ICLR 2026 Papers

Large Reasoning Models (LRMs) have achieved impressive performance on complex reasoning tasks by generating detailed chain-of-thought (CoT) explanations. However, these responses are often excessively long, containing redundant reasoning steps that inflate inference cost and reduce usability. Controlling the length of generated reasoning without sacrificing accuracy remains an open challenge. Through a systematic empirical analysis, we reveal a consistent positive correlation between model entropy and response length at different reasoning stages across diverse LRMs: the thinking phase exhibits higher entropy, reflecting exploratory behavior of longer responses, while the final answer phase shows lower entropy, indicating a more deterministic solution.This observation suggests that entropy at different reasoning stages can serve as a control knob for balancing conciseness and performance. Based on this insight, this paper introduces Phase Entropy Aware Reward (PEAR), a reward mechanism that incorporating phase-dependent entropy into the reward design. Instead of treating all tokens uniformly, PEAR penalize excessive entropy during the thinking phase and allowing moderate exploration at the final answer phase, which encourages models to generate concise reasoning traces that retain sufficient flexibility to solve the task correctly. This enables adaptive control of response length without relying on explicit length targets or rigid truncation rules. Extensive experiments across four benchmarks demonstrate that PEAR consistently reduces response length while sustaining competitive accuracy across model scales. In addition, PEAR demonstrates strong out-of-distribution (OOD) robustness beyond the training distribution.

We propose an always-feasible ``flexible'' quadratic programming (QP) optimizer, FlexQP, which is based on an exact relaxation of the QP constraints. If the original constraints are feasible, then the optimizer finds the optimal solution to the original QP. On the other hand, if the constraints are infeasible, the optimizer identifies a solution that minimizes the constraint violation in a sparse manner. FlexQP scales favorably with respect to the problem dimension, is robust to both feasible and infeasible QPs with minimal assumptions on the problem data, and can be effectively warm-started. We subsequently apply deep unfolding to improve our optimizer through data-driven techniques, leading to an accelerated version called Deep FlexQP. By learning dimension-agnostic feedback policies for the parameters from a small number of training examples, Deep FlexQP generalizes to problems with larger dimensions and can optimize for many more iterations than it was initially trained for. Our approach outperforms two recently proposed state-of-the-art accelerated QP approaches on a suite of benchmark systems including portfolio optimization, classification, and regression problems. We provide guarantees on the expected performance of our deep QP optimizer through probably approximately correct (PAC) Bayes generalization bounds. These certificates are used to design an accelerated sequential quadratic programming solver that solves nonlinear optimal control and predictive safety filter problems faster than traditional approaches. Overall, our approach is very robust and greatly outperforms existing non-learning and learning-based optimizers in terms of both runtime and convergence to the optimal solution across multiple classes of NLPs.

Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which cannot guarantee that the retrieved pattern has the strongest association with the query, failing correctness. We reframe this problem by proposing that a query is a generative variant of a stored memory pattern, and define a variant distribution to model this subtle context-dependent generative process. Consequently, correct retrieval should return the memory pattern with the maximum a posteriori probability of being the query's origin. This perspective reveals that an ideal similarity measure should approximate the likelihood of each stored pattern generating the query in accordance with variant distribution, which is impossible for fixed and pre-defined similarities used by existing associative memories. To this end, we develop adaptive similarity, a novel mechanism that learns to approximate this insightful but unknown likelihood from samples drawn from context, aiming for correct retrieval. We theoretically prove that our proposed adaptive similarity achieves optimal correct retrieval under three canonical and widely applicable types of variants: noisy, masked, and biased. We integrate this mechanism into a novel adaptive Hopfield network (`A-Hop`), and empirical results show that it achieves state-of-the-art performance across diverse tasks, including memory retrieval, tabular classification, image classification, and multiple instance learning. Our code is publicly available at https://anonymous.4open.science/r/Adaptive-Hopfield-Network-C137/.

