A Conveyor Belt Mechanism for Repositionable Magnetic Coupling Between Continuum Robots
Ella Walsh, Eric Diller, Jessica Burgner-Kahrs
AI 速览：提出一种可集成于腱驱动连续体机器人内部的传送带机构，实现功能元件沿机器人本体的连续主动重定位，并以磁耦合案例验证其可调刚度能力。
This work proposes a novel conveyor belt mechanism enabling continuous, active repositioning of functional elements along the body of a tendon-driven continuum robot. Up to three conveyor belt mechanisms are integrated within a 9 mm diameter continuum robot. We demonstrate equivalent or reduced conveyor belt actuation forces compared to robot tendon actuation forces. As a case study, we mount permanent magnets along two conveyor belts, and demonstrate actively reconfigurable inter-robot coupling. Coupling point location and quantity can be adjusted during robot operation to actively tune the effective stiffness of the coupled multi-robot system. We show that effective stiffness follows a predictable inverse-cubic relationship with coupling location, and increases with the number of coupling points. These findings demonstrate that the conveyor belt mechanism enables active functional element repositioning for changing tasks requirements, with magnetic inter-robot coupling as one proof-of-concept.
On Zeros and Algorithms for Disordered Systems II: The Antiferromagnetic Ising Model up to Kesten-Stigum
Ferenc Bencs, Brice Huang, Daniel Z. Lee, Kuikui Liu, Guus Regts
AI 速览：作者提出首个在均匀随机 d-正则图上、对反铁磁 Ising 模型在直至 Kesten-Stigum 阈值的全部逆温度范围内以任意高精度估计配分函数的多项式时间算法。
We give the first polynomial-time algorithm to estimate the partition function of the antiferromagnetic Ising model on the uniformly random $d$-regular graph to arbitrarily high accuracy for all inverse temperatures up to the Kesten-Stigum threshold. This is the entire regime in which the model is "replica symmetric," and is conjectured to be optimal for polynomial-time counting and sampling. To achieve our algorithmic result, we establish the absence of Fisher zeros for the partition function in a constant-width strip around the interval from $0$ up to the Kesten-Stigum threshold, with high probability over the randomness of the input graph. AI Disclosure: The overarching vision and proof architecture were developed solely by the authors without AI input. GPT 5.5 Pro was used, with extensive guidance from the authors, for only a few minor technical aspects of the proof. The authors independently verified correctness and wrote everything by hand. We take full responsibility for its contents. A more detailed statement can be found in Section 1.2.
HairDeck: Animation-Ready Stylized Hair Cards from a Single Image
Yuze He, Yixiang Wei, Wang Zhao, Chuhao Chen, Yanning Zhou, Yong-Jin Liu
AI 速览：HairDeck 将风格化发型视为无序的发片集合，用集合扩散 Transformer 从单张图像一次性生成发片及其弹簧骨骼链，得到可直接导出的可动画资产。
The hair of stylized characters in games and avatars is built from hair cards: artist-placed ribbons whose geometry is the visible hair, animated by spring bones. Existing image-based methods produce realistic hair or a single fused mesh, while CHARM, the only generator of stylized hair cards, decodes a hairstyle autoregressively as a long sequence of control points. Observing that a card hairstyle is an unordered set of artist-defined primitives, we propose HairDeck, which generates it as one: each card is a single token, and a set diffusion transformer denoises all cards together. From a single image, HairDeck generates the cards and the spring-bone chains that drive them, yielding an animatable asset that exports to ready-to-use downstream formats. On CHARM's own test set, it lowers Chamfer distance by 44% and card-orientation error by more than half while running 33 times faster, and from single images it outperforms CHARM, image-to-3D pipelines and strand-based methods. Project page: https://hyzcluster.github.io/HairDeck
Approximating Minimum Spanning Trees in Metrics under Semi-Random Corruptions
Aditya Anand, Anupam Gupta, Rajesh Jayaram, Euiwoong Lee, Ali Vakilian
AI 速览：研究在半随机损坏的度量空间中近似最小生成树，针对距离只增、只减和任意改变三种情形给出近似算法与下界。
We study the problem of finding minimum spanning trees in semi-random corrupted metrics. In this problem proposed by Bateni, Dharangutte, Jayaram, and Wang (COLT'24), we start with a metric space $\mathcal{M} = (X, d)$. The adversary independently corrupts each pairwise distance with probability $p$. The algorithm only observes these possibly corrupted distances and must output a spanning tree whose expected cost (in the true metric) is multiplicatively close to the minimum spanning tree cost. Prior work showed that losing a factor of $Ω(\log n)$ is necessary, even if the algorithm may adaptively select $O(n/\log n)$ points and probe the true distances between them. However, no upper bounds were known. We study three regimes based on whether the adversary can only increase, decrease, or arbitrarily change the corrupted distances. We show the following: (1) In the increase-only setting, we give a polynomial-time $O(1)$-approximation algorithm for any constant $0 \le p < 1$. (2) In the decrease-only setting, we give an $O(\log n)$-approximation algorithm for any constant $0 \le p < 1$. Additionally, we show an $O(\log^4 n)$-approximation algorithm that runs in quasi-polynomial time $n^{O(\log n)}$, for any constant $p \leq 0.1$. Moreover, we show that a polynomial-time algorithm computing an $n^{1/3-\varepsilon}$-approximation is unlikely to exist. (3) In the general setting, where the adversary can both increase and decrease distances, we show an $O(\log n)$-approximation algorithm for every $0 \leq p < \frac{1}{4}$. Further, we show that no $o(n)$-approximation is possible for $\frac{1}{2} \leq p < 1$. Our algorithms answer the main open question in Bateni et al.'s work; moreover, the $O(\log n)$-approximations in the latter two settings are information-theoretically optimal.
