Structure and Scale in Simplicial Sequence Modelling

• URL: http://arxiv.org/abs/2606.01302v1
• Date: Sun, 31 May 2026 15:44:57 GMT
• Title: Structure and Scale in Simplicial Sequence Modelling
• Abstract summary: We find a correlation between scaling patterns in performance and representations in small transformers trained to predict the outputs of a hidden Markov model.<n> residual activations are known to linearly encode a belief distribution over latent states in a probability simplex.
• Score: 4.830289654929358
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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