ICLR 2026 Papers

Due to their inherent complexity, reasoning tasks have long been regarded as rigorous benchmarks for assessing the capabilities of machine learning models, especially large language models (LLMs). Although humans can solve these tasks with ease, existing models, even after extensive pre-training and post-training at scale, still fail to perform reasoning reliably. In this paper, we revisit reasoning tasks from a causal perspective, seeking to understand their behavior in latent space and to offer insights for addressing their challenges. Specifically, we cast reasoning tasks as a selection mechanism, in which high-level logical concepts function as selection operators on the given observations, such as, identifying the correct answer in a math problem or filling the appropriate entry in Sudoku. We emphasize two key properties of this formulation that shed light on the difficulty of reasoning tasks. First, the latent space exceeds the observation space in complexity, even when the correct answer is fully determined by the observed input. Second, the latent variables, corresponding to logical thought, are densely structured and exhibit strong dependencies. Building on this formulation, we introduce a framework, called SR$^2$, that incorporates the estimated latent variables as feedback into the selection mechanism, thereby facilitating the learning of dense dependencies among latent representations. The framework consists of three key modules: reflective representation learning, dependency self-refinement, and periodic intermediate alignment. Experimentally, we show that our approach yields significant gains in reasoning accuracy, for example, attaining over 10% improvement in performance with 8$\times$ fewer parameters on the Sudoku and Maze tasks over the recent advances.

Existing time series forecasting methods primarily rely on the numerical data itself. However, real-world time series exhibit complex patterns associated with multimodal information, making them difficult to predict with numerical data alone. While several multimodal time series forecasting methods have emerged, they either utilize text with limited supplementary information or focus merely on representation extraction, extracting minimal textual information for forecasting. To unlock the Value of Text, we propose VoT, a method with Event-driven Reasoning and Multi-level Alignment. Event-driven Reasoning combines the rich information in exogenous text with the powerful reasoning capabilities of LLMs for time series forecasting. To guide the LLMs in effective reasoning, we propose the Historical In-context Learning that retrieves and applies historical examples as in-context guidance. To maximize the utilization of text, we propose Multi-level Alignment. At the representation level, we utilize the Endogenous Text Alignment to integrate the endogenous text information with the time series. At the prediction level, we design the Adaptive Frequency Fusion to fuse the frequency components of event-driven prediction and numerical prediction to achieve complementary advantages. Experiments on real-world datasets across 10 domains demonstrate significant improvements over existing methods, validating the effectiveness of our approach in the utilization of text. The code is made available at https://anonymous.4open.science/r/VoT-465C.

Current benchmarks for long-context reasoning in Large Language Models (LLMs) often blur critical factors like intrinsic task complexity, distractor interference, and task length. To enable more precise failure analysis, we introduce CogniLoad, a novel synthetic benchmark grounded in Cognitive Load Theory (CLT). CogniLoad generates natural-language logic puzzles with independently tunable parameters that reflect CLT's core dimensions: intrinsic difficulty ($d$) controls intrinsic load; distractor-to-signal ratio ($\rho$) regulates extraneous load; and task length ($N$) serves as an operational proxy for conditions demanding germane load. Evaluating 22 SotA reasoning LLMs, CogniLoad reveals distinct performance sensitivities, identifying task length as a dominant constraint and uncovering varied tolerances to intrinsic complexity and U-shaped responses to distractor ratios. By offering systematic, factorial control over these cognitive load dimensions, CogniLoad provides a reproducible, scalable, and diagnostically rich tool for dissecting LLM reasoning limitations and guiding future model development.

