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The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable" layer''in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis. We also open-source the code at\url {https://github. com/idealab-isu/DSA}. 

Humans understand videos from both the visual and audio aspects of the data. In this work, we present a self supervised cross modal representation approach for learning audio visual correspondence (AVC) for videos in the wild. After the learning stage, we explore retrieval in both cross modal and intra modal manner with the learned representations. We verify our experimental results on the VGGSound dataset and our approach achieves promising results. 

Efficiently and accurately simulating partial differential equations(PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a "good" adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of caring out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects.