Structure and Scale in Simplicial Sequence Modelling
For researchers studying deep learning theory, this work provides preliminary evidence linking two key phenomena, though it is incremental and limited to a simple synthetic setting.
The paper hypothesizes a connection between scaling laws and emergent mechanisms in deep learning, finding preliminary evidence of a correlation between performance scaling and representational structure in small transformers trained on hidden Markov model outputs.
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.