可解释量子学习的训练-剪枝-读出-重写工作流
A train--prune--readout--rewrite workflow for interpretable quantum learning
- Tongji University（同济大学）
- Shanghai Research Institute for Intelligent Autonomous Systems（上海智能无人系统研究院）
- State Key Laboratory of Autonomous Intelligent Unmanned Systems（自主无人系统国家重点实验室）
- Research & Development Center BMW, BMW China Services Ltd.（宝马中国研发中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出训练-剪枝-读出-重写工作流，用复值Kolmogorov-Arnold网络实现可解释量子学习，通过代数读出、符号重写和变换测试区分物理基础与计算结构，并在多量子比特任务中验证高精度。
AI中文摘要：
AI for Science 的目标不仅是从数据中预测复杂物理系统，还要从学习模型中提取数学结构和可物理检验的表征。本文开发了一种训练-剪枝-读出-重写工作流，将物理领域基础与三个日益严格的分析声明区分开来：对训练后预测器的代数等价读出、在采样物理域上的紧凑且忠于教师的符号重写，以及基于变换的学习内部表征测试。该工作流使用复值 Kolmogorov-Arnold 网络实现，其显式边函数支持剪枝后对保留计算的分析读出。在解析控制的单量子比特任务中，重写恢复了纯度（purity）的二次结构，而 von Neumann 熵仅产生域受限的符号替代；物理对齐的变量分组保持了符号保真度。对于双量子比特纠缠相关任务，共享学习暴露了共同的内部表征，其物理内容被直接探究。局部酉变换拒绝了直接的协变坐标解释，而固定解码器迁移表明共享激活以变换一致的形式携带泡利关联信息。随后通过低阶非线性读出恢复了与任务相关的不变谱特征。独立的预测测试在三量子比特分类和受控的十量子比特纯度回归（超过一百万个复值输入）中保持了高精度。这些结果建立了一个证据分辨框架，用于在受约束的复值科学学习中区分物理基础、可读计算、忠实符号压缩和变换检验的物理结构。
英文摘要：
AI for Science aims not only to predict complex physical systems from data, but also to extract mathematical structure and physically testable representations from learned models. Here, a train--prune--readout--rewrite workflow is developed that separates physical-domain grounding from three increasingly stringent analysis claims: algebraically equivalent readout of a trained predictor, compact teacher-faithful symbolic rewriting on the sampled physical domain, and transformation-based tests of learned internal representations. The workflow is implemented with complex-valued Kolmogorov--Arnold networks, whose explicit edge functions enable post-pruning analytic readout of the retained computation. In analytically controlled single-qubit tasks, rewriting recovered the quadratic structure of purity, whereas von Neumann entropy yielded only a domain-bounded symbolic surrogate; physics-aligned variable grouping preserved symbolic fidelity. For two-qubit entanglement-related tasks, shared learning exposed a common internal representation whose physical content was interrogated directly. Local-unitary transformations rejected a direct invariant-coordinate interpretation, while fixed-decoder transfer showed that the shared activation carries Pauli-correlation information in a transformation-consistent form. Task-related invariant spectral features were subsequently recovered through low-order nonlinear readouts. Separate predictive tests retained high accuracy for three-qubit classification and controlled ten-qubit purity regression with over one million complex inputs. These results establish an evidence-resolved framework for distinguishing physical grounding, readable computation, faithful symbolic compression and transformation-tested physical structure in constrained complex-valued scientific learning.
