Long-Horizon Reasoning

On-policy distillation (OPD) provides dense token-level supervision on student rollouts, but this supervision can become unreliable when the student and teacher diverge, either because of a large initial policy gap or compounding errors in long-horizon reasoning and tool use. We introduce Divergence-Triggered Dynamic Distillation (DTDD), an adaptive OPD framework that uses segment-level student-teacher divergence to trigger teacher takeover during training. When divergence triggers an intervention during reasoning, the student prefix continues to receive standard OPD supervision. The teacher then generates a recovery suffix, which the student learns through behavior cloning, using cross-entropy on the teacher-generated tokens. We evaluate DTDD in three regimes: long-horizon reasoning, distillation from a base initialization without offline supervised fine-tuning (SFT), and multi-turn agents. We also compare alternative trigger designs and teacher-intervention rates. DTDD reduces the post-warmup peak gradient norm by $8.6\times$ and, from a base initialization, reaches $21.3\%$ held-out math accuracy in $2.6\times$ fewer optimizer updates than OPD; both methods finish near $22\%$. It improves best-observed performance by $4.8$ and $4.1$ percentage points on ALFWorld with LoRA and agentic code, respectively. Ablations show that segment-averaged triggers outperform token-spike triggers. Behavior cloning is also more effective than the tested OPD surrogate for training teacher-generated recoveries. Across 23 experimental arms, takeover tends to help when the teacher substantially outperforms the OPD-trained student, provided that the teacher can recover from student-visited states, the student can learn those recoveries, and teacher intervention is neither excessive nor insufficient.

Long-horizon agents often struggle to recover from failures whose causes lie several steps earlier, beyond what local reflection or backtracking can resolve. We introduce BELIEFWEAVER, a framework that combines persistent evidence across attempts with prospective reasoning over repair directions. It maintains a relational belief state over frontiers, attempts, observations, and checkpoints. Execution evidence updates related frontier priorities across attempts and rollback, while diagnostic evidence gates execution. An implicit world model (IWM) evaluates repair hypotheses, predicts progress, and identifies relations among frontiers to guide exploration. We further distill these recurring IWM reasoning components into a 9B student through supervised fine-tuning and on-policy distillation (OPD). Across three terminal-based benchmarks, BELIEFWEAVER improves aggregate final score by 5.1 percentage points over native Terminus-2 continuation, with positive trends in exploration efficiency. The distilled 9B student improves final score by 9.8 percentage points over the reported native baseline while reducing estimated teacher API cost by 54.8% relative to the matched teacher. These results show that persistent evidence and prospective reasoning can improve recovery in long-horizon agent tasks while substantially reducing reliance on teacher-model inference.

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.

World models must predict how an environment evolves under sequences of actions, enabling agents to compare possible futures and reason about counterfactual actions before acting. Long-horizon prediction is commonly obtained by recursively applying a one-step transition model, but intermediate errors can compound over time. Multi-step dynamics models instead condition on a sequence of future actions and predict their consequences directly, but become harder to learn as horizon grows: the model must track interacting state changes across the trajectory, endpoint supervision provides weak credit assignment, and intermediate predictions can remain plausible while losing information needed for later states. We show that these challenges can be addressed by casting the internal evolution of a multi-step transition as structured reasoning over textual world states: reasoning over sparse state changes reduces the burden of state tracking, a predictive-gain objective rewards the learned state for improving over a matched predictor that conditions on raw history instead, and intermediate predictive rewards supervise each state along the trajectory. Because these intermediate states are explicit textual representations of the world, they provide semantically meaningful targets that can be inspected, scored, and corrected during training. Across ScienceWorld, Jericho, and CEO-Bench, our approach achieves the strongest average long-horizon performance against recursive and non-recursive baselines that condition directly on raw history, with gains increasing at longer horizons. In a controlled counterfactual study, our model is also the only one with statistically significant sensitivity to future actions.