Large Language Models (LLMs) excel at various reasoning tasks but still encounter challenges such as hallucination and factual inconsistency in knowledge-intensive tasks, primarily due to a lack of external knowledge and factual verification. These challenges could be mitigated by leveraging knowledge graphs (KGs) to support more reliable LLM reasoning. However, existing KG-augmented LLM frameworks still rely on static integration mechanisms that cannot adjust reasoning in response to evolving context and retrieved evidence, resulting in error propagation and incomplete reasoning. To alleviate these issues, we propose **V**erify-**o**n-**G**raph (**VoG**), a scalable and model-agnostic framework to enhance LLM reasoning via iterative retrieval, stepwise verification, and adaptive revision. Besides performing KG retrieval guided by an initially generated reasoning plan, VoG iteratively verifies and revises the reasoning plan, correcting intermediate errors in consideration of the varying contextual conditions. During plan revision, VoG leverages a context-aware multi-armed bandit strategy, guided by reward signals that capture uncertainty and semantic consistency, to enhance the alignment between the reasoning plan and retrieved evidence in a more adaptive and reliable way. Experimental results across three benchmark datasets show that VoG consistently improves both reasoning accuracy and efficiency. Our code is available at https://anonymous.4open.science/r/VoG-132C/.

Accurate prediction of protein-ligand bioactivity is a cornerstone of modern drug discovery, yet current deep learning methods often struggle with out-of-domain (OOD) generalization. The existing methods rely on access to source data, making them impractical in scenarios where data cannot be accessed due to confidentiality, privacy concerns or intellectual property restrictions. In this paper, we provide the first exploration of a more realistic setting for bioactivity prediction, where models are expected to adapt to out-of-domain distributions without access to source data. Motivated by the critical role of binding-relevant interactions in determining ligand-protein bioactivity, we introduce an uncertainty-weighted consistency strategy, in which original samples with high confidence guide their augmented counterparts by minimizing feature distance. This encourages the model to focus on informative interaction regions while suppressing reliance on spurious or non-causal substructures. To further enhance representation discriminability and prevent feature collapse, we integrate a contrastive optimization objective that pulls together augmented views of the same complex and pushes away views from different complexes. Together, these two components enable the learning of invariant, bioactivity-aware representations, allowing robust adaptation under distribution shifts. Extensive experiments across DTIGN, SIU 0.6, and DrugOOD demonstrate that our framework consistently outperforms state-of-the-art baselines under scaffold, protein, and assay based OOD settings. Especially on the eight subsets of DTIGN, it improves Pearson’s $R$ by 8.2\% and Kendall’s Tau $\tau$ by 5.8\% on average over the best baseline, underscoring its effectiveness as a source data-absent solution for OOD bioactivity prediction.

When continual test-time adaptation (TTA) persists over the long term, errors accumulate in a model and further lead it to predict only a few classes regardless of the input, known as model collapse. Recent studies have explored reset strategies that erase these accumulated errors completely. However, their periodic resets lead to suboptimal adaptation, as they occur independently of collapse. Also, their full resets cause the catastrophic loss of knowledge acquired over time, even though it could be beneficial in future. To this end, we propose 1) an Adaptive and Selective Reset (ASR) scheme that dynamically determines when and where to reset, 2) an importance-aware regularizer to recover essential knowledge lost from reset, and 3) an on-the-fly adaptation adjustment scheme to enhance adaptability under challenging domain shifts. Extensive experiments across long-term TTA benchmarks demonstrate the effectiveness of our approach, particularly under challenging conditions. Our code will be released.

Can Vision Language Models (VLMs) imagine the full scene from just a few views, like humans do? Humans form spatial mental models, internal representations of unseen space, to reason about layout, perspective, and motion. Our new MindCube benchmark with 21,154 questions across 3,268 images exposes this critical gap, where existing VLMs exhibit near-random performance. Using MindCube, we systematically evaluate how well VLMs build robust spatial mental models through representing positions (cognitive mapping), orientations (perspective-taking), and dynamics (mental simulation for "what-if" movements). We then explore three approaches to help VLMs approximate spatial mental models, including unseen intermediate views, natural language reasoning chains, and cognitive maps. The significant improvement comes from a synergistic approach, "map-then-reason", that jointly trains the model to first generate a cognitive map and then reason upon it. By training models to reason over these internal maps, we boosted accuracy from 37.8% to 60.8% (+23.0%). Adding reinforcement learning pushed performance even further to 70.7% (+32.9%). Our key insight is that such scaffolding of spatial mental models, actively constructing and utilizing internal structured spatial representations with flexible reasoning processes, significantly improves understanding of unobservable space.

