Scaling Laws for SAE Training Data
This paper investigates how the number of unique activations affects sparse autoencoder (SAE) training when the total training budget is fixed. It finds that quality improves rapidly with buffer size but then plateaus, where replaying the buffer is nearly as effective as using fresh activations. The authors propose a scaling law for limited data and validate it across various models, layers, and SAE variants. They provide a practical rule: choose the smallest buffer that reaches the quality plateau and replay it, reducing activation storage by 8-64x with negligible quality loss.