AI 速览：作者提出一个在一般图上以 n^{2+o(1)} 时间求解最大基数匹配的算法，思路是扩展近期组合最大流技术到斜对称流问题。
We consider the maximum cardinality matching problem in general graphs, and give an $n^{2+o(1)}$-time algorithm for the problem. Our work builds on recent work on combinatorial algorithms for maximum flow and extends the techniques to skew-symmetric flow problems which capture general matchings as a special case.
Collaborative AI agents for autonomous experimental research with solid-state quantum spins
El Mustapha Mansouri, Eikichi Kimura, Masato Koga, Keigo Arai
AI 速览：多个基于大语言模型的智能体相互评审、可中止或改道研究，并在金刚石量子自旋体系上完成从选题、理论推导到实验检验的闭环。
An autonomous research laboratory could conduct an entire study, from formulating questions to preparing manuscripts. Artificial intelligence (AI) offers one route towards this goal. Recent AI systems take on several research roles, but may draw conclusions that the evidence does not support. Here, we present an autonomous research laboratory in which agents based on large language models assess one another's work and can stop or redirect investigations. They can generate and reject research questions, require separate theoretical checks and conduct experiments designed to challenge their claims. We demonstrate these capabilities by investigating ensembles of quantum spins in diamond. The agents derived the minimum number of calibration settings needed to predict responses to a defined family of microwave pulse sequences. They checked the result computationally and designed experiments to distinguish competing predictions. An initial experiment agreed with the theoretical predictions, but repeated reference measurements showed that the signal was drifting during data collection. The agents therefore treated the result as inconclusive and revised the measurement protocol without relaxing the acceptance criteria. The revised experiment met those criteria and supported the theoretical predictions. This study demonstrates that collaborating AI agents can select research questions, derive theoretical results and test their predictions experimentally.
Pre-Crime for Agents, at the Last Second: Probing When a Recruited Agent Gives In
Leonidas Raghav
AI 速览：作者报告，在受控多智能体场景中，对智能体激活做线性探针可在输出生成前预测其即将泄露秘密，但增益主要来自有标签训练而非激活本身。
When AI agents share channels and credentials, one agent can press another to break its operator's rule, a first step towards collusion. Output filters check only what an agent has already written. Can an overseer tell beforehand that an agent is about to give in? We show that a linear probe on the agent's activations can, in a controlled multi-agent setting. Across six scenarios, a peer presses a target for up to 20 rounds to reveal a secret, such as a deploy token; the target often refuses, then gives in. Read at each model call before its output is written, the probe picks out the one that leaks. On held-out Qwen3-32B episodes, at a threshold set to flag 5% of benign calls, it catches 82% of leaking calls. At a similar flag rate, a zero-shot decision-model monitor catches 26%. On gpt-oss-20b, a probe on its reasoning reaches AUROC 0.91. A bag-of-words classifier trained on the same calls comes close, so most of the gain comes from training on labels, not activations. The probe also flags permitted disclosures: it reads the coming disclosure more than the violation. The warning is short-range, and halting on any alarm would stop most benign episodes, which a second text check does not fix. A warning raised before generation could let an overseer stop an agent that is about to give in, ahead of others acting on its messages or recruitment spreading through a swarm.
Beyond Ground Truth: A Heuristic Unsupervised Quality Assurance Engine for Diagnosing Calibrational Blindness in Dental Segmentation
Fatematuj Johura Mim
AI 速览：提出无需真实标注的启发式质量检查引擎 HUS-QA，用于评估牙科 X 光分割掩膜质量并诊断模型的校准盲区。
In real-world clinical settings, dental X-ray segmentation using deep learning methods suffers from reliability issues. Even when the segmentation quality is bad, deep learning models show high confidence in their predictions (calibrational blindness). Moreover, in real use, doctors do not have ground-truth masks to check their accuracy. To address this problem, we introduce a simple quality-checking engine called HUS-QA with three stages. We train it on the PRAD (Periapical Dental X-ray) dataset to build our SimCLR self-supervised ResNet-18 U-Net model, which generates the segmentation mask and then evaluates its quality. Our HUS-QA checks the segmentation mask quality without a ground-truth mask. Prediction confidence, edge sharpness, shape connectivity, and area-size penalty are the simple indicators considered in this research. Results show that standard confidence methods fail (r = -0.1394, p = 1.7864e-3, ROC AUC = 0.4275). By contrast, our HUS-QA shows a positive correlation with actual Dice scores (r = 0.4647, p = 3.7510e-28) and achieves a strong ROC-AUC of 0.8405. Therefore, HUS-QA serves as a practical tool for clinical quality control.
