Birth of a Learning Law

Defense Advanced Research Projects Agency; Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-92-J-1309

A ferrofluid based neural network: design of an analogue associative memory

We analyse an associative memory based on a ferrofluid, consisting of a system of magnetic nano-particles suspended in a carrier fluid of variable viscosity subject to patterns of magnetic fields from an array of input and output magnetic pads. The association relies on forming patterns in the ferrofluid during a trainingdphase, in which the magnetic dipoles are free to move and rotate to minimize the total energy of the system. Once equilibrated in energy for a given input-output magnetic field pattern-pair the particles are fully or partially immobilized by cooling the carrier liquid. Thus produced particle distributions control the memory states, which are read out magnetically using spin-valve sensors incorporated in the output pads. The actual memory consists of spin distributions that is dynamic in nature, realized only in response to the input patterns that the system has been trained for. Two training algorithms for storing multiple patterns are investigated. Using Monte Carlo simulations of the physical system we demonstrate that the device is capable of storing and recalling two sets of images, each with an accuracy approaching 100%.Comment: submitted to Neural Network

Adaptive Resonance Associative Map: A Hierarchical ART System for Fast Stable Associative Learning

This paper introduces a new class of predictive ART architectures, called Adaptive Resonance Associative Map (ARAM) which performs rapid, yet stable heteroassociative learning in real time environment. ARAM can be visualized as two ART modules sharing a single recognition code layer. The unit for recruiting a recognition code is a pattern pair. Code stabilization is ensured by restricting coding to states where resonances are reached in both modules. Simulation results have shown that ARAM is capable of self-stabilizing association of arbitrary pattern pairs of arbitrary complexity appearing in arbitrary sequence by fast learning in real time environment. Due to the symmetrical network structure, associative recall can be performed in both directions.Air Force Office of Scientific Research (90-0128

An associative memory for the on-line recognition and prediction of temporal sequences

This paper presents the design of an associative memory with feedback that is capable of on-line temporal sequence learning. A framework for on-line sequence learning has been proposed, and different sequence learning models have been analysed according to this framework. The network model is an associative memory with a separate store for the sequence context of a symbol. A sparse distributed memory is used to gain scalability. The context store combines the functionality of a neural layer with a shift register. The sensitivity of the machine to the sequence context is controllable, resulting in different characteristic behaviours. The model can store and predict on-line sequences of various types and length. Numerical simulations on the model have been carried out to determine its properties.Comment: Published in IJCNN 2005, Montreal, Canad

Sparse neural networks with large learning diversity

Coded recurrent neural networks with three levels of sparsity are introduced. The first level is related to the size of messages, much smaller than the number of available neurons. The second one is provided by a particular coding rule, acting as a local constraint in the neural activity. The third one is a characteristic of the low final connection density of the network after the learning phase. Though the proposed network is very simple since it is based on binary neurons and binary connections, it is able to learn a large number of messages and recall them, even in presence of strong erasures. The performance of the network is assessed as a classifier and as an associative memory

Deep Complex Networks

At present, the vast majority of building blocks, techniques, and architectures for deep learning are based on real-valued operations and representations. However, recent work on recurrent neural networks and older fundamental theoretical analysis suggests that complex numbers could have a richer representational capacity and could also facilitate noise-robust memory retrieval mechanisms. Despite their attractive properties and potential for opening up entirely new neural architectures, complex-valued deep neural networks have been marginalized due to the absence of the building blocks required to design such models. In this work, we provide the key atomic components for complex-valued deep neural networks and apply them to convolutional feed-forward networks and convolutional LSTMs. More precisely, we rely on complex convolutions and present algorithms for complex batch-normalization, complex weight initialization strategies for complex-valued neural nets and we use them in experiments with end-to-end training schemes. We demonstrate that such complex-valued models are competitive with their real-valued counterparts. We test deep complex models on several computer vision tasks, on music transcription using the MusicNet dataset and on Speech Spectrum Prediction using the TIMIT dataset. We achieve state-of-the-art performance on these audio-related tasks

Adiabatic Quantum Optimization for Associative Memory Recall

Hopfield networks are a variant of associative memory that recall information stored in the couplings of an Ising model. Stored memories are fixed points for the network dynamics that correspond to energetic minima of the spin state. We formulate the recall of memories stored in a Hopfield network using energy minimization by adiabatic quantum optimization (AQO). Numerical simulations of the quantum dynamics allow us to quantify the AQO recall accuracy with respect to the number of stored memories and the noise in the input key. We also investigate AQO performance with respect to how memories are stored in the Ising model using different learning rules. Our results indicate that AQO performance varies strongly with learning rule due to the changes in the energy landscape. Consequently, learning rules offer indirect methods for investigating change to the computational complexity of the recall task and the computational efficiency of AQO.Comment: 22 pages, 11 figures. Updated for clarity and figures, to appear in Frontiers of Physic