How do we know if two systems - biological or artificial - process information in a similar way? Similarity measures such as linear regression, Centered Kernel Alignment (CKA), Normalized Bures Similarity (NBS), and angular Procrustes distance are often used to quantify this similarity. However, it is currently unclear what drives high similarity scores and what constitutes a good score. Here, we introduce a novel tool to investigate these questions by differentiating through similarity measures to directly maximize the score.

The brain is a complex system, and as all complex systems, its dynamics is highly nonlinear with complexity at many different scales. Large scale properties emerge from interactions at smaller scales but cannot be understood from the mechanisms of the smaller scales only. For example, at the molecular level one can study the mechanisms that generate action potentials in neurons but a perfect understanding of these mechanisms is not enough to understand how the brain is able to perform complex cognitive abilities such as memory, reasoning, spatial navigation, language, etc. Instead, the large scale of brain networks is more appropriate to gain insights on how the brain achieves such remarkable abilities. This is why it is important to model the dynamics of large networks of neurons.

The brain can be viewed as a computing or information processing machine where the relevant information is extracted from the sensory inputs. Similarly to our computers, the computations can be described as a sequence of instructions with algorithms. However, the brain is also very different from our computers and others prefer to view it as a dynamical system with continuous time dynamics at multiple temporal and spatial scales. How can we combine these two points of view ?