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# End-to-end learning of convolutional neural net and dynamic programming for left ventricle segmentation

*Proceedings of the Third Conference on Medical Imaging with Deep Learning*, PMLR 121:555-569, 2020.

#### Abstract

Differentiable programming is able to combine different functions or modules in a data processing pipeline with the goal of applying gradient descent-based end-to-end learning or optimization. A significant impediment to differentiable programming is the non-differentiable nature of some functions. We propose to overcome this difficulty by using neural networks to approximate such modules. An approximating neural network provides synthetic gradients (SG) for backpropagation across a non-differentiable module. Our design is grounded on a well-known theory that gradient of an approximating neural network can approximate a sub-gradient of a weakly differentiable function. We apply SG to combine convolutional neural network (CNN) with dynamic programming (DP) in end-to-end learning for segmenting left ventricle from short axis view of heart MRI. Our experiments show that end-to-end combination of CNN and DP requires fewer labeled images to achieve a significantly better segmentation accuracy than using only CNN.