This repository provides the repsim package for comparing representational similarity in PyTorch.

See rsatoolbox for a more mature and fully-featured toolbox. In contrast, this repository

• does everything in PyTorch, so the outputs are in principle differentiable.
• provides kernel-based methods such as CKA.
• provides metric RSA methods of Williams et al. (2021) and Shahbazi et al. (2021).

• Here, a neural representation refers to a n by d matrix containing the activity of d neurons in response to n inputs.
• Similarity and distance are essentially inverses. Similarity is high when distance is low, and vice versa. Both are (with few exceptions) non-negative quantities.
• Pairwise similarity refers to a n by n matrix of similarity scores among all pairs of input-items for a given neural representation. Likewise, pairwise distance is n by n but contains distances rather than similarities.
• Representational similarity is a scalar score that is large when two neural representations are similar to each other. Representational distance is likewise a scalar that is large when two representations are dissimilar.

There are two core operations of any measure of representational similarity:

1. Computing pairwise similarity (or pairwise distance). The result is a n by n Representational Similarity Matrix (RSM) (or Representational Distance Matrix (RDM)).
2. Comparing two RSMs (or RDMs) to each other to get a scalar representational similarity (or distance) score.

Step 1 is handled by functions in the repsim.pairwise module. See the repsim.pairwise.compare() function to get started.

Step 2 is handled by the top-level repsim.compare() function.

In some special circumstances, we can take computational shortcuts bypassing Step 1, so most users will not explicitly call anything inside repsim.pairwise.

Applying the kernel trick is central to some of the representational similarity measures we use. The repsim.kernels module contains the kernel logic. By default, repsim makes all pairwise comparisons using a Squared Exponential kernel whose length scale adapts to the median Euclidean distance of the given data. This can be overridden in most places by specifying a kernel keyword argument to repsim.pairwise.compare, or a kernel_x and kernel_y argument to repsim.compare. For example:

import repsim
import repsim.kernels
import repsim.pairwise
import torch

n, d = 10, 3
x = torch.randn(n, d)

# Get pairwise distances using squared exponential kernel with an automatic length-scale (the default)
rdm_default = repsim.pairwise.compare(x)

# Get pairwise distances using laplace kernel with an automatic length-scale
k = repsim.kernels.Laplace()
rdm_laplace = repsim.pairwise.compare(x, kernel=k)

# Get pairwise distances using squared exponential kernel with a custom length-scale
k = repsim.kernels.SquaredExponential(length_scale=0.2)
rdm_sqexp_short = repsim.pairwise.compare(x, kernel=k)