arXiv AI
Scaling Laws for SAE Training Data
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Sparse autoencoders (SAEs) are usually trained on hundreds of millions to billions of activation tokens, but this study shows that the amount of data needed depends on the evaluation metric. Training four SAE architectures on three language models with token budgets from 5 M to 500 M revealed that reconstruction quality can reach near‑full‑data performance with far fewer tokens, while one‑to‑one feature reproducibility continues to improve as more data is used. The research also found that random sampling preserves activation distributions better for reconstruction, whereas diversity‑based sampling can enhance feature interpretability, and provided a theoretical framework distinguishing statistical consistency from the stricter conditions needed for exact feature recovery.
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