Understanding Why Neural Networks Generalize Well Through GSNR of Parameters

As deep neural networks (DNNs) achieve tremendous success across many application domains, researchers tried to explore in many aspects on why they generalize well. In this paper, we provide a novel perspective on these issues using the gradient signal to noise ratio (GSNR) of parameters during training process of DNNs. The GSNR of a parameter is defined as the ratio between its gradient's squared mean and variance, over the data distribution. Based on several approximations, we establish a quantitative relationship between model parameters' GSNR and the generalization gap. This relationship indicates that larger GSNR during training process leads to better generalization performance. Moreover, we show that, different from that of shallow models (e.g. logistic regression, support vector machines), the gradient descent optimization dynamics of DNNs naturally produces large GSNR during training, which is probably the key to DNNs' remarkable generalization ability.

Teaching Compositionality to CNNs

Convolutional neural networks (CNNs) have shown great success in computer vision, approaching human-level performance when trained for specific tasks via application-specific loss functions. In this paper, we propose a method for augmenting and training CNNs so that their learned features are compositional. It encourages networks to form representations that disentangle objects from their surroundings and from each other, thereby promoting better generalization. Our method is agnostic to the specific details of the underlying CNN to which it is applied and can in principle be used with any CNN. As we show in our experiments, the learned representations lead to feature activations that are more localized and improve performance over non-compositional baselines in object recognition tasks.

A backward pass through a CNN using a generative model of its activations

Neural networks have shown to be a practical way of building a very complex mapping between a pre-specified input space and output space. For example, a convolutional neural network (CNN) mapping an image into one of a thousand object labels is approaching human performance in this particular task. However the mapping (neural network) does not automatically lend itself to other forms of queries, for example, to detect/reconstruct object instances, to enforce top-down signal on ambiguous inputs, or to recover object instances from occlusion. One way to address these queries is a backward pass through the network that fuses top-down and bottom-up information. In this paper, we show a way of building such a backward pass by defining a generative model of the neural network's activations. Approximate inference of the model would naturally take the form of a backward pass through the CNN layers, and it addresses the aforementioned queries in a unified framework.