Long-horizon search requires agents to gather evidence across multiple steps and synthesize it into well-supported answers. The recent agent harnesses provide a natural and promising framework to support such long-running search processes. As interaction histories grow, one single agent in harnesses might get stuck and cause the policy to lose track of unresolved questions, overlook useful evidence, or terminate before sufficient support has been collected. One of promising way is to decouple three distinct responsibilities of proposing retrieval actions, updating persistent state, and deciding when to stop rather than concentrating them within a single policy. Targeted at it, we introduce Harness-Search, a multi-agent search harness to reduce the local errors propagating across subsequent exploration, evidence curation, and termination decisions. In particular, Harness-Search assigns these responsibilities to three permission-bounded authorities: a Retrieval Policy that proposes search operations, a Memory Operator that validates and commits persistent-state updates, and a Summary Auditor that accepts or rejects termination based on the sufficiency of the curated evidence. Together, these roles form a Propose-Commit-Audit loop in which actions are proposed, persistent evidence is selectively committed, and stopping decisions are subjected to an explicit sufficiency check. Across seven long-horizon search benchmarks, Harness-Search improves both retrieval and answer generation under the same policy backbone, increasing Recall by 4.60-27.92 points and Final-Answer Recall by 12.34-30.13 points over the strongest harness-based baseline on each evidence-retrieval benchmark. Moreover, trajectory-level analyses show that Harness-Search continues to accumulate useful evidence and expand evidence coverage with less redundant retrieval as the search history grows.

Long-horizon research agents must decide both how to investigate and what to investigate next as evidence accumulates. This is hard to learn because such decisions are sparse in long execution traces, and their consequences may emerge several investigations later. We introduce Meta-reasoning for Iterative Research Agents (MIRA), a hierarchical architecture separating research allocation from execution. An outer-loop meta-reasoner curates context from a persistent research record, then writes a work order for the next investigation or ends the episode. A fresh inner-loop executor carries out each work order, making execution part of the transition between meta-reasoning actions. Without policy training, MIRA improves long-horizon inference and allocates additional compute more effectively in theorem proving and open-ended neural-architecture research. Its decision boundaries also provide natural units for credit assignment. At each boundary, we train a generative critic to forecast expected remaining return from partial states, outperforming token-level alternatives. Cross-environment pretraining improves forecasting and adaptation, yielding a transferable prior for valuing partial progress. We use this prior to initialize MIRA-AC, a generative actor-critic jointly trained to forecast remaining return and choose the next investigation, without a separate critic model. MIRA-AC concentrates policy optimization on meta-reasoning decisions, enabling efficient long-horizon reinforcement learning without directly optimizing the longer execution traces they initiate. Training MIRA-AC on the model's own proxy hill-climbing signals improves gold performance across four autoresearch environments; the actor transfers with cross-environment value initialization. Together, these results show that meta-reasoning can be learned as an explicit policy for directing long-horizon autonomous research.

Random exploration reveals how an environment can be traversed before a goal is specified. Can this experience support long-range planning without policy-improvement training? Our random-walk analysis explains what temporal relations contain: short horizons reveal geodesic geometry in the diffusion limit, while longer horizons reveal connectivity between regions before mixing removes these distinctions. We learn these relations with a conditional energy-based model that estimates temporal log-density ratios through horizon-conditioned embeddings. The model is trained on observation pairs by noise-contrastive estimation, without action or reward labels. The planner queries these learned relations at different horizons as it moves toward the goal. At test time, a separate local dynamics model predicts candidate action outcomes, and the temporal model evaluates their progress toward the goal by selecting or aggregating estimated improvements across horizons. The agent executes one action and replans with both models fixed. Experiments demonstrate long-range maze planning from random exploration using states and images. Learned score fields, embedding probes, and planned routes exhibit properties of a multiscale cognitive map. We further demonstrate egocentric navigation from random exploration and manipulation planning from suboptimal data.

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 tasks require preserving and later recovering cross-session evidence under a bounded, query-blind memory budget. Existing compression can discard fine-grained visual cues or conflate semantically similar but incompatible observations. We present C3M, a cross-session multimodal memory organization that maintains a bounded active index over persistent source text-image evidence. Relation-aware updates consolidate safe redundancy while preserving complementary and incompatible records. At query time, budgeted routing selects useful index pages and expands their associated source evidence under a fixed reader budget. Together, these mechanisms establish a compact, provenance-preserving multimodal memory organization for cross-session long-horizon tasks, retaining temporal distinctions and source links required for reliable downstream reasoning. Code is available at https://github.com/HuzhouNLP/C3M.

