ICLR 2026 Papers

The MCP standardizes how LLMs interact with external systems, forming the foundation for general agents. However, existing MCP benchmarks remain narrow in scope: they focus on read-heavy tasks or tasks with limited interaction depth, and fail to capture the complexity and realism of real-world workflows. To address this, we propose \texttt{MCPMark}, a benchmark designed to evaluate realistic and comprehensive MCP use, comprising $127$ high-quality tasks collaboratively created by human experts and AI agents. Specifically, each task starts from a curated initial state and incldes a programmatic script for automatic verification. Moreover, these tasks require richer and more varied interactions with the environment, involving diverse create, read, update, and delete (CRUD) operations. We conduct comprehensive evaluation of cutting-edge LLMs using a minimal agent framework that operates in a tool-calling loop. Empirical results show that the best-performing model, \texttt{gpt-5-medium}, reaches only $52.56$\% pass@1 and $33.86$\% pass^4, while other widely regarded strong models, including \texttt{claude-sonnet-4} and \texttt{o3}, fall below $30$\% pass@1 and $15$\% pass^4. On average, LLMs require $16.18$ execution turns and $17.38$ tool calls per task, substantially exceeding those in previous MCP benchmarks and demonstrating the stress-testing nature of \texttt{MCPMark}.

Language model post-training has enhanced instruction-following and performance on many downstream tasks, but also comes with an often-overlooked cost on tasks with many possible valid answers. We characterize three desiderata: in-context steerability, valid output space coverage, and distributional alignment, and document across three model families how post-training can reduce these properties. In particular, we disambiguate between two kinds of in-context learning: ICL for eliciting existing underlying knowledge or capabilities, and in-context steerability, where a model must use in-context information to override its priors and steer to a novel data generating distribution. To better evaluate and improve these desiderata, we introduce Spectrum Suite, a large-scale resource compiled from $>40$ data sources and spanning $>90$ tasks requiring models to steer to and match diverse distributions. We find that while instruction-tuning helps elicit underlying capabilities and models, it hurts a model’s ability to flexibly steer in-context. To mitigate these issues, we propose Spectrum Tuning, a post-training method using Spectrum Suite to improve steerability and distributional coverage. We find that Spectrum Tuning often improves over pretrained models and their instruction-tuned counterparts, enhancing steerability, spanning more of the out- put space, and improving distributional alignment on held-out datasets.

In reinforcement learning (RL), critics traditionally learn absolute state values, estimating how good a particular situation is in isolation. Adding any constant to $V(s)$ leaves action preferences unchanged. Thus only value differences are relevant for decision making. Motivated by this fact, we ask the question whether these differences can be learned directly. For this, we propose \emph{Relative Value Learning} (RV), a framework that considers antisymmetric value differences $\Delta(s_i, s_j) = V(s_i) - V(s_j)$. We define a new pairwise Bellman operator and prove it is a $\gamma$-contraction with a unique fixed point equal to the true value differences, derive well-posed $1$-step/$n$-step/$\lambda$-return targets and reconstruct generalized advantage estimation from pairwise differences to obtain an unbiased policy-gradient estimator (R-GAE). Besides rigorous theoretical contributions, we integrate RV with PPO and achieve competitive performance on the Atari benchmark (49 games, ALE) compared to standard PPO, indicating that relative value estimation is an effective alternative to absolute critics. Source code will be made available.

We propose a general and computationally efficient framework for achieving differential privacy (DP) on Hadamard manifolds, which are complete and simply connected Riemannian manifolds with non-positive curvature. Leveraging the Cartan-Hadamard theorem, we introduce Exponential-Wrapped Laplace and Gaussian mechanisms that achieve $\epsilon$-DP, $(\epsilon, \delta)$-DP, Gaussian DP (GDP), and Rényi DP (RDP) without relying on computationally intensive MCMC sampling. Our methods operate entirely within the intrinsic geometry of the manifold, ensuring both theoretical soundness and practical scalability. We derive utility bounds for privatized Fréchet means and demonstrate superior utility and runtime performances on both synthetic data and real-world data in the space of symmetric positive definite matrices (SPDM) equipped with three different metrics. To our knowledge, this work constitutes the first unified extension of multiple DP notions to general Hadamard manifolds with practical and scalable implementations.

Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile scenarios and tasks, we theoretically investigate utilizing transformers as students to learn from a class of teacher models. Specifically, the teacher models covered in our analysis include convolution layers with average pooling, graph convolution layers, and various classic statistical learning models, including a variant of sparse token selection models [Sanford et al., 2023, Wang et al., 2024] and group-sparse linear predictors [Zhang et al., 2025]. When learning from this class of teacher models, we prove that one-layer transformers with simplified "position-only'' attention can successfully recover all parameter blocks of the teacher models, thus achieving the optimal population loss. Building upon the efficient mimicry of trained transformers towards teacher models, we further demonstrate that they can generalize well to a broad class of out-of-distribution data under mild assumptions. The key in our analysis is to identify a fundamental bilinear structure shared by various learning tasks, which enables us to establish unified learning guarantees for these tasks when treating them as teachers for transformers.

Sparsely-activated Mixture-of-Experts (SMoE) models offer efficient pre-training and low latency but their large parameter counts create significant memory overhead, motivating research into expert compression. Contrary to recent findings favouring expert *merging* on discriminative benchmarks, we find that expert *pruning* is a superior strategy for generative tasks. We demonstrate that existing merging techniques introduce an irreducible error due to the loss of fine-grained routing control over experts. Leveraging this insight, we propose Router-weighted Expert Activation Pruning (REAP), a novel pruning criterion that considers both router gate-values and expert activation norms to minimize the reconstruction error bound. Across a diverse set of SMoE models ranging from 20B to 1T parameters, REAP consistently outperforms merging and other pruning methods on generative benchmarks, especially at 50% compression. Notably, our method achieves near-lossless compression on code generation tasks with Qwen3-Coder-480B and Kimi-K2, even after pruning 50% of experts.

RL with Verifiable Rewards (RLVR) has emerged as a promising paradigm for improving the reasoning abilities of large language models (LLMs). Current methods rely primarily on policy optimization frameworks like PPO and GRPO, which follow generalized policy iteration that alternates between evaluating the current policy's value and improving the policy based on evaluation. While effective, they often suffer from training instability and diversity collapse, requiring complex heuristic tricks and careful tuning. We observe that standard RLVR in math reasoning can be formalized as a specialized finite-horizon Markov Decision Process with deterministic state transitions, tree-structured dynamics, and binary terminal rewards. Though large in scale, the underlying structure is simpler than general-purpose control settings for which popular RL algorithms (e.g., PPO) were developed, suggesting that several sophisticated techniques in existing methods may be reduced or even omitted. Based on this insight, we prove a surprising result: the optimal action can be recovered from the Q-function of a fixed uniformly random policy, thereby bypassing the generalized policy iteration loop and its associated heuristics. We introduce \underline{\textbf{R}}andom P\underline{\textbf{o}}licy \underline{\textbf{V}}aluation for Div\underline{\textbf{e}}rse \underline{\textbf{R}}easoning (ROVER) to translate this principle into a practical and scalable algorithm for LLM math reasoning, a minimalist yet highly effective RL method that samples actions from a softmax over these uniform-policy Q-values. ROVER preserves diversity throughout training, allowing sustained exploration of multiple valid pathways. Across multiple base models and standard math reasoning benchmarks, ROVER demonstrates superior performance in both \textbf{quality} (\textbf{+8.2} on pass@1, \textbf{+16.8} on pass@256) and \textbf{diversity} (\textbf{+20.5\%}), despite its radical simplification compared to strong, complicated existing methods.

Reinforcement Learning (RL) has played a central role in the recent surge of LLMs' math abilities by enabling verification-driven training through binary verifier signals. In contrast, Supervised Learning (SL) is rarely considered for such verification-driven training, largely due to its heavy reliance on reference answers and inability to reflect on mistakes. In this work, we challenge the prevailing notion that self-improvement is exclusive to RL and propose Negative-aware Fine-Tuning (NFT) --- a supervised approach that enables LLMs to reflect on their failures and improve autonomously with no external teachers. In online training, instead of throwing away self-generated negative answers, NFT constructs an \textit{implicit} negative policy to model them. This implicit policy is parameterized with the same positive LLM we target to optimize on positive data, enabling direct policy optimization on all LLMs' generations. We conduct experiments on 7B and 32B models in math reasoning tasks. Results consistently show that through the additional leverage of negative feedback, NFT significantly improves over SL baselines like rejection fine-tuning, matching, or even surpassing leading RL algorithms like GRPO and DAPO. Furthermore, we demonstrate that NFT and GRPO are actually equivalent in strict-on-policy training, even though they have entirely different theoretical foundations. Our experiments and theoretical findings bridge the gap between SL and RL methods in binary-feedback learning systems.

