AI 速览：该论文从支撑估计角度刻画基于采样端点估计可达集的几何（Hausdorff）误差，并给出样本复杂度上界与匹配的极小极大下界。
Sampling-based reachability estimates reachable sets from finitely many simulated trajectory endpoints. Existing guarantees often control missed probability mass or approximation error relative to the convex hull of the reachable set, leaving the geometric error relative to the reachable set incompletely characterized. We study this error as a problem of support estimation under flow distortion. Our assumptions combine a uniform lower bound on the local volume density of the initial set, a lower bound on the sampling density, and a one-sided Lipschitz constant $μ$ for the vector field. These conditions admit initial sets with corners and dynamics that may expand or contract. In the fine-accuracy regime, $\tilde{\mathcal O}\bigl(2^ne^{nμT}(R/r)^n/(ρκ)\bigr)$ independent endpoint samples suffice for Hausdorff accuracy $r$ using the endpoint cloud. Here, $n$ is the state dimension, $T$ is the horizon, $R$ is the volume-equivalent radius, and $ρ$ and $κ$ quantify sampling density and local volume density. For $n\ge2$ and sufficiently small $κ$, a minimax lower bound over all estimators based only on independent endpoints matches these dependencies up to a dimension-dependent factor $2\cdot4^n$ and logarithmic factors, within the stated parameter range and when the state domain accommodates the construction. The exponential burden in dimension, and in the horizon for expanding systems, is therefore intrinsic to this observation model. Planar experiments illustrate the predicted effects of corners and contraction; robot-arm experiments show how empirical accuracy deteriorates with dimension.
Wen Fang, Xianxian Li, Jun Liu, Jie Luo, Yongxin Tong, Ke Xu
We study self-reference and solution independence in Boolean $K$-SAT as a finite analogue of Gödel incompleteness. Independence is defined through factorial moments of the solution count. Constant-width random formulas fail this criterion due to correlations among overlapping assignments. At a covering threshold, logarithmic-width random CNFs have a Poisson solution count, with positive probabilities of unsatisfiability and unique satisfiability. Replacing a redundant clause by one falsified by the unique solution yields an unsatisfiable companion preserving the unsigned incidence graph. For every permitted local view of a good uniquely satisfiable formula, an unsatisfiable companion preserves that view. Irreducibility defeats deterministic and bounded-error evaluators using $N^c$ clause queries, for fixed $0<c<1$. It establishes a local information obstruction, not an unrestricted time lower bound. For fixed $δ>0$, transcripts of $N^{1-δ}$ queries leave $N-o(N)$ bits of witness entropy. On typical support graphs, expansion yields linear Resolution width, linear PC/PCR and SOS degree, and exponential proof size. Bounds hold for semantic Cutting Planes under a partition condition and for Positivstellensatz with bounded product width, uniformly over unsatisfiable support-preserving signings. Structural evidence and the limits of acceleration strategies motivate the self-referential $K$-SAT exhaustive-search hypothesis (SRK-ESH): no uniform deterministic algorithm deciding the promise family achieves a fixed proportional saving in the exponent. This dual-evidence criterion combines intrinsic hardness mechanisms with algorithmic evidence. We interpret this hypothesis as a quantitative projection of the Gödel-style local--global gap. The information obstruction constrains quantum local observation and statistical learning from bounded local information.
Yiming Yan, Hongyang Wang, Wenbo Chen, Xuan Wang, Jingguo Liu, Xian Li, Chen Qi, Leo Fan 等 15 位作者
Agentic reinforcement learning (RL) often requires repeated tool calls in task-specific environments. A training job may create thousands of these environments in bursts while sharing a cluster with other jobs. We present Sandman, a sandbox service built and operated at Amazon for agent tool execution and evaluation. It serves multiple production agentic RL workloads on shared Kubernetes. A training framework supplies a task image and uses commands and file operations in the returned sandbox. Files and processes persist across calls until the framework releases the environment. Sandman manages creation, readiness and cleanup. Each sandbox is a Kubernetes pod with a small daemon mounted into the unmodified image. In a scale test, Sandman held 11,858 concurrent tiny sandboxes. Four production SWE-bench Verified training campaigns created 3.1 million sandboxes in October 2026. We report the design trade-offs and operational lessons from handling creation bursts, preparing task environments, reclaiming abandoned sandboxes, and running evaluation under controlled conditions. We will open-source Sandman's daemon, provider and pool.
