A Primer in Post-Training Reasoning Data: What We Know About How It Works

Post-training has become a primary driver of recent progress in large reasoning models, and reasoning data are often the key variable determining whether this stage succeeds. Work on post-training reasoning data has grown rapidly, yet this literature remains scattered across dataset papers, reinforcement-learning recipes, reward-model studies, benchmarks, and frontier system reports. This paper is the first primer to synthesize over 150 key public studies and system reports on post-training reasoning data. We organize the field around four questions: what data objects exist, what makes them useful, how they are constructed, and how they scale. Together, this organization provides an attribution framework for future reasoning-data releases and post-training recipes.

Agentic Transformers Provably Learn to Search via Reinforcement Learning

Tree search is a central abstraction behind many language-agent reasoning and decision-making tasks: agents must explore actions, remember failures, and backtrack toward promising alternatives. Yet, we lack a theoretical understanding of how transformer-based policies acquire such search capabilities from the training dynamics of reinforcement learning (RL). We study this question in a stochastic $k$-ary tree environment, where an agentic transformer observes only its trajectory history through interaction and receives a terminal reward for reaching a hidden leaf goal node. We first construct a two-head transformer that implements randomized depth-first search (DFS): one head tracks previous actions, while the other detects failure outcomes and triggers backtracking. We then analyze the training dynamics of policy gradient under a depth-wise curriculum, showing that this same DFS mechanism emerges in stages from sparse reinforcement feedback without expert demonstrations. The resulting policy exhibits depth generalization: after training only on depth-$1$ and depth-$2$ trees, it succeeds on deeper full trees. We further show that, under imbalanced goal distributions, discounting the return leads to a ranked DFS policy that prioritizes higher-probability branches. Overall, our results identify a mechanistic normal form for transformer-based search, in which attention heads specialize and cooperate to extract decision-relevant traces from context and convert them into agentic action selection via RL training.

ConMoE: Expert-Pool Consolidation via Prototype Reassignment for MoE Compression

Mixture-of-Experts (MoE) language models reduce per-token computation but still require storing and serving all experts, making deployment memory-intensive. Existing post-training compression methods mainly shrink this cost by pruning experts or merging their weights. We formulate post-training MoE compression as expert-pool consolidation: retaining a smaller set of pretrained experts as reusable prototypes and deterministically remapping each original expert reference to one selected prototype. This view separates the reduced expert pool from the reuse structure that represents the original expert slots, and allows prototype sharing within local layer scopes while preserving the original router interface. We propose ConMoE, a train-free prototype remapping framework that selects retained experts using calibration-based contribution and replaceability signals, then redirects original expert calls to the selected prototypes without weight updates or post-compression fine-tuning. Experiments on three pretrained MoE language models show that ConMoE matches or outperforms strong pruning and merging baselines in several settings, achieving the best average score on deepseek-moe-16b-base at both 25% and 50% routed-expert reduction, while remaining competitive on Qwen3-30B-A3B and OLMoE-1B-7B-0125. Ablations indicate that deterministic reassignment is the most stable component, whereas broader cross-layer sharing and post-hoc weight fusion are model-dependent.

ESPO: Early-Stopping Proximal Policy Optimization

When a large language model under reinforcement learning commits a wrong reasoning step early in a trajectory, standard algorithms force it to keep generating until the maximum horizon, spending compute on tokens that never receive positive reward and polluting advantage estimates with post-failure noise. We propose ESPO (Early-Stopping Proximal Policy Optimization), which detects trajectory failure on-the-fly and terminates rollouts early. At each generation step, ESPO computes a surrogate regret using only the logits already computed during sampling, and terminates when the smoothed cumulative regret significantly exceeds its estimated values. Truncated trajectories are treated as absorbing failure states with a terminal reward, concentrating negative temporal-difference (TD) errors near the detected failure step without any additional reward model or human annotation. On DeepSeek-R1-Distill-Qwen-7B trained for mathematical reasoning, ESPO surpasses PPO on AIME~2024 (46.28% vs. 45.25%), AMC~2023 (85.83% vs. 82.94%), and MATH-500 (87.42% vs. 85.43%), while saving more than 20% rollout tokens cumulatively.

Harness-Bench: Measuring Harness Effects across Models in Realistic Agent Workflows

LLM agents are increasingly deployed as executable systems that use tools, modify workspaces, and produce concrete artifacts. In such workflows, performance depends not only on the base model, but also on the harness: the system layer that manages context, tools, state, constraints, permissions, tracing, and recovery. However, existing benchmarks typically abstract away execution, compare complete agent systems, or hold the harness fixed, making execution-layer variation difficult to study. We introduce Harness-Bench, a diagnostic benchmark for evaluating configuration-level harness effects in realistic agent workflows. Harness-Bench evaluates representative harness configurations across multiple model backends under shared task environments, budgets, and evaluation protocols, while preserving each harness's native execution behavior. The benchmark contains 106 sandboxed offline tasks constructed from practical agent-use patterns and manually reviewed for realism, solvability, oracle-checkability, and integrity. Each run records final artifacts, execution traces, usage statistics, and validator outputs, enabling analysis beyond final completion. Across 5,194 execution trajectories, we observe substantial variation in completion, process quality, efficiency, and failure behavior across model-harness pairings. These results suggest that agent capability should be reported at the model-harness configuration level rather than attributed to the base model alone. Our analysis further identifies recurring execution-alignment failures, where plausible reasoning becomes decoupled from tool feedback, workspace state, evidence, or verifiable output contracts. Harness-Bench provides a reproducible foundation for diagnosing and improving reliable, efficient, and auditable agent execution stacks.

