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.
@cite_28: We develop an intermediate representation for deformable part models and show that this representation has favorable performance characteristics for multi-class problems when the number of classes is high. Our model uses sparse coding of part filters to represent each filter as a sparse linear combination of shared dictionary elements. This leads to a universal set of parts that are shared among all object classes. Reconstruction of the original part filter responses via sparse matrix-vector product reduces computation relative to conventional part filter convolutions. Our model is well suited to a parallel implementation, and we report a new GPU DPM implementation that takes advantage of sparse coding of part filters. The speed-up offered by our intermediate representation and parallel computation enable real-time DPM detection of 20 different object classes on a laptop computer.
@cite_9: Learning filters to produce sparse image representations in terms of over complete dictionaries has emerged as a powerful way to create image features for many different purposes. Unfortunately, these filters are usually both numerous and non-separable, making their use computationally expensive. In this paper, we show that such filters can be computed as linear combinations of a smaller number of separable ones, thus greatly reducing the computational complexity at no cost in terms of performance. This makes filter learning approaches practical even for large images or 3D volumes, and we show that we significantly outperform state-of-the-art methods on the linear structure extraction task, in terms of both accuracy and speed. Moreover, our approach is general and can be used on generic filter banks to reduce the complexity of the convolutions.
@cite_29: This paper introduces a regularization method called Correlative Filter (CF) for Convolutional Neural Network (CNN), which takes advantage of the relevance between the convolutional kernels belonging to the same convolutional layer. During the process of training with the proposed CF method, several pairs of filters are designed in a manner of randomness to contain opposite weights in low-level layers. Regarding higher level layers where synthetical features are processed, the relation between correlative filters is explored as translation of various directions. The proposed CF method attempts to optimize the inner structure of convolutional layers and it can work jointly with other regularization techniques, such as stochastic pooling, Dropout, etc. The experimental results on the competitive image classification benchmark dataset CIFAR-10 demonstrates the performance of the proposed CF method, additionally, it is also verified that the proposed CF method is wonderful to be employed to enhance several state-of-the-art regularization models.
@cite_23: The focus of this paper is speeding up the evaluation of convolutional neural networks. While delivering impressive results across a range of computer vision and machine learning tasks, these networks are computationally demanding, limiting their deployability. Convolutional layers generally consume the bulk of the processing time, and so in this work we present two simple schemes for drastically speeding up these layers. This is achieved by exploiting cross-channel or filter redundancy to construct a low rank basis of filters that are rank-1 in the spatial domain. Our methods are architecture agnostic, and can be easily applied to existing CPU and GPU convolutional frameworks for tuneable speedup performance. We demonstrate this with a real world network designed for scene text character recognition, showing a possible 2.5x speedup with no loss in accuracy, and 4.5x speedup with less than 1 drop in accuracy, still achieving state-of-the-art on standard benchmarks.
@cite_12: 
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