Dataset-level heterogeneity introduces significant domain biases that fundamentally degrade generalization on general Time Series Foundation Models (TSFMs), yet this challenge remains underexplored. This paper rethinks the from-scratch training of TSFMs using the paradigm of federated learning. We propose a novel Federated Dataset Learning (FeDaL) approach to tackle heterogeneous time series by learning dataset-agnostic temporal representations. Specifically, the distributed architecture of federated learning is a nature solution to decompose heterogeneous TS datasets into shared generalized knowledge and preserved personalized knowledge. Moreover, based on the TSFM architecture, FeDaL explicitly mitigates both local and global biases by adding two complementary mechanisms: Domain Bias Elimination (DBE) and Global Bias Elimination (GBE). FeDaL`s cross-dataset generalization has been extensively evaluated in real-world datasets spanning eight tasks (including various regression and classification), against 54 baselines. We further analyze federated scaling behavior, showing how data volume, client count, and join rate affect model performance under decentralization.

As generative models become ubiquitous, there is a critical need for fine-grained control over the generation process. Yet, while controlled generation methods from prompting to fine-tuning proliferate, a fundamental question remains unanswered: are these models truly controllable in the first place? In this work, we provide a theoretical framework to formally answer this question. Framing human-model interaction as a control process, we propose a novel algorithm to estimate the controllable sets of models in a dialogue setting. Notably, we provide formal guarantees on the estimation error as a function of sample complexity: we derive probably-approximately correct bounds for controllable set estimates that are distribution-free, employ no assumptions except for output boundedness, and work for any black-box nonlinear control system (i.e., any generative model). We empirically demonstrate the theoretical framework on different tasks in controlling dialogue processes, for both language models and text-to-image generation. Our results show that model controllability is surprisingly fragile and highly dependent on the experimental setting. This highlights the need for rigorous controllability analysis, shifting the focus from simply attempting control to first understanding its fundamental limits.

Despite recent progress in text-to-image (T2I) generation, existing models often struggle to faithfully capture user intentions from short and under-specified prompts. While prior work has attempted to enhance prompts using large language models (LLMs), these methods frequently generate stylistic or unrealistic content due to insufficient grounding in visual semantics and real-world composition. Inspired by recent advances in reasoning for language model, we propose RePrompt, a novel reprompting framework that introduces explicit reasoning into the prompt enhancement process via reinforcement learning. Instead of relying on handcrafted rules or stylistic rewrites, our method trains a language model to generate structured, self-reflective prompts by optimizing for image-level outcomes. The tailored reward models assesse the generated images in terms of human preference, semantic alignment, and visual composition, providing indirect supervision to refine prompt generation. Our approach enables end-to-end training without human-annotated data. Experiments on GenEval and T2I-Compbench show that RePrompt significantly boosts spatial layout fidelity and compositional generalization across diverse T2I backbones, establishing new state-of-the-art results. Code: https://github.com/microsoft/DKI_LLM/tree/main/RePrompt.

Time series anomaly detection (TSAD) faces critical challenges from intrinsic data noisiness and temporal heterogeneity, which undermine the reconstruction fidelity of prevailing generative approaches. While diffusion models offer theoretical advantages in capturing complex temporal dynamics, their inherent stochasticity introduces irreducible variance in reconstructions. We present the ICDiffAD, a novel method that synergizes adaptive noise scheduling with semi-deterministic generation to address these limitations. ICDiffAD introduces two key innovations: (1) an *SNR Scheduler* that governs training through quantifiable noise scales, enabling robust learning of normative patterns across non-stationary regimes; and (2) an *SNR Implicit Conditioning Mechanism* that initializes reverse diffusion from partially corrupted inputs, preserving signal coherence while attenuating anomalous components. This dual strategy ensures high-fidelity reconstructions aligned with the input’s manifold, reconciling generative flexibility with detection accuracy. Across five multivariate benchmarks, ICDiffAD improves the F1 score by 20.2\% and reduces false positives by 60.23\% compared to existing diffusion model-based TSAD methods.

Submodular maximization has broad applications in machine learning, network design, and data mining. However, classical algorithms often suffer from prohibitively high computational costs, which severely limit their scalability in practice. In this work, we focus on maximizing Sums of Concave over Modular functions (SCMs), an important subclass of submodular functions, under three fundamental constraints: cardinality, knapsack, and partition matroids. Our method integrates three components: continuous relaxation, Accelerated Approximate Projected Gradient Ascent (AAPGA), and randomized rounding, to efficiently compute near-optimal solutions. We establish a $(1 - \varepsilon - \eta - e^{-\Omega(\eta^2)})$ approximation guarantee for both cardinality and partition matroid constraints, with query complexity $O\left(n^{1/2}\varepsilon^{-1/2} (T_1 + T_2)\right)$. For the knapsack constraint, the approximation ratio degrades by a factor of $1/2$, with query complexity $O\left(n T_1 + n^{1/2}\varepsilon^{-1/2} T_2\right)$, where $T_1$ denotes the computational cost of evaluating the concave extension, and $T_2$ denotes the computational cost of backpropagation. By leveraging efficient convex optimization techniques, our approach substantially accelerates convergence toward high-quality solutions. In empirical evaluations, we demonstrate that AAPGA consistently outperforms standard PGA. On small-scale experiments, AAPGA achieves superior results in significantly less time, being up to $32.3\times$ faster than traditional methods. On large-scale experiments, our parallel multi-GPU implementation further enhances performance, demonstrating the scalability of our approach.

