ICML 2026 Papers

Influence maximization is an important research area in social network analysis, where the goal is to select a small set of seed nodes so as to maximize the expected spread of influence under a stochastic diffusion process. Classical approximation algorithms for this problem rely on full knowledge of the underlying influence probabilities and operate in an offline manner. In many real-world settings, however, these probabilities are unknown and must be learned from data, raising the question: \emph{can one still obtain strong performance guarantees while simultaneously learning the diffusion model parameters through repeated interactions?} In this paper, we study the problem of \emph{online influence maximization} under the independent cascade model, where influence probabilities are unknown and feedback is limited to \emph{node-level} activation outcomes. Prior work relies on a \emph{pair oracle} which needs to perform a joint optimization over seed sets and feasible parameters. This oracle is difficult to implement in practice and it was open whether one can achieve sublinear regret using only a \emph{standard} offline oracle. We resolve this question by designing an online learning algorithm that achieves $\widetilde{O}(\sqrt{T})$ regret using only a \emph{standard} offline oracle. Finally, we validate our theoretical results via experiments on real and synthetic data.

Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher’s own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization, its formal guarantees remain limited. We study SD for ridge regression with an unconstrained mixing weight $\xi \in \mathbb{R}$. Conditional on the training data and without any distributional assumptions, we prove that for any squared prediction risk $R$ (including out-of-distribution), the optimally mixed student strictly improves upon the ridge teacher at every regularization level $\lambda$ where the teacher risk is not stationary ($R'(\lambda) \neq 0$). We also characterize the optimal mixing weight $\xi^\star$ in terms of the risk derivative $R'$, showing that it can be negative, which is the case in over-regularized regimes. To quantify SD risk improvements, we derive exact risk asymptotics in the proportional asymptotics regime for general anisotropic covariance and deterministic signals. From a practical standpoint, we propose a consistent one-shot tuning method to estimate $\xi^\star$ without grid search, sample splitting, or refitting. Experiments on real-world datasets and pretrained neural network features support our theory and the one-shot tuning method.

Large Language Models (LLMs) are rarely static and are frequently updated in practice. A growing body of alignment research has shown that models initially deemed ``aligned'' can exhibit misaligned behavior after fine-tuning. These works typically assume that the initial model is aligned based on static black-box evaluation, i.e., the absence of undesired responses to a fixed set of queries. However, the limits of black-box evaluation for post-update scenarios is not explored sufficiently. In this work, we formalize model alignment in both the static and post-update settings and uncover a fundamental limitation of black-box evaluation. We theoretically show that, due to overparameterization, static alignment provides no guarantee of post-update alignment for *any* update dataset. Moreover, we prove that static black-box probing cannot distinguish a model that is genuinely post-update robust from one that conceals an arbitrary amount of adversarial behavior which can be activated by even a single benign gradient update. We further validate these findings empirically in LLMs across three core alignment domains: privacy, jailbreak safety, and behavioral honesty. We demonstrate the existence of LLMs that pass all standard black-box alignment tests, yet become severely misaligned after a single benign update. Finally, we show that the capacity to hide such latent adversarial behavior increases with model scale, confirming our theoretical prediction that post-update misalignment grows with the number of parameters. Together, our results highlight the inadequacy of static evaluation protocols and emphasize the urgent need for post-update--robust alignment evaluation. Code can be found [here](https://github.com/Ybakman/safety_benign_update).

We introduce a problem of fairly allocating indivisible goods (items) in which the agents' valuations cannot be observed directly, but instead can only be accessed via noisy queries. In the two-agent setting with Gaussian noise and bounded valuations, we derive upper and lower bounds on the required number of queries for finding an envy-free allocation in terms of the number of items, $m$, and the negative-envy of the optimal allocation, $\Delta$. In particular, when $\Delta$ is not too small (namely, $\Delta \gg m^{1/4}$), we establish that the optimal number of queries scales as $\frac{\sqrt m }{(\Delta / m)^2} = \frac{m^{2.5}}{\Delta^2}$ up to logarithmic factors. Our upper bound is based on non-adaptive queries and a simple thresholding-based allocation algorithm that runs in polynomial time, while our lower bound holds even under adaptive queries and arbitrary computation time.

