ICLR 2026 Papers

A fundamental challenge in data synthesis is protecting the fairness and privacy of the individual, particularly in data-scarce environments where underrepresented groups are at risk of further marginalization by reproducing the biases inherent in the data modeling process. We introduce a privacy- and fairness-aware for a class of generative models, which fuses the conditional generator within the framework of Bayesian nonparametric learning (BNPL). This conditional structure imposes fairness constraints in our generative model by minimizing the mutual information between generated outcomes and protected attributes. Unlike existing methods that primarily focus on sensitive binary-valued attributes, our framework extends seamlessly to non-binary attributes. Moreover, our method provides a systematic solution to class imbalance, ensuring adequate representation of underrepresented protected groups. Our proposed approach offers a scalable, privacy-preserving framework for ethical and equitable data generation, which we demonstrate by theoretical guarantees and extensive experiments on sensitive empirical examples.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven to be a highly effective strategy for empowering Large Language Models (LLMs) with long chain-of-thought reasoning abilities. However, its design and optimizations remain tailored to purely textual domains, resulting in suboptimal performance when applied to multimodal reasoning tasks. In particular, we observe that a major source of error (67%) in current multimodal reasoning lies in the perception of visual inputs. To address this bottleneck, we propose PAPO, a novel policy gradient algorithm that encourages the model to generate visually grounded reasoning without external supervision. Specifically, we introduce the Implicit Perception Loss in the form of a KL divergence term, which maximizes the difference between two probability distributions over the same rollout sequence, conditioned on either the original or corrupted visual input. Notably, PAPO does not rely on any additional data annotation, reward models, or stronger teacher models, and can therefore be seamlessly integrated into mainstream RLVR algorithms such as GRPO and DAPO. To further enhance the training stability of PAPO, we introduce the Double Entropy Loss, which effectively regularizes the new KL objective without compromising performance. Despite its simplicity, PAPO yields significant overall improvements of 4.4%-17.5% on diverse multimodal benchmarks. The improvements are more pronounced, approaching 8.0%-19.1%, on tasks with high vision dependency. We also observe a substantial reduction of 30.5% in perception errors, indicating improved perceptual capabilities with PAPO. Overall, PAPO offers a new perspective on advancing multimodal RLVR via the optimization objective, moving beyond rollout or reward design and pointing toward deeper integration of perception and reasoning.

Evaluating the quality of a clustering result without access to ground truth labels is fundamental for research in data mining. However, most cluster validation indices (CVIs) do not consider the noise assignments by density-based clustering methods like DBSCAN or HDBSCAN, even though the ability to correctly determine noise is paramount to successful clustering. In this paper, we propose DISCO, a **D**ensity-based **I**nternal **S**core for **C**lusterings with n**O**ise, the first CVI to explicitly assess the *quality* of noise assignments rather than merely counting them. DISCO is based on the Silhouette Coefficient, but adopts density-connectivity to evaluate clusters of arbitrary shapes, and proposes explicit noise evaluation: it rewards correctly assigned noise labels and penalizes noise labels where a cluster label would have been more appropriate. The pointwise definition of DISCO allows for the seamless integration of noise evaluation into the final clustering evaluation, while also enabling explainable evaluations of the clustered data. In contrast to most state-of-the-art, DISCO is well-defined and also covers edge cases that regularly appear as output from clustering algorithms, such as singleton clusters or a single cluster plus noise.

Prompt evolution algorithms offer a powerful paradigm for enhancing AI systems based on closed-source models, while few work explores whether aggregating results from multiple prompts to reach a consensus can further advance the system capability boundary. In this paper, we introduce Consensus-Evolve (C-Evolve), an evolutionary algorithm that discovers a group of prompts whose aggregated outputs after majority voting achieve optimal performance. More specifically, C-Evolve employs an island-based evolutionary algorithm to maintain population diversity, and prompts from distinct islands are selected to form groups to aggregate their outputs. The key difference from single individual evolution is a voting score, which evaluates each individual prompt's contribution within groups. We take this as the fitness score for evolution instead of individual performance. Consequently, C-Evolve is more likely to produce and maintain prompts with higher potential to form a high-performing group and eliminate low-performing ones, gradually improving the group performance after reaching consensus. Our method achieves state-of-the-art performance across a wide range of tasks, including both open-ended tasks like HotpotQA and closed-ended tasks like MATH. On Qwen3-8B, C-Evolve achieves 70.67\% on HotpotQA and 43.88\% on IFBench, which are 4.95\% and 2.73\% higher than GEPA, respectively. For GPT-4.1-mini, the accuracy on IFBench is further improved to 47.96\% and reaches 95.33\% in the MATH benchmark. These results demonstrate the C-Evolve's competitive performance.

