As a result, our framework achieves over 200 times speedup compared to autoregressive models on the dataset with atomic trajectories while substantially reducing prediction error relative to non-autoregressive benchmarks across both types of datasets. Our code is available at https://github.com/jykim-git/MD.

The rapid evolution of generative models has unlocked new potentials in protein binder design, a pivotal task in structural biology, by facilitating end-to-end generation via joint sequence-structure modeling or hallucination. However, existing approaches are predominantly implemented under a single-target, single-state assumption, limiting their ability to model multi-target or multi-state interactions required for advanced function-oriented protein design. Here, we introduce Chamaileon, which unifies multi-target and multi-state binder design by formulating the problem as cross-context binding landscape modeling. The framework is underpinned by a training paradigm termed \textit{In-Context Complex Co-Design (I3CD)} for context-aware sequence-structure co-modeling. During inference, we employ \textit{Mixture-of-Paths Sampling (MoPS)}, a scalable strategy that optimizes a single sequence across contexts while alleviating the scarcity of high-quality multi-conformational paired data. Extensive evaluation on our newly constructed benchmark, \textit{CROSS}, demonstrates that Chamaileon effectively generates sequences adaptable to diverse conformational landscapes and multi-target requirements.

Antibodies originate from germline templates and are diversified by somatic hypermutation, producing sequences in which conserved germline residues scaffold structure while rare non-germline (NGL) substitutions refine antigen binding. Current antibody language models (ALMs) treat all residues equivalently and inherit a germline bias that systematically down-weights functionally critical NGL mutations as statistical noise. We introduce PRISM, a germline-aware ALM that explicitly represents germline and non-germline residues as distinct token types over a factorized 53-token vocabulary. PRISM achieves state-of-the-art pseudo-perplexity in hypervariable CDRs and is uniquely positively correlated with experimental binding affinity across three deep mutational scanning landscapes on which all compared ALMs anti-correlate. The dual-vocabulary further enables property-specific controllable generation previously unattainable with entangled ALMs. NGL-directed sampling improves physics-based binding scores while GL-directed sampling preserves stability and solubility. These results establish disentangled germline/non-germline representation as a substantive advance in antibody language modeling.

Molecular dynamics (MD) is a key tool for simulating the dynamical behavior of atomic systems. However, MD is inherently serial, which makes it difficult to increase single-system throughput with concurrent compute. To address this, we introduce **L**angevin **S**peculative **D**ynamics (**LSD**), a distributed and model-agnostic speculative sampler for accelerating MD *without adding relative error*. Inspired by speculative methods in language and diffusion modeling, LSD uses a draft model to propose fast simulation steps and verifies them in parallel with a slower target model, applying a transport map from the draft to the target distribution. We extend speculative sampling to second-order Langevin dynamics, derive the achievable speedup as a function of physical parameters, show that LSD generalizes across different systems and draft-target combinations with a 3-9x speedup, and confirm theoretically and empirically that LSD samples trajectories from the same distribution as its target model.

Medical diagnosis tasks often rely on heterogeneous information from multiple sources, such as medical images and clinical text. Multimodal fusion is therefore essential for improving classification performance and robustness. However, most existing methods assume a fixed and known modality set, making them less effective when the number or composition of modalities changes. To address this limitation, we propose a modality-agnostic medical multimodal fusion framework that can naturally accommodate an arbitrary number of input modalities. At the coarse-grained modality level, we represent each modality’s estimation of latent semantics as an uncertainty-aware probability distribution, and impose symmetric consistency constraints to achieve global cross-modal semantic alignment. At the fine-grained token level, we further design a token-level consistency constraint based on linear reconstruction. This constraint enables structured mutual verification of local semantics across modalities. Finally, for multimodal fusion, we adopt a multi-view consistency strategy to obtain a unified representation for diagnosis prediction. In particular, each modality is sequentially treated as a conditional view to suppress noise in the remaining modalities and extract shared semantics. Extensive experiments on five public and self-constructed multimodal medical datasets demonstrate the effectiveness and scalability of the proposed approach. Code is available at https://github.com/gjhgjbkg/SMMF.

State space models (SSMs) have emerged as efficient linear-time alternatives to attention for long-sequence modeling. However, existing SSMs often suffer from instability and memory degradation over extended horizons due to poorly conditioned first-order updates and unbalanced update geometry. We introduce MuonSSM, a general framework that stabilizes SSM training by explicitly conditioning the geometry of memory updates rather than the recurrent transition matrix. MuonSSM augments SSMs with a momentum-based pathway and a lightweight Newton-Schulz transformation on low-rank input injections, yielding bounded and spectrally conditioned updates while preserving parallel scan complexity. Theory shows that MuonSSM improves gradient propagation, mitigates spectral amplification, and enriches memory representations over long horizons. Extensive experiments across language, vision, and time-series benchmarks show consistent gains in accuracy, robustness, and long-context performance when integrated into diverse SSM backbones. These results establish geometric conditioning of updates as a principled pathway to stable, scalable sequence modeling.