Manifold Approximation leads to Robust Kernel Alignment
This work addresses a specific issue in representation comparison for machine learning and neuroscience, but it appears incremental as it builds on existing kernel alignment methods.
The authors tackled the problem that Centered Kernel Alignment (CKA) is not robust due to ignoring manifold geometry, and they proposed Manifold approximated Kernel Alignment (MKA), which showed improved robustness in empirical evaluations on synthetic and real-world datasets.
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.