Training modern AI models has become increasingly expensive, and updating deployed models can alter their internal feature representations, affecting applications built upon them. In retrieval systems, such updates often require complete gallery re-indexing, a computationally expensive process at scale. Existing backward-compatibility methods enable direct comparison of representations from updated and earlier models, avoiding re-indexing. However, they typically require compatibility-specific training, learned mapping functions, or architectural modifications, and often depend explicitly on the previous model. We propose hyperspherical simplex representations derived from softmax outputs and logits for backward-compatible retrieval across independently trained models. They leverage the simplex structure induced by softmax cross-entropy training with one-hot labels as a common geometric reference across model updates. Since this reference depends on the number of classes, adding new ones expands the simplex, misaligning existing class prototypes with their earlier counterparts. We therefore derive a deterministic linear transformation to restore their alignment. Our theoretical analysis of the formal backward-compatibility definition identifies two geometric conditions under which its inequalities hold in expectation, assuming von Mises--Fisher class distributions with increasing concentration across updates. Aligned regular-simplex representations satisfy these conditions, providing a theoretical basis for the proposed representations under the stated assumptions. Without using additional compatibility-specific losses, learned mappings, or architectural modifications, the proposed representations achieve competitive results on standard compatibility benchmarks, including expanded class sets, more expressive architectures, and independently trained models from public repositories.

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