Long-Horizon LLM Reasoning

Current frontier LLMs can theoretically process long contexts with 1M tokens or more. But to what extent can they go beyond simple retrieval and perform deeper reasoning over such long contexts? We empirically investigate long-horizon reasoning capabilities of LLMs, focusing on deductive logic expressed in Prolog. We construct ProloNg, a synthetic testbed to probe Prolog Long Reasoning, which systematically varies the complexity (reasoning depth) of problems, where the hardest case has a reasoning depth of 22 and 62k context length. We study 8 reasoning models across 5 families of frontier LLMs, and find that performance degrades substantially as reasoning depth grows, with the majority of models approaching chance beyond depth 10.

We present EdgeRock, a family of multimodal models that deliver strong reasoning at constant memory. Most models keep reasoning history in a key-value (KV) cache that grows with every token, consuming accelerator memory, limiting concurrent requests, and competing with perception and control on edge devices. With fixed history, memory is allocated once and never runs out, however long the model reasons. Constant memory alone is not new: bounded-state models (recurrent, state-space, and sliding-window) already achieve it, but often at the cost of reasoning, because they cannot keep the distant details that later reasoning needs. We therefore introduce Rock Memory Anchors (RMA): the model learns what is worth remembering and stores it as KV records in a fixed-size bank, directly readable however far back the source lies. EdgeRock-4B, our first open-source release, supports text and image reasoning and reaches 82.9% mean pass@1 on AIME 2024-2026, while the bounded-state models we evaluate reach at most 18.8%, even at 14B scale. This result is on par with leading compact models whose memory grows with reasoning. Compared with its source model, EdgeRock-4B uses up to 99.1% less KV cache and delivers up to 6.42$\times$ higher end-to-end batch throughput.

Large language models deployed as personalized assistants must reason over long, evolving interaction histories. However, in long-term dialogue reasoning, relevant evidence is scattered across sessions, preferences may be revised over time, and standard long-context training fails to address these challenges under data scarcity and prohibitive computational costs. We propose StateTree, a data-driven RL method that constructs a challenging auxiliary task from scarce dialogues with verifiable ground truth. StateTree augments multi-session dialogues with a tree-structured path-tracing task: key-value records are embedded across sessions to form a binary tree. Solving the task requires the model to traverse from root to leaf by retrieving records across sessions and comparing timestamps to resolve branches, then recover the hidden target question among distractor leaves. We apply curriculum RL training progressively increasing tree depth and introduce a compositional variant whose edges carry step-level reasoning fragments, training the model to compose partial cues into coherent queries. Trained on 10K-token contexts, StateTree generalizes to 128K tokens without full-length RL costs and exhibits capabilities including cross-session retrieval, temporal reasoning, knowledge update, and compositional multi-hop reasoning. StateTree outperforms both SFT and RL-based baselines while preserving short-context general reasoning. StateTree-7B achieves gains up to +23.60% on LongMemEval (128k), and StateTree-14B reaches 59.00% accuracy on LongMemEval, surpassing QwenLong-L1-32B (45.20%).

Beam-search-based test-time methods provide an effective way to improve large language model (LLM) performance on long-horizon generation by pruning invalid reasoning paths early, leading to significantly improved reasoning efficiency and more favorable test-time cost scaling. Despite strong empirical success, the theoretical understanding of beam search remains limited. In this paper, we study the test-time compute guarantee of the commonly used beam search framework that uses the model's internal log-likelihood for intermediate scoring, while relying on an external reward model only after a complete response is generated. We first establish a lower bound for vanilla beam search, showing that at least $Ω(C^\star(x)^2)$ samples are required for the optimal response to survive, where $C^\star(x)$ is the token-level coverage coefficient for prompt $x$. This motivates our modified confidence-filtered beam search (CF-Beam), which reduces the sufficient coverage dependence from quadratic to nearly linear under prefix competitiveness, for fixed horizon, gap, and target accuracy. We then show that the regret of CF-Beam is upper-bounded by the probability of rare failure events and the reward estimation error scaled by a path-level coverage coefficient, where the rare-failure term vanishes as per-step sampling increases. Our results highlight a fundamental advantage of beam search over sequence-level inference methods such as Best-of-N and Best-of-Majority. While the guarantees of these approaches typically involve coverage coefficients that grow exponentially with the horizon $L$, CF-Beam controls the dominant search-induced term through a token-level coverage coefficient that scales polynomially with $L$. Our numerical experiments further confirm that beam search is more robust on hard instances and under increasing reasoning horizons.