The recent advancement of Large Language Models (LLMs) has revolutionized the algorithm design patterns. A new paradigm, LLM-based Automated Algorithm Design (LLM-AAD), has emerged to generate code implementations for high-quality algorithms. Unlike the traditional expert-driven algorithm development, in the LLM-AAD paradigm, ideas behind the algorithm are often implicitly embedded within the generated code. Therefore, measuring similarity for algorithms may help identify whether a generated algorithm is innovative or merely a syntactic refinement of an existing code implementation. However, directly applying existing code similarity metrics to algorithms raises a critical limitation: they do not necessarily reflect the similarity between algorithms. To address this, we introduce a novel perspective that defines algorithm similarity through the lens of its problem-solving behavior. We represent the problem-solving trajectory of an algorithm as the sequence of intermediate solutions progressively generated by the algorithm. The behavioral similarity is calculated by the resemblance between two problem-solving trajectories. Our approach focuses on how an algorithm solves a problem, not just its code implementation or final output. We demonstrate the utility of our similarity measure in two use cases. (i) Improving LLM-AAD: Integrating our similarity measure into a search method demonstrates promising results across two AAD tasks, proving the effectiveness of maintaining behavioral diversity in the algorithm search. (ii) Algorithm analysis. Our similarity metric provides a new perspective for analyzing algorithms, revealing distinctions in their problem-solving behaviors.

Recent advancements in real-time super-resolution have enabled higher-quality video streaming, yet existing methods struggle with the unique challenges of compressed video content. Commonly used datasets do not accurately reflect the characteristics of streaming media, limiting the relevance of current benchmarks. To address this gap, we introduce a new comprehensive dataset - $\textbf{StreamSR}$ - sourced from YouTube, covering a wide range of video genres and resolutions representative of real-world streaming scenarios. We benchmark 11 state-of-the-art real-time super-resolution models to evaluate their performance for the streaming use-case. Furthermore, we propose $\textbf{EfRLFN}$, an efficient real-time model that integrates Efficient Channel Attention and a hyperbolic tangent activation function - a novel design choice in the context of real-time super-resolution. We extensively optimized the architecture to maximize efficiency and designed a composite loss function that improves training convergence. EfRLFN combines the strengths of existing architectures while improving both visual quality and runtime performance. Finally, we show that fine-tuning other models on our dataset results in significant performance gains that generalize well across various standard benchmarks. We made the dataset, the code, and the benchmark available at $\textit{https://github.com/EvgeneyBogatyrev/EfRLFN}$.

Recent work shows Tree-Sliced Optimal Transport to be an efficient and more expressive alternative to Sliced Wasserstein (SW), improving downstream performance. Tree-sliced metrics compare probability distributions by projecting measures onto tree metric spaces; a central example is the Tree-Sliced Wasserstein (TSW) distance, which applies the $1$-Wasserstein metric after projection. However, computing tree-based $p$-Wasserstein for general $p$ is costly, largely confining practical use to $p=1$. This restriction is a significant bottleneck, as higher-order metrics ($p > 1$) are preferred in gradient-based learning for their more favorable optimization landscapes. In this work, we revisit Sobolev integral probability metrics (IPM) on trees to obtain a practical generalization of TSW. Building on the insight that a suitably regularized Sobolev IPM admits a closed-form expression, we introduce TS-Sobolev, a tree-sliced metric that aggregates regularized Sobolev IPMs over random tree systems and remains tractable for all $p\ge1$; for $p>1$, TS-Sobolev has the same computational complexity as TSW at $p=1$. Notably, at $p=1$ it recovers TSW exactly. Consequently, TS-Sobolev serves as a drop-in replacement for TSW in practical applications, with an additional flexibility in changing $p$. Furthermore, we extend this framework to define a corresponding metric for probability measures on hyperspheres. Experiments on Euclidean and spherical datasets show that TS-Sobolev and its spherical variant improve downstream performance in gradient flows, self-supervised learning, generative modeling, and text topic modeling over recent SW and TSW variants.