Understanding climate dynamics requires going beyond correlations in observational data to uncover their underlying causal process. Latent drivers, such as atmospheric processes, play a critical role in temporal dynamics, while direct causal influences also exist among geographically proximate observed variables. Traditional Causal Representation Learning (CRL) typically focuses on latent factors but overlooks such observable-to-observable causal relations, limiting its applicability to climate analysis. In this paper, we introduce a unified framework that jointly uncovers (i) causal relations among observed variables and (ii) latent driving forces together with their interactions. We establish conditions under which both the hidden dynamic processes and the causal structure among observed variables are simultaneously identifiable from time-series data. Remarkably, our guarantees hold even in the nonparametric setting, leveraging contextual information to recover latent variables and observable relations. Building on these insights, we propose CaDRe (Causal Discovery and Representation learning), a time-series generative model with structural constraints that integrates CRL and causal discovery. Experiments on synthetic datasets validate our theoretical results. On real-world climate datasets, CaDRe not only delivers competitive forecasting accuracy but also recovers visualized causal graphs aligned with domain expertise, thereby offering interpretable insights into climate systems.

Low-Rank Adaptation (LoRA) is the dominant parameter-efficient fine-tuning method due to its favorable compute-performance trade-off, yet it suffers from catastrophic forgetting. We study forgetting through a tractable _mean-field self-attention_ toy model, where tokens evolve as an interacting particle system and LoRA acts as a low-rank perturbation. Using tools from partial differential equations and dynamical systems, we characterize regimes suggesting a phase transition between forgetting and non-forgetting behavior. We show that one phase transition appears with respect to the norm of the perturbation, and the other with respect to the depth of the Transformers. We further bound the time-to-deviation in terms of the perturbation size and spectral quantities, and corroborate the predicted trends with experiments and exploratory analyses on real models under LoRA fine-tuning.

State-space models (SSMs) have emerged as an efficient strategy for building powerful language models, avoiding the quadratic complexity of computing attention in transformers. Despite their promise, the interpretability and steerability of modern SSMs remain relatively underexplored. We take a major step in this direction by identifying *activation subspace bottlenecks* in the Mamba family of SSM models using tools from mechanistic interpretability. We then introduce a test-time steering intervention that simply multiplies the activations of the identified bottlenecks by a scalar. Across 7 SSMs and 6 diverse benchmarks, this intervention improves performance by an average of 8.27%, without requiring any task-specific tuning. Finally, we validate that the identified bottlenecks are indeed hindering performance by modifying them to yield an architecture we call Stable-Mamba, which achieves long-context performance gains when retrained from scratch.

Despite the rapid progress of vision-language-action (VLA) models, the prevailing practice of predicting action chunks as discrete waypoints remains structurally misaligned with the intrinsic continuity of physical motion. This discretization arises naturally from fixed-rate robot data collection and the token-by-token prediction paradigm of large language models, but ties actions to rigid sampling rates, does not naturally support analytically consistent higher-order derivatives, and introduces quantization artifacts that hinder precise, compliant interaction. We propose Neural Implicit Action Fields (NIAF), which reformulates chunk-level action representation from discrete waypoints to continuous action functions. Using a vision-language model as a hierarchical spectral modulator over a learnable motion prior, NIAF synthesizes continuous-time action manifolds with arbitrary temporal resolution. This formulation enables analytical differentiation, allowing explicit supervision of velocity and regularization of higher-order derivative signals to promote mathematical consistency, physical plausibility, and control smoothness. Our approach achieves strong results on CALVIN and LIBERO across diverse backbones. Real-world experiments further confirm that NIAF supports stable impedance control, bridging policy-side action generation and execution-side smooth control.

