Learned-Norm Pooling for Deep Feedforward and Recurrent Neural Networks

In this paper we propose and investigate a novel nonlinear unit, called $L_p$ unit, for deep neural networks. The proposed $L_p$ unit receives signals from several projections of a subset of units in the layer below and computes a normalized $L_p$ norm. We notice two interesting interpretations of the $L_p$ unit. First, the proposed unit can be understood as a generalization of a number of conventional pooling operators such as average, root-mean-square and max pooling widely used in, for instance, convolutional neural networks (CNN), HMAX models and neocognitrons. Furthermore, the $L_p$ unit is, to a certain degree, similar to the recently proposed maxout unit (Goodfellow et al., 2013) which achieved the state-of-the-art object recognition results on a number of benchmark datasets. Secondly, we provide a geometrical interpretation of the activation function based on which we argue that the $L_p$ unit is more efficient at representing complex, nonlinear separating boundaries. Each $L_p$ unit defines a superelliptic boundary, with its exact shape defined by the order $p$. We claim that this makes it possible to model arbitrarily shaped, curved boundaries more efficiently by combining a few $L_p$ units of different orders. This insight justifies the need for learning different orders for each unit in the model. We empirically evaluate the proposed $L_p$ units on a number of datasets and show that multilayer perceptrons (MLP) consisting of the $L_p$ units achieve the state-of-the-art results on a number of benchmark datasets. Furthermore, we evaluate the proposed $L_p$ unit on the recently proposed deep recurrent neural networks (RNN).Comment: ECML/PKDD 201

Learning Deep Structured Models

Many problems in real-world applications involve predicting several random variables which are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such relationships. The goal of this paper is to combine MRFs with deep learning algorithms to estimate complex representations while taking into account the dependencies between the output random variables. Towards this goal, we propose a training algorithm that is able to learn structured models jointly with deep features that form the MRF potentials. Our approach is efficient as it blends learning and inference and makes use of GPU acceleration. We demonstrate the effectiveness of our algorithm in the tasks of predicting words from noisy images, as well as multi-class classification of Flickr photographs. We show that joint learning of the deep features and the MRF parameters results in significant performance gains.Comment: 11 pages including referenc

Morphological Network: How Far Can We Go with Morphological Neurons?

In recent years, the idea of using morphological operations as networks has received much attention. Mathematical morphology provides very efficient and useful image processing and image analysis tools based on basic operators like dilation and erosion, defined in terms of kernels. Many other morphological operations are built up using the dilation and erosion operations. Although the learning of structuring elements such as dilation or erosion using the backpropagation algorithm is not new, the order and the way these morphological operations are used is not standard. In this paper, we have theoretically analyzed the use of morphological operations for processing 1D feature vectors and shown that this gets extended to the 2D case in a simple manner. Our theoretical results show that a morphological block represents a sum of hinge functions. Hinge functions are used in many places for classification and regression tasks (Breiman (1993)). We have also proved a universal approximation theorem -- a stack of two morphological blocks can approximate any continuous function over arbitrary compact sets. To experimentally validate the efficacy of this network in real-life applications, we have evaluated its performance on satellite image classification datasets since morphological operations are very sensitive to geometrical shapes and structures. We have also shown results on a few tasks like segmentation of blood vessels from fundus images, segmentation of lungs from chest x-ray and image dehazing. The results are encouraging and further establishes the potential of morphological networks.Comment: 35 pages, 19 figures, 7 table

A Deep Learning Approach to Recognizing Bees in Video Analysis of Bee Traffic

Colony Collapse Disorder (CCD) has been a major threat to bee colonies around the world which affects vital human food crop pollination. The decline in bee population can have tragic consequences, for humans as well as the bees and the ecosystem. Bee health has been a cause of urgent concern for farmers and scientists around the world for at least a decade but a specific cause for the phenomenon has yet to be conclusively identified. This work uses Artificial Intelligence and Computer Vision approaches to develop and analyze techniques to help in continuous monitoring of bee traffic which will further help in monitoring forager traffic. Bee traffic is the number of bees moving in a given area in front of the hive over a given period of time. And, forager traffic is the number of bees entering and/or exiting the hive over a given period of time. Forager traffic is an important variable to monitor food availability, food demand, colony age structure, impact of pesticides, etc. on bee hives. This will lead to improved remote monitoring and general hive status and improved real time detection of the impact of pests, diseases, pesticide exposure and other hive management problems

Deep Learning with S-shaped Rectified Linear Activation Units

Rectified linear activation units are important components for state-of-the-art deep convolutional networks. In this paper, we propose a novel S-shaped rectified linear activation unit (SReLU) to learn both convex and non-convex functions, imitating the multiple function forms given by the two fundamental laws, namely the Webner-Fechner law and the Stevens law, in psychophysics and neural sciences. Specifically, SReLU consists of three piecewise linear functions, which are formulated by four learnable parameters. The SReLU is learned jointly with the training of the whole deep network through back propagation. During the training phase, to initialize SReLU in different layers, we propose a "freezing" method to degenerate SReLU into a predefined leaky rectified linear unit in the initial several training epochs and then adaptively learn the good initial values. SReLU can be universally used in the existing deep networks with negligible additional parameters and computation cost. Experiments with two popular CNN architectures, Network in Network and GoogLeNet on scale-various benchmarks including CIFAR10, CIFAR100, MNIST and ImageNet demonstrate that SReLU achieves remarkable improvement compared to other activation functions.Comment: Accepted by AAAI-1