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
2036963181 1682403713
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. 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. Deep reinforcement learning has emerged as a powerful tool for a variety of learning tasks, however deep nets typically exhibit forgetting when learning multiple tasks in sequence. To mitigate forgetting, we propose an experience replay process that augments the standard FIFO buffer and selectively stores experiences in a long-term memory. We explore four strategies for selecting which experiences will be stored: favoring surprise, favoring reward, matching the global training distribution, and maximizing coverage of the state space. We show that distribution matching successfully prevents catastrophic forgetting, and is consistently the best approach on all domains tested. While distribution matching has better and more consistent performance, we identify one case in which coverage maximization is beneficial - when tasks that receive less trained are more important. Overall, our results show that selective experience replay, when suitable selection algorithms are employed, can prevent catastrophic forgetting. Catastrophic forgetting occurs when connectionist networks learn new information, and by so doing, forget all previously learned information. This workshop focused primarily on the causes of catastrophic interference, the techniques that have been developed to reduce it, the effect of these techniques on the networks' ability to generalize, and the degree to which prediction of catastrophic forgetting is possible. The speakers were Robert French, Phil Hetherington (Psychology Department, McGill University, het@blaise.psych.mcgill.ca), and Stephan Lewandowsky (Psychology Department, University of Oklahoma, lewan@constellation.ecn.uoknor.edu). 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. Local competition among neighboring neurons is common in biological neural networks (NNs). In this paper, we apply the concept to gradient-based, backprop-trained artificial multilayer NNs. NNs with competing linear units tend to outperform those with non-competing nonlinear units, and avoid catastrophic forgetting when training sets change over time. During training, model-free reinforcement learning (RL) systems can explore actions that lead to harmful or costly consequences. Having a human "in the loop'' and ready to intervene at all times can prevent these mistakes, but is prohibitively expensive for current algorithms. We explore how human oversight can be combined with a supervised learning system to prevent catastrophic events during training. We demonstrate this scheme on Atari games, with a Deep RL agent being overseen by a human for four hours. When the class of catastrophes is simple, we are able to prevent all catastrophes without affecting the agent's learning (whereas an RL baseline fails due to catastrophic forgetting). To use deep reinforcement learning in the wild, we might hope for an agent that can avoid catastrophic mistakes. Unfortunately, even in simple environments, the popular deep Q-network (DQN) algorithm is doomed by a Sisyphean curse. Owing to the use of function approximation, these agents eventually forget experiences as they become exceedingly unlikely under a new policy. Consequently, for as long as they continue to train, DQNs may periodically relive catastrophic mistakes. Many real-world environments where people might be injured exhibit a special structure. We know a priori that catastrophes are not only bad, but that agents need not ever get near to a catastrophe state. In this paper, we exploit this structure to learn a reward-shaping that accelerates learning and guards oscillating policies against repeated catastrophes. First, we demonstrate unacceptable performance of DQNs on two toy problems. We then introduce intrinsic fear, a new method that mitigates these problems by avoiding dangerous states. Our approach incorporates a second model trained via supervised learning to predict the probability of catastrophe within a short number of steps. This score then acts to penalize the Q-learning objective, shaping the reward function away from catastrophic states. 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. Abstract The ability to learn tasks in a sequential fashion is crucial to the development of artificial intelligence. Until now neural networks have not been capable of this and it has been widely thought that catastrophic forgetting is an inevitable feature of connectionist models. We show that it is possible to overcome this limitation and train networks that can maintain expertise on tasks that they have not experienced for a long time. Our approach remembers old tasks by selectively slowing down learning on the weights important for those tasks. We demonstrate our approach is scalable and effective by solving a set of classification tasks based on a hand-written digit dataset and by learning several Atari 2600 games sequentially. The ability to learn tasks in a sequential fashion is crucial to the development of artificial intelligence. Neural networks are not, in general, capable of this and it has been widely thought that catastrophic forgetting is an inevitable feature of connectionist models. We show that it is possible to overcome this limitation and train networks that can maintain expertise on tasks which they have not experienced for a long time. Our approach remembers old tasks by selectively slowing down learning on the weights important for those tasks. We demonstrate our approach is scalable and effective by solving a set of classification tasks based on the MNIST hand written digit dataset and by learning several Atari 2600 games sequentially. 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... 