Representational dissimilarity metric spaces for stochastic neural networks
This work addresses a gap in neural representation analysis for researchers in deep learning and neuroscience by providing a method to account for noise structure, though it is incremental as it builds on prior shape metrics.
The authors tackled the problem of quantifying similarity between stochastic neural representations, which existing deterministic methods ignore, by generalizing shape metrics to stochastic cases. They found that stochastic geometries of neurobiological data resemble untrained and trained deep network representations and improved prediction of network attributes like training hyperparameters.
Quantifying similarity between neural representations -- e.g. hidden layer activation vectors -- is a perennial problem in deep learning and neuroscience research. Existing methods compare deterministic responses (e.g. artificial networks that lack stochastic layers) or averaged responses (e.g., trial-averaged firing rates in biological data). However, these measures of _deterministic_ representational similarity ignore the scale and geometric structure of noise, both of which play important roles in neural computation. To rectify this, we generalize previously proposed shape metrics (Williams et al. 2021) to quantify differences in _stochastic_ representations. These new distances satisfy the triangle inequality, and thus can be used as a rigorous basis for many supervised and unsupervised analyses. Leveraging this novel framework, we find that the stochastic geometries of neurobiological representations of oriented visual gratings and naturalistic scenes respectively resemble untrained and trained deep network representations. Further, we are able to more accurately predict certain network attributes (e.g. training hyperparameters) from its position in stochastic (versus deterministic) shape space.