ICML 2026 Papers

Understanding cellular phenotypes and how they respond to perturbations is critical for disease biology and therapeutic design. Single-cell RNA sequencing enables characterization at cellular resolution, yet the combinatorial space of conditions makes exhaustive experimental mapping infeasible. We introduce single-cell Concept Bottleneck Generative Models (scCBGM), a framework for interpretable and precise counterfactual editing of individual cells. scCBGM adapts concept bottleneck architectures for single-cell data through decoder skip connections and a cross-covariance penalty that promotes disentanglement without dimensional constraints. We extend the framework to flow matching models, enabling concept-guided editing in both encoding-decoding and generation regimes. To enable rigorous evaluation, we develop a synthetic benchmark with ground-truth counterfactuals. Across multiple real datasets, scCBGM demonstrates superior performance in combinatorial generalization and counterfactual prediction, supported by cell-level validation on synthetic data and population-level benchmarks on real datasets.

Large-scale molecular dynamics simulations are essential in understanding chemical and biological processes, necessitating the accurate and efficient modeling of interatomic interactions. Existing learning-based methods are generally based on message passing mechanisms; they are either not scalable or too coarse to offer accurate modeling. We propose a new message passing framework that can effectively and efficiently model interatomic interactions for simulating large-scale molecular dynamics at full atomic resolution. Specifically, our framework is stacked with a sequence of message passing neural network layers, each realizing the message passing over a distinct and dilated star-structured path. These star-structured paths are constructed progressively along dilated regions to capture the distance-dependent interactions. The crux of our framework is that it resolves the problem of dense interatomic interactions of large-scale atomic systems with sparser and region-based message passing graphs. We evaluate the framework on four benchmarks: MD22 (molecules with 42–370 atoms), Chignolin (a 166-atom protein featuring diverse conformations), the AdK dataset (a protein trajectory with up to 3,000 atoms), and the MISATO dataset (over 10,000 heterogeneous protein-ligand complexes with systems up to 40,000 atoms). Comprehensive evaluations demonstrate that our approach delivers state-of-the-art performance overall across various benchmarks. The code is provided on [Github](https://github.com/WanyuGroup/ICML2026-DKMP).

Generative Flow Networks (GFlowNets) have emerged as a powerful framework for molecular generation, sampling diverse candidates proportionally to a reward function. However, the vast chemical space necessitates truncating trajectory length, forcing models to treat incomplete molecular fragments as terminal states alongside valid molecules. This conflation distorts the learned distribution by allocating probability mass to chemically meaningless states. We propose LeakGFN, a dual-head architecture that decomposes flow into two components: a chemical head modeling flow over the full chemical space, and a valid head estimating the fraction of flow reaching valid molecules within the truncation boundary. Through this decomposition, the valid head implicitly learns molecular reachability without explicit supervision. We prove that LeakGFN recovers the correct distribution over accessible molecules under mild assumptions. Experiments on five molecular optimization tasks demonstrate consistent improvements over flow matching baselines, achieving state-of-the-art performance on four out of five tasks. Our module integrates as a plug-and-play enhancement into existing frameworks, improving performance on both pocket-conditioned and multi-objective generation tasks.

Deploying GRPO on Flow Matching models has proven effective for text-to-image generation. However, existing paradigms typically propagate an outcome-based reward to all preceding denoising steps without distinguishing the local effect of each step. Moreover, current group-wise ranking mainly compares trajectories at matched timesteps and ignores within-trajectory dependencies, where certain early denoising actions can affect later states via delayed, implicit interactions. We propose TurningPoint-GRPO (TP-GRPO), a GRPO framework that alleviates step-wise reward sparsity and explicitly models long-term effects within the denoising trajectory. TP-GRPO makes two key innovations: (i) it replaces outcome-based rewards with step-level incremental rewards, providing a dense, step-aware learning signal that better isolates each denoising action’s ``pure" effect, and (ii) it identifies turning points—steps that flip the local reward trend and make subsequent reward evolution consistent with the overall trajectory trend—and assigns these actions an aggregated long-term reward to capture their delayed impact. Turning points are detected solely via sign changes in incremental rewards, making TP-GRPO efficient and hyperparameter-free. Extensive experiments also demonstrate that TP-GRPO exploits reward signals more effectively and consistently improves generation.

Tokenizing music to fit the general framework of language models is a compelling challenge, especially considering the diverse symbolic structures in which music can be represented (e.g., sequences, grids, and graphs). To date, most approaches tokenize symbolic music as sequences of musical events, such as onsets, pitches, time shifts, or compound note events. This strategy is intuitive and has proven effective in Transformer-based models, but it treats the regularity of musical time implicitly: individual tokens may span different durations, resulting in non-uniform time progression. In this paper, we instead consider whether an alternative tokenization is possible, where a uniform-length musical step (e.g., a beat) serves as the basic unit. Specifically, we encode all events within a single time step at the same pitch as one token, and group tokens explicitly by time step, which resembles a sparse encoding of a piano-roll representation. We evaluate the proposed tokenization on music continuation and accompaniment generation tasks, comparing it with mainstream event-based methods. Results show improved musical quality and structural coherence, while additional analyses confirm higher efficiency and more effective capture of long-range patterns with the proposed tokenization.

