Xiao Wei
Publications
Progressive Approximation in Deep Residual Networks: Theory and Validation
The Universal Approximation Theorem (UAT) guarantees universal function approximation but does not explain how residual models distribute approximation across layers. We reframe residual networks as a layer-wise approximation process that builds an approximation trajectory from input to target, and prove the existence of progressive trajectories where error decreases monotonically with depth. It reveals that residual networks can implement structured, step-by-step refinement rather than end-to-end (E2E) black-box mapping. Building on this, we propose Layer-wise Progressive Approximation (LPA), a theoretically grounded training principle that explicitly aligns each layer with its residual target to realize such trajectories. LPA is architecture-agnostic: we observe progressive behavior in residual FNNs, ResNets, and Transformers across tasks including complex surface fitting, image classification, and NLP with LLMs for generation and classification. Crucially, this enables ``train once, use $N$ models": a single network yields useful predictions at every depth, supporting efficient shallow inference without retraining. Our work unifies approximation theory with practical deep learning, providing a new lens on representation learning and a flexible framework for multi-depth deployment. The source code will be released unpon acceptance at https://(open\_upon\_acceptance).
Mol-Debate: Multi-Agent Debate Improves Structural Reasoning in Molecular Design
Text-guided molecular design is a key capability for AI-driven drug discovery, yet it remains challenging to map sequential natural-language instructions with non-linear molecular structures under strict chemical constraints. Most existing approaches, including RAG, CoT prompting, and fine-tuning or RL, emphasize a small set of ad-hoc reasoning perspectives implemented in a largely one-shot generation pipeline. In contrast, real-world drug discovery relies on dynamic, multi-perspective critique and iterative refinement to reconcile semantic intent with structural feasibility. Motivated by this, we propose Mol-Debate, a generation paradigm that enables such dynamic reasoning through an iterative generate-debate-refine loop. We further characterize key challenges in this paradigm and address them through perspective-oriented orchestration, including developer-debater conflict, global-local structural reasoning, and static-dynamic integration. Experiments demonstrate that Mol-Debate achieves state-of-the-art performance against strong general and chemical baselines, reaching 59.82% exact match on ChEBI-20 and 50.52% weighted success rate on S$^2$-Bench. Our code is available at https://github.com/wyuzh/Mol-Debate.