Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively such as hippocampus and olfactory cortex. Here we consider associative memories with noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprisingly, we show that internal noise actually improves the performance of the recall phase while the pattern retrieval capacity remains intact, i.e., the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks.
Designing neural networks to learn a set of patterns and recall them later in the presence of noise has been an active topic of research for the past three decades. Inspired by Hebbian learning @cite_53 , Hopfield introduced an auto-associative neural mechanism of size @math with binary state neurons in which patterns are assumed to be binary vectors of length @math @cite_28 . The capacity of a Hopfield network under vanishing block error probability was later shown to be @math @cite_33 . With the hope of increasing the capacity of the Hopfield network, extensions to non-binary states were explored @cite_16 . In particular, investigated a multi-state complex-valued neural associative memory with estimated capacity less than @math @cite_34 ; showed the capacity with a prohibitively complicated learning rule to increase to @math @cite_35 . Lee proposed the Modified Gradient Descent learning Rule (MGDR) to overcome this drawback @cite_31 .
@cite_35 @cite_33 @cite_28 @cite_53 @cite_34 @cite_31 @cite_16
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We consider the problem of neural association for a network of non-binary neurons. Here, the task is to recall a previously memorized pattern from its noisy version using a network of neurons whose states assume values from a finite number of non-negative integer levels. Prior works in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network. In our formulation of the problem, we consider storing patterns from a suitably chosen set of patterns, that are obtained by enforcing a set of simple constraints on the coordinates (such as those enforced in graph based codes). Such patterns may be generated from purely random information symbols by simple neural operations. Two simple neural update algorithms are presented, and it is shown that our proposed mechanisms result in a pattern retrieval capacity that is exponential in terms of the network size. Furthermore, using analytical results and simulations, we show that the suggested methods can tolerate a fair amount of errors in the input. The task of a neural associative memory is to retrieve a set of previously memorized patterns from their noisy versions by using a network of neurons. Hence, an ideal network should be able to 1) gradually learn a set of patterns, 2) retrieve the correct pattern from noisy queries and 3) maximize the number of memorized patterns while maintaining the reliability in responding to queries. We show that by considering the inherent redundancy in the memorized patterns, one can obtain all the mentioned properties at once. This is in sharp contrast with previous work that could only improve one or two aspects at the expense of the others. More specifically, we devise an iterative algorithm that learns the redundancy among the patterns. The resulting network has a retrieval capacity that is exponential in the size of the network. Lastly, by considering the local structures of the network, the asymptotic error correction performance can be made linear in the size of the network. 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. 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.