Representation Topology Divergence: A Method for Comparing Neural Network Representations
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；CNRS（法国国家科学研究中心）；Université Paris Cité（巴黎西岱大学）；Artificial Intelligence Research Institute (AIRI)（人工智能研究院（AIRI））
Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD), measuring the dissimilarity in multi-scale topology between two point clouds of equal size with a one-to-one correspondence between points. The data point clouds are allowed to lie in different ambient spaces. The RTD is one of the few TDA-based practical methods applicable to real machine learning datasets. Experiments show that the proposed RTD agrees with the intuitive assessment of data representation similarity and is sensitive to its topological structure. We apply RTD to gain insights on neural networks representations in computer vision and NLP domains for various problems: training dynamics analysis, data distribution shift, transfer learning, ensemble learning, disentanglement assessment.
Scalar Function Topology Divergence: Comparing Topology of 3D Objects
Skolkovo Institute of Science and Technology（斯克尔科夫科学与技术研究所）；AIRI（AI研究机构）；CNRS, IMJ, Paris Cité University（国家科学研究中心、巴黎城市大学）；AI Foundation and Algorithm Lab（AI基金会与算法实验室）
Manifold Topology Divergence: a Framework for Comparing Data Manifolds
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；CNRS（法国国家科学研究中心）；Paris University（巴黎大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Artificial Intelligence Research Institute (AIRI)（人工智能研究院（AIRI））
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Artificial Intelligence Research Institute (AIRI)（人工智能研究院（AIRI））；Huawei Noah’s Ark lab（华为诺亚方舟实验室）；CNRS（法国国家科学研究中心）；Université Paris Cité（巴黎西岱大学）
Learning Log-Determinant Divergences for Positive Definite Matrices
Mitsubishi Electric Research Labs (MERL)（三菱电机研究实验室）；Australian Centre for Robotic Vision, Australian National University（澳大利亚国立大学澳大利亚机器人视觉中心）；University of Minnesota（明尼苏达大学）；Research School of Engineering, The Australian National University（澳大利亚国立大学工程研究学院）；Monash University（莫纳什大学）；Data61-CSIRO（澳大利亚联邦科学与工业研究组织数据61）
