SSRA: Scale-Shared Recursive Attention — Design and Complexity Analysis

AI Assistance Disclosure This research was conducted as a human-directed AI collaboration. The researchgoal and the underlying inspiration (a fractal, tree-like structure over thesequence context as a path to more efficient attention) come from the author.The specific architecture design, its mathematical formulation, the complexityanalysis, and the PyTorch implementation were generated by AI systems(Anthropic Claude, primarily through Claude Code) under the author's direction. The author defined the research goal and requirements, reviewed and tested thegenerated work, ran the experiments and measurements, and takes responsibilityfor the published content. An automated verification suite (causality,equivalence and gradient-flow checks) and empirical measurements were used tovalidate the AI-generated components. The prior-art review was likewise conducted by AI under the author'sdirection. The text of this report was written by AI and reviewed by theauthor. This disclosure was added on 9 July 2026; the original publication didnot state the extent of AI involvement. Abstract We describe SSRA (Scale-Shared Recursive Attention), a causal language-modeling block in which a single weight-shared rule — one softmax attention block Attn_θ and one learned pooling operator Pool_φ per layer — generates the entire scale hierarchy of the sequence. The same (θ, φ) is applied at every level of a binary tree built over the sequence, and the same θ performs the token-level read-out: a token is treated as a level-0 node. Two further properties complete the mechanism: learned, discrete-slot compression at every node (m summary vectors per node, via latent-query attention or hard top-m selection), and fully bidirectional attention inside nodes that remains legal in a causal LM because causality is enforced structurally — a node becomes consumable only after its span is complete — rather than by masking. Training cost is Θ(N·(w + m·log N)·d) per layer and the autoregressive decoding state is O(m·d·log N) per layer; this is the same complexity class as Log-Linear Attention, and we explicitly do not claim a better class. The contribution of this note is the design itself, its causality proof, its derived complexity, and a pre-registered falsification plan: two ablation axes (cross-scale weight sharing on/off; pooling operator family) and a multi-needle retrieval suite decide, at matched compute, whether the mechanism earns its place. Either outcome — positive or negative — answers the underlying hypotheses and is intended for publication. Version 1.1 (2026-07-20): adds an in-file AI Assistance Disclosure section, anerratum to the §2.6 decode-retention rule (mirroring §2.8 of the stage-2 record,DOI 10.5281/zenodo.21439493), a "Status of empirical follow-up" section, and aversion history. The v1.0 file remains available unchanged under its version DOI.