# Beyond Position: the emergence of wavelet-like properties in Transformers

arXiv: https://arxiv.org/abs/2410.18067 · HTML: https://mlsanity.com/paper/2410.18067/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 23 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)

## Built on by (most cited first, 2 of 2)

- [What are you sinking? A geometric approach on attention sink](https://mlsanity.com/paper/2508.02546/) (2025)
- [Where does Absolute Position come from in decoder-only Transformers?](https://mlsanity.com/paper/2606.06160/) (2026)

## Abstract (arXiv)

This paper studies how Transformer models with Rotary Position Embeddings (RoPE) develop emergent, wavelet-like properties that compensate for the positional encoding's theoretical limitations. Through an analysis spanning model scales, architectures, and training checkpoints, we show that attention heads evolve to implement multi-resolution processing analogous to wavelet transforms. We demonstrate that this scale-invariant behavior is unique to RoPE, emerges through distinct evolutionary phases during training, and statistically adheres to the fundamental uncertainty principle. Our findings suggest that the effectiveness of modern Transformers stems from their remarkable ability to spontaneously develop optimal, multi-resolution decompositions to address inherent architectural constraints.