论文标题

部分可观测时空混沌系统的无模型预测

A Light Touch Approach to Teaching Transformers Multi-view Geometry

论文作者

Bhalgat, Yash, Henriques, Joao F., Zisserman, Andrew

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。

Transformers are powerful visual learners, in large part due to their conspicuous lack of manually-specified priors. This flexibility can be problematic in tasks that involve multiple-view geometry, due to the near-infinite possible variations in 3D shapes and viewpoints (requiring flexibility), and the precise nature of projective geometry (obeying rigid laws). To resolve this conundrum, we propose a "light touch" approach, guiding visual Transformers to learn multiple-view geometry but allowing them to break free when needed. We achieve this by using epipolar lines to guide the Transformer's cross-attention maps, penalizing attention values outside the epipolar lines and encouraging higher attention along these lines since they contain geometrically plausible matches. Unlike previous methods, our proposal does not require any camera pose information at test-time. We focus on pose-invariant object instance retrieval, where standard Transformer networks struggle, due to the large differences in viewpoint between query and retrieved images. Experimentally, our method outperforms state-of-the-art approaches at object retrieval, without needing pose information at test-time.

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