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. Multi-class supervised learning systems require the knowledge of the entire range of labels they predict. Often when learnt incrementally, they suffer from catastrophic forgetting. To avoid this, generous leeways have to be made to the philosophy of incremental learning that either forces a part of the machine to not learn, or to retrain the machine again with a selection of the historic data. While these hacks work to various degrees, they do not adhere to the spirit of incremental learning. In this article, we redefine incremental learning with stringent conditions that do not allow for any undesirable relaxations and assumptions. We design a strategy involving generative models and the distillation of dark knowledge as a means of hallucinating data along with appropriate targets from past distributions. We call this technique, phantom sampling.We show that phantom sampling helps avoid catastrophic forgetting during incremental learning. Using an implementation based on deep neural networks, we demonstrate that phantom sampling dramatically avoids catastrophic forgetting. We apply these strategies to competitive multi-class incremental learning of deep neural networks. Using various benchmark datasets and through our strategy, we demonstrate that strict incremental learning could be achieved. We further put our strategy to test on challenging cases, including cross-domain increments and incrementing on a novel label space. We also propose a trivial extension to unbounded-continual learning and identify potential for future development. Humans can learn in a continuous manner. Old rarely utilized knowledge can be overwritten by new incoming information while important, frequently used knowledge is prevented from being erased. In artificial learning systems, lifelong learning so far has focused mainly on accumulating knowledge over tasks and overcoming catastrophic forgetting. In this paper, we argue that, given the limited model capacity and the unlimited new information to be learned, knowledge has to be preserved or erased selectively. Inspired by neuroplasticity, we propose a novel approach for lifelong learning, coined Memory Aware Synapses (MAS). It computes the importance of the parameters of a neural network in an unsupervised and online manner. Given a new sample which is fed to the network, MAS accumulates an importance measure for each parameter of the network, based on how sensitive the predicted output function is to a change in this parameter. When learning a new task, changes to important parameters can then be penalized, effectively preventing important knowledge related to previous tasks from being overwritten. Further, we show an interesting connection between a local version of our method and Hebb’s rule, which is a model for the learning process in the brain. We test our method on a sequence of object recognition tasks and on the challenging problem of learning an embedding for predicting triplets. We show state-of-the-art performance and, for the first time, the ability to adapt the importance of the parameters based on unlabeled data towards what the network needs (not) to forget, which may vary depending on test conditions. Developments in deep generative models have allowed for tractable learning of high-dimensional data distributions. While the employed learning procedures typically assume that training data is drawn i.i.d. from the distribution of interest, it may be desirable to model distinct distributions which are observed sequentially, such as when different classes are encountered over time. Although conditional variations of deep generative models permit multiple distributions to be modeled by a single network in a disentangled fashion, they are susceptible to catastrophic forgetting when the distributions are encountered sequentially. In this paper, we adapt recent work in reducing catastrophic forgetting to the task of training generative adversarial networks on a sequence of distinct distributions, enabling continual generative modeling. This paper presents a method for adding multiple tasks to a single deep neural network while avoiding catastrophic forgetting. Inspired by network pruning techniques, we exploit redundancies in large deep networks to free up parameters that can then be employed to learn new tasks. By performing iterative pruning and network re-training, we are able to sequentially "pack" multiple tasks into a single network while ensuring minimal drop in performance and minimal storage overhead. Unlike prior work that uses proxy losses to maintain accuracy on older tasks, we always optimize for the task at hand. We perform extensive experiments on a variety of network architectures and large-scale datasets, and observe much better robustness against catastrophic forgetting than prior work. In particular, we are able to add three fine-grained classification tasks to a single ImageNet-trained VGG-16 network and achieve accuracies close to those of separately trained networks for each task. Humans can learn in a continuous manner. Old rarely utilized knowledge can be overwritten by new incoming information while important, frequently used knowledge is prevented from being erased. In artificial learning systems, lifelong learning so far has focused mainly on accumulating knowledge over tasks and overcoming catastrophic forgetting. In this paper, we argue that, given the limited model capacity and the unlimited new information to be learned, knowledge has to be preserved or erased selectively. Inspired by neuroplasticity, we propose an online method to compute the importance of the parameters of a neural network, based on the data that the network is actively applied to, in an unsupervised manner. After learning a task, whenever a sample is fed to the network, we accumulate an importance measure for each parameter of the network, based on how sensitive the predicted output is to a change in this parameter. When learning a new task, changes to important parameters are penalized. We show that a local version of our method is a direct application of Hebb's rule in identifying the important connections between neurons. We test our method on a sequence of object recognition tasks and on the challenging problem of learning an embedding in a continuous manner. We show state of the art performance and the ability to adapt the importance of the parameters towards what the network needs (not) to forget, which may be different for different test conditions. 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. We introduce the Kronecker factored online Laplace approximation for overcoming catastrophic forgetting in neural networks. The method is grounded in a Bayesian online learning framework, where we recursively approximate the posterior after every task with a Gaussian, leading to a quadratic penalty on changes to the weights. The Laplace approximation requires calculating the Hessian around a mode, which is typically intractable for modern architectures. In order to make our method scalable, we leverage recent block-diagonal Kronecker factored approximations to the curvature. Our algorithm achieves over 90 test accuracy across a sequence of 50 instantiations of the permuted MNIST dataset, substantially outperforming related methods for overcoming catastrophic forgetting.