Not all solutions are created equal: An analytical dissociation of functional and representational similarity in deep linear neural networks

A foundational principle of connectionism is that perception, action, and cognition emerge from parallel computations among simple, interconnected units that generate and rely on neural representations. Accordingly, researchers employ multivariate pattern analysis to decode and compare the neural codes of artificial and biological networks, aiming to uncover their functions. However, there is limited analytical understanding of how a network’s representation and function relate, despite this being essential to any quantitative notion of underlying function or functional similarity. We address this question using fully analysable two-layer linear networks and numerical simulations in nonlinear networks. We find that function and representation are dissociated, allowing representational similarity without functional similarity and vice versa. Further, we show that neither robustness to input noise nor the level of generalisation error constrain representations to the task. In contrast, networks robust to parameter noise have limited representational flexibility and must employ task-specific representations. Our findings suggest that representational alignment reflects computational advantages beyond functional alignment alone, with significant implications for interpreting and comparing the representations of connectionist systems

Artificial neural networks are computer systems inspired by the brain, consisting of interconnected units that process information to perform tasks like recognizing images. Scientists often use these systems as models to try to understand how biological brains work. In particular, they often compare the behaviour and internal activities of two different systems—for example, an artificial network next to a biological neural network—when placed in the same environments and performing the same or very similar tasks.When doing so, scientists commonly assume that if two neural networks perform the same task, they must organize and process information in similar ways internally. We mathematically analyzed how simple neural networks can solve identical problems to test this assumption. Our analysis revealed something surprising: networks can achieve exactly the same performance on a task while using completely different ways of organizing information internally. This means that what a network does and how it organizes information can be very much disconnected.However, we discovered an important exception. Networks that can handle errors well—particularly disruptions to their internal organization—tend to develop specialized internal patterns for particular tasks. This suggests there are advantages to certain types of internal organization that go beyond just solving the original task. We advocate that future studies should investigate whether this is true of the artificial neural networks people use in practice, as well as of biological brains.