ICLR 2026 论文列表

The representer theorem is a cornerstone of kernel methods, which aim to estimate latent functions in reproducing kernel Hilbert spaces (RKHSs) in a nonparametric manner. Its significance lies in converting inherently infinite-dimensional optimization problems into finite-dimensional ones over dual coefficients, thereby enabling practical and computationally tractable algorithms. In this paper, we address the problem of estimating the latent triggering kernels--functions that encode the interaction structure between events--for linear multivariate Hawkes processes based on observed event sequences within an RKHS framework. We show that, under the principle of penalized least squares minimization, a novel form of representer theorem emerges: a family of transformed kernels can be defined via a system of simultaneous integral equations, and the optimal estimator of each triggering kernel is expressed as a linear combination of these transformed kernels evaluated at the data points. Remarkably, the dual coefficients are all analytically fixed to unity, obviating the need to solve a costly optimization problem to obtain the dual coefficients. This leads to a highly efficient estimator capable of handling large-scale data more effectively than conventional nonparametric approaches. Empirical evaluations on synthetic datasets reveal that the proposed method attains competitive predictive accuracy while substantially improving computational efficiency over existing state-of-the-art kernel method-based estimators.

A core challenge in modern AI model development is obtaining high-quality evaluation metrics in a cost-effective way. Such evaluation often involves tradeoffs between expensive, high-quality measurements and a variety of lower-quality proxies. We introduce Multiple-Prediction-Powered Inference (MultiPPI), a general framework for constructing statistically efficient estimates by optimally allocating resources across these diverse data sources. We provide theoretical guarantees about the minimax optimality, finite-sample performance, and asymptotic normality of the MultiPPI estimator. Through experiments across three diverse large language model (LLM) evaluation scenarios, we show that MultiPPI consistently achieves lower estimation error than existing baselines. This advantage stems from its budget-adaptive allocation strategy, which strategically combines subsets of models by learning their complex cost and correlation structures.

We study differentially private continual release of the number of distinct items in a stream, where items may be both inserted and deleted. In this turnstile setting, a recent work of Jain, Kalemaj, Raskhodnikova, Sivakumar, and Smith (NeurIPS '23) showed that for streams of length $T$, polynomial additive error of $\Omega(T^{1/4})$ is necessary, even without any space restrictions. We show that this additive error lower bound can be circumvented if the algorithm is allowed to output estimates with *multiplicative* error. We give an algorithm for the continual release of the number of distinct elements with $\text{polylog} (T)$ multiplicative and $\text{polylog}(T)$ additive error. We also show a qualitatively similar phenomenon for estimating the $F_2$ moment of a turnstile stream, where we can obtain $1+o(1)$ multiplicative and $\text{polylog} (T)$ additive error. Both results can be achieved by polylogarithmic space streaming algorithms where some multiplicative error is necessary even without privacy. Lastly, we raise questions aimed at better understanding trade-offs between multiplicative and additive error in private continual estimation problems.

Spatial intelligence is essential for multimodal large language models (MLLMs) operating in the complex physical world. Existing benchmarks, however, probe only single-image relations and thus fail to assess the multi-image spatial reasoning that real-world deployments demand. We introduce MMSI-Bench, a VQA benchmark dedicated to multi-image spatial intelligence. Six 3D-vision researchers spent more than 300 hours meticulously crafting 1,000 challenging, unambiguous multiple-choice questions from over 120,000 images, each paired with carefully designed distractors and a stepwise reasoning process. We conduct extensive experiments and evaluate 37 open-source and proprietary MLLMs, observing a wide gap: the strongest open-source model attains roughly 30\% accuracy and OpenAI's GPT-5 reasoning model reaches 40\%, while humans score 97\%. These results underscore the challenging nature of MMSI-Bench and the substantial headroom for future research. Leveraging the annotated reasoning processes, we also provide an automated error analysis pipeline that diagnoses four dominant failure modes, including (1) grounding errors, (2) overlap-matching and scene-reconstruction errors, (3) situation-transformation reasoning errors, and (4) spatial-logic errors, offering insights for advancing spatial intelligence.