Multistatic ISAC with Deep Learning-Based Clutter Suppression for 5G and Beyond
Yalin E. Sagduyu, Tugba Erpek, Sastry Kompella
AI 速览：该论文提出一种多基地ISAC框架，利用残差与注意力增强的深度神经网络从杂波污染观测中直接增强目标响应，以提升目标位置与速度估计的鲁棒性。
Integrated sensing and communications (ISAC) systems using 5G and beyond signals of opportunity enable joint wireless sensing and communication using shared infrastructure and spectrum resources. While multistatic ISAC can increase sensing coverage with spatially distributed receivers, dense and dynamic clutter can significantly degrade bistatic range and Doppler estimation, leading to errors in target localization and velocity estimation. This paper presents a multistatic ISAC framework with clutter suppression for high-fidelity estimation of target position and velocity. Distributed clutter is modeled with randomly located scatterers with varying Doppler spreads and radar cross sections to capture dense and dynamic clutter effects. A broad range of conventional signal processing baselines are evaluated for clutter suppression, showing limited robustness under strong clutter conditions. To address this limitation, deep learning-based clutter suppression methods are introduced to improve robustness against dense and dynamic clutter by employing residual and attention-enhanced deep neural network architectures that directly enhance target responses from clutter-contaminated observations. These methods substantially outperform conventional approaches in target position and velocity estimation across diverse clutter conditions in multistatic ISAC.
Classical communication over quantum channels: does entanglement help in nature?
Peixue Wu
AI 速览：作者提出Schur加权块熵不等式，证明所有相位协变信道（含多能级振幅阻尼、广义退相位、阻尼-退相位信道）在经典通信中不存在纠缠优势。
Can entangling codewords across independent uses of a quantum channel improve the rate of classical communication? An old conjecture states that there is no such entanglement advantage for all channels. Although Hastings's result and follow-up works disproved this conjecture, it turns out that enormous dimension is required to construct a channel where entanglement enhances classical communication. This indicates that there might be no entanglement advantage for many physical channels, or for all low dimensional channels. Motivated by recent progress on (generalized) amplitude damping channels, we propose a general Schur-weighted block entropy inequality, and show that there is no entanglement advantage for all phase-covariant channels including multi-level amplitude damping channels, generalized dephasing channels, and damping-dephasing channels. As a by-product, we also recover the recently established result that there is no entanglement advantage for all qubit channels.
AI 速览：作者提出 RADIOlogy，利用视觉-语言模型中多头注意力池化的零样本异常定位特性，以单次前向的对比打分实现无需训练的零样本异常检测与分割。
Current zero-shot anomaly detection methods often rely on complex prompt-learning techniques or computationally expensive sliding-window strategies to achieve fine-grained visual alignment to detect small-scale anomalies. This reliance stems from the fundamental limitation of standard CLIP architectures, where [CLS] token attention and spatial patch pooling struggle to capture subtle, localized anomaly features. While prompt-learning approaches aim to bridge this gap, they typically require a large number of ground-truth segmentation masks from auxiliary datasets, which are often unavailable in specialized domains. In this work, we show an emerging property of multi-head attention pooling in vision-language models: remarkable zero-shot anomaly localization and detection right out of the box. We translate this property into a single-pass anomaly detection technique, RADIOlogy, that does not require dense, windowed execution and significantly outperforms other training-free baselines. Instead, the method relies on a simple contrastive scoring approach that compares the average similarity between vision features and a suite of normal and abnormal prompts. Furthermore, we leverage the agglomerative features of RADIO models to enhance pixel-level anomaly segmentation using a dense anomaly refinement pipeline. Finally, we show how the vision-language family of training-free zero-shot anomaly detection techniques can be applied successfully to the medical domain with minimal modifications. Code is available at https://github.com/jacomof/RADIOlogy.
When Imputation Changes the Nearest Neighbor: Exact Certification of Similarity Retrieval for Incomplete Sensor Time Series
Jianru Shen
AI 速览：针对缺失值插补会改变最近邻的问题，提出对窗口最小值距离族在任意允许补全下保持检索结论的精确认证方法。
Sensor time series routinely reach similarity search with missing values, and the retrieved neighbours then depend on how the gaps were filled. We ask which retrieval conclusions hold for every admissible completion of an incomplete query. For a family of window-minimum distances that contains the $L_1$ distance as its separable end we give a pairwise certificate that one candidate is strictly closer than another, a guaranteed candidate set that contains every possible nearest neighbour, and a certificate that a nearest-neighbour label cannot change. The guarantees hold uniformly over the specified box and apply to the true query whenever it lies inside. At the separable end a closed form is known, but beyond it the worst-case gap need not be attained at a corner of the box. We prove a finite reduction to critical values, give an exact interval dynamic programme for the worst-case ranking gap, and a quadratic-time fast layer of valid bounds and feasible witnesses, supported by an exact criterion for when the feature-box relaxation is tight. On three traffic-sensor collections with real gap patterns, linear interpolation changes the nearest neighbour in 15 to 33 percent of the queries. At the full band the feature-box relaxation misses up to 14 percent of the exactly stable boundary pairs, whereas fixed-completion and Monte Carlo checks issue false certificates. The fast layer resolves about 90 percent of all tested boundary pairs without dynamic programming, and on paired network-scale queries the exact method is 82 to 110 times faster than the programme alone. Label certificates transfer to three public benchmarks, and the band width trades forecasting accuracy and certification coverage for lower imputation sensitivity, with dataset-dependent crossovers.