MemAudit: Post-hoc Auditing of Poisoned Agent Memory via Causal Attribution and Structural Anomaly Detection

Large language model agents increasingly rely on persistent memory to store past interactions, retrieve relevant demonstrations, and improve long-horizon task execution. However, this memory mechanism also creates a practical security vulnerability: an adversarial user may inject malicious records into the agent's memory through ordinary interaction, and these records can later be retrieved to steer the agent's reasoning and actions. Existing defenses primarily focus on online intervention, such as prompt filtering or output blocking, but they do not address the post-hoc question of which stored memories are responsible after harmful behavior has already been observed. We propose \textbf{MemAudit}, a post-hoc causal memory auditing framework for memory-augmented LLM agents. The framework combines two complementary signals: (1) a counterfactual memory influence score that measures each memory's causal contribution to harmful outputs, and (2) a memory consistency graph that identifies structurally anomalous memories within the broader memory store. We evaluate MemAudit against MINJA, a query-only memory injection attack in which malicious records are generated and stored through normal agent interactions rather than direct memory-bank modification. Across both QA and reasoning-agent settings, MemAudit substantially reduces attack success rates under realistic post-hoc auditing scenarios. The results show that QA attack success is reduced from $70\%$ to $0\%$, while RAP attack success drops from $83.3\%$ to $0\%$.

Formal Skill: Programmable Runtime Skills for Efficient and Accurate LLM Agents

Large Language Model (LLM) agents increasingly act inside real workspaces, where tools and skills determine whether model reasoning becomes reliable action. Existing skills remain largely informal: Markdown skills and instruction packs encode procedures as long natural-language documents, while function calling, Model Context Protocol (MCP) servers, and framework tools structure individual actions but usually leave workflow state, policy enforcement, and completion discipline outside the skill itself. We introduce Formal Skill, a runtime-native abstraction that represents reusable capability with JSON metadata and action schemas, reliable Python executors, hook-governed control logic, Formal Skill routing, and skill-local runtime state. By moving reusable procedure from repeated prompt text into executable state machines and hook policies, Formal Skill gives agents a token-efficient and enforceable control surface. We implement the abstraction in FairyClaw, an open-source event-driven runtime for executable, observable, and composable Formal Skills. On Harness-Bench, FairyClaw obtains highly competitive average scores while using substantially fewer tokens, with especially strong results on tasks that expose the role of Formal Skill.

Multi-Depth Uniform Coverage Path Planning for Unmanned Surface Vehicle Surveying

This paper introduces a novel automatic coverage path planning algorithm for bathymetry surveying with unmanned surface vehicles. The detection range of the mapping sensor employed - a multibeam echo sounder - is heavily influenced by local seafloor depths. Hence, a path designed to uniformly cover the sea surface does not guarantee uniform coverage of the seafloor. Yet this is currently the typical process for bathymetric surveys, with the simplistic boustrophedon scheme along manually selected waypoints at constant depths being the most widespread planner used. The proposed scheme incorporates coarse prior depth information to pre-process the target region and adaptively guide path generation and sensing range configuration. By explicitly accounting for depth variations, the proposed algorithm designs a coverage path with optimised spacing between survey passes that adjusts the sensing beam aperture to achieve more consistent seafloor coverage. The proposed method is shown to offer significant improvements in both synthetic and real-world scenarios. Validations in challenging synthetic terrains achieves coverage ratios beyond 99%, a marked improvement when compared with traditional boustrophedon paths revealing a maximum 75% coverage. The same trend appears in realistic simulations using real bathymetric data from a coastal harbour, with coverage reaching over 92%, and significantly surpassing boustrophedon sweeps with coverage rates below 65%. Beyond improved performance, the scheme also brings a fully automated design, suitable for autonomous marine vehicles, thus offering practical utilities for real-world applications.

Thinking with Reasoning Skills: Fewer Tokens, More Accuracy

Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing \emph{reasoning from scratch} paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.

EdgeFormer: local patch-based edge detection transformer on point clouds

Edge points on 3D point clouds can clearly convey 3D geometry and surface characteristics, therefore, edge detection is widely used in many vision applications with high industrial and commercial demands. However, the fine-grained edge features are difficult to detect effectively as they are generally densely distributed or exhibit small-scale surface gradients. To address this issue, we present a learning-based edge detection network, named EdgeFormer, which mainly consists of two stages. Based on the observation that spatially neighboring points tend to exhibit high correlation, forming the local underlying surface, we convert the edge detection of the entire point cloud into a point classification based on local patches. Therefore, in the first stage, we construct local patch feature descriptors that describe the local neighborhood around each point. In the second stage, we classify each point by analyzing the local patch feature descriptors generated in the first stage. Due to the conversion of the point cloud into local patches, the proposed method can effectively extract the finer details. The experimental results show that our model demonstrates competitive performance compared to six baselines.