Frequency-Graded Directional Collapse in Full-Softmax Sequential Recommenders

Full-softmax sequential recommenders degrade on rare items, but the failure's locus and the mechanism of content-based repair remain unclear. We identify frequency-graded directional concentration after cross-entropy training in the output, rather than input, embedding table: rare-item directions form a low-rank cone anti-aligned with typical user states. Untied probes, capacity controls, and a frequency-capping ladder with volume-matched controls support an imbalance-driven optimization explanation. History dropout strengthens tail retrieval, whereas a frozen semantic residual favors popular items, consistent with an anisotropy-associated popularity prior. Whitening the semantic matrix before training reduces this anisotropy; tested post-hoc centering, normalization and gating do not reproduce the training-time gains. Across three Amazon corpora, the repaired retriever raises Recall@10 by 20–29% over the matched d = 192 pure-ID control. A 17.4K-parameter residual then reranks only the retrieved top-10 using training-set co-occurrence, preserving Recall@10 exactly. Under matched full-catalog evaluation, the final system achieves state-of-the-art performance against ten reproduced baselines, improving all four metrics across three corpora by approximately 17–48% over the strongest five-seed baseline per metric. Repeated tests reject frequency gating; excluding consumed items alone raises NDCG@10 by 28.7%. These results connect output-side geometry to ranking behavior under a frozen evaluation protocol.