Language models can produce plausible short proofs, but may still be unreliable on long-horizon research problems, where progress depends on a sequence of uncertain and interdependent decisions. We introduce Stellar Colosseum, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science. Colosseum explores alternative strategies before proof construction, uses a readiness gate to decide when a route is mature enough to decompose, represents the proof plan as interdependent section-level subproblems, and routes verifier findings back to the affected part of the argument. Across these stages, it generates candidates in parallel, attacks them with targeted falsification, and combines candidates and their critiques into a single research artifact through overlapping random-sample tree aggregation. The Colosseum workflow has been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. We demonstrate the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks. Using Colosseum with Gemini 3.1 Pro, we obtain several new results that address open problems arising from papers published at top venues such as FOCS and JMLR. On TCS-Bench, a benchmark of research-level theorem-proving tasks drawn from papers published at FOCS, STOC, and SODA, Colosseum achieves 71.0% accuracy using Gemini 3.1 Pro and Gemini 3.7 Flash. In a separate Codeforces evaluation using Gemini 3.1 Pro, the proof-oriented pipeline with execution feedback solves 218 of 222 problems.

Current paradigms for training language models via reinforcement learning rely heavily on sparse outcome rewards. However, as we pursue tasks that require longer and more complicated trajectories, such strategies result in slow learning. Prior work has attempted to address this problem by rewarding partial progress; however, naive formulations are often biased and converge to suboptimal policies. We show that a simple and unbiased dense reward formulation, which we term progressive point matching, scales exponentially more efficiently to long-horizon tasks by rewarding partial progress on a segment level, both theoretically and empirically via synthetic environments. We then show how progressive point matching can be practically instantiated using a single reference trajectory per task. On extremely hard math reasoning problems, sparse outcome rewards cannot make any progress, whereas segment-level rewards enable improvements at larger test-time token budgets when measured by success rate or pass@k.

Recursive self-improvement (RSI) remains hard in long-horizon tasks, where growing histories obscure the task state and misalign skill invocation. We introduce Recuris, a recursive Experiential-Working Memory architecture for long-horizon agent harnesses, in which Working Memory tracks task progress and guides skill selection from Experiential Memory, grounding skill use in current needs rather than the full history. This coupling also turns execution into structured evidence that localizes failures to specific memory components. Across tasks, a fixed Meta-Agent turns that evidence into localized, validation-gated updates to Skill Memory that reshape execution and yield new evidence, forming a bounded recursive memory-evolution loop. Across four long-horizon benchmarks and ten models, Recuris improves task success in 35 of the 37 completed model-benchmark pairs, carrying frontier models to SOTA-level task success: on tau-bench it adds +17.8 points to GPT-5.6 Sol and +15.6 to Claude Opus 5, taking Opus 5 to 87.9%, and +16.6/+13.5 points on Qwen3.6-27B/35B on SkillFlow. The advantage widens as the interaction horizon grows, to +32.2 points on the longest tasks, and common long-horizon failures fall by up to 80%. These results position recursively evolving memory as a scalable foundation for RSI, enabling agents to continuously transform accumulated experience into increasingly effective long-horizon behavior. Code: https://github.com/Gen-Verse/Recuris

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 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.

We present Seed2.0, a model series that takes a meaningful step toward solving complex, real-world tasks. Our approach begins with identifying users' genuine needs and constructing a reliable, forward-looking evaluation system by selecting and abstracting benchmarks grounded in these needs and in realistic, complex scenarios. Guided by this evaluation system, Seed2.0 targets two persistent challenges, long-tail knowledge and complex instruction following, substantially improving the model's reliability on intricate, long-horizon tasks. Beyond these, Seed2.0 delivers world-leading reasoning intelligence, visual understanding, and search capabilities that address the most common needs of a broad user base. Through extensive real-world use cases documented in this model card, we demonstrate that Seed2.0 begins to exhibit the ability to handle initial complex real-world tasks, delivering greater value to hundreds of millions of users.

