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arXiv · 2606.01302

Structure and Scale in Simplicial Sequence Modelling

Matthew Farrugia-Roberts
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Abstract

Modern large-scale deep learning exhibits two striking empirical phenomena: behavioural scaling laws (predictable performance gains with increasing scale) and emergent mechanisms (structured internal representations and circuits in deep neural networks). We hypothesise that these two phenomena are connected: that predictable changes in behaviour are the result of predictable changes in internal computational structure. In this paper, we report preliminary evidence of such a connection. We find a correlation between scaling patterns in performance and representations in small transformers trained to predict the outputs of a hidden Markov model, for which residual activations are known to linearly encode a belief distribution over latent states in a probability simplex.

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Matthew Farrugia-Roberts. 2026-05-31. Structure and Scale in Simplicial Sequence Modelling. https://arxiv.org/abs/2606.01302

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