Sequential recommendation models, particularly those based on attention, achieve strong accuracy but incur quadratic complexity, making long user histories prohibitively expensive. Sub-quadratic operators such as Hyena provide efficient alternatives in language modeling, but their potential in recommendation remains underexplored. We argue that Hyena faces challenges in recommendation due to limited representation capacity on sparse, long user sequences. To address these challenges, we propose HyenaRec, a novel sequential recommender that integrates polynomial-based kernel parameterization with gated convolutions. Specifically, we design convolutional kernels using Legendre orthogonal polynomials, which provides a smooth and compact basis for modeling long-term temporal dependencies. A complementary gating mechanism captures fine-grained short-term behavioral bursts, yielding a hybrid architecture that balances global temporal evolution with localized user interests under sparse feedback. This construction enhances expressiveness while scaling linearly with sequence length. Extensive experiments on multiple real-world datasets demonstrate that HyenaRec consistently outperforms Attention-, Recurrent-, and other baselines in ranking accuracy. Moreover, it trains significantly faster (up to 6x speedup), with particularly pronounced advantages on long-sequence scenarios where efficiency is maintained without sacrificing accuracy. These results highlight polynomial-based kernel parameterization as a principled and scalable alternative to attention for sequential recommendation.

翻译：序列推荐模型，尤其是基于注意力机制的模型，虽能实现高精度，但存在平方复杂度，导致长用户历史序列的处理成本过高。Hyena等次平方算子在语言建模中提供了高效的替代方案，但其在推荐领域的潜力尚未得到充分探索。我们认为，Hyena在推荐中面临表征能力受限的挑战，难以应对稀疏的长用户序列。为此，我们提出HyenaRec——一种新型序列推荐模型，将基于多项式的核参数化与门控卷积相结合。具体而言，我们利用勒让德正交多项式设计卷积核，为建模长期时间依赖提供平滑且紧凑的基础。互补的门控机制捕获细粒度的短期行为突发，从而构建出混合架构，在稀疏反馈条件下平衡全局时间演化与局部用户兴趣。这种设计增强了模型表达能力，同时使复杂度与序列长度呈线性关系。在多个真实数据集上的大量实验表明，HyenaRec在排序精度上持续优于基于注意力、递归及其他基线模型。此外，其训练速度显著提升（最高可达6倍加速），尤其在长序列场景中优势明显，实现了效率与精度的双赢。这些结果凸显了基于多项式的核参数化作为注意力机制的有原则且可扩展的替代方案在序列推荐中的潜力。