Estimating Neural Representation Alignment from Sparsely Sampled Inputs and Features

arxiv:2502.15104

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Representation alignment · 2025-02-20

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2. Part 2
3. Part 3
4. Part 4
5. Part 5

Contents

• Estimating Neural Representation Alignment from Sparsely Sampled Inputs and Features
• Abstract
• Introduction
• Problem Statement
• Our Contribution
• Definitions
• Centered Kernel Alignment
• Measurement matrix
• Existing CKA estimators
• Naive Estimator
• Stimulus-Corrected Estimator
• Bias of the Existing Estimator
• Stimulus-Neuron-Corrected Estimator
• Linear example
• Practical applications in neuroscience
• Brain-to-Brain alignment
• Brain-to-Model alignment
• Object disentanglement
• Trial-to-Trial Similarity
• Discussion
• Conclusion
• Supplementary Information
• Appendix A Full derivation of the ℋ \mathcal{H} estimators
• A.1 Expression of ℋ \mathcal{H} in terms of the uncentered kernel
• A.2 Identifying the source of bias in the naive estimator
• A.3 Derivation of the stimulus-corrected ℋ \mathcal{H} estimator
• A.4 Derivation of the stimulus-neuron-corrected ℋ \mathcal{H} estimator
• Appendix B Bias analysis
• B.1 Generative process framework
• B.2 Biases in CKA estimators contributed by the biases in HSIC estimators
• B.3 Analyzing the overall ℋ ^ \widehat{\mathcal{H}} -based CKA estimators
• Appendix C Additional results on neural data
• C.1 Brain-to-model alignment
• C.2 Object disentanglement
• Appendix D Code availability
• Instructions for reporting errors