ICML 2026 Papers

Empirically, option-based hierarchical reinforcement (HRL) learning often produces longer and more diverse options when a deliberation cost is charged at option boundaries. However, when options are executed for many steps under an approximate dynamics model, small model errors compound along the option, degrading the quality of the resulting plan. In this work, we introduce the commitment loss to formalize the tradeoff between deliberation cost and model error as a function of option duration. We characterize how optimal termination probabilities vary with this tradeoff under two model-error mechanisms. First, the model is learned from finite data via maximum-likelihood estimation, producing statistical error that interacts with option duration. Second, we consider an input-driven setting where an exogenous input is only observed at option boundaries and evolves unobserved between them, creating a drift-induced mismatch between planned and realized dynamics. In both cases, we solve for the optimal termination behavior as a function of deliberation cost and the error scale, clarifying the behavior of some popular HRL algorithms that approach the deliberation cost as a heuristic.

We present MoST (Mixture of Speech and Text), a novel multimodal large language model that seamlessly integrates speech and text processing through our proposed Modality-Aware Mixture of Experts (MAMoE) architecture. While current multimodal models typically process diverse modality representations with identical parameters—disregarding their inherent representational differences, we introduce specialized routing pathways that direct tokens to modality-appropriate experts based on input type. MAMoE simultaneously enhances modality-specific learning and cross-modal understanding through two complementary components: modality-specific expert groups that capture domain-specific patterns and shared experts that facilitate information transfer between modalities. Building on this architecture, we develop an efficient transformation pipeline that adapts the pretrained MoE language model through strategic post-training on ASR and TTS datasets, followed by fine-tuning with a carefully curated speech-text instruction dataset. A key feature of this pipeline is that it relies exclusively on fully accessible, open-source datasets to achieve strong performance and data efficiency. Comprehensive evaluations across ASR, TTS, audio language modeling, and spoken question answering benchmarks show that MoST consistently outperforms existing models of comparable parameter counts. Our ablation studies confirm that the modality-specific routing mechanism and shared experts design significantly contribute to performance gains across all tested domains. To our knowledge, MoST represents the first fully open-source speech-text LLM built on a Mixture of Experts architecture.

We study the problems of approximate sampling from and distribution testing of \emph{mixture models}, where the modes satisfy a functional inequality called \emph{approximate tensorization of entropy} (ATE). While it is known that ATE makes these tasks more efficient in the unimodal setting, mixtures of few distributions satisfying ATE do not necessarily satisfy ATE overall, leading to a lack of theoretical guarantees for multimodal distributions, which are a key challenging case of modern generative models. We show this gap can be overcome by establishing the following pair of results for mixtures of ATE distributions: 1) We show fast mixing of Glauber dynamics from a \emph{data-based initialization}, with \emph{optimal} sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities, building on similar results in (Koehler et al., 2024, Huang et al., 2024) for mixtures satisfying the weaker Poincaré inequality. 2) Answering an open question from (Blanca et al., 2023), we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.

Vision-language-action models exhibit an inherent trade-off in action chunk length (``horizon''): longer horizons improve global foresight but degrade fine-grained local control, while shorter ones yield the opposite. To mitigate the trade-off, we propose a $\textbf{mixture of horizons (MoH)}$ strategy. In brief, MoH rearranges the action chunk into several segments with different horizons, processes them in parallel with a shared action transformer, and fuses outputs with a light linear gate. It offers three appealing benefits. i) Long-term foresight and short-term precision are jointly exploited within a single model. ii) MoH is plug-and-play for full-attention action modules with minimal training or inference overhead. iii) MoH enables dynamic inference with adaptive horizons, which selects stable actions through cross-horizon consensus, achieving 2.5$\times$ higher throughput than baselines while preserving superior performance. Extensive experiments over flow-based and one-step regression policies demonstrate that MoH yields consistent and significant gains on both simulations and real-world tasks.

Vector quantization is a fundamental tool for compressing high-dimensional embeddings, yet existing multi-codebook methods rely on static codebooks that limit expressiveness under heterogeneous data geometry. While recent dynamic quantizers like QINCo adapt codebooks to individual inputs and improve expressiveness, their strict sequential dependencies create decoding bottlenecks. We propose Residual Quantization via Mixture of Experts (RQ-MoE), a framework combining a two-level MoE with dual-stream quantization to enable input-dependent codebook adaptation for efficient vector quantization. RQ-MoE enables dynamic codebook construction and decouples instruction from quantization, facilitating parallel decoding. Theoretically, we show that standard Residual Quantization and QINCo can be recovered as constrained special cases of RQ-MoE, and derive a guideline for setting expert dimensionality in RQ-MoE. Extensive experiments show that RQ-MoE achieves state-of-the-art or on-par performance in reconstruction and retrieval, while it can provide 6×–14× faster decoding than prior vector quantization methods. The implementation is available at https://github.com/KDEGroup/RQ-MoE.

Model merging has emerged as a cost-effective approach for consolidating the capabilities of multiple LLMs without retraining. However, existing merging techniques, largely based on linear parameter arithmetic or optimization, struggle when applied to Mixture-of-Experts (MoE) architectures. We identify a critical failure mode in MoE merging, termed *routing breakdown*, in which the merged router fails to dispatch tokens to suitable experts. Routing breakdown stems from the sensitivity of the non-linear softmax and discrete Top-$k$ routing mechanisms to parameter perturbations from merging, a sensitivity further amplified by load-balancing constraints imposed during MoE pretraining. Because fine-tuned experts exhibit distinct specializations, even modest misrouting can cause severe performance degradation. To address this issue, we propose Hessian-Aware Router Calibration (HARC), a training-free framework that leverages second-order curvature information to realign the merged router. This approach admits a closed-form solution that can be efficiently solved using a matrix-free conjugate gradient method. Experiments on mathematical reasoning and code generation tasks show that HARC effectively mitigates routing breakdown across diverse MoE merging baselines and leads to substantial performance improvements.