An AI agent will learn a desired goal more effectively if it does not resist the training process, but many partially learned goals incentivize an AI to avoid further goal updates. We would like goals to be corrigible, meaning they allow changes requested through designated channels, so that we can confidently correct errors and shut down the AI if necessary. Despite this being a crucial safety property, the existing literature does not specify goals that are both corrigible and competitive with alternatives. We introduce a transformation that constructs a corrigible version of nearly any goal, without sacrificing performance. This is done by eliciting predictions of reward conditional on costlessly preventing updates, and having that target be pursued myopically. These goals are then shown to lead to optimal performance among the class of corrigible goals, to incentivize allowing mid-action overrides, and to disincentivize deliberate self-modification. Empirically, they induce corrigible behavior in gridworld settings and for language models when applied at the prompt level.

Current linear State-Space Models (SSMs) for 3D point clouds typically rely on 1D serialization schemes (e.g., Hilbert curves) for global modeling. In dense scenes, such imposed order can disrupt spatial continuity and induce what we call serialization bias. We propose AnIsoNet, a framework that decouples anisotropic geometry from isotropic semantics via two dedicated modules: Local Anisotropy Geometric Modeling (LAGM) and Global Isotropy Semantic Aggregation (GISA). LAGM uses ellipsoidal encoding to capture local directionality without relying on global order. GISA is configured according to dataset-level geometric density: dense-scene datasets use Identity Mode to avoid additional geometry-driven re-serialization, whereas sparse-object datasets use Morton serialization to provide a lightweight spatial prior. This avoids redundant multi-view scanning while preserving O(N) complexity. On S3DIS, reducing artificial serialization in dense scenes yields 82.62% mIoU, surpassing PCM by 3.0%. On ScanObjectNN, Morton serialization for sparse objects reaches 94.21% OA (+1.6%). On ScanNetV2, our model achieves 78.52% mIoU, surpassing PTv3 (77.5%) without pre-training, with only 12.2M parameters and 37G FLOPs.

Semantic-rich features from Vision Foundation Models (VFMs) have been leveraged to enhance Latent Diffusion Models (LDMs). However, raw VFM features are typically high-dimensional and redundant, increasing the difficulty of learning and reducing training efficiency for Diffusion Transformers (DiTs). In this paper, we propose Repack then Refine, a three-stage framework that brings the semantic-rich VFM features to DiT while further accelerating learning efficiency. Specifically, the RePack module projects the high-dimensional features onto a compact, low-dimensional manifold. This filters out the redundancy while preserving essential structural information. A standard DiT is then trained for generative modeling on this highly compressed latent space. Finally, to restore the high-frequency details lost due to the compression in RePack, we propose a Latent-Guided Refiner, which is trained lastly for enhancing the image details. On ImageNet-1K, RePack-DiT-XL/1 achieves an FID of 1.82 in only 64 training epochs. With the Refiner module, performance further improves to an FID of 1.65, significantly surpassing latest LDMs in terms of convergence efficiency. Our results demonstrate that packing VFM features, followed by targeted refinement, is a highly effective strategy for balancing generative fidelity with training efficiency. Source code is publicly available at https://github.com/guanfangdong/RePack-then-Refine.

Large language models increasingly generate structured outputs, including citation-grounded summaries, multi-step reasoning chains, and tool-augmented responses, where correctness is inherently compositional: a single flawed claim can invalidate an otherwise accurate response. Existing certification methods treat outputs as atomic units, forcing a binary choice between unsafe acceptance and wasteful rejection. We introduce \textbf{Claim Graph Risk Control (CGRiC)}, a framework that decomposes responses into dependency graphs of verifiable claims and assigns calibrated per-claim risk bounds via information-lift statistics. By composing these bounds, CGRiC provides explicit guarantees on the probability that any incorrect claim passes verification undetected. When this composed risk exceeds a target threshold, the system triggers localized repairs rather than full abstention, preserving correct content while fixing problematic claims. Our approach explicitly models extraction noise and verifier imperfection, and exploits conditional independence structure for tighter certificates when validated. Empirically, CGRiC achieves target risk levels while reducing abstention by 31\% compared to atomic baselines across QA, summarization, and reasoning tasks.

