arXiv subjects

Shufan Wu

Publications and source records attributed to Shufan Wu.

4 recordsLinked to original sources

arXiv2026

A Geometrically-Grounded Drive for MDL-Based Optimization in Deep Learning

This paper introduces a novel optimization framework that fundamentally integrates the Minimum Description Length (MDL) principle into the training dynamics of deep neural networks. Moving beyond its conventional role as a model selection criterion, we reformulate MDL as an active, adaptive driving force within the optimization process itself. The core of our method is a geometrically-grounded cognitive manifold whose evolution is governed by a \textit{coupled Ricci flow}, enriched with a novel \textit{MDL Drive} term derived from first principles. This drive, modulated by the task-loss gradient, creates a seamless harmony between data fidelity and model simplification, actively compressing the internal representation during training. We establish a comprehensive theoretical foundation, proving key properties including the monotonic decrease of description length (Theorem~\ref{thm:convergence}), a finite number of topological phase transitions via a geometric surgery protocol (Theorems~\ref{thm:surgery}, \ref{thm:ultimate_fate}), and the emergence of universal critical behavior (Theorem~\ref{thm:universality}). Furthermore, we provide a practical, computationally efficient algorithm with $O(N \log N)$ per-iteration complexity (Theorem~\ref{thm:complexity}), alongside guarantees for numerical stability (Theorem~\ref{thm:stability}) and exponential convergence under convexity assumptions (Theorem~\ref{thm:convergence_rate}). Empirical validation on synthetic regression and classification tasks confirms the theoretical predictions, demonstrating the algorithm's efficacy in achieving robust generalization and autonomous model simplification. This work provides a principled path toward more autonomous, generalizable, and interpretable AI systems by unifying geometric deep learning with information-theoretic principles.

cs.LG↗

arXiv2026

HCP-DCNet: A Hierarchical Causal Primitive Dynamic Composition Network for Self-Improving Causal Understanding

The ability to understand and reason about cause and effect -- encompassing interventions, counterfactuals, and underlying mechanisms -- is a cornerstone of robust artificial intelligence. While deep learning excels at pattern recognition, it fundamentally lacks a model of causality, making systems brittle under distribution shifts and unable to answer ``what-if'' questions. This paper introduces the \emph{Hierarchical Causal Primitive Dynamic Composition Network (HCP-DCNet)}, a unified framework that bridges continuous physical dynamics with discrete symbolic causal inference. Departing from monolithic representations, HCP-DCNet decomposes causal scenes into reusable, typed \emph{causal primitives} organized into four abstraction layers: physical, functional, event, and rule. A dual-channel routing network dynamically composes these primitives into task-specific, fully differentiable \emph{Causal Execution Graphs (CEGs)}. Crucially, the system employs a \emph{causal-intervention-driven meta-evolution} strategy, enabling autonomous self-improvement through a constrained Markov decision process. We establish rigorous theoretical guarantees, including type-safe composition, routing convergence, and universal approximation of causal dynamics. Extensive experiments across simulated physical and social environments demonstrate that HCP-DCNet significantly outperforms state-of-the-art baselines in causal discovery, counterfactual reasoning, and compositional generalization. This work provides a principled, scalable, and interpretable architecture for building AI systems with human-like causal abstraction and continual self-refinement capabilities.

cs.LG↗

arXiv2025

Robust Probability Hypothesis Density Filtering: Theory and Algorithms

Multi-target tracking (MTT) serves as a cornerstone technology in information fusion, yet faces significant challenges in robustness and efficiency when dealing with model uncertainties, clutter interference, and target interactions. Conventional approaches like Gaussian Mixture PHD (GM-PHD) and Cardinalized PHD (CPHD) filters suffer from inherent limitations including combinatorial explosion, sensitivity to birth/death process parameters, and numerical instability. This study proposes an innovative minimax robust PHD filtering framework with four key contributions: (1) A theoretically derived robust GM-PHD recursion algorithm that achieves optimal worst-case error control under bounded uncertainties; (2) An adaptive real-time parameter adjustment mechanism ensuring stability and error bounds; (3) A generalized heavy-tailed measurement likelihood function maintaining polynomial computational complexity; (4) A novel partition-based credibility weighting method for extended targets. The research not only establishes rigorous convergence guarantees and proves the uniqueness of PHD solutions, but also verifies algorithmic equivalence with standard GM-PHD. Experimental results demonstrate that in high-clutter environments, this method achieves a remarkable 32.4% reduction in OSPA error and 25.3% lower cardinality RMSE compared to existing techniques, while maintaining real-time processing capability at 15.3 milliseconds per step. This breakthrough lays a crucial foundation for reliable MTT in safety-critical applications.

eess.SY↗

arXiv2021

A New Continuous Optimization Method for Mixed Integer Space Travelling Salesman Problem

The travelling salesman problem (TSP) of space trajectory design is complicated by its complex structure design space. The graph based tree search and stochastic seeding combinatorial approaches are commonly employed to tackle the time-dependent TSP due to their combinatorial nature. In this paper, a new continuous optimization strategy for the mixed integer combinatorial problem is proposed. The space trajectory combinatorial problem is tackled using continuous gradient based method. A continuous mapping technique is developed to map the integer type ID of targets on the sequence to a set of continuous design variables. Expected flyby targets are introduced as references and used as priori to select the candidate target to fly by. Bayesian based analysis is employed to model accumulated posterior of the sequence and a new objective function with quadratic form constraints is constructed. The new introduced auxiliary design variables of expected targets together with the original design variables are set to be optimized. A gradient based optimizer is used to search optimal sequence parameter. Performances of the proposed algorithm are demonstrated through a multiple debris rendezvous problem and a static TSP benchmark.

math.OC↗