T-RoPE: Time-Aware Rotary Position Embedding for Sequential Recommendation

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.

Positional encoding is a fundamental component of Transformer-based generative recommendation models, where user histories are modeled as autoregressive item sequences. Most positional encoding methods are inherited from natural language processing and mainly represent discrete item order. However, recommendation sequences go beyond ordered lists, as timestamps and temporal effects also shape item relations. Our work is motivated by a real-world food delivery and instant retail recommendation system, where user behavior exhibits multi-level temporal regularities, including recency effects, meal-time peaks, weekday-weekend shifts, and promotion-driven traffic bursts. Existing methods partially address this issue through timestamp features, interval embeddings, decay functions, or attention biases, but they usually inject heterogeneous temporal signals through a unified representation or a single modeling pathway, making it difficult to distinguish broad temporal dynamics from local order cues. To address this limitation, we propose Decoupled Temporal Encoding (DTE), a lightweight framework for generative recommendation. DTE separates temporal dynamics from order information through two complementary modules: a personalized macro-temporal module that injects compact temporal primitives into item embeddings, and a time-gated micro-sequential module that introduces relative-order bias only when interactions are temporally dense. DTE is also parameter-efficient and deployment-friendly, allowing easy integration into existing systems.

Every Transformer architecture dedicates enormous capacity to learning rich representations in semantic embedding space -- yet the rotation manifold acted upon by Rotary Positional Embeddings (RoPE) has been treated as a fixed, hand-crafted structure, populated only by discrete ordinal indices. We argue that this rotation space is a largely overlooked second dimension of expressivity in the attention mechanism, one whose systematic exploration may open a new door for attention-based architectures. The analogy to complex numbers is instructive: just as introducing the imaginary axis -- orthogonal to and independent of the real line -- unlocked new algebraic structure once believed impossible, treating the rotation manifold as a learnable, signal-conditioned space opens an orthogonal degree of freedom in attention. In this framing, the token embedding encodes the semantic (real) component of a representation -- what a token means -- while the rotation encodes its dynamic (imaginary) component -- how it relates to every other token across time, position, and context. We introduce SIREN-RoPE, a concrete instantiation of this idea, which populates the rotation dimension with heterogeneous signals -- continuous timestamps, cyclical temporal patterns, and categorical metadata -- via a dual-branch Sinusoidal Representation Network (SIREN). As a proof of concept, we evaluate on a production-scale news feed dataset from a major social network using a generative recommender as the ranking model, demonstrating that activating this hidden dimension yields consistent improvements across calibration and ranking objectives with negligible computational overhead. We invite the community to view the rotation space not as a solved positional-encoding detail, but as an untapped axis whose rich structure may prove as consequential for attention as the imaginary unit proved for algebra.