一个平稳（因而兼容）的表示就是您所需的一切

摘要

学习兼容表示的目标是，在模型更新时，能让特征表示随时间变化而可互换使用。本文证明，由d-Simplex固定分类器学习到的平稳表示在其正式定义下具备兼容性。这一结果奠定了未来研究的基础，并可直接应用于实际学习场景。我们探讨了在模型顺序微调时，利用d-Simplex固定分类器学习兼容性所面临的挑战。根据d-Simplex固定分类器结合交叉熵损失进行学习，能够对齐特征分布的一阶统计量，但可能无法充分捕捉模型更新间表示中的高阶依赖关系。为解决该问题，我们证明，通过交叉熵损失与对比损失的凸组合，使用d-Simplex固定分类器训练模型，不仅能够捕捉高阶依赖关系，而且在兼容性约束下等价于仅用交叉熵损失学习。我们通过大量实验验证了这一发现，并考虑了一种新场景：预训练模型被顺序微调，且偶尔被更优模型替换。实验表明，平稳表示能够实现不间断的检索服务（无需重新处理图库图像），同时在模型更新和替换过程中提升性能，达到了最优水平。代码见 https://github.com/miccunifi/iamcl2r。

English

Learning compatible representations aims to learn feature representations that can be used interchangeably over time whenever a model undergoes updates. In this paper, we demonstrate that stationary representations learned by d-Simplex fixed classifiers imply compatibility as in its formal definition. This result establishes a foundation for future works and can be directly exploited in practical learning scenarios. We address the challenge of learning compatibility using d-Simplex fixed classifiers when the model is sequentially fine-tuned. Learning according to a d-Simplex fixed classifier with the cross-entropy loss aligns feature distributions at the first-order statistics. Consequently, it may not fully capture higher-order dependencies in the representation between model updates. To address this issue, we demonstrate that training the model using a d-Simplex fixed classifier through a convex combination of the cross-entropy loss and a contrastive loss not only captures higher-order dependencies, but is also equivalent to learning with the cross-entropy under the compatibility constraints. We confirm our findings with extensive experiments also considering a new scenario where a pre-trained model is sequentially fine-tuned and occasionally replaced with an improved model. We show that stationary representations enable uninterrupted retrieval services (without reprocessing gallery images) while improving performance during model updates and replacements, achieving state-of-the-art. Code at https://github.com/miccunifi/iamcl2r.