Incomplete multi-view clustering is challenging due to view missingness and the entanglement of shared semantics with view-specific factors in latent representations. Existing methods often rely on heuristic fusion or direct completion strategies, which suffer from error propagation and unreliable generation under missing views. In this paper, we propose an **I**nformation-guided **D**isentangled latent modeling framework with **C**onditional **D**iffusion for incomplete multi-view clustering (IDCD). Specifically, we first encode each view into a latent representation that is variationally decomposed into a view-wise semantic latent and a view-specific factor. Information-theoretic objectives are introduced to guide the disentanglement of view-wise latents, preserving essential multi-view information while reducing the dependency between semantic and view-specific factors and encouraging cross-view semantic consistency. Besides, we aggregate the semantic latents via a mixture of Wasserstein distributions to obtain a unified global representation, where we impose a Gaussian mixture prior to explicitly couple representation learning with clustering. Based on the learned disentangled latent space, a conditional diffusion model guided by both the global semantic latent and view-specific factors is employed to generate missing views in a consistent manner. Extensive experiments on benchmark datasets demonstrate superior clustering performance and robust missing-view generation compared to state-of-the-art methods.

Deep learning has been widely regarded as a powerful tool for Koopman operator theory-based modeling, as it provides a promising architecture for data-driven learning of observable functions. To fully leverage this advantage, a well-designed training paradigm is required. However, the existing training paradigms typically either incur high optimization complexity or hinder effective end-to-end training, limiting modeling accuracy and training efficiency. To address this issue, we propose a differentiable quadratic programming (QP)-embedded deep Koopman framework (QPKO). In QPKO, a QP problem, which comprises a one-step accuracy-oriented objective function and a set of multi-step accuracy-oriented constraints, is formulated to introduce a mapping from observable functions to the global linear model. By doing so, the global linear model no longer needs to be treated as an independent trainable component, thereby effectively reducing optimization complexity. This QP-based mapping is implemented as a differentiable and computationally efficient module by leveraging OptNet (a differentiable QP layer), enabling effective end-to-end training. Experiments on four nonlinear dynamical systems show that QPKO achieves satisfactory improvements in modeling accuracy, training efficiency, and control performance.

Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from oversmoothing, where a node's features become increasingly similar to those of its neighbors. Unitary graph convolutions, which are mathematically constrained to preserve smoothness, have been proposed to address this issue. Despite this, in many physical systems, such as diffusion processes, smoothness naturally increases and unitarity may be overconstraining. In this paper, we systematically study the smoothing effects of different GNNs for dynamics modeling and prove that unitary convolutions hurt performance for such tasks. We propose relaxed unitary convolutions that balance smoothness preservation with the natural smoothing required for physical systems. We also generalize unitary and relaxed unitary convolutions from graphs to meshes. In experiments on PDEs such as the heat and wave equations over complex meshes and on weather forecasting, we find that our method outperforms several strong baselines, including mesh-aware transformers and equivariant neural networks. Our code is available at github.com/EdwardBerman/rayleigh_analysis

Flow Matching (FM) models have emerged as a leading paradigm for high-fidelity synthesis. However, their reliance on iterative Ordinary Differential Equation (ODE) solving creates a significant latency bottleneck. Existing solutions face a dichotomy: training-free solvers suffer from significant performance degradation at low Neural Function Evaluations (NFEs), while training-based methods incur prohibitive training costs and lack plug-and-play versatility. To bridge this gap, we propose the Bi-Anchor Interpolation Solver (BA-solver). BA-solver retains the versatility of standard training-free solvers while achieving significant acceleration by introducing a lightweight SideNet (1-2% backbone size) alongside the frozen backbone. Specifically, our method is founded on two synergistic components: 1) Bidirectional Temporal Perception, where the SideNet learns to approximate both future and historical velocities without retraining the heavy backbone; and 2) Bi-Anchor Velocity Integration, which utilizes the SideNet with two anchor velocities to efficiently approximate intermediate velocities for batched high-order integration. By utilizing the backbone to establish high-precision “anchors” and the SideNet to densify the trajectory, BA-solver enables large step sizes with minimized error. Empirical results on ImageNet-256 demonstrate that BA-solver achieves generation quality comparable to 100+ NFEs Euler solver in just 10 NFEs and maintains high fidelity in as few as 5 NFEs, incurring negligible training costs. Furthermore, BA-solver ensures seamless integration with existing generative pipelines, facilitating downstream tasks such as image editing.

To address the increasing long-context compute limitations of softmax attention, several subquadratic recurrent operators have been developed. This work includes models such as Mamba-2, DeltaNet, Gated DeltaNet (GDN), and Kimi Delta Attention (KDA). As the space of recurrences grows, a parallel line of work has arisen to taxonomize them. One compelling view is the test-time regression (TTR) framework, which interprets recurrences as performing online least squares updates that learn a linear map from the keys to values. Existing delta-rule recurrences can be seen as first-order approximations to this objective, but notably ignore the curvature of the least-squares loss during optimization. In this work, we address this by introducing preconditioning to these recurrences. Starting from the theory of online least squares, we derive equivalences between linear attention and the delta rule in the exactly preconditioned case. Next, we realize this theory in practice by proposing a diagonal approximation: this enables us to introduce preconditioned variants of DeltaNet, GDN, and KDA alongside efficient chunkwise parallel algorithms for computing them. Empirically, we find that our preconditioned delta-rule recurrences yield consistent performance improvements across synthetic recall benchmarks and language modeling at the 340M and 1B scale.

Generating long-horizon molecular dynamics (MD) is difficult due to error accumulation in time-domain autoregressive models, which causes drift, and fixed step-size constraints on temporal resolution. We propose **BioDynaSpec**, which reformulates protein dynamics as spatio-spectral generation: **Independent Windowed Fourier Decomposition (IWFD)** decomposes trajectories into window-wise spectral representations, and a generator combines low-to-high frequency autoregression with diffusion denoising to reconstruct continuous motion. This formulation is motivated by **a local near-equilibrium view of protein dynamics**: after per-window alignment, fluctuations around an anchor conformation are better characterized in spectral space, where local mode structure is more explicit than in frame-wise coordinates. To improve cross-residue and cross-frequency consistency, we introduce **Inter-Residue Frequency Coupling (IRFC)**, a learnable Gaussian distance bias in attention that injects a resonance-inspired structural prior. On ATLAS, BioDynaSpec improves 250-frame trajectory generation with $R_{250}=1.509$ Å, where $R_s$ denotes the mean per-frame C$\alpha$-RMSE over the first $s$ frames after alignment, reducing error by 60.4\% versus MDGEN and 57.2\% versus ProAR, while achieving the best PCA-2D displacement-profile correlation and stepwise distribution matching. For equilibrium conformational sampling, it achieves Root Mean $W_2=1.31$, MD PCA $W_2=0.90$, and Joint PCA $W_2=1.19$, improving over the next best method by 50.03\%, 35.25\%, and 47.58\%, respectively. It also improves near-equilibrium local-dynamics and covariance consistency, achieving PCA-PSD-LogCorr $=0.817$ and CFRE $=0.989$, corresponding to a 21.9\% gain and a 36.7\% reduction over the next best method, respectively. The source code is available at https://github.com/Linmj-Judy/BioDynaSpec.git.

Equivariant neural networks exploit underlying task symmetries to improve generalization, but strict equivariance constraints can induce more complex optimization dynamics that can hinder learning. Prior work addresses these limitations by relaxing strict equivariance during training, but typically relies on prespecified, explicit, or implicit target levels of relaxation for each network layer, which are task-dependent and costly to tune. We propose Recurrent Equivariant Constraint Modulation (RECM), a layer-wise constraint modulation mechanism that learns appropriate relaxation levels solely from the training signal and the symmetry properties of each layer's input-target distribution, without requiring any prior knowledge about the task-dependent target relaxation level. We demonstrate that under the proposed RECM update, the relaxation level of each layer provably converges to a value upper-bounded by its symmetry gap, namely the degree to which its input-target distribution deviates from exact symmetry. Consequently, layers processing symmetric distributions recover full equivariance, while those with approximate symmetries retain sufficient flexibility to learn non-symmetric solutions when warranted by the data. Empirically, RECM outperforms prior methods across diverse exact and approximate equivariant tasks, including the challenging molecular conformer generation on the GEOM-Drugs dataset.

While Mamba2's expanded state dimension enhances temporal modeling, it incurs substantial inference overhead that saturates bandwidth during autoregressive generation. Standard pruning methods fail to address this bottleneck: unstructured sparsity leaves activations dense, magnitude-based selection ignores runtime dynamics, and gradient-based methods impose prohibitive costs. We introduce GHOST (Grouped Hidden-state Output-aware Selection and Truncation), a structured pruning framework that approximates control-theoretic balanced truncation using only forward-pass statistics. By jointly measuring controllability and observability, GHOST rivals the fidelity of gradient-based methods without requiring backpropagation. As a highlight, on models ranging from 130M to 2.7B parameters, our approach achieves a 50% state-dimension reduction with approximately 1 perplexity point increase on WikiText-2. Code is available at https://github.com/Menezmic21/mamba2_ghost.