Flowcharts are widely used to represent processes and relationships through intuitive visual representations. However, accurately interpreting these diagrams remains challenging due to their structural complexity and high visual diversity. Existing flowchart datasets often lack fine-grained control over key properties such as graph complexity and rendering style, limiting their utility for training and testing of multimodal large language models (MLLMs) on visual reasoning tasks. To address these limitations, we introduce FlowGen, a controllable synthesizer that generates flowcharts that have customizable structural features and supports multiple renderer backends. FlowGen enables fine-grained control over graph properties such as graph order and size, branched arrows, and nested subgraphs, facilitating systematic evaluation of MLLMs' capabilities. Extensive experiments on open-source and proprietary MLLMs show that training on FlowGen substantially improves flowchart parsing and question answering (QA), while also enhancing generalization to other public datasets. Furthermore, FlowGen provides challenging test datasets that expose consistent weaknesses in current MLLMs, particularly related to high structural complexity and varied rendering styles. Our code and data are publicly available at https://github.com/nju-websoft/FlowGen.

Variational Autoencoders (VAEs) are a powerful alternative to matrix factorization for recommendation. A common technique in VAE-based collaborative filtering (CF) consists in applying binary input masking to user interaction vectors, which improves performance but remains underexplored theoretically. In this work, we analyze how collaboration arises in VAE-based CF and show it is governed by \emph{latent proximity}: we derive a latent sharing radius that informs when an SGD update on one user strictly reduces the loss on another user, with influence decaying as the latent Wasserstein distance increases. We further study the induced geometry: with clean inputs, VAE‑based CF primarily exploits \emph{local} collaboration between input‑similar users and under‑utilizes \emph{global} collaboration between far‑but‑related users. We compare two mechanisms that encourage \emph{global} mixing and characterize their trade‑offs: \ding{172} $\beta$‑KL regularization directly tightens the information bottleneck, promoting posterior overlap but risking representational collapse if too large; \ding{173} input masking induces stochastic \emph{geometric} contractions and expansions, which can bring distant users onto the same latent neighborhood but also introduce neighborhood drift. To preserve user identity while enabling global consistency, we propose an anchor regularizer that aligns user posteriors with item embeddings, stabilizing users under masking and facilitating signal sharing across related items. Our analyses are validated on the Netflix, MovieLens-20M, and Million Song datasets. We also successfully deployed our proposed algorithm on an Amazon streaming platform following a successful online experiment.

Decision-focused learning (DFL) integrates predictive modeling and optimization by training predictors to optimize the downstream decision target rather than merely minimizing prediction error. To date, existing DFL methods typically rely on deterministic point predictions, which are often insufficient to capture the intrinsic stochasticity of real-world environments. To address this challenge, we propose the first diffusion-based DFL approach, which trains a diffusion model to represent the distribution of uncertain parameters and optimizes the decision by solving a stochastic optimization with samples drawn from the diffusion model. Our contributions are twofold. First, we formulate diffusion DFL using the reparameterization trick, enabling end-to-end training through diffusion. While effective, it is memory and compute-intensive due to the need to differentiate through the diffusion sampling process. Second, we propose a lightweight score function estimator that uses only several forward diffusion passes and avoids backpropagation through the sampling. This follows from our results that backpropagating through stochastic optimization can be approximated by a weighted score function formulation. We empirically show that our diffusion DFL approach consistently outperforms strong baselines in decision quality. The source code for all experiments is available [here](https://anonymous.4open.science/r/e2e-model-444D/README.md).

Long chain-of-thought (CoT) is an essential ingredient in effective usage of modern large language models, but our understanding of the reasoning strategies underlying these capabilities remains limited. While some prior works have attempted to categorize CoTs using predefined strategy types, such approaches are constrained by human intuition and fail to capture the full diversity of model behaviors. In this work, we introduce the CoT Encyclopedia, a bottom-up framework for analyzing and steering model reasoning. Our method automatically extracts diverse reasoning criteria from model-generated CoTs, embeds them into a semantic space, clusters them into representative categories, and derives contrastive rubrics to interpret reasoning behavior. Human evaluations show that this framework produces more interpretable and comprehensive analyses than existing methods. Moreover, we show that this understanding translates into measurable improvements on both problem-solving and safety benchmarks. We can predict which strategy a model is likely to use and guide it toward more effective alternatives. Finally, we show that training data format (e.g., free-form vs. multiple-choice) impacts reasoning far more than data domain, highlighting the importance of format-aware model design. In short, the CoT Encyclopedia turns reasoning from a black box into a controllable asset, enabling LLMs that think more clearly, perform more reliably, and act more safely.

