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Abstract

This paper presents a novel methodology for determining representational structure, which builds upon the existing Spotlight Resonance method. This new tool is used to gain insight into how discrete representations can emerge and organise in autoencoder models, through a controlled ablation study in which only the activation function is altered. Using this technique, the validity of whether function-driven symmetries can act as implicit inductive biases on representations is determined. Representations are found to tend to discretise when the activation functions are defined through a discrete algebraic permutation-equivariant symmetry. In contrast, they remain continuous under a continuous algebraic orthogonal-equivariant definition. This confirms the hypothesis that the symmetries of network primitives can carry unintended inductive biases, which produce task-independent artefactual structures in representations. The discrete symmetry of contemporary forms is shown to be a strong predictor for the production of discrete representations emerging from otherwise continuous distributions -- a quantisation effect. This motivates further reassessment of functional forms in common usage due to such unintended consequences. Moreover, this supports a general causal model for one mode in which discrete representations may form, and could constitute a prerequisite for downstream interpretability phenomena, including grandmother neurons, discrete coding schemes, general linear features and possibly Superposition. Hence, this tool and proposed mechanism for the influence of functional form on representations may provide insights into interpretability research. Finally, preliminary results indicate that quantisation of representations appears to correlate with a measurable increase in reconstruction error, reinforcing previous conjectures that this collapse can be detrimental.