Attention mechanism remains the defining operator in Transformers since it provides expressive global credit assignment, yet its quadratic cost in sequence length N makes long-context modeling expensive and often forces truncation or other heuristics. Linear attention reduces complexity to O(Nd^2) by reordering computation through kernel feature maps, but this reformulation drops the softmax mechanism and shifts the attention score distribution. Lifelong recommendation requires efficient attention as well, for large-scale sequence modeling with user histories and candidate items under tight latency and resource constraints. We introduce SVD-Attention, a novel attention mechanism, and SOLAR, a set-aware framework built on it for lifelong recommendation. SVD-Attention factorizes low-rank embeddings into r principal components, computes candidate-to-interest scores in compact space, and applies softmax over those scores. Its bilinear reduction is exact on the rank-r reconstruction, while the normalized output approximates token-level softmax with an explicitly bounded residual. The resulting computation reduces the cost from O(N^2d) to O(Ndr), and supports 12,000 behaviors and 3,000 candidates per request without filtering. SOLAR achieves the best among compared methods on RecFlow and MIND, delivers 0.8531 AUC at approximately 19ms 95th-percentile latency in an industrial evaluation, and yields business gains with a 0.68% relative lift in Video Views in the real-world online A/B test. Following this evaluation, SOLAR has been fully deployed in Kuaishou's production recommendation system.

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