Mathematician, musician, hiking guide. Researcher residing in Australia jointly funded by Timaeus and the Gradient Institute. I am focused on understanding the generalisation properties of models based on Singular Learning Theory and Developmental Interpretability and relating this to alignment.
Website: https://www.liamcarroll.au/
If a model is singular, then Watanabe’s Free Energy Formula (FEF) can have big implications for the geometry of the loss landscape. Whether or not a particular neural network model is singular does indeed depend on its activation function, amongst other structures in its architecture.
In DSLT3 I will outline the ways simple two layer feedforward ReLU neural networks are singular models (ie I will show the symmetries in parameter space that produce the same input-output function), which is generalisable to deeper feedforward ReLU networks. There I will also discuss similar results for tanh networks, alluding to the fact that there are many (but not all) activation functions that produce these symmetries, thus making neural networks with those activation functions singular models, thus meaning the content and interpretation of Watanabe’s free energy formula is applicable.