We derive the calculation of two critical numbers predicting the behavior of perceptron networks. First, we derive the calculation of what we call the lossless memory (LM) dimension. The LM dimension is a generalization of the Vapnik--Chervonenkis (VC) dimension that avoids structured data and therefore provides an upper bound for perfectly fitting almost any training data. Second, we derive what we call the MacKay (MK) dimension. This limit indicates a 50 chance of not being able to train a given function. Our derivations are performed by embedding a neural network into Shannon's communication model which allows to interpret the two points as capacities measured in bits. We present a proof and practical experiments that validate our upper bounds with repeatable experiments using different network configurations, diverse implementations, varying activation functions, and several learning algorithms. The bottom line is that the two capacity points scale strictly linear with the number of weights. Among other practical applications, our result allows to compare and benchmark different neural network implementations independent of a concrete learning task. Our results provide insight into the capabilities and limits of neural networks and generate valuable know how for experimental design decisions.
Even though perceptrons have been utilized for a long time, its capacities have been rarely explored beyond discussion of linear separability. Moreover, catastrophic forgetting has so far not been explained satisfactorily. Catastrophic forgetting @cite_39 @cite_31 describes the effect that when the net is first trained on one set of labels and then on another set of labels, it very quickly looses its capability to classify the first set of labels. Our interpretation is that one cause for this would be a capacity overflow in the second round of training.
@cite_31 @cite_39
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Catastrophic forgetting is a problem of neural networks that loses the information of the first task after training the second task. Here, we propose a method, i.e. incremental moment matching (IMM), to resolve this problem. IMM incrementally matches the moment of the posterior distribution of the neural network which is trained on the first and the second task, respectively. To make the search space of posterior parameter smooth, the IMM procedure is complemented by various transfer learning techniques including weight transfer, L2-norm of the old and the new parameter, and a variant of dropout with the old parameter. We analyze our approach on a variety of datasets including the MNIST, CIFAR-10, Caltech-UCSD-Birds, and Lifelog datasets. The experimental results show that IMM achieves state-of-the-art performance by balancing the information between an old and a new network. Catastrophic forgetting is a problem faced by many machine learning models and algorithms. When trained on one task, then trained on a second task, many machine learning models "forget" how to perform the first task. This is widely believed to be a serious problem for neural networks. Here, we investigate the extent to which the catastrophic forgetting problem occurs for modern neural networks, comparing both established and recent gradient-based training algorithms and activation functions. We also examine the effect of the relationship between the first task and the second task on catastrophic forgetting. We find that it is always best to train using the dropout algorithm--the dropout algorithm is consistently best at adapting to the new task, remembering the old task, and has the best tradeoff curve between these two extremes. We find that different tasks and relationships between tasks result in very different rankings of activation function performance. This suggests the choice of activation function should always be cross-validated. Neural network algorithms such as multilayer perceptrons (MLPs) and radial basis function networks (RBFNets) have been used to construct learners which exhibit strong predictive performance. Two data related issues that can have a detrimental impact on supervised learning initiatives are class imbalance and labeling errors (or class noise). Imbalanced data can make it more difficult for the neural network learning algorithms to distinguish between examples of the various classes, and class noise can lead to the formulation of incorrect hypotheses. Both class imbalance and labeling errors are pervasive problems encountered in a wide variety of application domains. Many studies have been performed to investigate these problems in isolation, but few have focused on their combined effects. This study presents a comprehensive empirical investigation using neural network algorithms to learn from imbalanced data with labeling errors. In particular, the first component of our study investigates the impact of class noise and class imbalance on two common neural network learning algorithms, while the second component considers the ability of data sampling (which is commonly used to address the issue of class imbalance) to improve their performances. Our results, for which over two million models were trained and evaluated, show that conclusions drawn using the more commonly studied C4.5 classifier may not apply when using neural networks. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method.