Squared tensor networks (TNs) and their extension as computational graphs---squared circuits---have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces additional complexity when computing the partition function or marginalizing variables, which hinders their applicability in ML. To solve this issue, canonical forms of TNs are parameterized via unitary matrices to simplify the computation of marginals. However, these canonical forms do not apply to circuits, as they can represent factorizations that do not directly map to a known TN. Inspired by the ideas of orthogonality in canonical forms and determinism in circuits enabling tractable maximization, we show how to parameterize squared circuits to overcome their marginalization overhead. Our parameterizations unlock efficient marginalization even in factorizations different from TNs, but encoded as circuits, whose structure would otherwise make marginalization computationally hard. Finally, our experiments on distribution estimation show how our proposed conditions in squared circuits come with no expressiveness loss, while enabling more efficient learning.

As Vision Transformers (ViTs) become standard backbones across vision, a mechanistic account of their computational phenomenology is now essential. Despite architectural cues that hint at dynamical structure, there is no settled framework that interprets Transformer depth as a well-characterized flow. In this work, we introduce the $\textbf{Block-Recurrent Hypothesis (BRH)}$, arguing that trained ViTs admit a block-recurrent depth structure such that the computation of the original $L$ blocks can be accurately rewritten using only $k \ll L$ distinct blocks applied recurrently. Across diverse ViTs, between-layer representational similarity matrices suggest few contiguous phases. To determine whether this reflects reusable computation, we operationalize our hypothesis in the form of block recurrent surrogates of pretrained ViTs, which we call Recurrent Approximations to Phase-structured TransfORmers ($\texttt{Raptor}$). Using small-scale ViTs, we demonstrate that phase-structure metrics correlate with our ability to accurately fit $\texttt{Raptor}$ and identify the role of stochastic depth in promoting the recurrent block structure. We then provide an empirical existence proof for BRH in foundation models by showing that we can train a $\texttt{Raptor}$ model to recover $94$\% of DINOv2 ImageNet-1k linear probe accuracy in only 2 blocks. To provide a mechanistic account of these observations, we leverage our hypothesis to develop a program of $\textbf{Dynamical Interpretability}$. We find $\textit{\textbf{(i)}}$ directional convergence into class-dependent angular basins with self-correcting trajectories under small perturbations $\textit{\textbf{(ii)}}$ token-specific dynamics, where $\texttt{cls}$ executes sharp late reorientations while $\texttt{patch}$ tokens exhibit strong late-stage coherence reminiscent of a mean-field effect and converge rapidly toward their mean direction and $\textit{\textbf{(iii)}}$ a collapse of the update field to low rank in late depth, consistent with convergence to low-dimensional attractors. Altogether, we find that a compact recurrent program emerges along the depth of ViTs, pointing to a low-complexity normative solution that enables these models to be studied through principled dynamical systems analysis.

Identifying the vulnerabilities of large language models (LLMs) is crucial for improving their safety by addressing inherent weaknesses. Jailbreaks, in which adversaries bypass safeguards with crafted input prompts, play a central role in red-teaming by probing LLMs to elicit unintended or unsafe behaviors. Recent optimization-based jailbreak approaches iteratively refine attack prompts by leveraging LLMs. However, they often rely heavily on either binary attack success rate (ASR) signals, which are sparse, or manually crafted scoring templates, which introduce human bias and uncertainty in the scoring outcomes. To address these limitations, we introduce AMIS (Align to MISalign), a meta-optimization framework that jointly evolves jailbreak prompts and scoring templates through a bi-level structure. In the inner loop, prompts are refined using fine-grained and dense feedback using fixed scoring template. In the outer loop, the template is optimized using an ASR alignment score, gradually evolving to better reflect true attack outcomes across queries. This co-optimization process yields progressively stronger jailbreak prompts and more calibrated scoring signals. Evaluations on AdvBench and JBB-Behaviors demonstrate that AMIS achieves state-of-the-art performance, including 88.0% ASR on Claude-3.5-Haiku and 100.0% ASR on Claude-4-Sonnet, outperforming existing baselines by substantial margins.

