ICLR 2026 Papers

Recurrent neural networks (RNNs) with deep test-time memorization modules, such as Titans and TTT, represent a promising, linearly-scaling paradigm distinct from Transformers. While these expressive models do not yet match the peak performance of state-of-the-art Transformers, their potential has been largely untapped due to prohibitively slow training and low hardware utilization. Existing parallelization methods force a fundamental conflict governed by the chunksize hyperparameter: large chunks boost speed but degrade performance, necessitating a fixed, suboptimal compromise. To solve this challenge, we introduce TNT, a novel training paradigm that decouples training efficiency from inference performance through a two-stage process. Stage one is an efficiency-focused pre-training phase utilizing a hierarchical memory. A global module processes large, hardware-friendly chunks for long-range context, while multiple parallel local modules handle fine-grained details. Crucially, by periodically resetting local memory states, we break sequential dependencies to enable massive context parallelization. Stage two is a brief fine-tuning phase where only the local memory modules are adapted to a smaller, high-resolution chunksize, maximizing accuracy with minimal overhead. Evaluated on Titans and TTT models, TNT achieves a substantial acceleration in training speed—up to 17$\times$ faster than the most accurate baseline configuration—while simultaneously improving model accuracy. This improvement removes a critical scalability barrier, establishing a practical foundation for developing expressive RNNs and facilitating future work to close the performance gap with Transformers.

Large reasoning models (LRMs) combined with retrieval-augmented generation (RAG) have enabled deep research agents capable of multi-step reasoning with external knowledge retrieval. However, previous methods that extend reasoning with single-query search steps struggle to scale to complex tasks demanding broad document exploration. Meanwhile, approaches that generate multiple independent queries simultaneously may limit deeper, sequential reasoning. To address these limitations, we propose HybridDeepSearcher that dynamically integrates parallel and sequential search strategies to enable effective search scaling. To support training, we introduce HDS-QA, a novel dataset that seamlessly integrates broad parallel search with sequential search reasoning, providing answer trajectories in the form of reasoning-query-retrieval loops with parallel sub-queries. Across all five benchmarks, our approach significantly outperforms the state-of-the-art, improving F1 scores by +15.9 on FanOutQA and +11.5 on a subset of BrowseComp. Further analysis reveals that HybridDeepSearcher effectively scales performance with additional test-time search resources and demonstrates robustness on questions requiring more evidence, achieving higher evidence coverage. We include the code in the supplementary materials and will release the dataset and code publicly.

Recent trends in test-time scaling for reasoning models (e.g., OpenAI o1, DeepSeek-R1) have led to remarkable improvements through long Chain-of-Thought (CoT). However, existing benchmarks mainly focus on immediate, single-horizon tasks, failing to adequately evaluate models’ ability to understand and respond to complex, long-horizon scenarios. To address this incomplete evaluation of Large Reasoning Models (LRMs), we propose R-HORIZON, a method designed to stimulate long-horizon reasoning behaviors in LRMs through query composition. Based on R-HORIZON, we construct a long-horizon reasoning benchmark, comprising complex multi-step reasoning tasks with interdependent problems that span long reasoning horizons. Through comprehensive evaluation of LRMs using the R-HORIZON benchmark, we find that even the most advanced LRMs suffer significant performance degradation. Our analysis reveals that LRMs exhibit limited effective reasoning length and struggle to allocate thinking budget across multiple problems appropriately. Recognizing these limitations, we use R-HORIZON to construct long-horizon reasoning data for reinforcement learning with verified rewards (RLVR). Compared to training with single-horizon data, RLVR with R-HORIZON not only substantially improves performance on the multi-horizon reasoning tasks, but also promotes accuracy on standard reasoning tasks (+7.5 on AIME2024). These results position R-HORIZON as a scalable, controllable, and low-cost paradigm for enhancing and evaluating the long-horizon reasoning capabilities of LRMs.

Small Vision-Language Models (VLMs) provide a computationally efficient alternative to larger models, at the cost of weaker generalization abilities and downstream task performance. These shortcomings could be addressed by test-time scaling techniques, but existing methods are typically computationally demanding, contradicting the resource-efficient design goals of small models. To address these limitations, we propose two novel and efficient test-time scaling strategies that leverage the model-internal features rather than external supervision: (i) Test-Time Augmentation (TTAug), which generates multiple augmented inputs and aggregates outputs at the token level without parameter updates, and (ii) Test-Time Adaptation (TTAdapt), which adapts model parameters during inference using consensus-based pseudolabels from TTAug. Through extensive experiments across nine benchmarks, we demonstrate consistent performance improvements while maintaining computational efficiency suitable for resource-constrained environments. The generality of our approach is demonstrated both within models at different scales and across different VLMs without additional tuning.

