提出考虑数据流形结构的核对齐方法，提升表示度量的稳定性。
Manifold Approximation leads to Robust Kernel Alignment
- 基于流形几何改进核对齐，引入曼福德近似机制
- 在合成与真实数据上验证，多尺度下表现更稳定
- 适合关注表示学习鲁棒性的研究者
中心化核对齐（CKA）是衡量表示、判断网络等价性及神经科学应用中常用的度量方法。然而，CKA未考虑数据的底层流形结构，依赖大量启发式方法，导致在不同数据尺度下行为不一致。本文提出流形近似核对齐（MKA），将流形几何融入对齐任务。我们建立了MKA的理论框架，并在合成数据集和真实案例上进行实证评估，对比其与现有方法的性能。结果表明，感知流形的核对齐能为表示度量提供更稳健的基础，具有代表学习中的潜在应用价值。
原文摘要 · Abstract (English)
Centered kernel alignment (CKA) is a popular metric for comparing representations, determining equivalence of networks, and neuroscience research. However, CKA does not account for the underlying manifold and relies on numerous heuristics that cause it to behave differently at different scales of data. In this work, we propose Manifold approximated Kernel Alignment (MKA), which incorporates manifold geometry into the alignment task. We derive a theoretical framework for MKA. We perform empirical evaluations on synthetic datasets and real-world examples to characterize and compare MKA to its contemporaries. Our findings suggest that manifold-aware kernel alignment provides a more robust foundation for measuring representations, with potential applications in representation learning.
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