We study how large language models (LLMs) “think” through their representation space. We propose a novel geometric framework that models an LLM’s reasoning as flows—embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows’ velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomenon, offering a new lens for interpretability and formal analysis of LLMs' behavior.

Predictive coding networks (PCNs) offer a local-learning alternative to backpropagation in which layers communicate residual errors, aligning well with biological computation and neuromorphic hardware. In this work we introduce Difference Predictive Coding (DiffPC), a spike-native PC formulation for spiking neural networks. DiffPC replaces dense floating-point messages with sparse ternary spikes, provides spike-compatible target and error updates, and employs adaptive threshold schedules for event-driven operation. We validate DiffPC on fully connected and convolutional architectures, demonstrating competitive performance on MNIST (99.3\%) and Fashion-MNIST (89.6\%), and outperforming a backpropagation baseline on CIFAR-10. Crucially, this performance is achieved with high communication sparsity, reducing data movement by over two orders of magnitude compared to standard predictive coding. DiffPC thus establishes a faithful, hardware-aligned framework for communication-efficient training on neuromorphic platforms.

We present GRAPE (Group RepresentAtional Position Encoding), a unified framework for positional encoding based on group actions. GRAPE brings together two families of mechanisms: (i) multiplicative rotations (Multiplicative GRAPE) in $\operatorname{SO}(d)$ and (ii) additive logit biases (Additive GRAPE) arising from unipotent actions in the general linear group $\mathrm{GL}$. In Multiplicative GRAPE, a position $n\in\mathbb{Z}$ (or $t\in\mathbb{R}$) acts as $\mathbf{G}(n)=\exp(n\,\omega\,\mathbf{L})$ with a rank‑2 skew generator $\mathbf{L} \in \mathbb{R}^{d \times d}$, yielding a relative, compositional, norm‑preserving map with a closed‑form matrix exponential. RoPE is recovered exactly when the $d/2$ planes are the canonical coordinate pairs with log‑uniform spectrum. Learned commuting subspaces and compact non‑commuting mixtures strictly extend this geometry to capture cross-subspace feature coupling at $O(d)$ and $O(rd)$ cost per head, respectively. In Additive GRAPE, additive logits arise as rank‑1 (or low‑rank) unipotent actions, recovering ALiBi and the Forgetting Transformer (FoX) as exact special cases while preserving an exact relative law and streaming cacheability. Altogether, GRAPE supplies a principled design space for positional geometry in long‑context models, subsuming RoPE and ALiBi as special cases.

Transformer-based PDE surrogates achieve remarkable performance but face two key challenges: fixed patch sizes cause systematic error accumulation at harmonic frequencies, and computational costs remain inflexible regardless of problem complexity or available resources. We introduce Overtone, a unified solution through dynamic patch size control at inference. Overtone's key insight is that cyclically modulating patch sizes during autoregressive rollouts distributes errors across the frequency spectrum, preventing the systematic harmonic artifacts that plague fixed-patch models. We implement this through two architecture-agnostic modules—CSM (Cyclic Stride Modulator, using dynamic stride modulation) and CKM (Cyclic Kernel Modulator, using dynamic kernel resizing)—that together provide both harmonic mitigation and compute-adaptive deployment. The harmonic mitigation alone yields up to 40% error reduction in long rollouts, while the flexible tokenization allows users to trade accuracy for speed dynamically based on computational constraints. Applied to challenging 2D and 3D PDE benchmarks, a single Overtone model matches or exceeds multiple fixed-patch baselines across all compute budgets.