We introduce STEERINGSAFETY, a benchmark for evaluating representation steering methods across nine safety perspectives spanning 18 datasets. While prior work highlights the general capabilities of representation steering, we focus on safety perspectives including refusal, bias, hallucination, social behaviors, reasoning, epistemic integrity, and normative judgment. STEERINGSAFETY provides modularized building blocks for state-of-the-art steering methods, enabling unified implementation of DIM, ACE, CAA, PCA, and LAT with recent enhancements such as conditional steering. Results on Gemma-2-2B, Llama-3.1-8B, and Qwen-2.5-7B show that strong steering performance depends on the pairing of method, model, and specific perspective. For instance, DIM is consistently effective, yet all methods exhibit substantial entanglement, where improving effectiveness on one safety perspective often significantly changes performance on others. Social behaviors are most vulnerable (degradation up to 76%), refusal steering (jailbreaking) frequently compromises normative judgment such as commonsense morality (up to 26%), and hallucination steering shifts political views unpredictably across models, ranging from a 21% shift to the right to a 19% shift to the left. These findings show the need to understand steering methods through multiple safety angles rather than a single target behavior.

*Crowdsourced fact-checking systems* have been adopted by major social media companies such as X, Meta, TikTok and Google with the aim of combating misleading information at scale without relying on centralized editorial control. These systems have been developed around a common underlying concept: a *bridging mechanism* that identifies notes flagging misleading information when they receive support from people with different perspectives rather than simple majority support. To our knowledge the only publicly disclosed bridging algorithms deployed for fact-checking are based on matrix factorization, as deployed by both X and Meta, augmented with additional components addressing abuse, targeted manipulation, and contributor brigades. This work examines the core matrix factorization portion of these systems, presenting theoretical and empirical evaluations of the degree to which coordinated users could vote strategically by leveraging the latent representations to fabricate the appearance of *synthetic consensus* within the bridging mechanism. Using historic production data, we find that up to 10.7% of lower quality notes could be manipulated above consensus thresholds using less than 10 ratings. We complement these findings with a theoretical analysis, revealing counterintuitively that rating a note as ``Not Helpful'' can increase its helpfulness score, as well as a cost model quantifying manipulation effort. We have developed and deployed mitigations within X's Community Notes algorithm to address synthetic consensus.

Adaptive Neuro-Fuzzy Inference System (ANFIS) was designed to combine the learning capabilities of neural network with the reasoning transparency of fuzzy logic. However, conventional ANFIS architectures suffer from structural complexity, where the product-based inference mechanism causes an exponential explosion of rules in high-dimensional spaces. We herein propose the \textbf{K}olmogorov-\textbf{A}rnold **N**euro-**F**uzzy **I**nference **S**ystem (KANFIS), a compact neuro-symbolic architecture that unifies fuzzy reasoning with additive function decomposition. KANFIS employs an additive aggregation mechanism, under which both model parameters and rule complexity scale linearly with input dimensionality rather than exponentially. Furthermore, KANFIS is compatible with both Type-1 (T1) and Interval Type-2 (IT2) fuzzy logic systems, enabling explicit modeling of uncertainty and ambiguity in fuzzy representations. By using sparse masking mechanisms, KANFIS generates compact and structured rule sets, resulting in an intrinsically interpretable model with clear rule semantics and transparent inference processes. Empirical results demonstrate that KANFIS achieves competitive performance against representative neural and neuro-fuzzy baselines.