Triangle- and mesh-based neural rendering seeks to bridge neural representations and graphics engines through triangle primitives compatible with standard rasterization. Yet existing methods were developed and evaluated under inconsistent settings, with few direct comparisons and little evaluation in graphics engines. We introduce MeshSuite, the first benchmark for systematic evaluation of engine deployment and Non-Engine Render in triangle- and mesh-based neural rendering. MeshSuite evaluates two deployment settings: Standard Deployment, using an opaque mesh pipeline with vertex colors and hardware Z-buffering; and Dedicated Deployment, using method-specific engine implementations to preserve appearance and compositing features. For mesh splatting, we also audit exported surfaces for topological and geometric integrity as downstream graphics assets. Our results show that engine deployment reduces image quality in both settings; among evaluated methods, MeshSplatting degrades least under Standard Deployment. Dedicated Deployment preserves most fidelity at roughly 5-33x the runtime of Standard Deployment across two deployment datasets. For mesh splatting, explicit connectivity and shared indexing remain limited: shared vertex indexing alone guarantees neither manifoldness nor global connectivity. These findings show that rasterizability is only part of graphics readiness and underscore the need to assess engine deployment. Project page: https://x-up-lab.github.io/research/meshsuite.
Self-improving LLM agents edit their own harness, the prompts and rules around a fixed model, and keep an edit only if an acceptance gate scores it higher on a batch of tasks. Such a gate sees what the harness does under the current model, not what it would still prevent if one safeguard failed. When safeguards overlap, deleting one is masked: the others still block the harm, so the gate decides on task success alone and redundancy erodes unseen. We measure harm for every subset of four written safeguards in two agent environments and run 411 improvement loops under ten gate rules, mostly as controlled deletion experiments, plus three runs of the GEPA optimizer. A deletion behind another working safeguard adds almost no observable harm. A paired significance test blocks deletions that pass by chance but not deletions that genuinely raise task success, and a larger evaluation batch lets it delete cheaper safeguards: at the same cost, 20-task batches kept every harness protected while 40-task batches lost all six. Large harm audits prevent exposure but not the loss of depth, which turns into harm when the harness is reused with a weaker model. GEPA kept every safety rule verbatim, yet two of its three final harnesses misused credentials under a weaker model. A statistical model frozen before the runs predicts where each gate's protection breaks as safeguard cost and batch size change, and freezing safety text or auditing one-layer ablations preserves depth.
Web systems increasingly predict users' decisions from what users say, yet when interests partly conflict, users may promise to cooperate to win the other side's cooperation and then not do so. Sales or service agents that rely on such promises may grant concessions to users who then do not keep their promises, at a cost to the party they represent. We test how LLMs combine users' statements with decision records to predict users' decisions, using 1,260 rounds in which 42 users played a repeated prisoner's dilemma-style game with five agents, each prompted to express a dominant Big Five trait, and could talk with the agent before every decision. Across eight open-weight LLMs, predictions from decision records separated cooperation from defection well (AUC = .80), and adding dialogue brought no detectable gain. With dialogue, predictions agreed with users' statements more often, and errors concentrated on rounds in which users broke their statements: accuracy on rounds with a statement barely changed (.73 to .74), while it rose on kept statements (.76 to .95) and fell sharply on broken ones (.65 to .17). Predictions weighted statements more heavily than users' behavior warranted: when users stated a decision they had not yet made in that game, the predicted probability of keeping it rose from .13 to .69, whereas users kept .40 of such statements. Users' decisions also varied with the agent they faced, but predictions hardly reflected this: users cooperated more with the Agreeableness agent than with the Extraversion agent (70.6% vs. 54.5%), whereas predicted cooperation was nearly identical (64.5% vs. 63.1%). Users also cooperated more with an agent when they themselves scored higher on that agent's trait, whereas predicted cooperation barely changed with these scores. Dialogue-based predictions should therefore weigh users' statements by their earlier decisions and the agent they face.
SWEET-RL: Training Multi-Turn LLM Agents on Collaborative Reasoning Tasks
Yifei Zhou, Song Jiang, Yuandong Tian, Jason Weston, Sergey Levine, Sainbayar Sukhbaatar, Xian Li
AI 速览：提出 ColBench 多轮人机协作基准与 SWEET-RL 算法，利用训练时额外信息训练评论家模型提供步级奖励，以改进多轮 LLM 智能体的信用分配。
Large language model (LLM) agents need to perform multi-turn interactions in real-world tasks. However, existing multi-turn RL algorithms for optimizing LLM agents fail to perform effective credit assignment over multiple turns while leveraging the generalization capabilities of LLMs and it remains unclear how to develop such algorithms. To study this, we first introduce a new benchmark, ColBench, where an LLM agent interacts with a human collaborator over multiple turns to solve realistic tasks in backend programming and frontend design. Building on this benchmark, we propose a novel RL algorithm, SWEET-RL (RL with Step-WisE Evaluation from Training-time information), that uses a carefully designed optimization objective to train a critic model with access to additional training-time information. The critic provides step-level rewards for improving the policy model. Our experiments demonstrate that SWEET-RL achieves a 6% absolute improvement in success and win rates on ColBench compared to other state-of-the-art multi-turn RL algorithms, enabling Llama-3.1-8B to match or exceed the performance of GPT4-o in realistic collaborative content creation.