Convolutional Neural Networks (CNNs) show state-of-the-art performance in computer vision tasks. However, convolutional layers of CNNs are known to learn redundant features, still not being efficient in memory requirement. In this work, we explore the redundancy of learned features in the form of correlation between convolutional filters, and propose a novel layer to reproduce it efficiently. The proposed "LinearConv" layer generates a portion of convolutional filters as a learnable linear combination of the rest of the filters and introduces a correlation-based regularization to achieve flexibility and control over the correlation between filters, and the number of parameters, in turn. This is developed as a plug-in layer to conveniently replace a conventional convolutional layer without any modification required in the network architecture. Our experiments verify that the LinearConv-based models are able to achieve a performance on-par with counterparts with up to 50 of parameter reduction, and having same computational requirement in run time.
Linear combinations linked with convolutional layers have been proposed to improve CNNs in multiple aspects. Separable filters @cite_9 and Sparselet models @cite_28 explore the idea of approximating a set of convolutional filters as a linear combination of a smaller set of basis filters. One other direction suggests linearly combining feature maps, rather than the filters which generate them, to efficiently impose the feature redundancy @cite_23 . In @cite_29 @cite_12 , authors try to generate correlated filters as a matrix multiplication with a set correlation matrices. Here, the authors use a set of static correlation matrices, followed by enabling their parametric learning. Each primary filter is one-to-one mapped in to a dependent filter based on these learnable correlation matrices. We follow a procedure parallel to this, but instead of learning a one-to-one mapping, we linearly combine a group of learnable filters, scaled by learnable linear coefficients to generate a group of correlated filters
@cite_28 @cite_9 @cite_29 @cite_23 @cite_12
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Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. In contrast, in this paper we propose harmonic blocks that produce features by learning optimal combinations of spectral filters defined by the Discrete Cosine Transform. The harmonic blocks are used to replace conventional convolutional layers to construct partial or fully harmonic CNNs. We extensively validate our approach and show that the introduction of harmonic blocks into state-of-the-art CNN baseline architectures results in comparable or better performance in classification tasks on small NORB, CIFAR10 and CIFAR100 datasets. In many machine learning tasks it is desirable that a model's prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equivariance under translations and rotations by design. The proposed architecture employs steerable filters to efficiently compute orientation dependent responses for many orientations without suffering interpolation artifacts from filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize He's weight initialization scheme to filters which are defined as a linear combination of a system of atomic filters. Numerical experiments show a substantial enhancement of the sample complexity with a growing number of sampled filter orientations and confirm that the network generalizes learned patterns over orientations. The proposed approach achieves state-of-the-art on the rotated MNIST benchmark and on the ISBI 2012 2D EM segmentation challenge. Convolutional neural network (CNN) has achieved the state-of-the-art performance in many different visual tasks. Learned from a large-scale training data set, CNN features are much more discriminative and accurate than the handcrafted features. Moreover, CNN features are also transferable among different domains. On the other hand, traditional dictionary-based features (such as BoW and spatial pyramid matching) contain much more local discriminative and structural information, which is implicitly embedded in the images. To further improve the performance, in this paper, we propose to combine CNN with dictionary-based models for scene recognition and visual domain adaptation (DA). Specifically, based on the well-tuned CNN models (e.g., AlexNet and VGG Net), two dictionary-based representations are further constructed, namely, mid-level local representation (MLR) and convolutional Fisher vector (CFV) representation. In MLR, an efficient two-stage clustering method, i.e., weighted spatial and feature space spectral clustering on the parts of a single image followed by clustering all representative parts of all images, is used to generate a class-mixture or a class-specific part dictionary. After that, the part dictionary is used to operate with the multiscale image inputs for generating mid-level representation. In CFV, a multiscale and scale-proportional Gaussian mixture model training strategy is utilized to generate Fisher vectors based on the last convolutional layer of CNN. By integrating the complementary information of MLR, CFV, and the CNN features of the fully connected layer, the state-of-the-art performance can be achieved on scene recognition and DA problems. An interested finding is that our proposed hybrid representation (from VGG net trained on ImageNet) is also complementary to GoogLeNet and or VGG-11 (trained on Place205) greatly. Compared to earlier multistage frameworks using CNN features, recent end-to-end deep approaches for fine-grained recognition essentially enhance the mid-level learning capability of CNNs. Previous approaches achieve this by introducing an auxiliary network to infuse localization information into the main classification network, or a sophisticated feature encoding method to capture higher order feature statistics. We show that mid-level representation learning can be enhanced within the CNN framework, by learning a bank of convolutional filters that capture class-specific discriminative patches without extra part or bounding box annotations. Such a filter bank is well structured, properly initialized and discriminatively learned through a novel asymmetric multi-stream architecture with convolutional filter supervision and a non-random layer initialization. Experimental results show that our approach achieves state-of-the-art on three publicly available fine-grained recognition datasets (CUB-200-2011, Stanford Cars and FGVC-Aircraft). Ablation studies and visualizations are provided to understand our approach.