Cross-modal image translation remains brittle and inefficient. Standard diffusion approaches often rely on a single, global linear transfer between domains. We find that this shortcut forces the sampler to traverse off-manifold, high-cost regions, inflating the correction burden and inviting semantic drift. We refer to this shared failure mode as fixed-schedule domain transfer. In this paper, we embed domain-shift dynamics directly into the generative process. Our model predicts a spatially varying mixing field at every reverse step and injects an explicit, target-consistent restoration term into the drift. This in-step guidance keeps large updates on-manifold and shifts the model’s role from global alignment to local residual correction. We provide a continuous-time formulation with an exact solution form and derive a practical first-order sampler that preserves marginal consistency. Empirically, across translation tasks in medical imaging, remote sensing, and electroluminescence semantic mapping, our framework improves structural fidelity and semantic consistency while converging in fewer denoising steps.

First-last frame video generation has recently gained significant attention. It enables coherent motion generation between specified first and last frames. However, this approach suffers from semantic degradation in intermediate frames, causing scene distortion and subject deformation that undermine temporal consistency. To address this issue, we introduce **Anchor Frame Bridging (AFB)**, a novel plug-and-play method that explicitly bridges semantic continuity from boundary frames to intermediate frames, offering training-free adaptability and generalizability. By adaptively interpolating anchor frames at temporally critical locations exhibiting maximal semantic discontinuities, our approach effectively mitigates semantic drift in intermediate frames. Specifically, we propose an **adaptive anchor frame selection** module, which generates text-aligned candidate frames via frame order reversal and selects anchors based on semantic continuity. Subsequently, we develop **anchor frame guided generation**, which leverages the selected anchor frames to guide semantic propagation across intermediate frames, ensuring consistent boundary semantics and preserving temporal coherence throughout the video sequence. The final video is synthesized using the first frame, last frame, selected anchor frames, and the text prompt. The results demonstrate that our method significantly enhances the temporal consistency and overall quality of generated videos. Specifically, when applied to the Wan2.1-I2V model, it yields improvements of 16.58\% in FVD and 10.21\% in PSNR. The codes are provided in the supplementary material.

Agentic language model (LM) systems have rapidly become central to modern workflows, powering applications like "Deep Research" and "Claude Code." As contexts grow beyond what even the largest frontier models can process effectively, multi-LM architectures have emerged to overcome context limitations. Beneath their apparent diversity lies a recurring pattern: smaller "compressor" LMs distill raw context into compact text that is then consumed by larger "predictor" LMs that interact with the user. Despite their popularity, the design of compressor-predictor systems remains largely ad hoc. Little guidance exists on how compressor and predictor choices shape downstream performance. In practice, attributing gains to compression versus prediction requires exhaustive pairwise sweeps, which is costly and task-specific. We argue that these agentic system design questions are, at root, information-theoretic. Viewing the compressor LM as a "noisy channel", we introduce a simple estimator of the mutual information between the context and its compression to quantify compression quality in a task-independent way. We show that mutual information strongly predicts downstream performance, independent of any specific task. Through an information-theoretic framework, we perform a comprehensive empirical analysis across five datasets and three model families. Results reveal that larger compressors not only are more accurate, but also more token-efficient, conveying more bits of information per token. A 7B Qwen-2.5 compressor, for instance, is $1.6\times$ more accurate, $4.6\times$ more concise, and conveys $5.5\times$ more bits of mutual information per token. Across the datasets studied, scaling compressors is substantially more effective than scaling predictors, enabling larger on-device compressors to pair with smaller cloud predictors. When applied to a Deep Research system, these principles enable local compressors as small as 3B parameters to recover 99% of frontier-LM accuracy at 26% of API costs.