Large Language Models (LLMs) have made remarkable progress in mathematical reasoning, but still continue to struggle with high-precision tasks like numerical computation and formal symbolic manipulation. Integrating external tools has emerged as a promising approach to bridge this gap. Despite recent advances, existing methods struggle with three key challenges: constructing tool-integrated reasoning data, performing fine-grained optimization, and enhancing inference. To overcome these limitations, we propose THOR (Tool-Integrated Hierarchical Optimization via RL). First, we introduce TIRGen, a multi-agent based pipeline for constructing high-quality datasets of tool-integrated reasoning paths, aligning with the policy and generalizing well across diverse models. Second, to perform fine-grained hierarchical optimization, we introduce an RL strategy that jointly optimizes for both episode-level problem solving and step-level code generation. This is motivated by our key insight that the success of an intermediate tool call is a strong predictor of the final answer's correctness. Finally, THOR incorporates a self-correction mechanism that leverages immediate tool feedback to dynamically revise erroneous reasoning paths during inference. Our approach demonstrates strong generalization across diverse models, performing effectively in both reasoning and non-reasoning models. It further achieves state-of-the-art performance for models of a similar scale on multiple mathematical benchmarks, while also delivering consistent improvements on code benchmarks. Our code will be publicly available at https://github.com/JingMog/THOR.

Sudden concept drift makes previously trained predictors unreliable, yet deciding when to retrain and what post-drift data size is sufficient is rarely addressed. We propose CALIPER —a detector- and model-agnostic, data-only test that estimates the post-drift data size required for stable retraining. CALIPER exploits state dependence in streams generated by dynamical systems: we run a single-pass weighted local regression over the post-drift window and track a one-step proxy error as a function of a locality parameter $\theta$. When an effective sample size gate is satisfied, a monotonically non-increasing trend in this error with increasing a locality parameter indicates that the data size is sufficiently informative for retraining. We also provide a theoretical analysis of our method, and we show that the algorithm has a low per-update time and memory. Across datasets from four heterogeneous domains, three learner families, and two detectors, CALIPER consistently matches or exceeds the best fixed data size for retraining while incurring negligible overhead and often outperforming incremental updates. CALIPER closes the gap between drift detection and data-sufficient adaptation in streaming learning.

While Retrieval-Augmented Generation (RAG) has advanced knowledge-intensive tasks, we identify a fundamental vulnerability: the Correlation Trap. Existing systems cannot distinguish causally decisive evidence from overwhelmingly correlated yet misleading information, leading to systematic failures. We introduce Counterfactual RAG (CF-RAG), a new framework that operationalizes causal reasoning to overcome this limitation. CF-RAG systematically generates and evaluates counterfactual queries to identify causally relevant distinctions, and employs a parallel arbitration mechanism to reconcile conflicting evidence without interference. On challenging benchmarks, CF-RAG substantially improves robustness against the Correlation Trap, achieving state-of-the-art performance while maintaining comparable efficiency to standard RAG models.

Intervention-based model steering offers a lightweight and interpretable alternative to prompting and fine-tuning. However, by adapting strong optimization objectives from fine-tuning, current methods are susceptible to overfitting and often underperform, sometimes generating unnatural outputs. We hypothesize that this is because effective steering requires the faithful identification of internal model mechanisms, not the enforcement of external preferences. To this end, we build on the principles of *distributed alignment search (DAS)*, the standard for causal variable localization, to propose a new steering method: **Concept DAS (CDAS)**. While we adopt the core mechanism of DAS, *distributed interchange intervention (DII)*, we introduce a novel distribution matching objective tailored for the steering task by aligning intervened output distributions with counterfactual distributions. CDAS differs from prior work in two main ways: first, it learns interventions via weak-supervised distribution matching rather than probability maximization; second, it uses DIIs that naturally enable bi-directional steering and allow steering factors to be derived from data, reducing the effort required for hyperparameter tuning and resulting in more faithful and stable control. On AxBench, a large-scale model steering benchmark, we show that CDAS does not always outperform preference-optimization methods but may benefit more from increased model scale. In two safety-related case studies, overriding refusal behaviors of safety-aligned models and neutralizing a chain-of-thought backdoor, CDAS achieves systematic steering while maintaining general model utility. These results indicate that CDAS is complementary to preference-optimization approaches and conditionally constitutes a robust approach to intervention-based model steering.