Hierarchical Residuals widened the residual state while holding per-layer compute fixed, and the scaling fit showed a 1.30-fold FLOPs-efficiency gain
AspireAI community · arXiv
Residual connections in Transformers tie the residual width carried through depth to the compute width used inside each layer, so widening one widens the other. Hierarchical Residuals (HiRes) decouples them: standard d-dimensional PreNorm layers run inside each block, while a wider D-dimensional PostNorm outer residual connects the blocks, with learned projections bridging the two spaces at block boundaries and the individual Transformer layers left unchanged. Across model sizes and depths HiRes consistently beat vanilla residual addition, and the fitted scaling laws indicated a 1.30-fold improvement in FLOPs efficiency. On OLMoE-1B-7B pretraining for 500B tokens it reached 0.0208 lower training loss and 1.14 points higher downstream accuracy than vanilla residuals, while competing with VWN, mHC and AttnRes using less activation memory and I/O cost. The limitation is that the scaling-law gain is a fitted estimate rather than a wall-clock speedup, and the method was only exercised on one pretraining run at 1B-7B scale.
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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.