Active reasoning requires large language models (LLMs) to interact with external sources and strategically gather information to solve problems. Central to this process is belief tracking: maintaining a coherent understanding of the problem state and the missing information toward the solution. However, due to limited reasoning capabilities, LLM-based agents often suffer from belief deviation: they struggle to correctly model beliefs, lose track of problem states, and fall into uninformative or repetitive actions. Once this happens, errors compound and reinforcement learning (RL) training fails to properly credit the crucial exploratory steps. To address this issue, we propose to track the deviation of model beliefs and develop $\mathbf{T^3}$, a simple yet effective method that detects excessive belief deviation and truncates trajectories during training to remove uninformative tails. By preserving credit for informative prefixes, $\mathbf{T^3}$ systematically improves policy optimization. Across 5 challenging tasks, $\mathbf{T^3}$ consistently enhances training stability, token efficiency, and final performance, achieving up to 30\% gains while cutting rollout tokens by roughly 25\%. These results highlight belief control as a key principle for developing robust and generalizable LLM-based active reasoners.

We present SpinBench, a cognitively grounded diagnostic benchmark for evaluating spatial reasoning in vision language models (VLMs). SpinBench is designed around the core challenge of spatial reasoning: perspective taking, the ability to reason about how scenes and object relations change under viewpoint transformation. Since perspective taking requires multiple cognitive capabilities, such as recognizing objects across views, relative positions grounding, and mentally simulating transformations, SpinBench introduces a set of fine-grained diagnostic categories. Our categories target translation, rotation, object relative pose, and viewpoint change, and are progressively structured so that single-object simpler tasks scaffold toward the most demanding multi-object perspective-taking setting. We evaluate 43 state-of-the-art VLMs, both proprietary and open source. Results reveal systematic weaknesses: strong egocentric bias, poor rotational understanding, and inconsistencies under symmetrical and syntactic reformulations. Scaling analysis shows both smooth improvements and emergent capabilities. While human subjects achieve high accuracy (91.2\%), task difficulty as measured by human response time shows strong correlation with VLM accuracy, indicating that SpinBench captures spatial reasoning challenges shared across humans and VLMs. Together, our findings highlight the need for structured, cognitively inspired diagnostic tools to advance spatial reasoning in multimodal foundation models. Our website can be found [here](https://spinbench25.github.io/).

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the **magnitude** of these updates, largely overlooking their **direction**. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference $\Delta\log p$ between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that $\Delta\log p$ more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (e.g., divergence or entropy). Building on this insight, we propose two practical applications: (1) a *test-time extrapolation* method that amplifies the policy along the learned $\Delta\log p$ direction to improve reasoning accuracy without further training; (2) a *training-time reweighting* method that focuses learning on low-probability (corresponding to higher $\Delta\log p$) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

Recent advancements in Large Language Models (LLMs) have shifted from explicit Chain-of-Thought (CoT) reasoning to more efficient latent reasoning, where intermediate thoughts are represented as vectors rather than text. However, latent reasoning can be brittle on challenging, out-of-distribution tasks where robust reasoning is most critical. To overcome these limitations, we introduce Latent Thought Policy Optimization (LTPO), a parameter-free framework that enhances LLM reasoning entirely at test time, without requiring model parameter updates. LTPO treats intermediate latent "thought" vectors as dynamic parameters that are actively optimized for each problem instance. It employs an online policy gradient method guided by an intrinsic, confidence-based reward signal computed directly from the frozen LLM's own output distributions, eliminating the need for external supervision or expensive text generation during optimization. Extensive experiments on five reasoning benchmarks show that LTPO not only matches or surpasses strong baselines on standard tasks but also demonstrates remarkable robustness where others fail. Most notably, on highly challenging AIME benchmarks where existing latent reasoning baselines collapse to near-zero accuracy, LTPO delivers substantial improvements, showcasing a unique capability for complex reasoning.