We study a sampling problem whose target distribution is $\pi \propto \exp(-f-r)$ where the data fidelity term $f$ is Lipschitz smooth while the regularizer term $r=r_1-r_2$ is a non-smooth difference-of-convex (DC) function, i.e., $r_1,r_2$ are convex. By leveraging the DC structure of $r$, we can smooth out $r$ by applying Moreau envelopes to $r_1$ and $r_2$ separately. In line with DC programming, we then redistribute the concave part of the regularizer to the data fidelity and study its corresponding proximal Langevin algorithm (termed DC-LA). We establish convergence of DC-LA to the target distribution $\pi$, up to discretization and smoothing errors, in the $q$-Wasserstein distance for all $q \in \mathbb{N}^*$, under the assumption that $V$ is distant dissipative. Our results improve previous work on non-log-concave sampling in terms of a more general framework and assumptions. Numerical experiments show that DC-LA produces accurate distributions in synthetic settings and provides qualitatively reasonable uncertainty quantification in a real-world Computed Tomography application.

Mixture-of-Experts (MoE) models scale large language models efficiently by sparsely activating experts, but once an expert is selected, it is executed fully. Hence, the trade-off between accuracy and computation in an MoE model typically exhibits large discontinuities. We propose Mixture of Slimmable Experts (MoSE), an MoE architecture in which each expert has a nested, slimmable structure that can be executed at variable widths. This enables conditional computation not only over which experts are activated but also over how much of each expert is utilized. Consequently, a single pretrained MoSE model can support a more continuous spectrum of accuracy-compute trade-offs at inference time. We present a simple and stable training recipe for slimmable experts under sparse routing, combining multi-width training with standard MoE objectives. During inference, we explore strategies for runtime width determination, including a lightweight test-time training mechanism that learns how to map router confidence/probabilities to expert widths under a fixed budget. Experiments on GPT-style models, various routing regimes, zero-shot downstream reasoning benchmarks, and continual pre-training adaptation of DeepSeek model show that MoSE matches or improves standard MoE at full width and consistently shifts the compute-quality frontier toward lower inference FLOPs. The code can be found at: https://github.com/tnurbek/mose.

The forest matrix of a signed graph plays an important role in network science and social opinion dynamics, yet existing algorithms are mainly designed for unsigned graphs and are difficult to extend to signed graphs. In this paper, we study the problem of efficiently estimating the forest matrix of signed graphs with \(n\) nodes and introduce the signed forest matrix theorem, which establishes the relationship between generalized spanning converging forests and the forest matrix. Based on this result, we propose a novel algorithm \textsc{GSCF}, built on a variant of loop-erased random walks, to generate generalized spanning converging forests in expected \(O(n)\) time. We further develop two sampling algorithms, \textsc{FMDE} and \textsc{FMDE+}, for estimating the diagonal of the forest matrix, both with time complexity \(O(ln)\), where \(l\) is the number of samples. Extensive experiments on various signed graphs show that our methods achieve high estimation accuracy, significantly improve computational efficiency, and scale to graphs with over twenty million nodes. Our source code is publicly available on \url{https://github.com/HaoxinSun98/SignedForestDiagonal}.

Static fine-tuning paradigms impose rigid structural constraints on foundation models like the Segment Anything Model 2 (SAM2), limiting their adaptability to the varying complexity of specialized downstream tasks. To overcome this limitation, we propose **ACO-MoE-LoRA**, a dynamic framework that introduces an "Evolving-while-Training" strategy by synergizing Ant Colony Optimization (ACO) with a Latent Space Mixture-of-Experts (MoE) architecture. Central to our method is the ACO-ConvLoRA module, which employs a pheromone-guided routing mechanism to actively govern expert selection and topological evolution. By formulating expert assignment as an evolutionary pathfinding problem, this module effectively mitigates the standard routing collapse issue and enables elastic adjustment of LoRA ranks via weight slicing, bridging discrete structural search with continuous parameter training. Extensive experiments across 16 challenging datasets demonstrate that our framework consistently outperforms leading static adapters, while effectively addressing the local optimality limitations of recent dynamic heuristics. This work presents a self-organizing solution that harmonizes swarm intelligence with gradient optimization for efficiently adapting foundation models to specialized domains.

Out-of-distribution (OOD) generalization has attracted increasing research attention in recent years, owing to its promising empirical results in real-world applications. However, theoretical studies on OOD generalization remain limited, particularly with respect to lower bounds on the generalization error. To better understand how source data contributes to improved OOD generalization performance, we take an initial step toward establishing a lower bound on the OOD generalization error, and subsequently investigate upper bounds from the perspective of statistical learning theory. Interestingly, we find that under the RCS and empirical-RCS conditions, simply minimizing the average empirical risk over the source domains can yield a nearly optimal error rate (up to a logarithmic factor) \textit{without} requiring knowledge or estimation of distributional parameters or the discrepancy between source and target domains. This conditional result provides a theoretical perspective on the surprising phenomenon observed in DomainBed, where carefully designed OOD generalization algorithms fail to outperform the simple empirical risk minimization (ERM) algorithm. Our results also imply a no-free-lunch theorem and provide an optimistic bound for OOD generalization.