Learning to Coordinate Symbolic Tools: LLM Agents for Verified Sum-of-Squares Certificates

Tool calling allows large language models (LLMs) to invoke external computation during problem solving, a useful capability in various fields including AI for mathematics. We study this setting through weighted sum-of-squares (SOS) decomposition, a machine-checkable route to proving polynomial nonnegativity and hence polynomial inequalities. A candidate decomposition can be checked exactly, but finding one requires choosing among non-unique regroupings and coordinating multiple symbolic transformations. We develop an agent that combines algebraic task training, symbolic tools, and verifier-grounded optimization for this task. Rather than training only on the composite SOS task, we construct 1.35 million synthetic examples covering eight supporting polynomial tasks together with weighted-SOS decomposition. We first apply supervised fine-tuning (SFT) to direct algebra problems and simulated symbolic traces, and then use Group Relative Policy Optimization (GRPO) with task-specific symbolic rewards. The SFT corpus contains no native tool-calling messages; at evaluation, the agent uses native SymPy calls for expansion, collection, reordering, and factorization. Every final SOS answer is checked by exact expansion and coefficient comparison. On held-out, same-generator synthetic problems, the full SFT+GRPO+tools system is the strongest of four evaluated configurations, reaching 78.96% verified success on weighted SOS, compared with 44.73% for the base model with the same tools, and 91.75% macro accuracy across nine polynomial tasks. Within this controlled setting, our work provides a case study of combining domain-specific skill training, executable tools, and verifier feedback, and may inform the design of tool-calling agents in other domains with exactly checkable outputs.

ScratchSim: A Procedural Synthetic Data Pipeline for Surface Scratch Detection

While automated defect detection such as the detection of surface scratched is an important aspect in industrial quality control, the scarcity of annotated defect data make this task challenging. This paper presents a procedural rendering pipeline that generates large-scale annotated synthetic training data using BlenderProc, with configurable material appearance, camera modes, and domain randomization, producing automatic COCO-format annotations. To show the potential of our approach, we evaluate four training strategies, namely synthetic-only, real-only, mixed, and fine-tuning from synthetic weights, across two objects with different material properties and three lightweight edge-deployable detectors, YOLOX, YOLO26, and LW-DETR. Our evaluation show that fine-tuning from synthetic weights consistently outperforms real-only training, and that mixed training effectively recovers performance under scarce real-data conditions, with findings validated across both convolutional and transformer-based architectures. The proposed approach enables scalable defect detection without the burden of large real annotated datasets, making it practical for on-device industrial inspection. The pipeline scripts, 3D model, and both synthetic and real annotated scratch datasets for a glossy toy Ferrari car will be made available through the project website upon acceptance.

Graphon Mean-Field Subsampling for Cooperative Heterogeneous Multi-Agent Reinforcement Learning

Coordinating large populations of interacting agents is a central challenge in multi-agent reinforcement learning (MARL), where the size of the joint state-action space scales exponentially with the number of agents. Mean-field methods alleviate this burden by aggregating agent interactions, but these approaches assume homogeneous interactions. Recent graphon-based frameworks capture heterogeneity, but are computationally expensive as the number of agents grows. Therefore, we introduce $\texttt{GMFS}$, a $\textbf{G}$raphon $\textbf{M}$ean-$\textbf{F}$ield $\textbf{S}$ubsampling framework for scalable cooperative MARL with heterogeneous agent interactions. By subsampling $κ$ agents according to interaction strength, we approximate the graphon-weighted mean-field and learn a policy with sample complexity $\mathrm{poly}(κ)$ and optimality gap $O(1/\sqrtκ)$. We verify our theory with numerical simulations in robotic coordination, showing that $\texttt{GMFS}$ achieves near-optimal performance.

Practical Adversarial Attacks on Stochastic Bandits via Fake Data Injection

Adversarial attacks on stochastic bandits have traditionally relied on some unrealistic assumptions, such as per-round reward manipulation and unbounded perturbations, limiting their relevance to real-world systems. We propose a more practical threat model, Fake Data Injection, which reflects realistic adversarial constraints: the attacker can inject only a limited number of bounded fake feedback samples into the learner's history, simulating legitimate interactions. We design efficient attack strategies under this model, explicitly addressing both magnitude constraints (on reward values) and temporal constraints (on when and how often data can be injected). Our theoretical analysis shows that these attacks can mislead both Upper Confidence Bound (UCB) and Thompson Sampling algorithms into selecting a target arm in nearly all rounds while incurring only sublinear attack cost. Experiments on synthetic and real-world datasets validate the effectiveness of our strategies, revealing significant vulnerabilities in widely used stochastic bandit algorithms under practical adversarial scenarios.

Object-Pose Estimation With Neural Population Codes

Robotic assembly tasks require object-pose estimation, particularly for tasks that avoid costly mechanical constraints. Object symmetry complicates the direct mapping of sensory input to object rotation, as the rotation becomes ambiguous and lacks a unique training target. Some proposed solutions involve evaluating multiple pose hypotheses against the input or predicting a probability distribution, but these approaches suffer from significant computational overhead. Here, we show that representing object rotation with a neural population code overcomes these limitations, enabling a direct mapping to rotation and end-to-end learning. As a result, population codes facilitate fast and accurate pose estimation. On the T-LESS dataset, we achieve inference in 3.2 milliseconds on an Apple M1 CPU and a Maximum Symmetry-Aware Surface Distance accuracy of 84.7% using only gray-scale image input, compared to 69.7% accuracy when directly mapping to pose.