Learning filter scale and orientation in convolutional neural networks

Convolutional neural networks have many hyper-parameters such as filter size, number of filters, and pooling size, which require manual tuning. Though deep stacked structures are able to create multi-scale and hierarchical representations, manually fixed filter sizes limit the scale of representations that can be learned in a single convolutional layer. Can we adaptively learn to scale the filters on training time? Proposed adaptive filter model can learn the scale and orientation parameters of filters can be learned using back propagation. Therefore, in a single convolution layer, we can create filters of different scale and orientation that can adapt to small or large features and objects. The proposed model uses a relatively large base size (grid) for filters. In the grid, a differentiable function acts as an envelope for the filters. The envelope function guides effective filter scale and shape/orientation by masking the filter weights before the convolution. Therefore, only the weights in the envelope are updated during training. In this work, we employed a multivariate (2D) Gaussian as the envelope function and showed that it can grow, shrink, or rotate by updating its covariance matrix during back propagation training . We tested the model with its basic settings to show the collaboration of weight matrix and envelope function is possible. We used a deeper architecture to show the performance on deeper and wider networks. We tested the new filter model on MNIST, MNIST-cluttered, and CIFAR-10 and compared the results with the networks that used conventional convolution layers. The results demonstrate that the new model can effectively learn and produce filters of different scales and orientations in a single layer. Moreover, the experiments show that the adaptive convolution layers perform equally; or better, especially when data includes objects of varying scale and noisy backgrounds