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Correcting Biased Centered Kernel Alignment Measures in Biological and Artificial Neural Networks (2405.01012v1)

Published 2 May 2024 in q-bio.NC and cs.CV

Abstract: Centred Kernel Alignment (CKA) has recently emerged as a popular metric to compare activations from biological and artificial neural networks (ANNs) in order to quantify the alignment between internal representations derived from stimuli sets (e.g. images, text, video) that are presented to both systems. In this paper we highlight issues that the community should take into account if using CKA as an alignment metric with neural data. Neural data are in the low-data high-dimensionality domain, which is one of the cases where (biased) CKA results in high similarity scores even for pairs of random matrices. Using fMRI and MEG data from the THINGS project, we show that if biased CKA is applied to representations of different sizes in the low-data high-dimensionality domain, they are not directly comparable due to biased CKA's sensitivity to differing feature-sample ratios and not stimuli-driven responses. This situation can arise both when comparing a pre-selected area of interest (e.g. ROI) to multiple ANN layers, as well as when determining to which ANN layer multiple regions of interest (ROIs) / sensor groups of different dimensionality are most similar. We show that biased CKA can be artificially driven to its maximum value when using independent random data of different sample-feature ratios. We further show that shuffling sample-feature pairs of real neural data does not drastically alter biased CKA similarity in comparison to unshuffled data, indicating an undesirable lack of sensitivity to stimuli-driven neural responses. Positive alignment of true stimuli-driven responses is only achieved by using debiased CKA. Lastly, we report findings that suggest biased CKA is sensitive to the inherent structure of neural data, only differing from shuffled data when debiased CKA detects stimuli-driven alignment.

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Summary

  • The paper demonstrates that biased CKA produces misleading high similarity scores in low-data, high-dimensional scenarios.
  • It employs comparative experiments with fMRI, MEG, and CNN layer data to validate the robustness of debiased CKA.
  • The findings imply that debiased CKA enhances both neuroimaging analysis and the alignment accuracy of neural network models.

A Deeper Dive into the Pitfalls of Biased CKA in Neural Data Analysis

Overview of the Research

Recent research has critically evaluated the efficacy of Centered Kernel Alignment (CKA) as an alignment metric for comparing activations from biological and artificial neural networks. While biased CKA has been a popular choice, this paper exposes its shortcomings, especially in cases involving low-data and high-dimensionality scenarios, typical of neural data like fMRI or MEG. The findings throw light on the advantages of using debiased CKA to achieve more accurate and stimuli-driven responses. Here's a walkthrough of what was discovered, the experimental approach, and the implications of these findings.

The Trouble with Biased CKA

The heart of the problem with biased CKA lies in its sensitivity to the ratio of features to samples. This intrinsic characteristic can lead to misleadingly high similarity scores for random matrices, which do not genuinely reflect proper alignment between biological responses and model architectures:

  • Erroneous High Similarity: Biased CKA can generate high similarity scores even between completely random matrices, especially if these matrices have a large number of columns (features) relative to rows (samples).
  • False Positive Alignments: The biased version of CKA may suggest an alignment between different layers of a neural network and regions of interest (ROIs) in the brain, which could be falsely attributed to similar processing of stimuli.

Debiasing the CKA

To combat the vulnerabilities of biased CKA, researchers have refined the metric to a debiased version, which demonstrates resilience to the pitfalls of its predecessor:

  • Robust to Dimensionality Issues: The debiased CKA doesn't produce artificially high similarities when faced with varying dimensions across the datasets.
  • Genuine Stimuli-driven Responses: Only the debiased CKA has shown consistency in representing actual, stimuli-driven neural responses, making it a more reliable tool in neuroimaging studies.

Experimental Insights

To bolster their arguments, the researchers conducted comprehensive experiments across different conditions using fMRI and MEG data; along with ANN layers from popular CNN models like ResNet18 and CORnet-S:

  1. Sensitivity Tests: Trials where both random and structured (real) data were exposed to biased and debiased CKA revealed significant flaws in the biased approach. For instance, shuffling sample-feature pairs did not significantly alter biased CKA results, underscoring its insensitivity to the actual stimuli-driven changes.
  2. Comparison Across Networks: Analyses of neural data in relation to layers of CNNs showed that debiased CKA is sensitive to true variations in stimuli, which biased CKA often misconstrued as random similarities.
  3. Real versus Random: Testing with a mix of real and randomized data further confirmed that debiased CKA could discern genuine similarities driven by real stimuli, which biased CKA could not distinguish from random data alignments.

Theoretical and Practical Implications

The paper sheds light not only on the theoretical understanding of neural alignment metrics but also poses significant practical implications for designing more effective neural network models and analyzing neuroimaging data:

  • Enhanced Model Accuracy: Using debiased CKA could help in developing neural network models that are better aligned with human brain responses, which may enhance the accuracy and robustness against adversarial attacks.
  • Better Neuroimaging Analysis: This metric can significantly improve the reliability of neuroimaging data analyses, directly impacting clinical and research outcomes in neuroscience.

Looking Ahead: Future Developments in AI

Reflecting on these findings, one can anticipate further refinements in neural alignment metrics. The robust attributes of debiased CKA could pave the way for new methodologies that not only tackle the dimensional disparities in data but also enhance the fidelity of cross-domain neural data analysis. Moreover, this could be a stepping stone towards creating AI systems that genuinely mimic human brain processes, a key pursuit in cognitive neuroscience and artificial intelligence.

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