Large Language Models (LLMs) have shown remarkable capabilities in solving various programming tasks, such as code generation. However, their potential for code optimization, particularly in performance enhancement, remains largely unexplored. This paper investigates the capabilities of LLMs in optimizing code for minimal execution time, addressing a critical gap in current research. The recently proposed code optimization methods constructs program optimization pairs based on iterative submissions from the same programmer for the same problem. However, this approach confines LLMs to local performance improvements, neglecting global algorithmic innovation. To overcome this limitation, we adopt a completely different perspective by reconstructing the optimization pairs into a problem-oriented approach. This allows for the integration of various ideas from multiple programmers tackling the same problem. Furthermore, we observe that code optimization presents greater challenges compared to code generation, often accompanied by "optimization tax". Recognizing the inherent trade-offs in correctness and efficiency, we introduce a novel anchor verification framework to mitigate this "optimization tax." Ultimately, the problem oriented perspective combined with anchor verification framework significantly enhances both the correct optimization ratio and speedup to new levels.

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of the problem. A practical way to apply such a scheme is to compute subspaces for a selected set of parameters in the computationally demanding offline stage and in the online stage approximate subspace for unknown parameters by interpolation. For realistic problems the space of parameters is high dimensional, which renders classical interpolation strategies infeasible or unreliable. We propose to relax the interpolation problem to regression, introduce several loss functions suitable for subspace data, and use a neural network as an approximation to high-dimensional target function. To further simplify a learning problem we introduce redundancy: in place of predicting subspace of a given dimension we predict larger subspace. We show theoretically that this strategy decreases the complexity of the mapping for elliptic eigenproblems with constant coefficients and makes the mapping smoother for general smooth function on the Grassmann manifold. Empirical results also show that accuracy significantly improves when larger-than-needed subspaces are predicted. With the set of numerical illustrations we demonstrate that subspace regression can be useful for a range of tasks including parametric eigenproblems, deflation techniques, relaxation methods, optimal control and solution of parametric partial differential equations.

Direct Preference Optimization (DPO) has recently been extended from text-only models to vision-language models. However, existing methods rely on oversimplified pairwise comparisons, generating a single negative image via basic perturbations or similarity-based retrieval, which fail to capture the complex nature of multimodal preferences, inducing optimization bias and hallucinations. To address this issue, we propose MISP-DPO, the first framework to incorporate \emph{multiple}, semantically \emph{diverse} negative images in multimodal DPO via the Plackett-Luce model. Our method embeds prompts and candidate images in CLIP (Contrastive Language–Image Pre-training) space and applies a sparse autoencoder to uncover semantic deviations into interpretable factors. Negative samples are selected based on reconstruction difficulty, semantic deviation from the positive, and mutual diversity, yielding broader and more informative supervision. To handle multi-negative comparisons, we adopt a Plackett–Luce objective and introduce an importance sampling strategy that improves training efficiency. Experiments across five diverse benchmarks demonstrate that MISP-DPO consistently improves multimodal alignment over prior methods, validating the effectiveness of semantic-aware, multi-negative sampling in preference-based learning.

Urban embodied AI agents, ranging from delivery robots to quadrupeds, are increasingly populating our cities, navigating chaotic streets to provide last-mile connectivity. Training such agents requires diverse, high-fidelity urban environments to scale, yet existing human-crafted or procedurally generated simulation scenes either lack scalability or fail to capture real-world complexity. We introduce UrbanVerse, a data-driven real-to-sim system that converts crowd-sourced city-tour videos into physics-aware, interactive simulation scenes. UrbanVerse consists of: (i) UrbanVerse-100K, a repository of 100k+ annotated urban 3D assets with semantic and physical attributes, and (ii) UrbanVerse-Gen, an automatic pipeline that extracts scene layouts from video and instantiates metric-scale 3D simulations using retrieved assets. Running in IsaacSim, UrbanVerse offers 160 high-quality constructed scenes from 24 countries, along with a curated benchmark of 10 artist-designed test scenes. Experiments show that UrbanVerse scenes preserve real-world semantics and layouts, achieving human-evaluated realism comparable to manually crafted scenes. In urban navigation, policies trained in UrbanVerse exhibit scaling power laws and strong generalization, improving success by +6.3% in simulation and +30.1% in zero-shot sim-to-real transfer comparing to prior methods, accomplishing a 300 m real-world mission with only two interventions.