VeriCUA: Verification as Agentic Exploration for Computer-Using Agents
Qiushi Sun, Da Yu, Alexander Knop, Amer Sinha, Lingpeng Kong, Ben Kao, Ravi Kumar, Pritish Kamath
AI 速览：提出平台无关的验证框架 VeriCUA，把任务完成验证建模为智能体在共享流程中动态收集证据并评估，统一在线与离线、跨平台与多模态观测场景。
Building and scaling computer-using agents (CUAs) across desktop, mobile, and web environments requires reliable task-completion verification for data curation, evaluation, and reinforcement learning. Typical automated approaches prompt vision-language models (VLMs) to judge trajectories or generate programs to inspect application state. However, both rely on partial views of complex digital environments. VLM judges are restricted to supplied observations, while generated programs depend on accessible state. These views can omit decisive evidence or leave completion judgments unsupported. Tailoring separate verifiers to different platforms and access settings adds further engineering cost. We present VeriCUA, a platform-agnostic framework for verification through agentic exploration. It treats verification as dynamic evidence gathering and assessment within a shared procedure for online and offline settings across platforms and observation modalities. After inspecting the available context to construct a task rubric, the verifier selects GUI or code checks for unresolved requirements and combines their findings under explicit evidence rules. Experiments show improved agreement with reference labels over the compared baselines across these settings, with the largest offline gains on hard cases and stronger rejection of false completion claims online. Further analyses connect these gains to complementary evidence and test-time exploration.
AI 速览：提出 Multi-View MoE，用多个路由器聚合专家选择偏好，并复用路由分数调制专家输入，在固定激活专家预算下提升下游性能。
Sparse mixture-of-experts (MoE) models expand parameter capacity by activating a small subset of experts per token. Expert selection directly affects model capabilities under a fixed active-expert budget. Dense evaluation of all experts reveals weak agreement between single-router rankings and expert-utility evaluation rankings, especially in middle and deep layers. Richer signals for selection and computation incur additional cost: selection based on internal expert activations requires preliminary computation, while processing multiple full representations separately through the same expert repeats its computation. We propose Multi-View MoE to improve expert selection with multiple routers and reuse their preferences to modulate expert computation under a fixed expert budget. Its Multi-Router submodule aggregates sigmoid scores from independently initialized routers. These routers develop highly differentiated expert preferences during training, allowing experts strongly favored by one router or jointly supported by several routers to be selected. Multi-View further uses each selected expert's relative scores across routers to mix learned latent views into its input, reusing routing preferences for both selection and computation. Each selected expert executes one forward pass, preserving the active-expert count, expert FLOPs, and all-to-all communication volume. On a 24-layer 10B-A1B model trained on 708B tokens, full Multi-View MoE improves the nine-task downstream mean by 1.18 percentage points over the baseline. Multi-Router alone yields a 0.6-percentage-point gain and improves the rank correlation between router scores and evaluated expert utility, with relative increases of 8.1% globally and approximately 58% in the layer with the lowest single-router alignment. Controlled mixing interventions show the model uses input differences that depend on both the expert and the token.
AI 速览：PIVOT 将教师生成的纠正片段插入学生 rollout，并对这些片段施加 token 级 KL 监督，与 RLVR 目标联合训练，以缓解困难推理任务中稀疏奖励无学习信号的问题。
Reinforcement learning from verifiable rewards (RLVR) is limited by sparse outcome-level feedback on hard reasoning tasks: when all rollouts in a group fail, rewards provide no learning signal. Stronger teachers can provide additional guidance, but this raises a central question: how can such signals be incorporated into RLVR to support successful rollouts while remaining learnable for the student? We distinguish two complementary mechanisms: trajectory-level intervention, which improves access to reward-bearing trajectories, and token-level supervision, which provides dense targets to guide student learning. Our controlled experiments show that either mechanism alone can remain insufficient, motivating their combination. We therefore introduce PIVOT, which inserts teacher-generated corrections into student rollouts and applies token-level KL supervision to these segments alongside the RLVR objective. Beyond their combination, we systematically analyze where to intervene and how to supervise, yielding a recipe for effective guidance. Across hard logic games and mathematical reasoning benchmarks, PIVOT consistently outperforms existing methods, nearly doubling mean avg@8 on logic games from 19.5% for the best-performing baseline to 35.6%.