The Model Context Protocol (MCP) standardizes how large language model (LLM) agents discover, describe, and call external tools. While MCP unlocks broad interoperability, it also enlarges the attack surface by making tools first-class, composable objects with natural-language metadata, and standardized I/O. We present MSB (MCP Security Benchmark), the first end-to-end evaluation suite that systematically measures how well LLM agents resist MCP-specific attacks throughout the full tool-use pipeline: task planning, tool invocation, and response handling. MSB contributes: (1) a taxonomy of 12 attacks including name-collision, preference manipulation, prompt injections embedded in tool descriptions, out-of-scope parameter requests, user-impersonating responses, false-error escalation, tool-transfer, retrieval injection, and mixed attacks; (2) an evaluation harness that executes attacks by running real tools (both benign and malicious) via MCP rather than simulation; and (3) a robustness metric that quantifies the trade-off between security and performance: Net Resilient Performance (NRP). We evaluate nine popular LLM agents across 10 domains and 405 tools, producing 2,000 attack instances. Results reveal the effectiveness of attacks against each stage of MCP. Models with stronger performance are more vulnerable to attacks due to their outstanding tool calling and instruction following capabilities. MSB provides a practical baseline for researchers and practitioners to study, compare, and harden MCP agents.

Is bigger always better for time series foundation models? With the question in mind, we explore an alternative to training a single, large monolithic model: building a portfolio of smaller, pretrained forecasting models. By applying ensembling or model selection over these portfolios, we achieve competitive performance on large-scale benchmarks using much fewer parameters. We explore strategies for designing such portfolios and find that collections of specialist models consistently outperform portfolios of independently trained generalists. Remarkably, we demonstrate that post-training a base model is a compute-effective approach for creating sufficiently diverse specialists, and provide evidences that ensembling and model selection are more compute-efficient than test-time fine-tuning.

Text-to-image (T2I) generation aims to synthesize images from textual prompts, which jointly specify what must be shown and imply what can be inferred, which thus correspond to two core capabilities: \textbf{\textit{composition}} and \textbf{\textit{reasoning}}. Despite recent advances of T2I models in both composition and reasoning, existing benchmarks remain limited in evaluation. They not only fail to provide comprehensive coverage across and within both capabilities, but also largely restrict evaluation to low scene density and simple one-to-one reasoning. To address these limitations, we propose \textbf{\textsc{T2I-CoReBench}}, a comprehensive and complex benchmark that evaluates both composition and reasoning capabilities of T2I models. To ensure comprehensiveness, we structure composition around scene graph elements (\textit{instance}, \textit{attribute}, and \textit{relation}) and reasoning around the philosophical framework of inference (\textit{deductive}, \textit{inductive}, and \textit{abductive}), formulating a 12-dimensional evaluation taxonomy. To increase complexity, driven by the inherent real-world complexities, we curate each prompt with higher compositional density for composition and greater reasoning intensity for reasoning. To facilitate fine-grained and reliable evaluation, we also pair each evaluation prompt with a checklist that specifies individual \textit{yes/no} questions to assess each intended element independently. In statistics, our benchmark comprises $1,080$ challenging prompts and around $13,500$ checklist questions. Experiments across 28 current T2I models reveal that their composition capability still remains limited in high compositional scenarios, while the reasoning capability lags even further behind as a critical bottleneck, with all models struggling to infer implicit elements from prompts.

Reinforcement learning from human feedback (RLHF) has proven effectiveness for aligning text-to-image (T2I) diffusion models with human preferences. Although Direct Preference Optimization (DPO) is widely adopted for its computational efficiency and avoidance of explicit reward modeling, its applications to diffusion models have primarily relied on pairwise preferences. The precise optimization of listwise preferences remains largely unaddressed. In practice, human feedback on image preferences often contains implicit ranked information, which conveys more precise human preferences than pairwise comparisons. In this work, we propose Diffusion-LPO, a simple and effective framework for Listwise Preference Optimization in diffusion models with listwise data. Given a caption, we aggregate user feedback into a ranked list of images and derive a listwise extension of the DPO objective under the Plackett–Luce model. Diffusion-LPO enforces consistency across the entire ranking by encouraging each sample to be preferred over all of its lower-ranked alternatives. We empirically demonstrate the effectiveness of Diffusion-LPO across various tasks, including text-to-image generation, image editing, and personalized preference alignment. Diffusion-LPO consistently outperforms pairwise DPO baselines on visual quality and preference alignment.

