We are presenting our work “Discriminating image representations with principal distortions” at #ICLR2025 today (4/24) at 3pm! If you are interested in comparing model representations with other models or human perception, stop by poster #63. Highlights in 🧵 openreview.net/forum?id=ugX...

Recent work suggests that many models are converging to representations that are similar to each other and (maybe) to human perception. However, similarity often focuses on stimuli that are far apart in stimulus space. Even if global geometry is similar, the local geometry can be quite different.

We propose a framework for comparing a set of image representations in terms of their local geometries. We quantify the local geometry of a representation using the Fisher information matrix (FIM), a standard statistical tool for characterizing the sensitivity to local stimulus distortions.

We use the FIM to define a metric on the local geometry of an image representation near a base image. This metric can be related to previous work investigating the sensitivities of one or two models.

We then extend this work to show that the metric may be used to optimally differentiate a set of *many* models, by finding a pair of “principal distortions” that maximize the variance of the models under this metric.

This provides an efficient method to generate stimulus distortions that discriminate image representations. These distortions can be used to test which model is closest to human perception.

As an example, we use this framework to compare a set of simple models of the early visual system, identifying a novel set of image distortions that allow immediate comparison of the models by visual inspection.

In a second example, we apply our method to a set of deep neural network models and reveal differences in the local geometry that arise due to architecture and training types, illustrating the method's potential for revealing interpretable differences between computational models.

These examples demonstrate how our framework can be used to probe for informative differences in local sensitivities between complex models, and suggest how it could be used to compare model representations with human perception.