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在算法统计学中，字符串x由包含它的有限集解释，Kolmogorov结构函数记录每一复杂度层级上最小的此类模型。Vereshchagin的强模型，即可由全算法从数据中计算的模型，本质上是简单划分的胞元。我们将二进制串的划分视为假设，将包含x的胞元作为其模型，并在此基础上发展针对对称划分（即群作用于串的轨道划分）的算法统计学。子群与划分间的Galois连接赋予每个环境群一个对称划分格，以及规范凭证、规范代价和假设代数。由此得到的结构函数与对称精巧度测量了x的规律性中具有对称性的部分。对全对称群而言，任何划分都是对称的：胞元还原了所有Kolmogorov模型，廉价划分的胞元恰好还原了强模型，正常串与奇异串由对称性刻画。对GL(n,2)而言，胞元恰为线性齐次集，因此线性对称性是受限模型类。对非零x，线性对称结构函数位于充分线与平凡界之间的带状区域，且两条边界均可达到：存在随机正常串，其简单结构对线性对称不可见。我们还给出了置换群空间上的坐标：每个群是Burnside环的一个元素（其类型）连同一次置换（其位置），且限制操作通过Mackey公式加细划分。在这些坐标下，对称群的坍缩是关于位置的陈述，线性假设由其类型决定且精确到n^2比特，而最大间隙定理表明，任何小到足以搜索的对称假设空间，都小到足以遗漏简单结构。
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Recent autonomous machine learning engineering (MLE) agents have made significant progress on public leaderboards. Often motivated by progress stagnation over long-horizon cycles and limited Large Language Model (LLM) primitives, modern MLE agents are deployed on top of increasingly elaborate machinery：multi-agent orchestrators, dedicated retrieval subagents, and more. While such harnesses expand, the use of more primitive but improved coding agents - where LLMs have direct access to the execution environment through read, write, and bash primitives - has received little attention in the field. In this paper we find that, under an equal time budget and the same frontier LLM backbone, open-source state-of-the-art harnesses provide no advantages over a single session of a minimal-harness coding agent baseline, pointing to the backbone as the primary driver for performance. Via a series of large-scale systematic ablation studies, we argue that the machinery layers become redundant in the coding agent setting. We conclude that the effort spent elaborating hand-crafted harnesses around strong models yields poor returns for current MLE benchmarks.
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Pretrained robot policies provide useful action priors, but long-horizon manipulation still requires coordination between semantic reasoning and physical execution. Semantic reasoning operates at a coarser timescale than physical interaction, while episode-level failures provide limited guidance on which system component should be revised. We propose DynaHarness, a dynamic physical harness that couples semantic reasoning with physical governance through a shared execution contract and turns failure evidence into validated capability revisions. To be more specific, the slow brain proposes capabilities and symbolic arguments, while the fast brain grounds and monitors commands, refuses unresolved actions, substitutes capabilities, and requests replans when needed. The physical execution contract bounds each accepted command and records execution evidence across analytic skills, recovery skills, and the frozen VLA. Failure attribution localizes faults in these records and directs targeted revisions of reusable capabilities or execution mechanisms. Paired regression checks govern admission or rejection, closing the self-evolution loop. On LIBERO-Pro, DynaHarness achieves 75.2% on 800 newly sampled initial states, compared with 17.5% for the frozen policy. With the same capability library, full dynamic execution reaches 74.0% versus 63.9% under nominal one-step replanning. This demonstrates the value of DynaHarness as a dynamic physical harness that governs how existing capabilities are grounded, monitored, and coordinated during execution. Our project page is at
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循环Transformer与混合专家模型（Mixture-of-Experts, MoE）为高效扩展提供了互补路径：循环在固定参数量下增加了计算深度，而MoE稀疏性在固定活跃计算量下扩展了总容量。然而，现有的扩展法则仅孤立地对循环或稀疏性进行建模。在本文中，我们引入了Loop Scaling Laws，这是首个将循环与稀疏性连同模型规模和数据一起进行联合建模的扩展法则。其核心是一个有界的、以稀疏性为条件的循环映射，该映射刻画了由循环带来的有效参数增益，以及稀疏性如何提升这一增益。该法则比先前的替代方法更准确地预测了循环模型的留出损失（held-out loss），并将标准的稠密模型与MoE扩展法则作为特例还原。除了预测功能外，拟合后的法则还为在计算与内存约束下设计循环MoE模型提供了原则性基础。下游评估进一步展示了这两个维度的互补优势：稀疏性带来了约3倍的活跃参数效率，循环在推理任务上带来了约2倍的总参数效率，而联合扩展进一步推进了性能前沿。作为一项实际扩展，我们证明了这些收益在万亿token规模下依然成立：在训练计算量匹配的情况下，具有法则推导循环的循环MoE在推理基准测试上与参数量约为其2倍的非循环MoE表现相当，同时通过循环实现了测试时扩展。
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Material generation should produce not only an appearance, but also the rules that construct it. We introduce MatLoom, a compact, layer-oriented language for text-to-material generation with pretrained language models. Each program composes alpha-masked layers whose shared spatial expressions define coverage and physically based rendering (PBR) channels, making dependencies between patterns, color, and relief explicit. A standalone interpreter evaluates the program into material maps, while the source retains named fields and layer parameters for subsequent authoring. Without task-specific fine-tuning, our pipeline uses parser-guided repair and preview-based critique to revise material designs, then searches noise seeds while keeping each candidate's remaining source fixed. On a curated benchmark of 141 prompts evaluated with six backbones, our best-performing configuration achieves higher mean scores than three diffusion baselines on all four flat-layout prompt-alignment metrics. Its initial programs already exceed all three baselines on mean BLIPScore, before critique or seed search. Retained programs have a median length of 21 lines when pooled across backbones. In a blind four-way comparison involving 30 participants and 20 prompts, our renders receive 59.2% of choices, compared with 19.3% for the most-preferred baseline. Compact executable programs thus offer a way to generate prompt-aligned materials while retaining their construction as part of the asset.
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我们提出Cogentic，一种面向开放研究问题自动证明发现的多智能体框架。前沿语言模型能单次产生有力的数学思想，但对需探索多种竞争性猜想、克服细微技术障碍及长期保留中间进展的开放问题，单次生成往往不足。Cogentic通过迭代的证明-验证循环解决这些挑战：协调器将一批独立证明器分配至不同证明方向，将其输出交由数个专用组件进行对抗性验证，并将确认的中间结果提升至持久化的已验证账本，供后续轮次基于此构建。该框架旨在解决研究级数学与理论计算机科学问题。以Gemini为基础模型，Cogentic在在线学习、拍卖理论与机制设计的五个开放问题上取得了新结果。每项结果均由领域专家独立验证，并在配套论文中进行了完整阐述。我们在 列出这些结果，新结果经验证后亦将列于此。
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