arXiv:2409.12135v3 Announce Type: replace-cross Abstract: Temporal difference (TD) learning with linear function approximation (linear TD) is a classic and powerful prediction algorithm in reinforcement learning. While it is well-understood that linear TD converges almost surely to a unique point, this convergence traditionally requires the assumption that the features used by the approximator are linearly independent. However, this linear independence assumption does not hold in many practical scenarios. This work is the first to establish the almost sure convergence of linear TD without requiring linearly independent features. We prove that the weight iterates of linear TD converge to a bounded set, and that the value estimates derived from the weights in that set are the same almost everywhere. We also establish a notion of local stability of the weight iterates. Importantly, we do not impose assumptions tailored to feature dependence and do not modify the linear TD algorithm. Key to our analysis is a novel characterization of bounded invariant sets of the mean ODE of linear TD.

arXiv:2601.07315v4 Announce Type: replace-cross Abstract: Vision Language Models (VLMs) have demonstrated remarkable potential in multimodal reasoning, yet they inherently suffer from spatial blindness and logical hallucinations when interpreting densely structured engineering content, such as analog circuit schematics. To address these challenges, we propose a Vision Language Model-Optimized Collaborative Agent Design Workflow for Analog Circuit Sizing (VLM-CAD) designed for robust, step-by-step reasoning over multimodal evidence. VLM-CAD bridges the modality gap by integrating a neuro-symbolic structural parsing module, Image2Net, which transforms raw pixels into explicit topological graphs and structured JSON representations to anchor VLM interpretation in deterministic facts. To ensure the reliability required for engineering decisions, we further propose ExTuRBO, an Explainable Trust Region Bayesian Optimization method. ExTuRBO serves as an explainable grounding engine, employing agent-generated semantic seeds to warm-start local searches and utilizing Automatic Relevance Determination to provide quantified evidence for the VLM's decisions. Experimental results on two complex circuit benchmarks demonstrate that VLM-CAD significantly enhances spatial reasoning accuracy and maintains physics-based explainability. VLM-CAD consistently satisfies complex specification requirements while achieving low power consumption, with a total runtime under 66 minutes, marking a significant step toward robust, explainable multimodal reasoning in specialized technical domains.