Long-context reasoning requires accurately identifying relevant information in extensive, noisy input contexts. In this work, we propose PERK (Parameter Efficient Reasoning over Knowledge), a scalable approach for learning to encode long contexts using gradient updates at test time. Specifically, PERK employs two nested optimization loops in a meta-training phase. The inner loop rapidly encodes contexts into a low-rank adapter (LoRA) that serves as a parameter-efficient memory module for the base model. Concurrently, the outer loop learns to use the updated adapter to accurately recall and reason over relevant information from the encoded long context. Our evaluations on several long-context reasoning tasks show that PERK significantly outperforms the standard long-context finetuning, achieving average absolute performance gains of up to 20% for Qwen-2.5 (0.5B & 7B) on synthetic and real-world long-context reasoning. PERK also maintains its advantages across model scales and families. Compared to specialized long-context LLMs, PERK matches or surpasses their performance. Finally, our analyses show PERK is more robust to reasoning complexity, length extrapolation, and the positions of relevant information in contexts.

Reinforcement Learning (RL) has demonstrated its potential to improve the reasoning ability of Large Language Models (LLMs), yet most existing Reinforcement Finetuning (RFT) methods are inherently \textit{on-policy} RL, failing to reuse historical data and thus preventing efficient scaling. In this work, we explore the potential of \textit{off-policy} RL to leverage historical data for rollout-efficient RFT. Specifically, we propose \textbf{Re}incarnating \textbf{Mix}-policy Proximal Policy Gradient (\textbf{ReMix}), which enables on-policy RFT methods to leverage off-policy data. ReMix consists of three major components: (1) Mix-policy proximal policy gradient with an increased Update-To-Data (UTD) ratio that utilizes the data from both current and past policies for efficient training; (2) KL-Convex policy constraint that combines the KL constraints on the base and precedent model to balance stability and flexibility; (3) Policy reincarnation that replaces the base model with the mix-policy RFT model in the mid way of training and restarts on-policy training, to achieve a seamless transition from early efficiency to steady convergence. In our experiments, we train a series of ReMix models based on PPO, GRPO from 1.5B, 7B base models. On five math reasoning benchmarks (i.e., AIME'24, AMC'23, Minerva, OlympiadBench, and MATH500), ReMix achieves an average Pass@1 accuracy of \textbf{52.10\%} (with \textbf{0.079M rollouts}) and \textbf{64.39\%} (with \textbf{0.011M rollouts}) on 1.5B and 7B models, respectively. Compared with 15 recent advanced models, ReMix shows SOTA-level performance with an over \textbf{30x to 450x reduction in training cost in terms of rollout data volume}, demonstrating superior training efficiency. Additionally, our multifaceted analysis reveals insightful findings, including the implicit preference for shorter responses of off-policy RFT, the collapse mode of self-reflection under severe off-policyness, etc.

Protein interaction modeling is central to protein design, which has been transformed by machine learning with broad applications in drug discovery and beyond. In this landscape, structure-based de novo binder design is most often cast as either conditional generative modeling or sequence optimization via structure predictors ("hallucination"). We argue that this is a false dichotomy and propose Complexa, a novel fully atomistic binder generation method unifying both paradigms. We extend recent flow-based latent protein generation architecture and leverage the domain-domain interactions of monomeric computationally predicted protein structures to construct Teddymer, a new large-scale dataset of synthetic binder-target pairs for pretraining. Combined with high-quality experimental multimers, this enables training a strong base model. We then perform inference-time optimization with this generative prior, unifying the strengths of previously distinct generative and hallucination methods. Complexa sets a new state of the art in computational binder design benchmarks: it delivers markedly higher in-silico success rates than existing generative approaches, and our novel test-time optimization strategies greatly outperform previous hallucination methods under normalized compute budgets. We further demonstrate explicit interface hydrogen bond optimization, fold class-guided binder generation, and extensions to small molecule targets and enzyme design tasks, again surpassing prior methods. Code, models and new data will be publicly released.

