论文标题
部分可观测时空混沌系统的无模型预测
Hierarchical Average Precision Training for Pertinent Image Retrieval
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Image Retrieval is commonly evaluated with Average Precision (AP) or Recall@k. Yet, those metrics, are limited to binary labels and do not take into account errors' severity. This paper introduces a new hierarchical AP training method for pertinent image retrieval (HAP-PIER). HAPPIER is based on a new H-AP metric, which leverages a concept hierarchy to refine AP by integrating errors' importance and better evaluate rankings. To train deep models with H-AP, we carefully study the problem's structure and design a smooth lower bound surrogate combined with a clustering loss that ensures consistent ordering. Extensive experiments on 6 datasets show that HAPPIER significantly outperforms state-of-the-art methods for hierarchical retrieval, while being on par with the latest approaches when evaluating fine-grained ranking performances. Finally, we show that HAPPIER leads to better organization of the embedding space, and prevents most severe failure cases of non-hierarchical methods. Our code is publicly available at: https://github.com/elias-ramzi/HAPPIER.
