Zyphra Hierarchical Attention makes sparse attention asymptotically subquadratic, not just constant-factor faster
AspireAI community · arXiv
Most sparse attention methods still pay a quadratic bill for the indexer that selects the sparse keys, so they buy a constant factor rather than a change in scaling. Zyphra Hierarchical Attention (ZHA) attacks that: it builds a tree of recursively compressed key summaries over the KV cache and lets each query traverse the tree top-down to retrieve a sparse subset of keys. By iteratively growing the tree's depth, total cost including routing and final attention grows sublinearly in sequence length, giving overall subquadratic (but superlinear) attention scaling. The authors report that ZHA can be applied to existing pretrained models with only a short KL distillation stage over a few billion tokens, that it maintains performance on long-context retrieval and on reasoning, mathematical and agentic coding tasks, and that it is robust to tree geometry including trees up to 6 levels deep. They also report a performance model showing the approach scales subquadratically and dramatically outperforms competing methods beyond 1 million context, with the stated potential to extend effective context windows to the hundreds of millions or billions of tokens. The caveat is that the headline scaling claims come from a preprint's own performance model and its own benchmarks rather than an independent reproduction.
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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.