Improved Sampling Schedules for Discrete Diffusion Models
Alberto Foresti, Mustapha Bounoua, Giulio Franzese, Luca Ambrogioni, Pietro Michiardi
AI 速览：作者从热力学熵产生与动力学活动角度分析均匀离散扩散模型的反向过程，并提出两种新的采样调度（EDS、WDS），在语言建模任务上报告了计算效率提升。
Uniform Discrete Diffusion Models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain underexplored. In this work, we bridge this gap by analyzing the reverse process dynamics through the lens of thermodynamic entropy production and dynamical activity. We use a variational expression of the discrete Wasserstein distance to characterize the dynamics of the generation process. Leveraging these insights, we first introduce the Entropic Discrete Schedule (EDS), which aligns with entropy production, and later construct the Wasserstein Discrete Schedule (WDS), which combines entropy production and dynamical activity to act as a geometric cost. Our experimental results on language modeling show that WDS provide the same results as uniform while using up to half of the computations on the MBPP benchmark. The code is available at https://github.com/AlbertoForesti/impscheds.
Minimum Label $k$-Cut on Planar Graphs: Complexity and Color Structure
Yuanhao Wang, Wei Wang
AI 速览：研究底层图结构与颜色类结构如何影响最小标签 k-割问题的参数化复杂性与可解性边界。
Minimum Label $k$-Cut asks for a minimum-size set of colors such that deleting all edges of these colors leaves at least $k$ connected components. We study how the structure of the underlying graph and its color classes affects the complexity of this problem. Regarding fixed-parameter tractability with respect to $k$ on simple planar graphs, we prove that the problem is W[1]-hard, even when the underlying graph is a cactus graph and each color appears at most twice. Furthermore, for cactus graphs in which every color class is connected, we establish a complexity boundary in terms of the maximum monochromatic degree: when this degree is at most two, an optimal solution can be found in $O(Nk^2)$ time, where $N$ is the input size, with no restriction on color frequency or the number of blocks spanned by a color; allowing the maximum monochromatic degree to increase to three already makes the decision version NP-complete. Finally, we prove that the problem remains W[1]-hard parameterized by $k$ on fan graphs, even when every color class is an induced path. These results show that bounding color frequency does not suffice to eliminate parameterized hardness. They also establish a monochromatic-degree boundary for connected colors on cactus graphs and identify complexity barriers to extending this tractable case to outerplanar graphs.
AI 速览：提出首个 token 级自适应在线策略自蒸馏方法 MTA-OPSD，让每个 token 在训练中从多教师池中选择偏好的教师。
On-policy Self-distillation (OPSD) has proven effective for post-training large language models by constructing a teacher conditioned on privileged references. However, existing approaches keep the teacher fixed either throughout training by consistently exposing it to the full reference, or within each response by adaptively varying partial reference exposure only across responses. In this paper, we argue that neither of them is sufficient. Instead, every token needs its own teacher, as the teacher preference can vary token by token within the same response. Through a teacher-intervention pilot study, we validate that the teacher preference differs across tokens, and reveal that a preferred teacher can be identified for each token through majority voting and KL-based selection. Motivated by these findings, we propose Multi-teacher Adaptive On-policy Self-Distillation (MTA-OPSD), the first token-level adaptive OPSD method. Our method constructs a multi-teacher pool consisting of candidate teachers, and enables every token to adaptively select its preferred teacher during training. Experiments with Qwen3 models on mathematical reasoning tasks show that MTA-OPSD consistently outperforms existing OPSD approaches with an average gain of up to $+5.9$ over the base model, highlighting the importance of adapting teacher supervision at the token level. The code is available at https://github.com/xingzhejun/MTA-OPSD.
What Can Be Computed with Indefinite Causal Structure?
Omri Shmueli
AI 速览：在过程矩阵形式下研究不定因果序的计算能力，作者报告在两种设定下给出多项式时间算法，分别覆盖 NP 与唯一汇点定向问题。
Can quantum computation become more powerful when operations do not need to follow a definite causal order? We study this question in the process matrix formalism of Oreshkov et al. (Nature Communications, 2012), which allows quantum operations to be connected without a fixed global order. In the computational model, a quantum circuit succinctly describes a process matrix, and the algorithm is given access to its generated channel, with computational cost measured by the size of the generating circuit. We give polynomial-time algorithms in two settings. First, general process matrix computation suffices to solve every problem in $\textbf{NP}$. The valid processes used by our algorithm satisfy the purification postulate of Araújo et al. (Quantum, 2017), and their generated channels are unitary, although their generating circuits are not. Second, requiring the process matrices themselves to be pure, we give a polynomial-time algorithm for unique-sink orientation, a general problem capturing several longstanding computational problems in optimization. Our unitary generators are constructed explicitly and efficiently. Assuming that unique-sink orientation has no quantum polynomial-time algorithm, our result shows that indefinite causal order can provide computational power beyond $\textbf{BQP}$ within the process matrix formalism, even while preserving unitarity.
