# ClockRoPE: Random Fourier Rotations for Temporal Routine Modeling

arXiv: https://arxiv.org/abs/2607.26369 · HTML: https://mlsanity.com/paper/2607.26369/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Rotary Position Embedding for Vision Transformer](https://mlsanity.com/paper/2403.13298/) (2024)
- [Time2Vec: Learning a Vector Representation of Time](https://mlsanity.com/paper/1907.05321/) (2019)
- [Music Transformer](https://mlsanity.com/paper/1809.04281/) (2018)
- [Actions Speak Louder than Words: Trillion-Parameter Sequential Transducers for Generative Recommendations](https://mlsanity.com/paper/2402.17152/) (2024)
- [Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding](https://mlsanity.com/paper/2106.02795/) (2021)
- [Self-attention with Functional Time Representation Learning](https://mlsanity.com/paper/1911.12864/) (2019)
- [Stable, Fast and Accurate: Kernelized Attention with Relative Positional Encoding](https://mlsanity.com/paper/2106.12566/) (2021)
- [LONGER: Scaling Up Long Sequence Modeling in Industrial Recommenders](https://mlsanity.com/paper/2505.04421/) (2025)
- [From block-Toeplitz matrices to differential equations on graphs: towards a general theory for scalable masked Transformers](https://mlsanity.com/paper/2107.07999/) (2021)
- [Learning the RoPEs: Better 2D and 3D Position Encodings with STRING](https://mlsanity.com/paper/2502.02562/) (2025)
- [Kunlun: Establishing Scaling Laws for Massive-Scale Recommendation Systems through Unified Architecture Design](https://mlsanity.com/paper/2602.10016/) (2026)
- [nD-RoPE: A Generalized RoPE for n-Dimensional Position Embedding](https://mlsanity.com/paper/2606.12146/) (2026)
- [Learning to Rotate: Temporal and Semantic Rotary Encoding for Sequential Modeling](https://mlsanity.com/paper/2604.24717/) (2026)
- [RelFlexformer: Efficient Attention 3D-Transformers for Integrable Relative Positional Encodings](https://mlsanity.com/paper/2605.10706/) (2026)

## Abstract (arXiv)

Rotary Position Embedding (RoPE) has been widely adopted in transformer-based large language models. However, its log-linear frequency schedule, originally designed to produce long-term attention decay, limits its adoption in domains with more complex distance-correlation patterns, such as temporal periodicity in sequential recommendation. We investigate the expressiveness of general query/key rotations and find that any normalized continuous positive-definite attention modulation function can be approximated by random rotations induced by its own Fourier transform, which we term Random Fourier Rotations. Building on this theory, we propose ClockRoPE for routine modeling in sequential recommendation, where rotation frequencies are derived from periodic attention modulation functions. In online A/B tests, ClockRoPE demonstrates consistent improvements in valued engagement metrics, and has been successfully deployed in production-scale generative retrieval system at a major video-sharing platform.