深度网络中的神经分化：表达性与表征多样性的理论框架
Neural Differentiation in Deep Networks: A Theoretical Framework for Expressivity and Representational Diversity
提出神经元级可微性指标 NDI 与训练时结构化剪枝方法 NDP，为视觉模型压缩提供可证明的误差上界与自适应稀疏化流程，可直接用于 CNN/ViT 等骨干网络的轻量化。
原文依据 NDP leverages NDI to perform adaptive, training-time neuron sparsification, followed by targeted fine-tuning
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论我们首先在单个神经元层面构建神经分化的数学框架。该框架形式化了每个神经元应在网络中获得独特表征角色、从而避免冗余并最大化集体表达性的原则。分化程度通过神经分化指数（NDI）量化，这是一种损失感知的度量，在统一框架内从几何、信息和曲率角度刻画神经元重要性。NDI 能够严格表征神经元在功能与重要性上与同侪的偏离程度，并支撑理论保证：我们建立了 NDI 引导消除下误差增加的形式化上界，从而为网络压缩提供可证明的安全裕度。在此基础上，我们提出神经分化剪枝（NDP）作为实际实现。NDP 利用 NDI 执行自适应、训练时的神经元稀疏化，随后进行定向微调，引导网络趋向紧凑且高度分化的骨干。尽管术语从生物分化中借用了直观类比，该框架完全是数学的且与架构无关。在现代视觉基准和架构上的实验表明，NDP 在实现显著结构化稀疏性的同时保持甚至提升准确率与鲁棒性，凸显了分化框架的实际影响。
英文原文摘要 1528 字符
We begin by developing a mathematical framework of neural differentiation, formulated at the level of individual neurons. This framework formalizes the principle that each neuron should acquire a distinct representational role within the network, thereby avoiding redundancy and maximizing collective expressivity. Differentiation is quantified through the Neural Differentiation Index (NDI), a loss-aware measure that characterizes neuron significance from geometric, informational, and curvature-based perspectives within a unified framework. The NDI enables a rigorous characterization of how strongly a neuron diverges from its peers in both function and importance, and supports theoretical guarantees: we establish formal bounds on the error increase under NDI-guided elimination, thereby providing provable safety margins for network compression. Building on this foundation, we introduce Neural Differentiation Pruning (NDP) as a practical instantiation. NDP leverages NDI to perform adaptive, training-time neuron sparsification, followed by targeted fine-tuning, guiding networks toward compact yet highly differentiated backbones. Although the terminology draws loose intuition from biological differentiation, the framework is fully mathematical and architecture-agnostic. Experiments on modern vision benchmarks and architectures show that NDP achieves substantial structured sparsity while maintaining--or even improving--accuracy and robustness, underscoring the practical impact of the differentiation framework.