Morphological Network: How Far Can We Go with Morphological Neurons?

In recent years, the idea of using morphological operations as networks has received much attention. Mathematical morphology provides very efficient and useful image processing and image analysis tools based on basic operators like dilation and erosion, defined in terms of kernels. Many other morphological operations are built up using the dilation and erosion operations. Although the learning of structuring elements such as dilation or erosion using the backpropagation algorithm is not new, the order and the way these morphological operations are used is not standard. In this paper, we have theoretically analyzed the use of morphological operations for processing 1D feature vectors and shown that this gets extended to the 2D case in a simple manner. Our theoretical results show that a morphological block represents a sum of hinge functions. Hinge functions are used in many places for classification and regression tasks (Breiman (1993)). We have also proved a universal approximation theorem -- a stack of two morphological blocks can approximate any continuous function over arbitrary compact sets. To experimentally validate the efficacy of this network in real-life applications, we have evaluated its performance on satellite image classification datasets since morphological operations are very sensitive to geometrical shapes and structures. We have also shown results on a few tasks like segmentation of blood vessels from fundus images, segmentation of lungs from chest x-ray and image dehazing. The results are encouraging and further establishes the potential of morphological networks.Comment: 35 pages, 19 figures, 7 table

An Online Unsupervised Structural Plasticity Algorithm for Spiking Neural Networks

In this article, we propose a novel Winner-Take-All (WTA) architecture employing neurons with nonlinear dendrites and an online unsupervised structural plasticity rule for training it. Further, to aid hardware implementations, our network employs only binary synapses. The proposed learning rule is inspired by spike time dependent plasticity (STDP) but differs for each dendrite based on its activation level. It trains the WTA network through formation and elimination of connections between inputs and synapses. To demonstrate the performance of the proposed network and learning rule, we employ it to solve two, four and six class classification of random Poisson spike time inputs. The results indicate that by proper tuning of the inhibitory time constant of the WTA, a trade-off between specificity and sensitivity of the network can be achieved. We use the inhibitory time constant to set the number of subpatterns per pattern we want to detect. We show that while the percentage of successful trials are 92%, 88% and 82% for two, four and six class classification when no pattern subdivisions are made, it increases to 100% when each pattern is subdivided into 5 or 10 subpatterns. However, the former scenario of no pattern subdivision is more jitter resilient than the later ones.Comment: 11 pages, 10 figures, journa

Hardware-Amenable Structural Learning for Spike-based Pattern Classification using a Simple Model of Active Dendrites

This paper presents a spike-based model which employs neurons with functionally distinct dendritic compartments for classifying high dimensional binary patterns. The synaptic inputs arriving on each dendritic subunit are nonlinearly processed before being linearly integrated at the soma, giving the neuron a capacity to perform a large number of input-output mappings. The model utilizes sparse synaptic connectivity; where each synapse takes a binary value. The optimal connection pattern of a neuron is learned by using a simple hardware-friendly, margin enhancing learning algorithm inspired by the mechanism of structural plasticity in biological neurons. The learning algorithm groups correlated synaptic inputs on the same dendritic branch. Since the learning results in modified connection patterns, it can be incorporated into current event-based neuromorphic systems with little overhead. This work also presents a branch-specific spike-based version of this structural plasticity rule. The proposed model is evaluated on benchmark binary classification problems and its performance is compared against that achieved using Support Vector Machine (SVM) and Extreme Learning Machine (ELM) techniques. Our proposed method attains comparable performance while utilizing 10 to 50% less computational resources than the other reported techniques.Comment: Accepted for publication in Neural Computatio

Liquid State Machine with Dendritically Enhanced Readout for Low-power, Neuromorphic VLSI Implementations

In this paper, we describe a new neuro-inspired, hardware-friendly readout stage for the liquid state machine (LSM), a popular model for reservoir computing. Compared to the parallel perceptron architecture trained by the p-delta algorithm, which is the state of the art in terms of performance of readout stages, our readout architecture and learning algorithm can attain better performance with significantly less synaptic resources making it attractive for VLSI implementation. Inspired by the nonlinear properties of dendrites in biological neurons, our readout stage incorporates neurons having multiple dendrites with a lumped nonlinearity. The number of synaptic connections on each branch is significantly lower than the total number of connections from the liquid neurons and the learning algorithm tries to find the best 'combination' of input connections on each branch to reduce the error. Hence, the learning involves network rewiring (NRW) of the readout network similar to structural plasticity observed in its biological counterparts. We show that compared to a single perceptron using analog weights, this architecture for the readout can attain, even by using the same number of binary valued synapses, up to 3.3 times less error for a two-class spike train classification problem and 2.4 times less error for an input rate approximation task. Even with 60 times larger synapses, a group of 60 parallel perceptrons cannot attain the performance of the proposed dendritically enhanced readout. An additional advantage of this method for hardware implementations is that the 'choice' of connectivity can be easily implemented exploiting address event representation (AER) protocols commonly used in current neuromorphic systems where the connection matrix is stored in memory. Also, due to the use of binary synapses, our proposed method is more robust against statistical variations.Comment: 14 pages, 19 figures, Journa