Hyperspherical Simplex Representations for Backward-Compatible Retrieval
Read the original on arXiv Machine Learning →The paper introduces hyperspherical simplex representations derived from softmax outputs and logits to enable backward-compatible retrieval across independently trained models. By exploiting the simplex geometry induced by cross‑entropy training, the authors propose a deterministic linear transformation that realigns class prototypes when new classes are added, eliminating the need for compatibility‑specific training or architectural changes. Theoretical analysis under von Mises–Fisher assumptions shows that these aligned regular‑simplex representations satisfy the formal backward‑compatibility conditions, and empirical results demonstrate competitive performance on standard benchmarks without extra losses or mappings.
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