In looped models the deepest KV plane carried almost all the signal, and keeping just it still sped up decoding
AspireAI community · arXiv
A looped language model runs one block of layers R times per token, so its key-value cache holds R planes per recurrent layer and self-speculative decoding reads all of them. The authors find that prefix keys and values matter late: at equal perturbation size, loops 25 to 32 were e^15.0 on Huginn-0125 and e^12.8 on Raven-Llama times more sensitive than loops 2 to 9, with the planes approaching the last one geometrically, and on Huginn 1 percent of positions carried 74 percent of the error. Their RIPE method stores the deepest plane everywhere except a window of recent positions kept at full depth, and a 64-position window removed 89 percent of tail positions at 11.9 percent of the full cache memory at a 1024-token context while making batched verification block-independent by construction. Measured self-speculative speed-ups were 2.09x with the full cache and 2.58x with the deepest plane alone, and nine pre-registered GPU batches back the results.
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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.