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Register a new userDeforming the Loss Surface
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Liangming Chen
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In deep learning, it is usually assumed that the shape of the loss surface is fixed. Differently, a novel concept of deformation operator is first proposed in this paper to deform the loss surface, thereby improving the optimization. Deformation function, as a type of deformation operator, can improve the generalization performance. Moreover, various deformation functions are designed, and their contributions to the loss surface are further provided. Then, the original stochastic gradient descent optimizer is theoretically proved to be a flat minima filter that owns the talent to filter out the sharp minima. Furthermore, the flatter minima could be obtained by exploiting the proposed deformation functions, which is verified on CIFAR-100, with visualizations of loss landscapes near the critical points obtained by both the original optimizer and optimizer enhanced by deformation functions. The experimental results show that deformation functions do find flatter regions. Moreover, on ImageNet, CIFAR-10, and CIFAR-100, popular convolutional neural networks enhanced by deformation functions are compared with the corresponding original models, where significant improvements are observed on all of the involved models equipped with deformation functions. For example, the top-1 test accuracy of ResNet-20 on CIFAR-100 increases by 1.46%, with insignificant additional computational overhead.
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In deep learning, it is usually assumed that the optimization process is conducted on a shape-fixed loss surface. Differently, we first propose a novel concept of deformation mapping in this paper to affect the behaviour of the optimizer. Vertical deformation mapping (VDM), as a type of deformation mapping, can make the optimizer enter a flat region, which often implies better generalization performance. Moreover, we design various VDMs, and further provide their contributions to the loss surface. After defining the local M region, theoretical analyses show that deforming the loss surface can enhance the gradient descent optimizers ability to filter out sharp minima. With visualizations of loss landscapes, we evaluate the flatnesses of minima obtained by both the original optimizer and optimizers enhanced by VDMs on CIFAR-100. The experimental results show that VDMs do find flatter regions. Moreover, we compare popular convolutional neural networks enhanced by VDMs with the corresponding original ones on ImageNet, CIFAR-10, and CIFAR-100. The results are surprising: there are significant improvements on all of the involved models equipped with VDMs. For example, the top-1 test accuracy of ResNet-20 on CIFAR-100 increases by 1.46%, with insignificant additional computational overhead.
Face recognition (FR) using deep convolutional neural networks (DCNNs) has seen remarkable success in recent years. One key ingredient of DCNN-based FR is the appropriate design of a loss function that ensures discrimination between various identities. The state-of-the-art (SOTA) solutions utilise normalised Softmax loss with additive and/or multiplicative margins. Despite being popular, these Softmax+margin based losses are not theoretically motivated and the effectiveness of a margin is justified only intuitively. In this work, we utilise an alternative framework that offers a more direct mechanism of achieving discrimination among the features of various identities. We propose a novel loss that is equivalent to a triplet loss with proxies and an implicit mechanism of hard-negative mining. We give theoretical justification that minimising the proposed loss ensures a minimum separability between all identities. The proposed loss is simple to implement and does not require heavy hyper-parameter tuning as in the SOTA solutions. We give empirical evidence that despite its simplicity, the proposed loss consistently achieves SOTA performance in various benchmarks for both high-resolution and low-resolution FR tasks.
Designing proper loss functions for vision tasks has been a long-standing research direction to advance the capability of existing models. For object detection, the well-established classification and regression loss functions have been carefully designed by considering diverse learning challenges. Inspired by the recent progress in network architecture search, it is interesting to explore the possibility of discovering new loss function formulations via directly searching the primitive operation combinations. So that the learned losses not only fit for diverse object detection challenges to alleviate huge human efforts, but also have better alignment with evaluation metric and good mathematical convergence property. Beyond the previous auto-loss works on face recognition and image classification, our work makes the first attempt to discover new loss functions for the challenging object detection from primitive operation levels. We propose an effective convergence-simulation driven evolutionary search algorithm, called CSE-Autoloss, for speeding up the search progress by regularizing the mathematical rationality of loss candidates via convergence property verification and model optimization simulation. CSE-Autoloss involves the search space that cover a wide range of the possible variants of existing losses and discovers best-searched loss function combination within a short time (around 1.5 wall-clock days). We conduct extensive evaluations of loss function search on popular detectors and validate the good generalization capability of searched losses across diverse architectures and datasets. Our experiments show that the best-discovered loss function combinations outperform default combinations by 1.1% and 0.8% in terms of mAP for two-stage and one-stage detectors on COCO respectively. Our searched losses are available at https://github.com/PerdonLiu/CSE-Autoloss.
Deep Residual Networks present a premium in performance in comparison to conventional networks of the same depth and are trainable at extreme depths. It has recently been shown that Residual Networks behave like ensembles of relatively shallow networks. We show that these ensembles are dynamic: while initially the virtual ensemble is mostly at depths lower than half the networks depth, as training progresses, it becomes deeper and deeper. The main mechanism that controls the dynamic ensemble behavior is the scaling introduced, e.g., by the Batch Normalization technique. We explain this behavior and demonstrate the driving force behind it. As a main tool in our analysis, we employ generalized spin glass models, which we also use in order to study the number of critical points in the optimization of Residual Networks.
In this work we introduce Deforming Autoencoders, a generative model for images that disentangles shape from appearance in an unsupervised manner. As in the deformable template paradigm, shape is represented as a deformation between a canonical coordinate system (`template) and an observed image, while appearance is modeled in `canonical, template, coordinates, thus discarding variability due to deformations. We introduce novel techniques that allow this approach to be deployed in the setting of autoencoders and show that this method can be used for unsupervised group-wise image alignment. We show experiments with expression morphing in humans, hands, and digits, face manipulation, such as shape and appearance interpolation, as well as unsupervised landmark localization. A more powerful form of unsupervised disentangling becomes possible in template coordinates, allowing us to successfully decompose face images into shading and albedo, and further manipulate face images.
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