## Abstract

Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has been recent interest in developing stricter notions of representational (dis)similarity that require neurons to be individually matched across networks. When two networks have the same size (i.e. same number of neurons), a distance metric can be formulated by optimizing over neuron index permutations to maximize tuning curve alignment. However, it is not clear how to generalize this metric to measure distances between networks with different sizes. Here, we leverage a connection to optimal transport theory to derive a natural generalization based on “soft” permutations. The resulting metric is symmetric, satisfies the triangle inequality, and can be interpreted as a Wasserstein distance between two empirical distributions. Further, our proposed metric avoids counter-intuitive outcomes suffered by alternative approaches, and captures complementary geometric insights into neural representations that are entirely missed by rotation-invariant metrics.

Original language | English (US) |
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Pages (from-to) | 133-143 |

Number of pages | 11 |

Journal | Proceedings of Machine Learning Research |

Volume | 243 |

State | Published - 2023 |

Event | 1st Workshop on Unifying Representations in Neural Models, UniReps 2023 - New Orleans, United States Duration: Dec 15 2023 → … |

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability