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This paper analytically dissociates functional and representational similarity in deep linear and non-linear neural networks, revealing that these two aspects can diverge. Specifically, it demonstrates that representational similarity does not guarantee functional similarity, and vice versa, challenging the assumption that multivariate pattern analysis directly equates representational alignment with functional alignment. The study further shows that robustness to parameter noise constrains representations towards task-specific solutions, unlike robustness to input noise or generalization error.
Representational similarity in neural networks can be high even when their functions are entirely different, and vice versa.
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 analysable two-layer linear networks and numerical simulations in non-linear 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 generalization 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.