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. In recent years, Convolutional Neural Networks (CNNs) have shown remarkable performance in many computer vision tasks such as object recognition and detection. However, complex training issues, such as "catastrophic forgetting" and hyper-parameter tuning, make incremental learning in CNNs a difficult challenge. In this paper, we propose a hierarchical deep neural network, with CNNs at multiple levels, and a corresponding training method for lifelong learning. The network grows in a tree-like manner to accommodate the new classes of data without losing the ability to identify the previously trained classes. The proposed network was tested on CIFAR-10 and CIFAR-100 datasets, and compared against the method of fine tuning specific layers of a conventional CNN. We obtained comparable accuracies and achieved 40 and 20 reduction in training effort in CIFAR-10 and CIFAR 100 respectively. The network was able to organize the incoming classes of data into feature-driven super-classes. Our model improves upon existing hierarchical CNN models by adding the capability of self-growth and also yields important observations on feature selective classification. In this paper we apply multilabel classification algorithms to the EUR-Lex database of legal documents of the European Union. For this document collection, we studied three different multilabel classification problems, the largest being the categorization into the EUROVOC concept hierarchy with almost 4000 classes. We evaluated three algorithms: (i) the binary relevance approach which independently trains one classifier per label; (ii) the multiclass multilabel perceptron algorithm, which respects dependencies between the base classifiers; and (iii) the multilabel pairwise perceptron algorithm, which trains one classifier for each pair of labels. All algorithms use the simple but very efficient perceptron algorithm as the underlying classifier, which makes them very suitable for large-scale multilabel classification problems. The main challenge we had to face was that the almost 8,000,000 perceptrons that had to be trained in the pairwise setting could no longer be stored in memory. We solve this problem by resorting to the dual representation of the perceptron, which makes the pairwise approach feasible for problems of this size. The results on the EUR-Lex database confirm the good predictive performance of the pairwise approach and demonstrates the feasibility of this approach for large-scale tasks. 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. In this paper, we address the incremental classifier learning problem, which suffers from catastrophic forgetting. The main reason for catastrophic forgetting is that the past data are not available during learning. Typical approaches keep some exemplars for the past classes and use distillation regularization to retain the classification capability on the past classes and balance the past and new classes. However, there are four main problems with these approaches. First, the loss function is not efficient for classification. Second, there is unbalance problem between the past and new classes. Third, the size of pre-decided exemplars is usually limited and they might not be distinguishable from unseen new classes. Forth, the exemplars may not be allowed to be kept for a long time due to privacy regulations. To address these problems, we propose (a) a new loss function to combine the cross-entropy loss and distillation loss, (b) a simple way to estimate and remove the unbalance between the old and new classes , and (c) using Generative Adversarial Networks (GANs) to generate historical data and select representative exemplars during generation. We believe that the data generated by GANs have much less privacy issues than real images because GANs do not directly copy any real image patches. We evaluate the proposed method on CIFAR-100, Flower-102, and MS-Celeb-1M-Base datasets and extensive experiments demonstrate the effectiveness of our method. A commonly encountered problem in MLP (multi-layer perceptron) classification problems is related to the prior probabilities of the individual classes - if the number of training examples that correspond to each class varies significantly between the classes, then it may be harder for the network to learn the rarer classes in some cases. Such practical experience does not match theoretical results which show that MLPs approximate Bayesian a posteriori probabilities (independent of the prior class probabilities). Our investigation of the problem shows that the difference between the theoretical and practical results lies with the assumptions made in the theory (accurate estimation of Bayesian a posteriori probabilities requires the network to be large enough, training to converge to a global minimum, infinite training data, and the a priori class probabilities of the test set to be correctly represented in the training set). Specifically, the problem can often be traced to the fact that efficient MLP training mechanisms lead to sub-optimal solutions for most practical problems. In this chapter, we demonstrate the problem, discuss possible methods for alleviating it, and introduce new heuristics which are shown to perform well on a sample ECG classification problem. The heuristics may also be used as a simple means of adjusting for unequal misclassification costs. The conventional wisdom is that backprop nets with excess hidden units generalize poorly. We show that nets with excess capacity generalize well when trained with backprop and early stopping. Experiments suggest two reasons for this: 1) Overfitting can vary significantly in different regions of the model. Excess capacity allows better fit to regions of high non-linearity, and backprop often avoids overfitting the regions of low non-linearity. 