Achieving optimality and adversarial robustness in deep reinforcement learning has long been regarded as conflicting goals. Nonetheless, recent theoretical insights presented in CAR suggest a potential alignment, raising the important question of how to realize this in practice. This paper first identifies a key gap between theory and practice by comparing standard policy optimization (SPO) and adversarially robust policy optimization (ARPO). Although they share theoretical consistency, *a fundamental tension between robustness and optimality arises in practical policy gradient methods*. SPO tends toward convergence to vulnerable first-order stationary policies (FOSPs) with strong natural performance, whereas ARPO typically favors more robust FOSPs at the expense of reduced returns. Furthermore, we attribute this tradeoff to the *reshaping effect of the strongest adversaries* in ARPO, which significantly complicates the global landscape by inducing *deceptive sticky FOSPs*. This improves robustness but makes navigation more challenging. To alleviate this, we develop the *BARPO*, a bilevel framework unifying SPO and ARPO by modulating adversary strength, thereby facilitating navigability while preserving global optima. Extensive empirical results demonstrate that BARPO consistently outperforms vanilla ARPO, providing a practical approach to reconcile theoretical and empirical performance.

Large language models (LLMs) are increasingly trained on tabular data, which, unlike unstructured text, often contains personally identifiable information (PII) in a highly structured and explicit format. As a result, privacy risks arise, since sensitive records can be inadvertently retained by the model and exposed through data extraction or membership inference attacks (MIAs). While existing MIA methods primarily target textual content, their efficacy and threat implications may differ when applied to structured data, due to its limited content, diverse data types, unique value distributions, and column-level semantics. In this paper, we present Tab-MIA, a benchmark dataset for evaluating MIAs on tabular data in LLMs and demonstrate how it can be used. Tab-MIA comprises five data collections, each represented in six different encoding formats. Using our Tab-MIA benchmark, we conduct the first evaluation of state-of-the-art MIA methods on LLMs fine-tuned with tabular data across multiple encoding formats. In the evaluation, we analyze the memorization behavior of pretrained LLMs on structured data derived from Wikipedia tables. Our findings show that LLMs memorize tabular data in ways that vary across encoding formats, making them susceptible to extraction via MIAs. Even when fine-tuned for as few as three epochs, models exhibit high vulnerability, with AUROC scores approaching 90% in most cases. Tab-MIA enables systematic evaluation of these risks and provides a foundation for developing privacy-preserving methods for tabular data in LLMs.

Reinforcement Learning (RL) can directly enhance the reasoning capabilities of large language models without extensive reliance on Supervised Fine-Tuning (SFT). In this work, we revisit the traditional Policy Gradient (PG) mechanism and propose a minimalist RL approach termed Group Policy Gradient (GPG). Unlike conventional methods, GPG directly optimizes the original RL objective, thus obviating the need for surrogate loss functions. By eliminating the critic and reference models, avoiding KL divergence constraints, and addressing the advantage and gradient estimation bias, our approach significantly simplifies the training process compared to Group Relative Policy Optimization (GRPO). Our approach achieves superior performance without relying on auxiliary techniques or adjustments. As illustrated in Figure 1, extensive experiments demonstrate that our method not only reduces computational costs but also consistently outperforms GRPO across various unimodal and multimodal tasks.

This paper investigates the application of Large Language Models (LLMs) in Automated Heuristic Design (AHD), where their integration into evolutionary frameworks reveals a significant gap in global control and long-term learning. We propose the Hindsight-Foresight Prompt (HiFo-Prompt), a novel framework for LLM-based AHD designed to overcome these limitations. This is achieved through two synergistic strategies: Foresight and Hindsight. Foresight acts as a high-level meta-controller, monitoring population dynamics(e.g., stagnation and diversity collapse) to switch the global search strategy between exploration and exploitation explicitly. Hindsight builds a persistent knowledge base by distilling successful design principles from past generations, making this knowledge reusable. This dual mechanism ensures that the LLM is not just a passive operator but an active reasoner, guided by a global plan (Foresight) while continuously improving from its cumulative experience (Hindsight). Empirical results demonstrate that HiFo-Prompt significantly outperforms a comprehensive suite of state-of-the-art AHD methods, discovering higher-quality heuristics with substantially improved convergence speed and query efficiency. Our code is available at https://github.com/Challenger-XJTU/HiFo-Prompt.