Policy gradient algorithms have been successfully applied to enhance the reasoning capabilities of large language models (LLMs). KL regularization is ubiquitous, yet the design surface, choice of KL direction (forward vs. reverse), normalization (normalized vs. unnormalized), and estimator ($k_1/k_2/k_3$), is scattered across the literature and often intertwined with off-policy estimation. We ask a focused question: under the off-policy setting, what weighting is required for each KL variant so that the surrogate we optimize yields the exact gradient of the intended KL-regularized objective? We answer this with a compact, unified derivation we call the Regularized Policy Gradient (\textbf{RPG}) view. RPG (i) unifies normalized and unnormalized KL variants and shows that the widely-used $k_3$ penalty is exactly the unnormalized KL; (ii) specifies conditions under which REINFORCE-style losses with stop-gradient are gradient-equivalent to fully differentiable surrogates; (iii) identifies and corrects an off-policy importance-weighting mismatch in GRPO's KL term; and (iv) introduces RPG-Style Clip, a truncated-importance-sampling step within RPG-REINFORCE that enables stable, off-policy policy-gradient training at scale. On mathematical reasoning benchmarks (AIME24, AIME25), RPG-REINFORCE with RPG-Style Clip improves accuracy by up to $+6$ absolute percentage points over DAPO. Notably, RPG is a \emph{stable and scalable} RL algorithm for LLM reasoning, realized via (a) a KL-correct objective, (b) truncated importance sampling, and (c) an iterative reference-policy update scheme.

Vision-Language Models (VLMs) have demonstrated remarkable performance across a variety of real-world tasks. However, existing VLMs typically process visual information by serializing images, a method that diverges significantly from the parallel nature of human vision. Moreover, their opaque internal mechanisms hinder both deeper understanding and architectural innovation. Inspired by the dual-stream hypothesis of human vision, which distinguishes the "what" and "where" pathways, we deconstruct the visual processing in VLMs into object recognition and spatial perception for separate study. For object recognition, we convert images into text token maps and find that the model's perception of image content unfolds as a two-stage process from shallow to deep layers, beginning with attribute recognition and culminating in semantic disambiguation. For spatial perception, we theoretically derive and empirically verify the geometric structure underlying the positional representation in VLMs. Based on these findings, we introduce an instruction-agnostic token compression algorithm based on a plug-and-play visual decoder to improve decoding efficiency, and a RoPE scaling technique to enhance spatial reasoning. Through rigorous experiments, our work validates these analyses, offering a deeper understanding of VLM internals and providing clear principles for designing more capable future architectures.

Large Language Models (LLMs) have demonstrated impressive generalization ability by learning from extensive unlabeled text. However, they still exhibit reasoning mistakes, which can affect their trustworthiness and reliability. Although users can interact with LLMs and provide diverse and comprehensive queries to expose the flaws of LLMs, obtaining sufficient and effective feedback is demanding. Furthermore, comprehensively evaluating LLMs with limited labeled samples is difficult. These make it a challenge to diagnose and remedy the deficiencies in LLMs through rich label-free user queries. To tackle this challenge and considersing that LLMs' reasoning mistakes often stem from knowledge deficiencies, we propose label-free curricular meaningful learning (LaMer), which first employs relative entropy to diagnose and quantify knowledge deficiencies of LLMs in a label-free setting. Then, LaMer adaptively synthesizes augmentation data based on deficiency severity and progressively remedies them with a curricular remedy strategy. Experiments show that LaMer effectively diagnoses and remedies knowledge deficiencies in LLMs, improving various LLMs across seven out-of-distribution (OOD) reasoning benchmarks, achieving comparable results to baselines with only 40% training data. LaMer even surpasses methods that rely on labeled data for deficiency diagnosis. In application, LaMer offers a diagnostic tool for efficient LLM development.

Counterfactual reasoning has emerged as a crucial technique for generalizing the reasoning capabilities of large language models (LLMs). By generating and analyzing counterfactual scenarios, researchers can assess the adaptability and reliability of model decision-making. Although prior work has shown that LLMs often struggle with counterfactual reasoning, it remains unclear which factors most significantly impede their performance across different tasks and modalities. In this paper, we propose a decompositional strategy that breaks down the counterfactual generation from causality construction to the reasoning over counterfactual interventions. To support decompositional analysis, we investigate 11 datasets spanning diverse tasks, including natural language understanding, mathematics, programming, and vision-language tasks. Through extensive evaluations, we characterize LLM behavior across each decompositional stage and identify how modality type and intermediate reasoning influence performance. By establishing a structured framework for analyzing counterfactual reasoning, this work contributes to the development of more reliable LLM-based reasoning systems and informs future elicitation strategies.

Chain-of-thought (CoT) reasoning has become the standard paradigm for enabling Large Language Models (LLMs) to solve complex problems. However, recent studies reveal a sharp performance drop in *reasoning hop generalization* scenarios, where the required number of reasoning steps exceeds training distributions while the underlying algorithm remains unchanged. The internal mechanisms driving this failure remain poorly understood. In this work, we conduct a systematic study on tasks from multiple domains, and find that errors concentrate at token positions of a few critical error types, rather than being uniformly distributed. Closer inspection reveals that these token-level erroneous predictions stem from internal *competition mechanisms*: certain attention heads, termed *erroneous processing heads* (ep heads), tip the balance by amplifying incorrect reasoning trajectories while suppressing correct ones. Notably, removing individual ep heads during inference can often restore the correct predictions. Motivated by these insights, we propose test-time correction of reasoning, a lightweight intervention method that dynamically identifies and deactivates ep heads in the reasoning process. Extensive experiments across different tasks and LLMs show that it consistently improves reasoning hop generalization, highlighting both its effectiveness and potential.

Designing system algorithms remains challenging, where the discontinuous nature of the solution space often forces system engineers to rely on generic heuristics at the expense of performance. We study whether LLMs can practically drive algorithm generation, and find that they are biased towards well-known generic designs, rather than making the creative leaps needed to navigate the discontinuous solution space. To address this limitation, we introduce MetaMuse, a framework for creative ideation built on three self-reflection principles: (1) quantifying solution diversity and usefulness in measurable performance space, rather than abstract idea space, (2) steering ideation through external stimuli, rather than internal randomness, and (3) constructing executable solutions using waypoint reasoning, rather than free-form chain-of-thought. Extensive evaluation shows that MetaMuse can generate high-performing solutions for two critical problems at a global cloud provider: cache replacement (reducing cache misses by up to 35.76%) and online bin packing (reducing bin usage by up to 30.93%).

Scaled post‑training now drives many of the largest capability gains in language models (LMs), yet its effect on pretrained knowledge remains poorly understood. Not all forgetting is equal: Forgetting one fact (e.g., a U.S. president or an API call) does not “average out” by recalling another. Hence, we propose a sample-wise paradigm to measure what is forgotten and when backward transfer occurs. Our metric counts 1→0 transitions (correct before post‑training, incorrect after) to quantify forgetting and 0→1 transitions to quantify backward transfer. Traditional task averages conflate these effects and obscure large changes. For multiple‑choice benchmarks, we add chance‑adjusted variants that subtract the expected contribution of random guessing from pre‑ and post‑training accuracies. We apply this framework across post‑training stages, model sizes, and data scales. Our large‑scale analysis across nearly 30 model pairs and 100 sub-benchmarks with up to 32,768 generated tokens per sample shows that: (1) Domain-continual pretraining induces moderate forgetting with low backward backward transfer; (2) RL/SFT post-training applied to base models and Instruction tuning yield substantial backward transfer with minimal forgetting; (3) Applying RL/SFT to instruction‑tuned models is sensitive on data scale: at small scales, both forgetting and backward transfer are small; at larger scales, effects are mixed and warrant further study with better controls; (4) Model merging does not reliably mitigate forgetting. Overall, our framework offers a practical yardstick for mapping how post‑training alters pretrained knowledge at scale -- enabling progress towards generally capable AI systems.

Monitoring Large Language Model (LLM) outputs is crucial for mitigating risks from misuse and misalignment. However, LLMs could evade monitoring through steganography: Encoding hidden information within seemingly benign generations. In this paper, we evaluate the steganography capabilities in frontier LLMs to better understand the risk they pose. We focus on two types of steganography: passing encoded messages and performing encoded reasoning. We find that current models are unable to encode short messages in their outputs without a monitor noticing under standard affordances. They can succeed, however, if given additional affordances like using an unmonitored scratchpad and coordinating on what encoding scheme to use. We additionally find early signs that models can perform basic encoded reasoning in a simple state-tracking problem. This includes some ability to reason with their own and pre-defined schemes, including encoding schemes such as Hexadecimal. Despite this, they can rarely hide reasoning subtly within a cover task to fool a monitor. Overall, our results indicate that current LLMs exhibit nascent steganographic capabilities. While these capabilities are likely insufficient to bypass well-designed monitors at present, this could change in the future.