Electronic structure predictions are relevant for a wide range of applications, from drug discovery to materials science. Since the cost of purely quantum mechanical methods can be prohibitive, machine learning surrogates are used to predict the result of these calculations. This work introduces the Basis Overlap Architecture (BOA), an equivariant graph neural network architecture based on a novel message passing scheme that utilizes the overlap matrix of the basis functions used to represent the ground state electron density. BOA is evaluated on QM9 and MD density datasets, surpassing the previous state-of-the-art in predicting accurate electron densities. Excellent generalization to larger molecules of up to nearly 200 atoms is demonstrated using a model trained only on QM9 molecules of up to 9 heavy atoms.

Data-free continual model merging (DFCMM) aims to fuse independently fine-tuned models into a single backbone that evolves with incoming tasks without accessing task data. This paper formulate two fundamental desiderata for DFCMM: transparency, avoiding interference with earlier tasks, and fidelity, adapting faithfully to each new task. This poses a challenge that existing approaches fail to address: how to bridge data-level desiderata with parameter-space optimization to ensure transparency and fidelity in the absence of task data. To this end, we propose NUFILT (NUll-space FILTering), a data-free framework that directly links these desiderata to optimization. Our key observation is that task vectors approximately align with representation subspaces, providing structural surrogates for enforcing transparency and fidelity. Accordingly, we design a null-space projector that preserves prior responses by filtering out overlapping components of new task vectors, thereby ensuring transparency, and a lightweight LoRA adapter that injects complementary task-specific signals, enabling fidelity in adapting to new tasks. The adapter is trained with a projection-based surrogate loss to retain consistency with previous knowledge while introducing novel directions. This joint filtering–adaptation process allows the backbone to absorb new knowledge while retaining existing behaviors, and the updates are finally fused back in a layer-wise linear fashion without extra parameters or inference cost. Theoretically, we establish approximate subspace alignment guarantees that justify null-space filtering. Empirically, NUFILT achieves state-of-the-art performance with minimal forgetting on both vision and NLP benchmarks, improving average accuracy by 4–7\% over OPCM and WUDI-Merging, while narrowing the gap to fine-tuning and reducing computation overhead.

Diffusion large language models (dLLMs), which offer bidirectional context and flexible masked-denoising generation, are emerging as a compelling alternative to autoregressive (AR) LLMs. However, like AR LLMs, their model sizes continue to grow, motivating weight compression for deployment. Although post-training quantization (PTQ) is effective for AR LLMs, directly transferring it to dLLMs at 2-bit leads to unsatisfactory performance. To tackle these challenges, we propose Quant-dLLM, an ultra-low-bit PTQ framework tailored to dLLMs. Since masked-denoising activations in dLLMs differ from the fully visible signals assumed by standard PTQ methods, we introduce Masked Calibration Simulation (MCS) to align calibration with the timestep-dependent masking, which yields more reliable calibrations. Moreover, we propose a Data-aware Any-order Quantizer (DAQ) that learns ultra-low-bit weight representations via an optimization algorithm. It performs iterative approximation guided by our simulated calibration data. In addition, under a strict 2-bit budget, we introduce Adaptive Blockwise Mixed Precision (ABMP), a sensitivity-based precision allocation scheme that adaptively assigns bit width across channel groups. When restricted to 2-bit precision, Quant-dLLM consistently achieves higher accuracy than state-of-the-art (SOTA) AR-transfer PTQ methods on dLLMs. We will release the code and models soon.

We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with step sizes that incorporate primal-dual guarantees, offering practical stopping criteria. We present a new Frank-Wolfe algorithm utilizing an optimistic framework and provide a primal-dual convergence proof. Additionally, we propose a generalized short-step strategy aimed at optimizing a computable primal-dual gap. Interestingly, this new generalized short-step strategy is also applicable to gradient descent algorithms beyond Frank-Wolfe methods. Empirical results demonstrate that our optimistic algorithm outperforms existing methods, highlighting its practical advantages.