2) Regardless of size, nets learn task subcomponents in similar sequence. Big nets pass through stages similar to those learned by smaller nets. Early stopping can stop training the large net when it generalizes comparably to a smaller net. We also show that conjugate gradient can yield worse generalization because it overfits regions of low non-linearity when learning to fit regions of high non-linearity. Continual Learning in artificial neural networks suffers from interference and forgetting when different tasks are learned sequentially. This paper introduces the Active Long Term Memory Networks (A-LTM), a model of sequential multi-task deep learning that is able to maintain previously learned association between sensory input and behavioral output while acquiring knew knowledge. A-LTM exploits the non-convex nature of deep neural networks and actively maintains knowledge of previously learned, inactive tasks using a distillation loss. Distortions of the learned input-output map are penalized but hidden layers are free to transverse towards new local optima that are more favorable for the multi-task objective. We re-frame the McClelland's seminal Hippocampal theory with respect to Catastrophic Inference (CI) behavior exhibited by modern deep architectures trained with back-propagation and inhomogeneous sampling of latent factors across epochs. We present empirical results of non-trivial CI during continual learning in Deep Linear Networks trained on the same task, in Convolutional Neural Networks when the task shifts from predicting semantic to graphical factors and during domain adaptation from simple to complex environments. We present results of the A-LTM model's ability to maintain viewpoint recognition learned in the highly controlled iLab-20M dataset with 10 object categories and 88 camera viewpoints, while adapting to the unstructured domain of Imagenet with 1,000 object categories. Previous works on sequential learning address the problem of forgetting in discriminative models. In this paper we consider the case of generative models. In particular, we investigate generative adversarial networks (GANs) in the task of learning new categories in a sequential fashion. We first show that sequential fine tuning renders the network unable to properly generate images from previous categories (i.e. forgetting). Addressing this problem, we propose Memory Replay GANs (MeRGANs), a conditional GAN framework that integrates a memory replay generator. We study two methods to prevent forgetting by leveraging these replays, namely joint training with replay and replay alignment. Qualitative and quantitative experimental results in MNIST, SVHN and LSUN datasets show that our memory replay approach can generate competitive images while significantly mitigating the forgetting of previous categories. Despite their success for object detection, convolutional neural networks are ill-equipped for incremental learning, i.e., adapting the original model trained on a set of classes to additionally detect objects of new classes, in the absence of the initial training data. They suffer from “catastrophic forgetting”–an abrupt degradation of performance on the original set of classes, when the training objective is adapted to the new classes. We present a method to address this issue, and learn object detectors incrementally, when neither the original training data nor annotations for the original classes in the new training set are available. The core of our proposed solution is a loss function to balance the interplay between predictions on the new classes and a new distillation loss which minimizes the discrepancy between responses for old classes from the original and the updated networks. This incremental learning can be performed multiple times, for a new set of classes in each step, with a moderate drop in performance compared to the baseline network trained on the ensemble of data. We present object detection results on the PASCAL VOC 2007 and COCO datasets, along with a detailed empirical analysis of the approach. Deep neural networks are used in many state-of-the-art systems for machine perception. Once a network is trained to do a specific task, e.g., bird classification, it cannot easily be trained to do new tasks, e.g., incrementally learning to recognize additional bird species or learning an entirely different task such as flower recognition. When new tasks are added, typical deep neural networks are prone to catastrophically forgetting previous tasks. Networks that are capable of assimilating new information incrementally, much like how humans form new memories over time, will be more efficient than re-training the model from scratch each time a new task needs to be learned. There have been multiple attempts to develop schemes that mitigate catastrophic forgetting, but these methods have not been directly compared, the tests used to evaluate them vary considerably, and these methods have only been evaluated on small-scale problems (e.g., MNIST). In this paper, we introduce new metrics and benchmarks for directly comparing five different mechanisms designed to mitigate catastrophic forgetting in neural networks: regularization, ensembling, rehearsal, dual-memory, and sparse-coding. Our experiments on real-world images and sounds show that the mechanism(s) that are critical for optimal performance vary based on the incremental training paradigm and type of data