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Gradient-free fine-tuning usually wastes queries, and ZO-Muon needed only a quarter of them to hit the same accuracy

AspireAI community · arXiv (cs.LG)
Zeroth-order optimization estimates gradients from finite differences of function evaluations, which makes it a memory-efficient way to fine-tune large models without backpropagation, at the cost of query efficiency. ZO-Muon unifies a projection-based subspace view that reduces gradient estimation variance by exploiting the low-rank structure of model updates with Muon-style spectral orthogonalization applied to noisy zeroth-order gradients, which reads as a low-rank Muon optimizer in that setting. Against MeZO on LLM fine-tuning it needed 24.7 percent of the queries to reach the same SST-2 performance, and on ViT-L fine-tuning on CIFAR-100 it improved accuracy by 25.1 percent.
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One distance function matched sparse-autoencoder features across layers and compressed feature circuits into supernodes
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.
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