Long-horizon agents can archive large histories, but future answers still incur retrieval, rereading, and context costs. When retained memory misses answer-relevant evidence, the system must return to larger portions of the raw history. We study budgeted evidence survival: before the query is known, which source evidence should be retained so that it remains recoverable and usable under a fixed retained source-evidence token budget? We instantiate this setting as Budgeted Pre-Query Retention, where memory is written during ingestion and later read without access to the full raw stream. We introduce EMBER, a learned retention policy that constructs a compact, source-backed evidence state. EMBER stores evidence capsules: verbatim source excerpts paired with retrieval keys and update metadata, preserving both grounding and read-time access. Post-query outcome feedback trains the writer to preserve evidence across the ingestion-retrieval-answer chain. On LongMemEval-RR, our LongMemEval-derived retained-evidence protocol, EMBER-14B reaches 0.3017 F1 at the 8192-token retained-evidence comparison point, compared with 0.1765 for the strongest non-EMBER budgeted baseline. Across retained source-evidence budgets, EMBER improves F1, Retain-Recall, and Read-Recall, indicating that long-horizon memory depends on retaining evidence within the budget rather than rereading larger histories.

Long-horizon reasoning requires a system to commit to medium-horizon intent without becoming rigid: re-plan too often and computation never coheres into multi-step structure; commit too long and the plan goes stale. We study this stability-adaptivity tradeoff in the latent reasoning setting, where multi-step computation occurs inside hidden state rather than externalized token traces. We extend the Hierarchical Reasoning Model (HRM) with a feudal-style manager-worker interface: a slow high-level module periodically emits a normalized directional subgoal that persists for P low-level steps, biasing the worker's hidden-state updates and supplying an intrinsic cosine alignment loss. On ARC and ConceptARC, we find that subgoal persistence -- not subgoal injection alone -- is the central knob: moderate periods P in [3, 6] consistently outperform both very frequent (P=1) and very long horizons, with a clear minimum LM loss at P=3 (1.544 vs. 1.674 at P=1, 1.640 baseline; replicated over 5 seeds at mean 1.595, std 0.045). The intrinsic alignment weight lambda shows a complementary narrow optimum (lambda approximately 0.05). A controlled ablation at past-sweet-spot lambda isolates learned directional structure -- not architectural capacity or auxiliary loss alone -- as the source of interference when the alignment signal exceeds its optimum. Together these findings implicate a design principle for compositional planning in latent reasoning systems: medium-horizon intent must be coherent across enough computational steps for compositional structure to form.

Deep research, in which an agent searches the open web, collects evidence, and derives an answer through extended reasoning, is a prominent use case for frontier language models. Frontier deep research products score high on existing benchmarks, making it difficult to distinguish their capabilities from current evaluation data alone. We introduce DeepWeb-Bench, a deep research benchmark that is substantially harder than existing benchmarks for the current frontier. Difficulty comes from three properties of the data itself: each task requires massive evidence collection, cross-source reconciliation, and long-horizon multi-step derivation. We represent these three sources of difficulty as four capability families (Retrieval, Derivation, Reasoning, and Calibration) and report results sliced by family. Every reference answer is accompanied by a source-provenance record with four disclosure levels and cross-source checks where available, making scores easier to audit against the underlying evidence. We evaluate DeepWeb-Bench on nine frontier models and report three findings: (1) retrieval is not the bottleneck, as retrieval failures account for only 12-14% of errors while derivation and calibration failures account for over 70%; (2) strong and weak models fail in qualitatively different ways, with strong models' errors dominated by incomplete derivation and weak models' by hallucinated precision; and (3) models exhibit genuine specialization across domains, with cross-model agreement of only rho = 0.61 and per-case disagreement reaching 18.8 percentage points. The public benchmark release includes the data, rubrics, and evaluation code.