Large language models (LLMs) excel at generating fluent text, but their internal reasoning remains opaque and difficult to control. Sparse autoencoders (SAEs) make hidden activations more interpretable by exposing latent features that often align with human concepts. Yet, these features are fragile and passive, offering no mechanism for systematic reasoning or model control. To address this, we introduce ActivationReasoning (AR), a framework that embeds explicit logical reasoning into the latent space of LLMs. It proceeds in three stages: (1) Finding latent representations, first latent concept representations are identified (e.g., via SAEs) and organized into a dictionary; (2) Activating propositions, at inference time AR detects activating concepts and maps them to logical propositions; and (3)Logical reasoning, applying logical rules over these propositions to infer higher-order structures, compose new concepts, and steer model behavior. We evaluate AR on multi-hop reasoning (PrOntoQA), abstraction and robustness to indirect concept cues (Rail2Country), reasoning over natural and diverse language (ProverQA), and context-sensitive safety (BeaverTails). Across all tasks, AR scales robustly with reasoning complexity, generalizes to abstract and context-sensitive tasks, and transfers across model backbones. These results demonstrate that grounding logical structure in latent activations not only improves transparency but also enables structured reasoning, reliable control, and alignment with desired behaviors, providing a path toward more reliable and auditable AI.

The classical optimal transport such as Kantorovich's optimal transport and partial optimal transport could be too restrictive in applications due to the full-mass or fixed-mass preservation constraints. To remedy this limitation, we propose elastic optimal transport (ELOT) which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It aims to answer the problem of how to transport the probability mass adaptively between probability distributions, which is a fundamental topic in various areas of artificial intelligence. The strength of elastic optimal transport is its capability to transport adaptive-mass in the light of the geometry structure of the problem itself. As an application example in machine learning, we apply elastic optimal transport to both unsupervised domain adaptation and partial domain adaptation tasks. It adaptively transports masses from source domain to target domain by taking domain shift into consideration and respecting the ubiquity of noises or outliers in the data, in order to improve the generalization performance. The experiment results on the benchmarks show that ELOT significantly outperforms the state-of-the-art methods. As a powerful distribution matching tool, elastic optimal transport might be of interests to the broad areas such as artificial intelligence, healthcare, physics, operations research, urban science, etc. The source code is available in the supplementary material.

Large language models (LLMs) are increasingly deployed in multi-agent systems (MAS) as components of collaborative intelligence, where peer interactions dynamically shape individual decision-making. While prior work has largely focused on conformity bias, we broaden the scope to examine how LLMs build rapport from previous interactions, resist misinformation, and integrate peer input during collaboration, which are key factors for achieving collective intelligence under complex social dynamics. We introduce KAIROS, a benchmark simulating quiz contests with peer agents of varying reliability, offering fine-grained control over conditions such as expert–novice roles, noisy crowds, and adversarial peers. LLMs receive both historical interactions and current peer responses, allowing systematic investigation into how rapport, peer action, and self-confidence influence decisions. To mitigate this vulnerability, we evaluate prompting, supervised fine-tuning, and reinforcement learning using Group Relative Policy Optimization (GRPO) across multiple models. Our results show that model size plays a central role in moderating susceptibility to social influence: larger models exhibit stronger resilience and benefit from prompting-based mitigation, whereas smaller models are more vulnerable. For the latter, carefully configured GRPO training improves both robustness and overall performance. Our code and datasets are available at: https://anonymous.4open.science/r/KAIROS-4F71

The alignment of representations from different modalities has recently been shown to provide insights on the structural similarities and downstream capabilities of different encoders across diverse data types. While significant progress has been made in aligning images with text, the temporal nature of _video_ data remains largely unexplored in this context. In this work, we conduct the first comprehensive study of video-text representation alignment, probing the capabilities of modern video and language encoders. Our findings reveal several key insights. First, we demonstrate that cross-modal alignment highly depends on the richness of both visual (static images vs. multi-frame videos) and text (single caption vs. a collection) data _provided at test time_, especially when using state-of-the-art video encoders. We propose parametric test-time scaling laws that capture this behavior and show remarkable predictive power against empirical observations. Secondly, we investigate the correlation between semantic alignment and performance on both semantic and non-semantic downstream tasks, providing initial evidence that strong alignment against text encoders may be linked to _general-purpose_ video representation and understanding. Finally, we correlate temporal reasoning with cross-modal alignment providing a challenging test-bed for vision and language models. Overall, our work introduces video-text alignment as an informative zero-shot way to probe the representation power of different encoders for spatio-temporal data.

Density ratio estimation (DRE) is fundamental in machine learning and statistics, with applications in domain adaptation and two-sample testing. However, DRE methods are highly sensitive to hyperparameter selection, with suboptimal choices often resulting in poor convergence rates and empirical performance. To address this issue, we propose a novel model aggregation algorithm for DRE that trains multiple models with different hyperparameter settings and aggregates them. Our aggregation provably achieves minimax-optimal error convergence without requiring prior knowledge of the smoothness of the unknown density ratio. Our method surpasses cross-validation-based model selection and model averaging baselines for DRE on standard benchmarks for DRE and large-scale domain adaptation tasks, setting a new state of the art on image and text data.

