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.

提出了一种基于“软”置换的度量方式，用于衡量具有不同大小的神经网络之间的距离，并避免了其他方式所遭受的违反直觉的结果，从而提供了对神经表示的补充几何洞见。

软匹配距离：一种捕捉单神经元调谐的神经表示度量