Long-Context Reasoning in Language Models

Visual long-document understanding is critical for enterprise, legal, and scientific applications, yet the best performing open recipes have not explored reasoning, a capability which has driven leaps in math and code performance. We introduce a synthetic data pipeline for reasoning in long-document understanding that generates thinking traces by scoring each page for question relevance, extracting textual evidence and ordering it from most to least relevant. We apply SFT to the resulting traces within <think> tags, gated by a <cot> control token, and the resulting reasoning capability is internalized via low-strength model merging. We study Qwen3 VL 32B and Mistral Small 3.1 24B. With Qwen3 VL, we achieve 58.3 on MMLongBenchDoc, surpassing the 7$\times$ larger Qwen3 VL 235B A22B (57.0). With Mistral, we show that synthetic reasoning outperforms distillation from the Thinking version's traces by 3.8 points on MMLBD-C, and internalized reasoning exhibits 12.4$\times$ fewer mean output tokens compared to explicit reasoning. We release our pipeline for reproducibility and further exploration.

As real-world tasks grow increasingly complex, long-context reasoning has become a core capability for Large Language Models (LLMs). However, few studies explore which data types are effective for long-context reasoning and why. We find that structured table data with periodic structures shows strong potential for long-context reasoning. Motivated by this observation, we mathematically analyze tabular dependency structures using mutual information, revealing periodic non-vanishing dependencies in table data. Furthermore, we systematically analyze the capabilities of structured table data, conduct relevant scaling experiments, and validate its underlying mechanisms for enhancing long-context reasoning, yielding several meaningful insights. Leveraging these insights, we propose a simple yet scalable pipeline(TableLong) for synthesizing high-quality, diverse, and verifiable structured table data to boost long-context reasoning via RL. Extensive experimental results demonstrate that table data significantly enhances the long-context reasoning capability of LLMs across multiple long-context benchmarks (+8.24% on average), and even improves performance on out-of-domain benchmarks (+8.06% on average). We hope that our insights provide practical guidance for effective post-training data to enhance long-context reasoning in LLMs.

Long-context language modeling is commonly framed as a scalability challenge of token-level attention, yet local-to-global information structuring remains largely implicit in existing approaches. Drawing on cognitive theories of discourse comprehension, we propose HiCI (Hierarchical Construction--Integration), a hierarchical attention module that constructs segment-level representations, integrates them into a shared global context, and broadcasts both to condition segment-level attention. We validate HiCI through parameter-efficient adaptation of LLaMA-2 with only <5.5% additional parameters, extending context from 4K to 100K tokens (7B) and 64K tokens (13B). Across language modeling, retrieval, and instruction-following benchmarks, HiCI yields consistent improvements over strong baselines, including matching proprietary models on topic retrieval and surpassing GPT-3.5-Turbo-16K on code comprehension. These results demonstrate the effectiveness of explicit hierarchical structuring as an inductive bias for long-context modeling.

LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet existing RLMs depend on an open-ended read-eval-print loop (REPL) in which the model generates arbitrary control code, making execution difficult to verify, predict, and analyse. We introduce $λ$-RLM, a framework for long-context reasoning that replaces free-form recursive code generation with a typed functional runtime grounded in $λ$-calculus. It executes a compact library of pre-verified combinators and uses neural inference only on bounded leaf subproblems, turning recursive reasoning into a structured functional program with explicit control flow. We show that $λ$-RLM admits formal guarantees absent from standard RLMs, including termination, closed-form cost bounds, controlled accuracy scaling with recursion depth, and an optimal partition rule under a simple cost model. Empirically, across four long-context reasoning tasks and nine base models, $λ$-RLM outperforms standard RLM in 29 of 36 model-task comparisons, improves average accuracy by up to +21.9 points across model tiers, and reduces latency by up to 4.1x. These results show that typed symbolic control yields a more reliable and efficient foundation for long-context reasoning than open-ended recursive code generation. The complete implementation of $λ$-RLM, is open-sourced for the community at: https://github.com/lambda-calculus-LLM/lambda-RLM.

Language models struggle to generalize beyond pretraining context lengths, limiting long-horizon reasoning and retrieval. Continued pretraining on long-context data can help but is expensive due to the quadratic scaling of Attention. We observe that most tokens do not require (Global) Attention over the entire sequence and can rely on local context. Based on this, we propose L2A (Learning To Attend), a layer that enables conditional (token-wise) long-range memory access by deciding when to invoke global attention. We evaluate L2A on Qwen 2.5 and Qwen 3 models, extending their effective context length from 32K to 128K tokens. L2A matches the performance of standard long-context training to within 3% while skipping Global Attention for $\sim$80% of tokens, outperforming prior baselines. We also design custom Triton kernels to efficiently implement this token-wise conditional Attention on GPUs, achieving up to $\sim$2$\times$ improvements in training throughput and time-to-first-token over FlashAttention. Moreover, L2A enables post-training pruning of highly sparse Global Attention layers, reducing KV cache memory by up to 50% with negligible performance loss. Our code is released under Apache 2.0 at https://github.com/awslabs/hybrid-model-factory/tree/main/examples/research/L2A.