Compositional diffusion models offer a promising route to long-horizon planning by denoising multiple overlapping sub-trajectories while ensuring that together they constitute a global solution. However, enforcing local behavior over long chains is often insufficient for a coherent global structure to emerge. Recent works tackle this limitation through intrinsic search, which explores multiple paths during the denoising process. While intrinsic search improves global coherence, it comes at the cost of repeated evaluations of an already compute-heavy model. In this work, we argue that extrinsic search, performed outside the denoising process, offers a more effective mode of exploration for long-horizon planning while naturally enabling the use of classical algorithms to solve unseen combinatorial tasks at test time. Our eXtrinsic search-guided Diffuser (XDiffuser) first computes a plan over a state-space graph -- serving as a lightweight local connectivity oracle for the diffusion model. The plan is then used to guide denoising for a single trajectory, effectively offloading the burden of exploration. XDiffuser outperforms diffusion-based baselines on long-horizon tasks, with particularly large gains in the low-quality data regime and on unseen tasks beyond goal-reaching, including multi-agent coordination and TSP-style reasoning. Project website: https://yanivhass.github.io/XDiffuser-site/

Long-horizon reasoning requires deciding not only what actions to take, but how many to execute open-loop before replanning. This number, the execution depth, balances replanning cost against compounding execution errors. Most current systems either fix the execution depth as a hand-tuned scalar or adjust it at inference time with heuristic rules decoupled from the policy; we argue both can be suboptimal. In this work, we treat the execution depth as a learnable, history-conditioned variable of the policy itself, and propose PACE, a model-native VLM policy that jointly predicts what to execute and for how long under a hard decision budget. We evaluate PACE on four long-horizon environments spanning fully and partially observable settings and visual and textual modalities: Sliding Puzzle, Sokoban, ALFWorld, and ScienceWorld. Across all settings, PACE improves success rate by 3.1 to 15.6 percentage points, while using fewer decisions on average, achieving empirical success-decision Pareto dominance.

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.

Existing web agent benchmarks have largely converged on short, single-site tasks that frontier models are approaching saturation on. However, real world web use consists of long-horizon, multi-site workflows. Common web navigation tasks, such as comparing products across different domains, planning trips across multiple services, or summarizing information from multiple search queries, require sustained context and cross-site reasoning over potentially hours of browsing. To capture and evaluate such behaviors, we introduce Odysseys: a benchmark of 200 long-horizon web tasks derived from real world browsing sessions evaluated on the live Internet. We find that binary pass/fail evaluation is inadequate for long-horizon settings and introduce a rubric-based evaluation, annotating each Odysseys task with an average of 6.1 graded rubrics. We demonstrate that this yields higher agreement with humans and provides a more fine-grained signal than commonly used trajectory-level LLM-as-a-judge evaluation metrics. We tested several leading frontier models and find that the strongest models achieve a success rate of 44.5%, which leaves substantial room for future improvements. Beyond task success, we argue that efficiency is a first-class concern for long-horizon agents. We introduce a Trajectory Efficiency metric (rubric score per step) and find that even frontier agents achieve only 1.15%, marking an evident need for agents that can succeed efficiently and not simply eventually. Odysseys isolates the critical evaluation of long-horizon proficiency in open-web environments, providing a realistic benchmark to measure progress towards computer-use agents that can potentially productively operate for hours. We release our tasks, evaluation scripts, and other results at https://odysseys-website.pages.dev

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.

Multimodal large language models (MLLMs) are increasingly considered as a foundation for embodied agents, yet it remains unclear whether they can reliably reason about the long-term physical consequences of actions from an egocentric viewpoint. We study this gap through a new task, Egocentric Scene Prediction with LOng-horizon REasoning: given an initial-scene image and a sequence of atomic action descriptions, a model is asked to predict the final scene after all actions are executed. To enable systematic evaluation, we introduce EXPLORE-Bench, a benchmark curated from real first-person videos spanning diverse scenarios. Each instance pairs long action sequences with structured final-scene annotations, including object categories, visual attributes, and inter-object relations, which supports fine-grained, quantitative assessment. Experiments on a range of proprietary and open-source MLLMs reveal a significant performance gap to humans, indicating that long-horizon egocentric reasoning remains a major challenge. We further analyze test-time scaling via stepwise reasoning and show that decomposing long action sequences can improve performance to some extent, while incurring non-trivial computational overhead. Overall, EXPLORE-Bench provides a principled testbed for measuring and advancing long-horizon reasoning for egocentric embodied perception.

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.