Long-horizon reasoning remains a central challenge for large language models (LLMs) under sparse-reward regimes. We argue that this brittleness arises from two biases induced by complex reasoning spaces: an exploration bias, where models are drawn toward locally plausible but structurally unstable branches, and a compounding bias, where small local deviations accumulate across depth and suppress rare rewards. We introduce Symbolic Closure Analysis (SCA) as a theoretical lens characterizing how branching structures and sparse rewards induce these biases in long-horizon reasoning with local admissibility, and as a design principle for structural priors in less formal reasoning tasks. Motivated by this analysis, we propose SAGE (Structural Admissibility-Guided Exploration), a unified framework that injects structural guidance to alleviate exploration bias and compounding bias in long-horizon reasoning. SAGE combines two complementary structural guidance: algebraic sparsification, which projects locally admissible candidates onto operator-indexed algebraic subspaces to suppress spurious branching and mitigate exploration bias, and hyperbolic structural guidance, which embeds reasoning states into a negatively curved space to provide dense depth-wise signals and mitigate compounding bias. Across 12 benchmarks and 7 model families, SAGE outperforms competitive baselines. In particular, SAGE achieves up to an 8-fold improvement on the Andrews-Curtis problem, an open real-world long-horizon task. Code is available at: https://github.com/Susan571/SAGE-NeurIPS2026.

Long-horizon reasoning is vulnerable to early errors that compromise later decisions. We present QART, the Quantum-Augmented Reasoning Transformer, a quantum--classical hybrid architecture combining a backbone language model with quantum encoding, CIM-based QUBO optimization, and quantum decoding. Semantic information can come from hidden representations or model-generated text; detailed encoding and optimization procedures remain proprietary. Under explicit assumptions, we establish a conditional asymptotic reliability separation from single-trajectory autoregressive LLMs. For a common task family with aligned optimality and acceptance criteria, autoregressive acceptance probability tends to zero when cumulative conditional risk of irreversible errors diverges. QART's task-optimal-path recovery probability remains bounded away from zero if conditional probabilities for optimal-path coverage and semantic fidelity, spectral certification, dynamical reachability, and faithful readout remain uniformly positive under a specified resource schedule. The architecture alone does not imply these bounds. Paired measurements on six long-horizon benchmarks using DeepSeek V4 Flash, GLM-5.3, and GPT-5.5 xhigh in a Codex agent environment favor QART in 14 of 15 backbone--benchmark pairs. Relative gains reach 84.0% on SciCode, 47.6% on $τ^3$-Bench, and 44.4% on Terminal-Bench 4.0; the DeepSeek V4 Flash configuration regresses by 7.8% on DeepSWE. These results do not directly validate the asymptotic separation. Potential quantum scaling laws are formulated as conditional hypotheses. A quantum-advantage interpretation requires a demonstrated CIM quantum advantage over strong classical solvers and its transfer to end-to-end reasoning after all system overheads.