Understanding how anatomical shapes evolve in response to developmental covariates—and quantifying their spatially varying uncertainties—is critical in healthcare research. Existing approaches typically rely on global time-warping formulations that ignore spatially heterogeneous dynamics. We introduce \texttt{PRISM}, a novel framework that bridges implicit neural representations with uncertainty-aware statistical shape analysis. \texttt{PRISM} models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation. Experiments on three synthetic datasets and one clinical dataset demonstrate \texttt{PRISM}'s strong performance across diverse tasks—from modeling shape evolution to anomaly detection—within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.

Traditional neural topic models are typically optimized by reconstructing the document's Bag-of-Words (BoW) representations, overlooking contextual information and struggling with data sparsity. In this work, we introduce a novel topic model training framework by Distilling Soft Labels (DSL) from Language Models (LMs). To construct the contextually enriched reconstruction signals, we project the next token probabilities, conditioned on a specialized prompt, onto a pre-defined vocabulary, and train the topic models to reconstruct the soft labels using the LM hidden states. This produces higher-quality topics that are more closely aligned with the underlying thematic structure of the corpus. Extensive experiments demonstrate that DSL achieves substantial improvements in topic coherence and assignment accuracy over existing baselines. Additionally, we also introduce a retrieval-based metric, which shows that our approach significantly outperforms existing methods in identifying semantically similar documents, highlighting its effectiveness for retrieval-oriented applications.

Protein function is often controlled by ligands that bias the direction of state transitions, such as agonists and antagonists, rather than stabilizing a single conformation. This is especially important for clinically relevant G protein-coupled receptors (GPCRs), where therapeutic efficacy depends on functional directionality. Structure-based design methods optimize binding to static conformations and cannot represent non-reversible, directional effects or systematically distinguish agonist from antagonist behavior. To address this gap, we introduce **T**ransition-**D**irected **D**iscrete **D**iffusion for allosteric**B**inder design (**TD3B**), a sequence-based generative framework that designs binders with specified agonist or antagonist behavior via a directional transition control objective. TD3B combines a target-aware Direction Oracle, a soft binding-affinity gate, and amortized fine-tuning of a pre-trained discrete diffusion model, enabling targeted agonist and antagonist generation decoupled from binding affinity and unattainable by equilibrium-based or inference-only guidance baselines. The code and checkpoints are available at https://huggingface.co/ChatterjeeLab/TD3B.

Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift away from the target distribution. In this work, we theoretically analyze this phenomenon in the setting of score-based diffusion models. For a realistic pipeline where each training round uses a combination of synthetic data and fresh samples from the target distribution, we obtain upper and lower bounds on the accumulated divergence between the generated and target distributions. Notably, to the best of our knowledge, this is the first lower bound on the divergence between the learned and target distributions, even for standard diffusion models. Our results allow us to characterize different regimes of drift, depending on the score estimation error and the proportion of fresh data used in each generation. In a certain regime, the accumulated divergence after several retraining rounds can be expressed as a discounted sum of score estimation errors made at each generation. We also provide empirical results on synthetic data and images to illustrate the theory.

Deep Multi-View Clustering (MVC) aims to learn a unified semantic representation from diverse data sources without supervision. However, current approaches relying on flat Euclidean embeddings often fail to model data uncertainty, resulting in rigid alignment where high-quality views are forced to drift toward corrupted ones. To address these challenges, we propose the Hyperbolic Asymmetric Multi-view Clustering (HAMC) framework. HAMC maps view-specific features into the Poincaré ball and uses radial geometry as a confidence proxy, encouraging confident representations to occupy larger radial distances while allowing ambiguous or noisy samples to remain closer to the origin. To mitigate noise, we introduce an asymmetric view alignment mechanism, enabling reliable views to unidirectionally guide unreliable ones. Furthermore, a consensus-aware cluster learning strategy is designed to construct robust global pseudo-labels via a confidence-based screening scheme, refining the cluster structure. Extensive experiments against 13 baselines demonstrate that HAMC achieves state-of-the-art performance.

In standard causal attention, each token's query, key, and value (QKV) are static and encode only preceding context. We introduce CAuSal aTtention with Lookahead kEys (CASTLE), an attention mechanism that continually updates each token's keys as the context unfolds. We term these updated keys lookahead keys because they belong to earlier positions yet integrate information from tokens that appear later relative to those positions, while strictly preserving the autoregressive property. Although the mechanism appears sequential, we derive a mathematical equivalence that avoids explicitly materializing lookahead keys at each position and enables efficient parallel training. On language modeling benchmarks, CASTLE consistently outperforms standard causal attention across model scales, reducing validation perplexity and improving average performance on a range of downstream tasks.