Existing red-teaming benchmarks, when adapted to new languages via direct translation, fail to capture socio-technical vulnerabilities rooted in local culture and law, creating a critical blind spot in LLM safety evaluation. To address this gap, we introduce CAGE (Culturally Adaptive Generation), a framework that systematically adapts the adversarial intent of proven red-teaming prompts to new cultural contexts. At the core of CAGE is the Semantic Mold, a novel approach that disentangles a prompt's adversarial structure from its cultural content. This approach enables the modeling of realistic, localized threats rather than testing for simple jailbreaks. As a representative example, we demonstrate our framework by creating KoRSET, a Korean benchmark, which proves more effective at revealing vulnerabilities than direct translation baselines. CAGE offers a scalable solution for developing meaningful, context-aware safety benchmarks across diverse cultures.

Following OpenAI's introduction of the ``thinking with images'' concept, recent efforts have explored stimulating the use of visual information in the reasoning process to enhance model performance in perception and reasoning tasks. However, to the best of our knowledge, no open-source work currently offers a feature set as rich as proprietary models (OpenAI O3), which can perform diverse image manipulations and simultaneously enhance logical reasoning capabilities through code. In this paper, we make a preliminary attempt in this direction by introducing \textbf{Thyme} (\textbf{Th}ink Be\textbf{y}ond I\textbf{m}ag\textbf{e}s), a novel paradigm for enabling multimodal large language models to transcend existing ``think with images'' approaches by autonomously generating and executing diverse image processing and computational operations via executable code (Figure 2). This approach not only facilitates a rich, on-the-fly set of image manipulations (e.g., cropping, rotation, contrast enhancement), but also allows for mathematical computations, all while maintaining high autonomy in deciding when and how to apply these operations. We activate this capability through a two-stage training strategy: an initial Supervised Fine-Tuning (SFT) on a curated dataset of 500K samples to teach code generation, followed by a Reinforcement Learning (RL) phase to refine decision-making. For the RL stage, we manually collect and design high-resolution question-answer pairs to increase the learning difficulty, and we propose \textbf{GRPO-ATS} (Group Relative Policy Optimization with Adaptive Temperature Sampling), an algorithm that applies distinct temperatures to text and code generation to balance reasoning exploration with code execution precision. We conduct extensive experimental analysis and ablation studies. As shown in Figure 1, comprehensive evaluations on nearly 20 benchmarks show that Thyme yields significant and consistent performance gains, particularly in challenging high-resolution perception and complex reasoning tasks.

AI tasks differ in complexity and are best addressed with different computation strategies (e.g., combinations of models and decoding methods). Hence, an effective routing system that maps tasks to the appropriate strategies is crucial. Most prior methods build the routing framework by training a *single* model across *all* strategies, which demands full retraining whenever new strategies appear and leads to high overhead. Attempts at such continual routing, however, often face difficulties with generalization. Prior models also typically use a *single* input representation, limiting their ability to capture the full complexity of the routing problem and leading to sub-optimal routing decisions. To address these gaps, we propose CONCUR, a **con**tinual routing framework that supports both **c**onstrained and **u**nconstrained **r**outing (i.e., routing with or without a budget). Our *modular* design trains a separate predictor model for each strategy, enabling seamless incorporation of new strategies with low additional training cost. Our predictors also leverage *multiple* representations of both tasks and computation strategies to better capture overall problem complexity. Experiments on both in-distribution and out-of-distribution, knowledge- and reasoning-intensive tasks show that our method outperforms the best single strategy and strong existing routing techniques with higher end-to-end accuracy and lower inference cost in both continual and non-continual settings, while also reducing training cost in the continual setting.

