Weight-normalized pretraining gains came from the effective learning rate it induces, and a schedule designed for that cut terminal loss by about 0.01 against cosine at 128B tokens
AspireAI community · arXiv (Yu, Ma, Bin, Di He)
Weight-normalized training is emerging as an alternative to weight decay, with recent studies reporting substantial pretraining loss gains. This paper shows those gains are driven primarily by the induced effective learning rate trajectory rather than by normalization alone - matching effective learning rate trajectories largely collapses the training loss dynamics of the two, which means schedule design should target effective learning rate rather than the nominal learning rate alone. Building on that principle, AIR (Affine Inverse-square-Root decay) combines a theoretically derived 1/sqrt(t) decay with an affine adjustment to satisfy prescribed peak and terminal learning rates over a finite horizon. Late-stage effective learning rate scheduling is identified as a key source of the gains, because a shared late schedule attenuates the effect of earlier choices. Experiments on 128B-token mixture-of-experts pretraining show AIR beats cosine and other candidate schedules on training loss, downstream performance and hyperparameter robustness, reducing terminal training loss by approximately 0.01 relative to cosine at matched cumulative learning rate, and applying the same effective learning rate trajectory to weight decay reproduces the dynamics. The limitation is the 0.01 effect size - real but modest - and the evidence comes from one MoE pretraining setup.
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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.