SpiralFormer: Looped Transformers Can Learn Hierarchical Dependencies via Multi-Resolution Recursion

TL;DR

SpiralFormer introduces a multi-resolution recursive Transformer that learns hierarchical dependencies efficiently, outperforming existing looped and non-looped models across various scales.

Contribution

It proposes a novel multi-resolution recursion schedule for looped Transformers, enabling hierarchical dependency learning and improved efficiency.

Findings

SpiralFormer achieves better parameter and compute efficiency than baselines.

Multi-resolution recursion induces functional specialization across scales.

Sequence resolution is a key axis for scaling recursive architectures.

Abstract

Recursive (looped) Transformers decouple computational depth from parameter depth by repeatedly applying shared layers, providing an explicit architectural primitive for iterative refinement and latent reasoning. However, early looped Transformers often underperform non-recursive baselines of equal compute. While recent literature has introduced more effective recursion mechanisms to mitigate this gap, existing architectures still operate at a fixed, full-token resolution, neglecting the potential efficiency of computing over compressed latent representations. In this paper, we propose SpiralFormer, a looped Transformer that executes recurrence under a multi-resolution recursion schedule. We provide probing evidence that multi-resolution recursion enables the model to learn hierarchical dependencies by inducing iteration-wise functional specialization across different scales. Empirically, SpiralFormer achieves better parameter and compute efficiency than both looped and non-looped baselines across model scales from 160M to 1.4B, establishing sequence resolution as a potential axis for scaling recursive architectures.