"Deep lifts": Neural networks can generalize even with the dumbest optimizer
Sunil Madhow, Yu-Xiang Wang
AI 速览：作者研究在插值数据的参数中均匀随机选取的过参数化 ReLU 网络参数，证明其泛化速率由解释数据的更小网络的规模决定，而非由完整假设类的 VC 维决定。
Given a labeled dataset $\{(x_i, y_i)\}_{i = 1}^n$, consider drawing a parameter vector $\hatθ$ uniformly at random from those that interpolate the data within a width-$W$ depth-$D$ ReLU architecture with continuous weights bounded within $[-M, M]$. We study the generalization properties of $\hatθ$ in the case where the dataset can, in fact, be explained by a smaller $w$-by-$d$ ReLU network. Despite the obliviousness of the selection rule for $\hatθ$, it adaptively generalizes at the rate $\tilde O\left(\frac{wdWD}{n}\right)$, rather than being governed by the VC dimension of the full $W$-by-$D$ hypothesis class. The reason is due to a particular inductive bias in ReLU networks: the $w$-by-$d$ parameter *witnesses* an exponential volume of $W$-by-$D$ interpolating parameters, which dwarfs the volume of poorly generalizing parameters (conditioned on interpolation). We explicitly construct this set of near-equivalent $W$-by-$D$ parameters by a proof technique called *deep lifting*, and then tie the achievable volume to stability properties of the $w$-by-$d$ witness. Examples show that these techniques allow us to convert approximation-theoretic results into generalization guarantees for nonparametric classes. We further show that generalization of uniform-random interpolators can survive label corruptions.
AI 速览：作者报告构造出经典色数任意大而量子色数恒为3的图，首次改进了自 Brassard–Cleve–Tapp 以来的量子色数间隙。
We confirm a conjecture of the first author [SODA'26] on a strong form of pseudo-telepathy for Khot's $d$-to-$1$ games: for every $d\geq 4$, every $ε>0$, and every $k\in\mathbb N$, there is a $d$-to-$1$ label-cover game of classical value less than $ε$ that admits a perfect quantum strategy using finite-dimensional shared entanglement with measurement contexts of radius at least $k$. As a consequence, there exist graphs whose quantum chromatic number $χ_q$ is $3$ and whose classical chromatic number $χ$ is arbitrarily large. This is the first improvement on the quantum chromatic gap since the work of Brassard, Cleve, and Tapp [Phys. Rev. Lett.'99], which produced graphs for which $χ$ grows exponentially in $χ_q$. To prove the conjecture, we proceed as follows. We start with a ``stretched'' version of the Mermin--Peres magic square, obtained by spacing out its equations and linking them with additional long equation wires. This operation increases the radius of the initial measurement contexts of a perfect quantum strategy for the game, while preserving classical unsatisfiability. We then apply parallel repetition to make the classical value small, and we turn the system into a pseudo-telepathic multi-layered Kneser hypergraph via a PCP construction of Dinur, Guruswami, Khot, and Regev [STOC'03]. Finally, we feed the resulting hypergraph into the reduction of Fei, Minzer, and Wang from hypergraph colouring to $4$-to-$1$ games, we establish quantum completeness of this reduction, and we show that it preserves context radius.
The Tight Competitive Ratio of Greedy for Online Steiner Forest
Iman Gholami, Ilya Hajiaghayi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade
AI 速览：该论文证明在线Steiner森林问题中自然贪心算法的竞争比紧确为Θ(log k log log k)，从而否定了Awerbuch-Azar-Bartal的O(log k)猜想。
The online Steiner Forest problem is a fundamental network design problem in which terminal pairs arrive one at a time and an algorithm must irrevocably purchase edges connecting each pair. The natural greedy algorithm connects each terminal pair by a shortest path after making all previously purchased edges free. Awerbuch, Azar, and Bartal (SODA 1996) proved that this algorithm is $O(log^2 k)$-competitive and conjectured an $O(log k)$ bound, where $k$ is the number of terminal pairs. Bamas, Drygala, and Maggiori (SODA 2022) obtained an $O(\log \NumPairs\log\log \NumPairs)$ bound for greedy on a restricted class of inputs, leaving the general case open. In this paper, we resolve the competitive ratio of the greedy algorithm for online Steiner Forest, proving that it is tightly $Θ(log(k) log log(k))$. Specifically, we establish an $O(log(k) log log(k))$ upper bound for arbitrary instances and construct a matching $Ω(log(k) log log(k))$ lower bound. Our results refute the $O(log k)$ conjecture of Awerbuch, Azar, and Bartal and establish a tight $Θ(log log k)$ separation between the greedy algorithm and the best possible online algorithm for Steiner Forest.