Graph structured data is commonly used to represent complex relationships such as transactions between accounts, communications between devices, and dependencies among machines or processes. Correspondingly, graph anomaly detection (GAD) plays a critical role in identifying anomalies across various domains, including finance, cybersecurity, manufacturing, etc. Facing the large-volume and multi-domain graph data, recent efforts aim to develop foundational generalist models capable of detecting anomalies in unseen graphs without retraining. To the best of our knowledge, the different feature semantics and dimensions of cross-domain graph structured data heavily hinders the development of graph foundation model, and leaves the further in-depth continual learning and inference capabilities in the evolving setting a quite nascent problem. To address these above challenges, we propose OWLEYE, a novel zero-shot GAD framework that learns transferable patterns of normal behavior from multiple graphs. Systematically, OWLEYE first introduces a cross-domain feature alignment module to harmonize feature distributions, which preserves domain-specific semantics during aligning more than the simple but widely-used Principle Component Analysis. Second, with aligned features, to enable method with continuous and scaling-up learning and inference capabilities, OWLEYE designs the multi-domain pattern dictionary learning to encode shared structural and attribute-based patterns. Third, for achieving the in-context learning ability, OWLEYE presents a truncated attention-based reconstruction module to robustly detect anomalies without requiring labeled data for unseen graph structured data. Extensive experiments on real-world datasets demonstrate that OWLEYE achieves superior performance and generalizability compared to state-of-the-art baselines, establishing a strong foundation for scalable and label-efficient anomaly detection.

The widespread deployment of large language models (LLMs) across linguistic communities necessitates reliable multilingual safety alignment. However, recent efforts to extend alignment to other languages often require substantial resources, either through large-scale, high-quality supervision in the target language or through pairwise alignment with high-resource languages, which limits scalability. In this work, we propose a resource-efficient method for improving multilingual safety alignment. We introduce a plug-and-play Multi-Lingual Consistency (MLC) loss that can be integrated into existing monolingual alignment pipelines. By improving collinearity between multilingual representation vectors, our method encourages directional consistency at the multilingual semantic level in a single update. This allows simultaneous alignment across multiple languages using only multilingual prompt variants without requiring additional response-level supervision in low-resource languages. We validate the proposed method across different model architectures and alignment paradigms, and demonstrate its effectiveness in enhancing multilingual safety with limited impact on general model utility. Further evaluation across languages and tasks indicates improved cross-lingual generalization, suggesting the proposed approach as a practical solution for multilingual consistency alignment under limited supervision.

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs) parallelize across positions and thus appear promising for language generation, yet standard discrete diffusion typically needs hundreds to thousands of model evaluations to reach high quality, trading serial depth for iterative breadth. We introduce **FS-DFM**, Few-Step Discrete Flow-Matching. A discrete flow-matching model designed for speed without sacrificing quality. The core idea is simple: make the number of sampling steps an explicit parameter and train the model to be consistent across step budgets, so one big move lands where many small moves would. We pair this with a reliable update rule that moves probability in the right direction without overshooting, and with strong teacher guidance distilled from long-run trajectories. Together, these choices make few-step sampling stable, accurate, and easy to control. On language modeling benchmarks, FS-DFM with 8 sampling steps achieves perplexity parity with a 1\,024-step discrete-flow baseline for generating 1\,024 tokens using a similar-size model, delivering up to 128× faster sampling and corresponding latency/throughput gains.

Spiking Neural Networks (SNNs) have emerged as an efficient neuromorphic computing paradigm, offering low energy consumption and strong representational capacity through binary spike-based information processing. However, their performance is heavily shaped by the input encoding method. While direct encoding has gained traction for its efficiency and accuracy, it proves less robust than traditional rate encoding. To illuminate this issue, we introduce Gradient Temporal Collinearity (GTC), a principled measure that quantifies the directional alignment of gradient components across time steps, and we show—both empirically and theoretically—that elevated GTC in direct encoding undermines robustness. Guided by this insight, we propose Structured Temporal Orthogonal Decorrelation (STOD), which integrates parametric orthogonal kernels with structured constraints into the input layer of direct encoding to diversify temporal features and effectively reduce GTC. Extensive experiments on visual classification benchmarks, show that STOD consistently outperforms state-of-the-art methods in robustness, highlighting its potential to drive SNNs toward safer and more reliable deployment.

