Scaling laws describe power-law improvements in model performance with dataset size and parameter count, yet their underlying mechanisms are not fully understood. To explain the parameter count scaling, existing theory posits power-law scaling with model depth. In linear-attention models, this scaling is tied to a powe …
Large language models are thought to represent features by vectors in a hidden space of dimension given by the model's width. Superposition, in which more features are represented than the width by letting representation vectors overlap, is a leading account of how representation vectors are organized. However, how mod …
Neural scaling, in which loss falls as a power law with training, is central to large language models, and one recent proposal is that a $1/3$ exponent emerges from learning peaked distributions. That account describes SGD, but models in practice are trained with adaptive optimizers. Here we separate two exponents the …