Large language models (LLMs) have achieved strong performance on a wide range of natural language tasks, and recent benchmarks suggest that they are increasingly adept at multi-hop reasoning. However, these benchmarks are typically short-horizon, requiring only a small number of retrieval or inference steps, and provide limited evidence of reliability on real-world tasks that involve following manuals spanning hundreds of pages with complex, interdependent guidelines. In this paper, we introduce Tasks over Application Manuals (TAM), a benchmark for evaluating long-horizon procedural reasoning. We construct TAM by curating real-world tasks from two domains: ICD-10-CM clinical coding (mapping medical conditions to diagnostic codes) and U.S. federal sentencing (computing crime sentencing guideline outcomes, specifically offense levels), with human-validated labels. Each task requires following an authoritative manual with tens of thousands of rules and executing a sequence of interdependent steps across different sections to produce an exact answer. We evaluate general-purpose prompting approaches, including retrieval-augmented generation, ReAct-style prompting, and an agent-harness baseline on GPT-5, and find that the best exact-match performance remains extremely low: 1% on ICD-10-CM coding and 15.5% on sentencing tasks. These results show that current benchmarks may overestimate LLM reasoning ability and miss a key challenge: reliably following long, rule-based procedures. The complete TAM data and code are publicly available.

Large Language Models (LLMs) increasingly act as autonomous agents executing complex, long-running procedural skills. Existing agent runtimes maintain execution by continually appending observations, actions, and intermediate reasoning traces to an ever-growing conversation history, causing latency degradation and context-poisoning failures over long horizons. We present SKILL. state, a runtime architecture that replaces append-only conversational history with an explicit, mutable execution state. At each execution step, the model receives only the immutable skill specification, the current structured execution state, and the latest observation. Intermediate reasoning is discarded immediately after producing a validated state update, preventing prompt growth with execution history. Across diverse datasets, models, and execution environments, SKILL. state improves task accuracy while substantially reducing cumulative token consumption. Our results demonstrate that explicit execution state is an effective and architecture-agnostic abstraction for scalable long-horizon agent skills.

Frontier language models solve reasoning problems in a single forward pass that would have been research contributions years ago, yet fail at multi-hour tasks: losing track of earlier decisions, declaring half-finished work done, or drifting from goals. We call this the horizon gap and survey 1,547 arXiv papers (2024-2026) collected via systematic seed harvest with a disclosed 26.8% bleed filter, extended by targeted supplementation. We disambiguate three routinely conflated properties: long-horizon (task property: required steps), long-context (model property: token capacity), and long-term memory (system property: persistence across steps/sessions). We organize the corpus into six categories tracking a long-horizon task's lifecycle -- planning, memory, execution, training, evaluation, and foundations/safety -- crossed with an axis capturing where horizons are carried (within-context, within-task-beyond-context, or cross-task-persistent). Across all categories, we find the same pattern: outcome-only signals grow uninformative as horizons lengthen, and the field's response -- whether process reward models, credit assignment, or trajectory-level diagnostics -- manufactures denser step-level signals. We treat critical and diagnostic literature as first-class threads throughout, arguing that segregating critique from method would routinely split single papers across chapters. We close by naming open measurement problems: decomposing model versus harness capability, managing correlated bias in process-level signals used for both training and evaluation, and whether long-horizon reliability admits general predictive theory.

Long-horizon reasoning in recent LLMs demands that the model switch between distinct skills inside a reasoning chain, such as first doing a math derivation, then using the result to plan a schedule. We call such problems cross-skill long-horizon tasks: multi-step tasks whose steps require different reasoning skills and depend on earlier outputs. Existing benchmarks often evaluate individual skills, lacking a principled way to measure how well a model switches between skills. We address this gap from both the evaluation and training sides. We introduce Skill Entropy, a measure of the difficulty of switching from one skill to another. We then propose Skill^2-Bench, a benchmark of cross-skill long-horizon tasks built over 558 skills across 9 verifiable and open-ended domains. Each task is assigned a task-level skill-entropy score and grouped into three difficulty levels. Evaluating 8 frontier and 4 open-source models on Skill^2-Bench reveals a skill-switching gap: accuracy decreases on higher-entropy tasks. We then turn skill entropy from a benchmark scale into a training signal. We propose Skill-Entropy RL, an RL framework where the model predicts not only the answer at each step but also the skill used to produce it. The reward combines step-level correctness with a skill-entropy reward that measures the alignment between the model-predicted skill sequence and the gold skill sequence. On Qwen3-4B-Instruct and Qwen3-1.7B, Skill-Entropy RL improves the Skill^2-Bench score from 34.4% to 68.4% and from 14.6% to 40.1%, respectively, outperforming competitive baselines. The same pipeline can be applied to off-the-shelf training data such as OpenR1-Math, indicating that skill entropy is a reusable training signal. Code available at: https://github.com/Gen-Verse/Skill-Entropy-RL