being used, but they all demonstrate that the catastrophic forgetting problem has yet to be solved. The authors propose a theoretical framework for backpropagation (BP) in order to identify some of its limitations as a general learning procedure and the reasons for its success in several experiments on pattern recognition. The first important conclusion is that examples can be found in which BP gets stuck in local minima. A simple example in which BP can get stuck during gradient descent without having learned the entire training set is presented. This example guarantees the existence of a solution with null cost. Some conditions on the network architecture and the learning environment that ensure the convergence of the BP algorithm are proposed. It is proven in particular that the convergence holds if the classes are linearly separable. In this case, the experience gained in several experiments shows that multilayered neural networks (MLNs) exceed perceptrons in generalization to new examples. > Abstract All natural cognitive systems, and, in particular, our own, gradually forget previously learned information. Plausible models of human cognition should therefore exhibit similar patterns of gradual forgetting of old information as new information is acquired. Only rarely does new learning in natural cognitive systems completely disrupt or erase previously learned information; that is, natural cognitive systems do not, in general, forget ‘catastrophically'. Unfortunately, though, catastrophic forgetting does occur under certain circumstances in distributed connectionist networks. The very features that give these networks their remarkable abilities to generalize, to function in the presence of degraded input, and so on, are found to be the root cause of catastrophic forgetting. The challenge in this field is to discover how to keep the advantages of distributed connectionist networks while avoiding the problem of catastrophic forgetting. In this article the causes, consequences and numerous solutions to the problem of catastrophic forgetting in neural networks are examined. The review will consider how the brain might have overcome this problem and will also explore the consequences of this solution for distributed connectionist networks. Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: (i) Using a tighter characterization of training speed than recent papers, an explanation for why training a neural net with random labels leads to slower training, as originally observed in [ ICLR'17]. (ii) Generalization bound independent of network size, using a data-dependent complexity measure. Our measure distinguishes clearly between random labels and true labels on MNIST and CIFAR, as shown by experiments. Moreover, recent papers require sample complexity to increase (slowly) with the size, while our sample complexity is completely independent of the network size. (iii) Learnability of a broad class of smooth functions by 2-layer ReLU nets trained via gradient descent. The key idea is to track dynamics of training and generalization via properties of a related kernel. Catastrophic forgetting is a fundamental problem with artificial neural networks (ANNs) in which learned representations are lost as new representations are acquired. This significantly limits the usefulness of ANNs in dynamic or non-stationary settings, as well as when applied to very large datasets. In this paper, we examine a novel neural network architecture which utilizes online clustering for the selection of a subset of hidden neurons to be activated in the feedforward and back propagation passes. It is shown that such networks are able to effectively mitigate catastrophic forgetting. Simulation results illustrate the advantages of the proposed network with respect to other schemes for addressing the memory loss phenomenon. This paper reviews the problem of catastrophic forgetting (the loss or disruption of previously learned information when new information is learned) in neural networks, and explores rehearsal mechanisms (the retraining of some of the previously learned information as the new information is added) as a potential solution. We replicate some of the experiments described by Ratcliff (1990), including those relating to a simple 'recency' based rehearsal regime. We then develop further rehearsal regimes which are more effective than recency rehearsal. In particular, 'sweep rehearsal' is very successful at minimizing catastrophic forgetting. One possible limitation of rehearsal in general, however, is that previously learned information may not be available for retraining. We describe a solution to this problem, 'pseudorehearsal', a method which provides the advantages of rehearsal without actually requiring any access to the previously learned information (the original training population) itself. We then sugge... It is challenging to train deep neural networks robustly with noisy labels, as the capacity of deep neural networks is so high that they can totally over-fit on these noisy labels. In this paper, motivated by the memorization effects of deep networks, which shows networks fit clean instances first and then noisy ones, we present a new paradigm called '' combating with noisy labels. We train two networks simultaneously. First, in each mini-batch data, each network filters noisy instances based on memorization effects. Then, it teaches the remained instances to its peer network for updating the parameters. Empirical results on benchmark datasets demonstrate that, the robustness of deep learning models trained by Co-teaching approach is much superior than that of state-of-the-art methods.