Modern language models reason within bounded context, an inherent constraint that poses a fundamental barrier to long-horizon reasoning. We identify recursion as a core principle for overcoming this barrier, and propose recursive models as a minimal realization, where the model can recursively invoke itself to solve subtasks in isolated contexts. We prove that any computable problem admits a recursive decomposition of reasoning in which each subtask requires only exponentially smaller active context than standard autoregressive models; this strictly surpasses any context management approach confined to a single sequence, such as summarization. We further generalize our framework to modern agentic systems with arbitrary context processing and control flows, and prove that recursive models can achieve optimal power within this broader class. Experimentally, we test two settings: fine-tuning a pretrained base model for recursive SAT solving, and training a small model from scratch on Go traces generated by exact game-tree search. Both show improved long-horizon accuracy with small active contexts.

Understanding and reasoning over long contexts is a crucial capability for language models (LMs). Although recent models support increasingly long context windows, their accuracy often deteriorates as input length grows. In practice, models often struggle to keep attention aligned with the most relevant context throughout decoding. In this work, we propose DYSCO, a novel decoding algorithm for improving long-context reasoning. DYSCO leverages retrieval heads--a subset of attention heads specialized for longcontext retrieval--to identify task-relevant tokens at each decoding step and explicitly up-weight them. By doing so, DYSCO dynamically adjusts attention during generation to better utilize relevant context. The method is training-free and can be applied directly to any off-the-shelf LMs. Across multiple instruction-tuned and reasoning models, DYSCO consistently improves performance on challenging long-context reasoning benchmarks, yielding relative gains of up to 25% on MRCR and LongBenchV2 at 128K context length with modest additional compute. Further analysis highlights the importance of both dynamic attention rescaling and retrievalhead guided selection for the effectiveness of the method, while providing interpretability insights into decoding-time attention behavior. Our code is available at https://github.com/princeton-pli/DySCO.

Rapidly increasing context lengths have led to the assumption that large language models (LLMs) can directly reason over entire codebases. Concurrently, recent advances in LLMs have enabled strong performance on software engineering benchmarks, particularly when paired with agentic workflows. In this work, we systematically evaluate whether current LLMs can reliably perform long-context code debugging and patch generation. Using SWE-bench Verified as a controlled experimental setting, we first evaluate state-of-the-art models within an agentic harness (mini-SWE-agent), where performance improves substantially: GPT-5-nano achieves up to a 31% resolve rate on 100 samples, and open-source models such as Deepseek-R1-0528 obtain competitive results. However, token-level analysis shows that successful agentic trajectories typically remain under 20k-30k tokens, and that longer accumulated contexts correlate with lower success rates, indicating that agentic success primarily arises from task decomposition into short-context steps rather than effective long-context reasoning. To directly test long-context capability, we construct a data pipeline where we artificially inflate the context length of the input by placing the relevant files into the context (ensuring perfect retrieval recall); we then study single-shot patch generation under genuinely long contexts (64k tokens). Despite this setup, performance degrades sharply: Qwen3-Coder-30B-A3B achieves only a 7% resolve rate at 64k context, while GPT-5-nano solves none of the tasks. Qualitative analysis reveals systematic failure modes, including hallucinated diffs, incorrect file targets, and malformed patch headers. Overall, our findings highlight a significant gap between nominal context length and usable context capacity in current LLMs, and suggest that existing agentic coding benchmarks do not meaningfully evaluate long-context reasoning.

Reinforcement Learning (RL) has emerged as a key driver for LLM reasoning. This capability is equally pivotal in long-context scenarios---such as long-dialogue understanding and structured data analysis---where the challenge extends beyond consuming tokens to performing rigorous deduction. While existing efforts focus on data synthesis or architectural changes, recent work points out that relying solely on sparse, outcome-only rewards yields limited gains, as such coarse signals are often insufficient to effectively guide the complex long-context reasoning. To address this, we propose LongR, a unified framework that enhances long-context performance by integrating a dynamic ``Think-and-Read'' mechanism---which interleaves reasoning with document consultation---with a contextual density reward based on relative information gain to quantify the utility of the relevant documents, without evidence annotations. Empirically, LongR achieves a gain of over 9% on LongBench v2 and consistent improvements on RULER and InfiniteBench, demonstrating robust efficiency in navigating extensive contexts. Furthermore, LongR consistently enhances performance across diverse RL algorithms (e.g., DAPO, GSPO). Finally, we conduct in-depth analyses to investigate the impact of reasoning chain length on efficiency and the model's robustness against distractors.

As model context lengths continue to grow, concerns about whether models effectively use the full context length have persisted. While several carefully designed long-context evaluations have recently been released, these evaluations tend to rely on retrieval from one or more sections of the context, which allows nearly all of the context tokens to be disregarded as noise. This represents only one type of task that might be performed with long context. We introduce Oolong, a benchmark of long-context reasoning tasks that require analyzing individual chunks of text on an atomic level, and then aggregating these analyses to answer distributional questions. Oolong is separated into two task sets: Oolong-synth, a set of naturalistic synthetic tasks, where we can easily ablate components of the reasoning problem; and Oolong-real, a downstream setting which requires reasoning over real-world conversational data. Oolong requires models to reason over large quantities of examples, to perform both classification and counting in-context, and to reason over temporal and user relations. Even frontier models struggle on Oolong, with GPT-5, Claude-Sonnet-4, and Gemini-2.5-Pro all achieving less than 50% accuracy on both splits at 128K. We release the data and evaluation harness for Oolong to enable further development of models that can reason over large quantities of text.

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. https://perk-long-context.web.app