Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensions

This study investigates the optimization aspects of imposing hard inequality constraints on the outputs of CNNs. In the context of deep networks, constraints are commonly handled with penalties for their simplicity, and despite their well-known limitations. Lagrangian-dual optimization has been largely avoided, except for a few recent works, mainly due to the computational complexity and stability/convergence issues caused by alternating explicit dual updates/projections and stochastic optimization. Several studies showed that, surprisingly for deep CNNs, the theoretical and practical advantages of Lagrangian optimization over penalties do not materialize in practice. We propose log-barrier extensions, which approximate Lagrangian optimization of constrained-CNN problems with a sequence of unconstrained losses. Unlike standard interior-point and log-barrier methods, our formulation does not need an initial feasible solution. Furthermore, we provide a new technical result, which shows that the proposed extensions yield an upper bound on the duality gap. This generalizes the duality-gap result of standard log-barriers, yielding sub-optimality certificates for feasible solutions. While sub-optimality is not guaranteed for non-convex problems, our result shows that log-barrier extensions are a principled way to approximate Lagrangian optimization for constrained CNNs via implicit dual variables. We report comprehensive weakly supervised segmentation experiments, with various constraints, showing that our formulation outperforms substantially the existing constrained-CNN methods, both in terms of accuracy, constraint satisfaction and training stability, more so when dealing with a large number of constraints

An Adaptive Sampling Scheme to Efficiently Train Fully Convolutional Networks for Semantic Segmentation

Deep convolutional neural networks (CNNs) have shown excellent performance in object recognition tasks and dense classification problems such as semantic segmentation. However, training deep neural networks on large and sparse datasets is still challenging and can require large amounts of computation and memory. In this work, we address the task of performing semantic segmentation on large data sets, such as three-dimensional medical images. We propose an adaptive sampling scheme that uses a-posterior error maps, generated throughout training, to focus sampling on difficult regions, resulting in improved learning. Our contribution is threefold: 1) We give a detailed description of the proposed sampling algorithm to speed up and improve learning performance on large images. We propose a deep dual path CNN that captures information at fine and coarse scales, resulting in a network with a large field of view and high resolution outputs. We show that our method is able to attain new state-of-the-art results on the VISCERAL Anatomy benchmark

A Comparison and Strategy of Semantic Segmentation on Remote Sensing Images

In recent years, with the development of aerospace technology, we use more and more images captured by satellites to obtain information. But a large number of useless raw images, limited data storage resource and poor transmission capability on satellites hinder our use of valuable images. Therefore, it is necessary to deploy an on-orbit semantic segmentation model to filter out useless images before data transmission. In this paper, we present a detailed comparison on the recent deep learning models. Considering the computing environment of satellites, we compare methods from accuracy, parameters and resource consumption on the same public dataset. And we also analyze the relation between them. Based on experimental results, we further propose a viable on-orbit semantic segmentation strategy. It will be deployed on the TianZhi-2 satellite which supports deep learning methods and will be lunched soon.Comment: 8 pages, 3 figures, ICNC-FSKD 201