Long-horizon tasks require sustained perception, reasoning, and exploration, and are a persistent challenge for large language model (LLM) agents. This gap is reflected in their limited performance on continual learning benchmarks such as ARC-AGI-3 and NetHack, especially when evaluated without specialized harnesses. Various agent harnesses have been proposed to close the gap, and each commits to a strategy for handling long sequences of observations, i.e., what information to save from the environment and how to load it into model context, a choice we argue is particularly consequential. Existing methods for context management have typically been designed around a tradeoff, where preserving more information makes relevant details harder to retrieve. Recent progress in coding agents, however, makes new approaches to memory viable. We propose PRO-LONG, a minimal context management framework built around programmatic memory for LLM agents in long-horizon, exploratory settings. PRO-LONG addresses the tradeoff by keeping a complete, structured interaction log and using programmatic tools to search this history efficiently. On NetHack, we find increasing gains from using PRO-LONG for cross-episodic memory, with scores reaching up to 2.2x those of a base coding agent. On the full ARC-AGI-3 public game set, PRO-LONG improves over this baseline agent by an average of 18.0 percentage points across frontier models, and matches or exceeds state-of-the-art specialized harnesses (up to 97.4% best@2) while using 4.2-5.8x fewer tokens. Relevant code and logs are available at https://github.com/alexisfox7/PRO-LONG.

Reinforcement learning (RL) has been applied to improve large language model (LLM) reasoning, yet the systematic study of how training scales with task difficulty has been hampered by the lack of controlled, scalable environments. Observed LLM shortcomings in long-horizon reasoning have raised the prospect that they are fundamental to the autoregressive transformer architecture. To address this, we introduce ScaleLogic, a synthetic logical reasoning framework that offers independent control over two axes of difficulty: the depth of the required proof planning (i.e., the horizon) and the expressiveness of the underlying logic. Our proposed framework supports a wide range of logics: from simple implication-only logic ("if-then") towards more expressive first-order reasoning with conjunction ("and"), disjunction ("or"), negation ("not"), and universal quantification ("for all"). Using this framework, we show that the RL training compute $T$ follows a power law with respect to reasoning depth $D$ ($T \propto D^γ$, $R^{2} > 0.99$), and that the scaling exponent $γ$ increases monotonically with logical expressiveness, from $1.04$ to $2.60$. On downstream mathematics and general reasoning benchmarks, more expressive training settings yield both larger performance gains (up to $+10.66$ points) and more compute-efficient transfer compared to less expressive settings, demonstrating that what a model is trained on, not just how much it is trained, shapes downstream transfer. We further show that the power-law relationship holds across multiple RL methods, and curriculum-based training substantially improves scaling efficiency. More broadly, our results demonstrate that LLM shortcomings in long-horizon reasoning are not fundamental to the underlying architecture, and can be addressed by improved training methodology and data.