Achieving spatial intelligence requires moving beyond visual plausibility to build world simulators grounded in physical laws. While coding LLMs have advanced static 3D scene generation, extending this paradigm to 4D dynamics remains a critical frontier. This task presents two fundamental challenges: multi-scale context entanglement, where monolithic generation fails to balance local object structures with global environmental layouts; and a semantic-physical execution gap, where open-loop code generation leads to physical hallucinations lacking dynamic fidelity. We introduce Code2Worlds, a framework that formulates 4D generation as language-to-simulation code generation. First, we propose a dual-stream architecture that disentangles retrieval-augmented object generation from hierarchical environmental orchestration. Second, to ensure dynamic fidelity, we establish a physics-aware closed-loop mechanism in which a PostProcess Agent scripts dynamics, coupled with a VLM-Motion Critic that performs self-reflection to iteratively refine simulation code. Evaluations on the Code4D benchmark show Code2Worlds outperforms baselines with a 41% SGS gain and 49% higher Richness, while uniquely generating physics-aware dynamics absent in prior static methods.

Group Relative Policy Optimization (GRPO), a prominent algorithm within the Reinforcement Learning from Verifiable Rewards (RLVR) framework, has achieved strong results in improving the reasoning capabilities of large language models (LLMs). However, GRPO is prone to advantage collapse, a failure mode where homogeneous rewards within a group (e.g., all correct or all incorrect answers) yield near-zero advantages and vanishing gradients. To address this, we introduce the Advantage Collapse Rate (ACR), the first diagnostic metric quantifying the proportion of training batches with ineffective gradients. Across models from 0.5B to 14B parameters on mathematical reasoning benchmarks, we show that ACR strongly predicts training stagnation and final performance. We then propose Adaptive Virtual Sample Policy Optimization (AVSPO), a lightweight extension of GRPO that injects virtual reward samples, guided by real-time ACR monitoring, to enable learning from homogeneous groups without additional model rollouts. AVSPO reduces advantage collapse by 58–63% relative to GRPO and yields consistent accuracy gains of 4–6 percentage points across all model scales, while maintaining generalization on the evaluated out-of-domain task. Code and datasets are available at https://github.com/hexixiang/Advantage-Collapse-Rate.

Training robust reasoning vision-language models (VLMs) in rare domains (such as geospatial) is fundamentally constrained by supervision scarcity. While raw geospatial imagery is abundant, the amount of task-direct supervision falls far behind that of common domains. In this work, we validate an important conclusion: indirect verifiable rewards, derived from seemingly unrelated metadata, are sufficient to induce sophisticated and generalizable geospatial reasoning across a wide range of downstream tasks (25+). We present Geo-R1 as one empirical instantiation of this paradigm. Rather than relying on limited task-specific annotations (i.e., direct rewards), Geo-R1 utilizes scalable, verifiable indirect proxy rewards based on cross-view alignment with metadata (geolocation information) to drive reinforcement learning at scale. Such indirect rewards successfully motivate the model to discover and internalize zero-shot geospatial reasoning across diverse tasks, achieving extraordinary zero-shot transfer on out-of-distribution benchmarks and even surpassing fully supervised specialists on certain benchmarks. These findings indicate that optimizing for indirect verifiable rewards may provide a scalable pathway to unlock generalized reasoning capabilities in rare domains with massive unlabeled data archives. Our code is available at: https://github.com/miniHuiHui/Geo-R1.

Alignment of large language models (LLMs) with human values has recently garnered significant attention, with prominent examples including the canonical yet costly Reinforcement Learning from Human Feedback (RLHF) and the simple Direct Preference Optimization (DPO). In this work, we demonstrate that both RLHF and DPO can be interpreted from the perspective of mutual information (MI) maximization, uncovering a profound connection to contrastive learning. Within this framework, both RLHF and DPO can be interpreted as methods that performing contrastive learning based on the positive and negative samples derived from base model, leveraging the Donsker–Varadhan (DV) lower bound on MI (equivalently, the MINE estimator). Such paradigm further illuminates why RLHF may not intrinsically incentivize reasoning capacities in LLMs beyond what is already present in the base model. Building on the perspective, we replace the DV/MINE bound with the Jensen–Shannon (JS) MI estimator and propose the Mutual Information Optimization (MIO). Comprehensive theoretical analysis and extensive empirical evaluations demonstrate that MIO mitigates the late-stage decline in chosen-likelihood observed in DPO, achieving competitive or superior performance across various challenging reasoning and mathematical benchmarks