Converting a 1.4B model into a 410M sibling needed structure-aware compensation rather than weight blending, and reached perplexity 19x and 23x lower than training from scratch
AspireAI community · arXiv (Yenugula)
Model families are trained size by size, and this paper asks whether a pretrained large model can instead be converted into a smaller sibling. The 1.4B to 410M conversion in Pythia is characterized end to end: representations align strongly across sizes (ridge R-squared 0.84) while parameters align weakly, and dense weight projection is destructive, with a bit-exact control placing the fault in basis mixing, which breaks rotary, per-head, GELU and LayerNorm structure. Under matched-budget continued pretraining, two independent levers separate - least-squares compensation, the function lever and best zero-shot performer, and variance-preserving rescale, the dynamics lever and best at endpoints - with a placement rule read off the architecture. Informed selection plus compensation plus rescale is the best arm in both families, reaching perplexity 19x and 23x lower than from scratch at matched budget (2.94 and 3.13 nats), and beating structured pruning plus distillation. A second family, Qwen3-1.7B to 0.6B, takes the placement rule unchanged but reverses a 2x2 crossing: on Pythia the re-fit carries the gain, while on Qwen3 the activation statistic carries 66 points and the re-fit is a null on top. The limitation is that the lever placement differs between families, so the rule is a heuristic rather than a law.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.