Current reasoning paradigms for LLMs include chain-of-thought, ReAct, and post-hoc self-critique. These paradigms rely on two assumptions that fail on long-horizon, multi-stage tasks. As a result, errors accumulate silently across reasoning steps, leaving an open question: can a reasoning system effectively detect and recover from its own failures? We present ReFlect, a harness system for LLM reasoning that creates standalone error detection and recovery logic as a deterministic wrapper around the model. Controlled experiments across 6 reasoning domains show that prompt-level self-critique produces formulaic templates that flag no issues in 90 of 100 audited reflection blocks, and the investigated LLMs wrongly accept a wrong answer in at least 76% of cases. Our ReFlect harness achieves task success rates ranging from 41% on gpt-4o-mini to 56% on Claude Sonnet 4.5 across six models spanning small and frontier scale, with per-model gains over Direct CoT ranging from +7 pp on Qwen2.5-72B to +29 pp on Claude Sonnet 4.5, and additionally raises SWE-bench patch-structural quality from 0% (Direct CoT) to between 82% (Qwen2.5-72B) and 87% (GPT-4o). Notably, the harness gain is inversely proportional to the model's Direct CoT task success rate (the fitted slope is -1.69 with r=-0.76): each pp lost in baseline success rate is mechanically recovered by 1.69 pp of harness gain. We spot that adding structured reasoning state and operators yields only 15.0--18.7% pair-mean on Llama-3.3-70B and Qwen2.5-72B because models at this scale cannot reliably populate the state its operators require. ReFlect is model-agnostic, training-free, and operates entirely at inference time.

As language models are increasingly deployed for complex autonomous tasks, their ability to reason accurately over longer horizons becomes critical. An essential component of this ability is planning and managing a long, complex chain-of-thought (CoT). We introduce LongCoT, a scalable benchmark of 2,500 expert-designed problems spanning chemistry, mathematics, computer science, chess, and logic to isolate and directly measure the long-horizon CoT reasoning capabilities of frontier models. Problems consist of a short input with a verifiable answer; solving them requires navigating a graph of interdependent steps that span tens to hundreds of thousands of reasoning tokens. Each local step is individually tractable for frontier models, so failures reflect long-horizon reasoning limitations. At release, the best models achieve <10% accuracy (GPT 5.2: 9.8%; Gemini 3 Pro: 6.1%) on LongCoT, revealing a substantial gap in current capabilities. Overall, LongCoT provides a rigorous measure of long-horizon reasoning, tracking the ability of frontier models to reason reliably over extended periods.

Long-horizon execution in Large Language Models (LLMs) remains unstable even when high-level strategies are provided. Evaluating on controlled algorithmic puzzles, we demonstrate that while decomposition is essential for stability, extreme decomposition creates a "no-recovery bottleneck". We show that this bottleneck becomes critical due to highly non-uniform error distribution, where consistent errors on a few "hard" steps become irreversible. To address this, we propose Lookahead-Enhanced Atomic Decomposition (LEAD). By incorporating short-horizon future validation and aggregating overlapping rollouts, LEAD provides enough isolation to maintain stability while retaining enough local context to correct errors. This enables the o4-mini model to solve Checkers Jumping up to complexity $n=13$, whereas extreme decomposition fails beyond $n=11$.

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.

The test-time compute strategy, such as Chain-of-Thought (CoT), has significantly enhanced the ability of large language models to solve complex tasks like logical reasoning. However, empirical studies indicate that simply increasing the compute budget can sometimes lead to a collapse in test-time performance when employing typical task decomposition strategies such as CoT. This work hypothesizes that reasoning failures with larger compute budgets stem from static planning methods, which hardly perceive the intrinsic boundaries of LLM reasoning. We term it as the Limited Reasoning Space hypothesis and perform theoretical analysis through the lens of a non-autonomous stochastic dynamical system. This insight suggests that there is an optimal range for compute budgets; over-planning can lead to redundant feedback and may even impair reasoning capabilities. To exploit the compute-scaling benefits and suppress over-planning, this work proposes Halo, a model predictive control framework for LLM planning. Halo is designed for long-horizon tasks with reason-based planning and crafts an entropy-driven dual controller, which adopts a Measure-then-Plan strategy to achieve controllable reasoning. Experimental results demonstrate that Halo outperforms static baselines on complex long-horizon tasks by dynamically regulating planning at the reasoning boundary.