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

arXiv:2609.38998v1 Announce Type: new Abstract: 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.

Abstract: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.

28 pages, 5 figures. ICML 2025 camera-ready version. Presented at ICML 2025 and CCN 2025

Machine Learning (cs.LG); Neurons and Cognition (q-bio.NC)

arXiv:2609.38998 [cs.LG]

(or arXiv:2609.38998v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.38998 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

Proc. ICML 2025, PMLR 267:5355-5382

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

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