Large Language Models (LLMs) have recently demonstrated strong capabilities in tool use, yet progress in tool retrieval remains hindered by incomplete and heterogeneous tool documentation. To address this challenge, we introduce Tool-DE, a new benchmark and framework that systematically enriches tool documentation with structured fields to enable more effective tool retrieval, together with two dedicated models, Tool-Embed and Tool-Rank. We design a scalable document expansion pipeline that leverages both open- and closed-source LLMs to generate, validate, and refine enriched tool profiles at low cost, producing large-scale corpora with 50k instances for embedding-based retrievers and 200k for rerankers. On top of this data, we develop two models specifically tailored for tool retrieval: Tool-Embed, a dense retriever, and Tool-Rank, an LLM-based reranker. Extensive experiments on ToolRet and Tool-DE demonstrate that document expansion substantially improves retrieval performance, with Tool-Embed and Tool-Rank achieving new state-of-the-art results on both benchmarks. We further analyze the contribution of individual fields to retrieval effectiveness, as well as the broader impact of document expansion on both training and evaluation. Overall, our findings highlight both the promise and limitations of LLM-driven document expansion, positioning Tool-DE, along with the proposed Tool-Embed and Tool-Rank, as a foundation for future research in tool retrieval.

Diffusion language models (DLMs) have recently emerged as an alternative to autoregressive approaches, offering parallel sequence generation and flexible token orders. However, their inference remains slower than that of autoregressive models, primarily due to the cost of bidirectional attention and the large number of refinement steps required for high-quality outputs. In this work, we highlight and leverage an overlooked property of DLMs, **early answer convergence**: in many cases, the correct answer can be internally identified by half steps before the final decoding step, both under semi-autoregressive and random re-masking schedules. For example, on GSM8K and MMLU, up to 97\% and 99\% of instances, respectively, can be decoded correctly using only half of the refinement steps. Building on this observation, we introduce **Prophet**, a training-free fast decoding paradigm that enables **early commit decoding**. Specifically, Prophet dynamically decides whether to continue refinement or to go ''all-in'' (i.e., decode all remaining tokens in one step), using the confidence gap between the top-2 prediction candidates as the criterion. It integrates seamlessly into existing DLM implementations, incurs negligible overhead, and requires no additional training. Empirical evaluations of LLaDA-8B and Dream-7B across multiple tasks show that Prophet reduces the number of decoding steps by up to 3.4$\times$ while preserving high generation quality. These results recast DLM decoding as a problem of ''when to stop refinement'', and demonstrate that early decode convergence provides a simple yet powerful mechanism for accelerating DLM inference, complementary to existing speedup techniques. Our code is submitted.

Deep learning models excel in stationary settings but suffer from loss of plasticity (LoP) in non-stationary environments. While prior literature characterizes LoP through symptoms like rank collapse of representations, it often lacks a mechanistic explanation for why gradient descent fails to recover from these states. This work presents a first-principles investigation grounded in dynamical systems theory, formally defining LoP not merely as a statistical degradation, but as an entrapment of gradient dynamics within invariant sub-manifolds of the parameter space. We identify two primary mechanisms that create these traps: frozen units from activation saturation and cloned-unit manifolds from representational redundancy. Crucially, our framework uncovers a fundamental tension: the very mechanisms that promote generalization in static settings, such as low-rank compression, actively steer the network into these LoP manifolds. We validate our theoretical analysis with numerical simulations and demonstrate how architectural interventions can destabilize these manifolds to restore plasticity.

Incorporating knowledge graphs (KGs) into large language model (LLM) reasoning has shown promise in alleviating hallucinations and factual errors. Although existing paradigms of KG-augmented LLMs have achieved encouraging results, they still exhibit notable limitations when handling multi-hop reasoning and complex logical queries: (1) search space truncation bias: current methods generate linear entity-relation reasoning paths, which can prune correct candidates prematurely during iterative exploration; and (2) entity error amplification: existing methods typically follow the retrieve-and-answer paradigm which causes LLMs to over-rely on retrieved evidence, exacerbating the impact of incorrect entities during reasoning. To alleviate the existing challenges, we propose Plan-Answer-Refine-on-Graph (PARoG), a novel framework for LLM reasoning on knowledge graphs. First, PARoG leverages SPARQL queries from KG data as references, decomposing them into structured step-by-step plans. We further train LLMs to construct such structured plans, which improves the logical consistency of reasoning, ensures uniform step granularity, and facilitates effective execution on the graph. Second, during reasoning over KGs, PARoG adopts a plan-answer-refine paradigm: the model first attempts to answer each sub-query independently, and then refines its prediction by integrating evidence retrieved from the KG. This process mitigates knowledge conflicts between LLM and KG, substantially reducing hallucinations. Experimental results on multiple KG reasoning benchmarks demonstrate that PARoG significantly outperforms state-of-the-art approaches, achieving especially superior accuracy on multi-hop and logically complex queries.