发表机构
Queen Mary University of London; University of Campinas (Unicamp)（伦敦玛丽女王大学; 坎皮纳斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用Fisher信息度量下的测地距离，提出一种基于微分几何的神经架构剪枝方法，在MNIST和CIFAR-10上超越幅度剪枝，实现最优性能。
AI 中文摘要
本文提出了一种新的参数剪枝方案，该方案源于模型空间中的微分几何距离。剪枝一个参数将其值设为零，这表示模型位移到该参数消失的超曲面上。从未剪枝模型到该超曲面的最小距离，自然通过由Fisher信息度量确定的模型空间中的测地距离来计算。该距离决定了剪枝下模型的真实变化及其性能。通过分析该测地距离逐渐更精确的近似，确定了剪枝方法最优性的自然层级。这从传统的幅度剪枝开始，然后发展为新的更复杂且有效的剪枝方案。该方法在MNIST和CIFAR-10上，对全连接网络和视觉变换器进行了演示，覆盖完整的0%-100%剪枝范围，并跨越五个随机种子。在考虑的每种架构和数据集组合上，它在准确性和Matthews相关系数方面均优于按参数幅度和仅局部Fisher信息的剪枝。此外，对不同级别测地近似的分析产生了计算高效且保持接近最优性能的中间剪枝方案。这种几何视角不仅为AI模型提供了一种最先进的剪枝方法，也为剪枝方案提供了经过验证且具有数学动机的合理性证明。
英文摘要
A new scheme for parameter pruning is introduced, derived from the differential-geometric distance in model space. Pruning a parameter sets its value to zero, representing a displacement of the model to the hypersurface on which that parameter vanishes. The minimal distance from the unpruned model to this hypersurface is naturally computed via the geodesic distance in the model space as determined by the Fisher information metric. This distance determines the true change in the model, and its performance, under pruning. By analysing progressively more faithful approximations of this geodesic distance a natural hierarchy of optimality for pruning methods is determined. This starts with the traditional magnitude pruning, then develops into new more sophisticated and effective pruning schemes. The method is demonstrated for both fully-connected networks and vision transformers, on MNIST and CIFAR-10, over the complete $0$-$100\%$ pruning range and across five random seeds. It outperforms pruning by parameter magnitude and by the local Fisher information alone in every architecture and dataset combination considered, on both accuracy and the Matthews correlation coefficient. Additionally, analysis of different levels of geodesic approximation produces intermediate pruning schemes that are computationally efficient and maintain near-optimal performance. This geometric picture supplies not only a state-of-the-art pruning methodology for AI models, but also a verified and mathematically-motivated justification for pruning schemes.
Comments21 pages, 4 figures, 4 tables