We study the problem of online learning in Stackelberg games with side information between a leader and a sequence of followers. In every round the leader observes contextual information and commits to a mixed strategy, after which the follower best-responds. We provide learning algorithms for the leader which achieve O(T^{1/2}) regret under bandit feedback, an improvement from the previously best-known rates of O(T^{2/3}). Our algorithms rely on a reduction to linear contextual bandits in the utility space: In each round, a linear contextual bandit algorithm recommends a utility vector, which our algorithm inverts to determine the leader's mixed strategy. We extend our algorithms to the setting in which the leader's utility function is unknown, and also apply it to the problems of bidding in second-price auctions with side information and online Bayesian persuasion with public and private states. Finally, we observe that our algorithms empirically outperform previous results on numerical simulations.

Speech emotion recognition (SER) hinges on front-ends that expose informative time-frequency (TF) structure from raw speech. Classical short-time Fourier and wavelet transforms impose fixed resolution trade-offs, while prior "superlet" variants rely on integer orders and hand-tuned hyperparameters. We revisit TF analysis from first principles and formulate a learnable continuum of superlet transforms. Starting from DC-corrected analytic Morlet wavelets, we define superlets as multiplicative ensembles of wavelet responses and realize learnable fractional orders via softmax-normalized weights over discrete orders, computed as a log-domain geometric mean. We establish admissibility (zero mean) and continuity in order and frequency, and characterize approximate analyticity by bounding negative-frequency leakage as a function of an effective cycle parameter. Building on these results, we introduce the Learnable Fractional Superlet Transform (LFST), a fully differentiable front-end that jointly optimizes (i) a monotone, log-spaced frequency grid, (ii) frequency-dependent base cycles, and (iii) learnable fractional-order weights, all trained end-to-end. LFST further includes a learnable asymmetric hard-thresholding (LAHT) module that promotes sparse, denoised TF activations while preserving transients; we provide sufficient conditions for boundedness and stability under mild cycle and grid constraints. To exploit LFST for SER, we design the Spectro-Temporal Emotion Encoder (STEE), which consumes two-channel TF maps, magnitude $S$ and phase-congruency $\kappa$, through a compact multi-scale stack with residual temporal and depthwise-frequency blocks, Adaptive FiLM gating, axial (time-axis) self-attention, global attentive pooling, and a lightweight classifier. The full LFST+STEE system is trained in a standard train-validate-test regime using focal loss with optional class rebalancing, and is validated on IEMOCAP, EMO-DB, and the private NSPL-CRISE dataset under standard protocols. By unifying a principled, learnable TF transform with a compact encoder, LFST+STEE replaces ad hoc front-ends with a mathematically grounded alternative that is differentiable, stable, and adaptable to data, enabling systematic ablations over frequency grids, cycle schedules, and fractional orders within a single end-to-end model. The source code for this paper is shared in this anonymous repository: https://anonymous.4open.science/r/LFST-for-SER-C5D2.

Objective assessment of audio source‑separation systems still mismatches subjective human perception, especially when interference from competing talkers and distortion of the target signal interact. We introduce Perceptual Separation (PS) and Perceptual Match (PM), a complementary pair of measures that, by design, isolate these leakage and distortion factors. Our intrusive approach generates a set of fundamental distortions, e.g., clipping, notch filter, and pitch shift from each reference waveform signal in the mixture. Distortions, references, and system outputs from all sources are independently encoded by a pre-trained self-supervised model, then aggregated and embedded with a manifold learning technique called diffusion maps, which aligns Euclidean distances on the manifold with dissimilarities of the encoded waveform representations. On this manifold, PM captures the self‑distortion of a source by measuring distances from its output to its reference and associated distortions, while PS captures leakage by also accounting for distances from the output to non‑attributed references and distortions. Both measures are differentiable and operate at a resolution as high as 75 frames per second, allowing granular optimization and analysis. We further derive, for both measures, frame-level deterministic error radius and non-asymptotic, high-probability confidence intervals. Experiments on English, Spanish, and music mixtures show that, against 14 widely used measures, the PS and PM are almost always placed first or second in linear and rank correlations with subjective human mean-opinion scores.