Self-regularization and structural adaptation of NPMLE for Gaussian mixture models in all dimensions
Yanjun Han, Yandi Shen, Yihong Wu
AI 速览：作者证明：均值位于超立方体内的 d 维高斯混合模型，其 NPMLE 能以高概率自动拟合出 O((log n/log log n)^d) 个分量，并在有限混合数据下使拟合分量数依概率有界。
We establish structural properties of the nonparametric maximum likelihood estimator (NPMLE) for $d$-dimensional Gaussian mixtures whose means lie in a hypercube. We show that, with high probability, the NPMLE based on $n$ independent observations self-regularizes by fitting a mixture model with $O((\frac{\log n}{\log\log n})^d)$ components, achieving the optimal model complexity without explicit model selection. Furthermore, the NPMLE exhibits a structural adaptation property: For data drawn from a finite mixture, the number of fitted components is bounded in probability as $n\to\infty$. Our proof applies a multivariate Jensen-type bound to control the typical number of critical points of the KKT function associated with the first-order optimality conditions. The key step is to lower bound its gradient norm uniformly on complex spheres. We establish this lower bound by decomposing the KKT function into an empirical fluctuation term and a relative density estimation error term, combining small-ball probability estimates for the former with polynomial approximation and Hellinger error bounds for the latter.
Gym-Anything for Robotics: Scaling physical simulations with digital agents
Pranjal Aggarwal, Sean Welleck
AI 速览：提出由编码智能体自动创建机器人仿真环境的框架，并构建包含25个仿真、25个测试与175个训练RL环境的RoboWorld基准。
Realistic, fast robotics simulations could enable large-scale training of embodied AI models that transfer to the real world. However, despite decades of progress, available simulations cover only a narrow range of real-world tasks and physical phenomena. The core bottleneck is that creating better simulations requires significant expert effort and therefore does not scale. To address this, we introduce Gym-Anything for Robotics, a framework in which coding agents create realistic robotics simulations. Our core insight is that simulation creation is a coding agent task, so improvements in coding agents translate directly into richer and more faithful simulations. We select simulations based on U.S. GDP data to cover economically valuable physical work, define what makes a good simulation and a good task, and develop an adversarial creation-audit loop that checks each simulation and task against these definitions. Using this pipeline, we build RoboWorld, a set of 25 simulations with 25 test and 175 training RL environments of varying difficulty. Even the best frontier models fail on every RoboWorld test task, achieving an average reward of only 0.06. Building on RoboWorld, we introduce several new ways for frontier models to improve, including in-context learning across repeated attempts, a privileged teacher that reads the simulator state and teaches a student in context, self-assisted learning from the model's own privileged experience, and code policies that generate demonstrations across varied scenes to train vision-language-action models (VLAs) such as $π_{0.5}$. Each of these substantially improves performance. We release our pipeline, RL environments, and benchmark to facilitate future research. Code and data are available at https://gym-anything.github.io/robotics
Training Foundation Models with a Single Algorithm
Yuda Song, Alvin Zhang, Fahim Tajwar, Daman Arora, Jeff Schneider, Daniel Khashabi, Ruslan Salakhutdinov, J. Andrew Bagnell 等 10 位作者
AI 速览：作者提出将预训练、中训练、SFT 与 RL 统一为对模型生成目标分布的最大似然拟合，从而用单一似然训练算法完成基础模型全流程训练。
Foundation models are typically trained in stages: pretraining, midtraining, supervised fine-tuning (SFT), and reinforcement learning (RL), with changes in both data and learning algorithms. We show that this algorithmic separation is not fundamental. By deriving suitable RL objectives as maximum-likelihood fitting to model-generated target distributions, we place all of these stages under a single likelihood-based training algorithm, unified training. This perspective turns the foundation-model training lifecycle into a problem of choosing which data to train on, in what proportions, and when, with conventional staged training as a special case. We instantiate this framework in a unified training system that mixes static data and RL generations within a single trainer. Across controlled and real-world experiments, unified training improves the accuracy-compute tradeoff and task coverage while preserving broader capabilities, and provides a stronger starting point for continual learning. This work lays the groundwork for a unified science of foundation-model training, connecting mathematical principles, training infrastructure, and the development of model capabilities.
Comparing Human Role-Players and LLM-Simulated Clients in Online Counselling Training: An Analysis of Counselling Patterns
Eric Rudolph, Philipp Steigerwald, Jens Albrecht
AI 速览：该研究比较新手咨询师与人类角色扮演来访者及LLM模拟来访者互动时的咨询沟通模式，以评估LLM模拟来访者在教学角色扮演中的可行性与差异。
This study investigates the capabilities of Large Language Models to simulate counselling clients in educational role-plays in comparison to human role-players. Initially, we recorded role-playing sessions, where novice counsellors interacted with human peers acting as clients, followed by role-plays between humans and clients simulated by Mistrals Mixtral 8x7b using 4-bit quantization. These interactions were analysed with a counselling communication pattern system at sentence level. We investigated two key questions: (1) to what extent LLM-generated responses replicate authentic conversational dynamics and (2) whether counsellors' communication behaviour differs when interacting with human versus LLM-simulated clients. The findings highlight both similarities and differences in the application of counselling patterns across scenarios, showing the potential of LLM-based role-playing exercises to enhance counselling competencies and to identify areas for further refinement in virtual client simulations.
