The prominence of deep learning, large amount of annotated data and increasingly powerful hardware made it possible to reach remarkable performance for supervised classification tasks, in many cases saturating the training sets. However, adapting the learned classification to new domains remains a hard problem due to at least three reasons: (1) the domains and the tasks might be drastically different; (2) there might be very limited amount of annotated data on the new domain and (3) full training of a new model for each new task is prohibitive in terms of memory, due to the shear number of parameter of deep networks. Instead, new tasks should be learned incrementally, building on prior knowledge from already learned tasks, and without catastrophic forgetting, i.e. without hurting performance on prior tasks. To our knowledge this paper presents the first method for multi-domain task learning without catastrophic forgetting using a fully tensorized architecture. Our main contribution is a method for multi-domain learning which models groups of identically structured blocks within a CNN as a high-order tensor. We show that this joint modelling naturally leverages correlations across different layers and results in more compact representations for each new task domain over previous methods which have focused on adapting each layer separately. We apply the proposed method to 10 datasets of the Visual Decathlon Challenge and show that our method offers on average about 7.5x reduction in number of parameters and superior performance in terms of both classification accuracy and Decathlon score. In particular, our method outperforms all prior work on the Visual Decathlon Challenge.
@cite_30: 
@cite_38: We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call "cardinality" (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, named ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart. The code and models are publicly available online.
@cite_32: Although the latest high-end smartphone has powerful CPU and GPU, running deeper convolutional neural networks (CNNs) for complex tasks such as ImageNet classification on mobile devices is challenging. To deploy deep CNNs on mobile devices, we present a simple and effective scheme to compress the entire CNN, which we call one-shot whole network compression. The proposed scheme consists of three steps: (1) rank selection with variational Bayesian matrix factorization, (2) Tucker decomposition on kernel tensor, and (3) fine-tuning to recover accumulated loss of accuracy, and each step can be easily implemented using publicly available tools. We demonstrate the effectiveness of the proposed scheme by testing the performance of various compressed CNNs (AlexNet, VGGS, GoogLeNet, and VGG-16) on the smartphone. Significant reductions in model size, runtime, and energy consumption are obtained, at the cost of small loss in accuracy. In addition, we address the important implementation level issue on 1?1 convolution, which is a key operation of inception module of GoogLeNet as well as CNNs compressed by our proposed scheme.
@cite_3: Given an existing trained neural network, it is often desirable to learn new capabilities without hindering performance of those already learned. Existing approaches either learn sub-optimal solutions, require joint training, or incur a substantial increment in the number of parameters for each added domain, typically as many as the original network. We propose a method called (DAN) that constrains newly learned filters to be linear combinations of existing ones. DANs precisely preserve performance on the original domain, require a fraction (typically 13 , dependent on network architecture) of the number of parameters compared to standard fine-tuning procedures and converge in less cycles of training to a comparable or better level of performance. When coupled with standard network quantization techniques, we further reduce the parameter cost to around 3 of the original with negligible or no loss in accuracy. The learned architecture can be controlled to switch between various learned representations, enabling a single network to solve a task from multiple different domains. We conduct extensive experiments showing the effectiveness of our method on a range of image classification tasks and explore different aspects of its behavior.
@cite_27: Convolutional Neural Networks (CNNs) has shown a great success in many areas including complex image classification tasks. However, they need a lot of memory and computational cost, which hinders them from running in relatively low-end smart devices such as smart phones. We propose a CNN compression method based on CP-decomposition and Tensor Power Method. We also propose an iterative fine tuning, with which we fine-tune the whole network after decomposing each layer, but before decomposing the next layer. Significant reduction in memory and computation cost is achieved compared to state-of-the-art previous work with no more accuracy loss.
@cite_31: 
. A detailed review of tensor methods falls outside the scope of this section. Herein, we focus on methods which have been used to re-parametrize existing individual convolutional layers. This is done mainly to speed up computation or to reduce the number of parameters. The authors in @cite_30 propose to decompose each of the 4D tensors representing the convolutional layers of a pretrained network into a sum of rank-- (1 ) tensors using CP decomposition. @cite_32 propose a similar approach but use Tucker decomposition instead of CP. @cite_27 also used CP decomposition, but optimize this using the tensor power method. The method of @cite_31 proposed a method to share parameters within a ResNext-like block @cite_38 by applying a Generalized Block Decomposition to a 4-th order tensor. As we show a straightforward extension of existing multi-domain adaptation methods (e.g. @cite_3 ) using tensors results in an adaptation model with a large number of parameters. To improve this, we propose to model groups of identically structured blocks within a CNN with a single high-order tensor.