Within-layer Diversity Reduces Generalization Gap

Neural networks are composed of multiple layers arranged in a hierarchical structure jointly trained with a gradient-based optimization, where the errors are back-propagated from the last layer back to the first one. At each optimization step, neurons at a given layer receive feedback from neurons belonging to higher layers of the hierarchy. In this paper, we propose to complement this traditional 'between-layer' feedback with additional 'within-layer' feedback to encourage diversity of the activations within the same layer. To this end, we measure the pairwise similarity between the outputs of the neurons and use it to model the layer's overall diversity. By penalizing similarities and promoting diversity, we encourage each neuron to learn a distinctive representation and, thus, to enrich the data representation learned within the layer and to increase the total capacity of the model. We theoretically study how the within-layer activation diversity affects the generalization performance of a neural network and prove that increasing the diversity of hidden activations reduces the estimation error. In addition to the theoretical guarantees, we present an empirical study on three datasets confirming that the proposed approach enhances the performance of state-of-the-art neural network models and decreases the generalization gap.Comment: 18 pages, 1 figure, 3 Table

Multi-layer ratio semi-definite classifiers

We develop a novel extension to the Ratio Semi-definite Classifier, a discriminative model formulated as a ratio of semi-definite polynomials. By adding a hidden layer to the model, we can efficiently train the model, while achieving higher accuracy than the original version. Results on artificial 2-D data as well as two separate phone classification corpora show that our multi-layer model still avoids the overconfidence bias found in models based on ratios of exponentials, while remaining competitive with state-of-the-art techniques such as multi-layer perceptrons. Index Terms — Pattern recognition, Speech recognition 1