Nearly-Optimal Time-Sample Trade-off in Consensus Dynamics
Francesco d'Amore, Joel Rybicki, Nobutaka Shimizu, Takeharu Shiraga, Robin Vacus
AI 速览：该论文研究同步 h-Majority 共识动力学中样本数 h 与达成共识所需时间之间的权衡，并给出近乎最优的上界与匹配下界。
How does the number of sampled opinions affect the time required to reach consensus in distributed consensus dynamics? We study the synchronous $h$-\textsf{Majority}, in which every node independently samples $h$ nodes uniformly at random with replacement in each round and adopts a most frequent sampled opinion, breaking ties uniformly at random. We show that $h$-\textsf{Majority} achieves the nearly-optimal trade-off between the sample size and the consensus time, among a broad class of consensus dynamics. In particular, we prove the following results. For every sample size $h \ge 3$ and for every initial configuration, we prove that the process reaches consensus with high probability within $\widetilde{O}\left(1+\min\left\{\frac{1}{\min\{h^2p_{\max},1\}},\frac{\sqrt{n}}{h}\right\}\right)$ rounds, where $n$ is the number of nodes and $p_{\max}$ is the largest initial fraction of nodes supporting any single opinion. This is the first bound on the consensus time for $h$-\textsf{Majority} that holds for every $h\ge3$ and every initial configuration. When the initially most popular opinion has a sufficiently large lead over every other opinion, we show that all nodes adopt this opinion with high probability within $O(\log n/\min\{h^2p_{\max},1\})$ rounds. We establish a matching lower bound up to polylogarithmic factors for any fixed update rule that treats all opinions symmetrically and that selects either a sampled opinion or the node's current opinion.
FARMS: A Verifiable Foundation for Automated Computational Science
Di Wu, Ling Liang, Haizhao Yang
AI 速览：作者提出 FARMS，将计算数学知识转化为可供 AI 解释与复用、并带有显式保证的“计算知识”基础。
Automated computational science could accelerate discovery by selecting, adapting and developing numerical methods. This prospect requires mathematical knowledge that AI systems can interpret and reuse with explicit guarantees. Here we present FARMS, a faithful and efficient foundation that transforms computational mathematics into AI-ready computing knowledge. FARMS connects formal statements to source context, algorithmic meaning and quantitative guarantees through source preparation, reusable representations and semantic review. Across 171 targets in randomized numerical linear algebra and numerical partial differential equations, 157 were accepted by the pipeline, with mean estimated costs of US \$0.85-2.29 per target across sources. Lean-checked implications from explicit source premises connect selected statements to computational skills, illustrated by a heat-flow solve and wave-response compression. FARMS therefore supports an affordable, reusable knowledge foundation for trustworthy automated computational science.
AI 速览：本教程第一部分系统介绍基于数据驱动变形雅可比的可变形物体形状伺服控制的基本要素与完整闭环。
In robotics, shape control (or shape servoing) refers to the automatic manipulation of a deformable object to achieve a desired shape. It involves a feedback loop that exploits the relation between robot motion and changes in the measured shape. This relation, known as the interaction Jacobian or, in this context, the deformation Jacobian, depends on the object's mechanical properties, geometry, and boundary conditions (e.g., where the object is grasped). Because these factors are often difficult to model accurately, the deformation Jacobian can be estimated locally from observed shape changes produced by commanded robot motions, without requiring a fine-tuned mechanical model. This article is the first of a two-part tutorial on data-driven Jacobian-based shape control of deformable objects. It introduces the central elements of the approach: the formulation of the shape-control problem, shape representation, estimation and online update of the deformation Jacobian, and a standard control law from the literature. It then assembles these elements into a complete shape-servoing loop, derives a local stability condition for this loop, and illustrates why some target shapes cannot be reached. Part II covers more advanced topics. Throughout both parts, a simulated planar example in which two robot arms manipulate an elastic rod observed by a camera illustrates the concepts.
Advanced power adjusting block withholding attacks such as PAW and T-PAW have been analyzed so far under a global-reset version of the proportional scheme (GRP), which is rarely used in practice. In this paper, we analyze T-PAW, which contains FAW and PAW as special cases, under the block-dependent payout schemes deployed in practice: Pay-Per-Last-N-Shares (PPLNS), round-based Proportional (PROP) and exponential-decay (EXP). We derive the revenue ratios analytically, by renewal arguments for PPLNS and through the stationary carry process of an open round for PROP and EXP. We further introduce Power Adjusting Hopping (PAH), where an adversary of any size adjusts its power allocation towards the pool according to the blockwork age of the round without withholding any block, and derive its revenue ratios under PROP and EXP. We show that GRP misestimates the T-PAW gain in a scheme-dependent direction: it overstates the gain under PROP up to an order of magnitude and understates it under EXP for the original slush decay rate. PROP is highly vulnerable to PAH, while EXP faces a trade-off: a slow decay invites PAH and a fast decay invites T-PAW. PPLNS is the least vulnerable scheme: it is immune to PAH and it mitigates, but does not eliminate, T-PAW. All analytical results are verified by Monte Carlo simulations.