scholarly journals A "Thermal" Perceptron Learning Rule

1992 ◽  
Vol 4 (6) ◽  
pp. 946-957 ◽  
Author(s):  
Marcus Frean
Keyword(s):  
Gradient Descent ◽  
Learning Rule ◽  
Training Period ◽  
Simple Extension ◽  
Linear Threshold ◽  
Initial Setting ◽  
Separable Problems ◽  
Temperature Parameter ◽  
Perceptron Learning

The thermal perceptron is a simple extension to Rosenblatt's perceptron learning rule for training individual linear threshold units. It finds stable weights for nonseparable problems as well as separable ones. Experiments indicate that if a good initial setting for a temperature parameter, T0, has been found, then the thermal perceptron outperforms the Pocket algorithm and methods based on gradient descent. The learning rule stabilizes the weights (learns) over a fixed training period. For separable problems it finds separating weights much more quickly than the usual rules.

scholarly journals Implementation of a spike-based perceptron learning rule using TiO2−x memristors

2015 ◽  
Vol 9 ◽  
Author(s):  
Hesham Mostafa ◽  
Ali Khiat ◽  
Alexander Serb ◽  
Christian G. Mayr ◽  
Giacomo Indiveri ◽  
...  
Keyword(s):  
Learning Rule ◽  
Perceptron Learning

TRAINING RECURRENT NEURAL NETWORKS — THE MINIMAL TRAJECTORY ALGORITHM

1992 ◽  
Vol 03 (01) ◽  
pp. 83-101 ◽  
Author(s):  
D. Saad
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Learning Rule ◽  
Weight Matrix ◽  
Training Methods ◽  
Input Output ◽  
Feed Forward ◽  
End Point ◽  
Common Weight ◽  
Perceptron Learning

The Minimal Trajectory (MINT) algorithm for training recurrent neural networks with a stable end point is based on an algorithmic search for the systems’ representations in the neighbourhood of the minimal trajectory connecting the input-output representations. The said representations appear to be the most probable set for solving the global perceptron problem related to the common weight matrix, connecting all representations of successive time steps in a recurrent discrete neural networks. The search for a proper set of system representations is aided by representation modification rules similar to those presented in our former paper,1 aimed to support contributing hidden and non-end-point representations while supressing non-contributing ones. Similar representation modification rules were used in other training methods for feed-forward networks,2–4 based on modification of the internal representations. A feed-forward version of the MINT algorithm will be presented in another paper.5 Once a proper set of system representations is chosen, the weight matrix is then modified accordingly, via the Perceptron Learning Rule (PLR) to obtain the proper input-output relation. Computer simulations carried out for the restricted cases of parity and teacher-net problems show rapid convergence of the algorithm in comparison with other existing algorithms, together with modest memory requirements.

scholarly journals Alopex: A Correlation-Based Learning Algorithm for Feedforward and Recurrent Neural Networks

1994 ◽  
Vol 6 (3) ◽  
pp. 469-490 ◽  
Author(s):  
K. P. Unnikrishnan ◽  
K. P. Venugopal
Keyword(s):  
Neural Networks ◽  
Gradient Descent ◽  
Transfer Functions ◽  
Learning Algorithm ◽  
Recurrent Networks ◽  
Error Measure ◽  
Scaling Properties ◽  
Error Measures ◽  
Local Correlations ◽  
Temperature Parameter

We present a learning algorithm for neural networks, called Alopex. Instead of error gradient, Alopex uses local correlations between changes in individual weights and changes in the global error measure. The algorithm does not make any assumptions about transfer functions of individual neurons, and does not explicitly depend on the functional form of the error measure. Hence, it can be used in networks with arbitrary transfer functions and for minimizing a large class of error measures. The learning algorithm is the same for feedforward and recurrent networks. All the weights in a network are updated simultaneously, using only local computations. This allows complete parallelization of the algorithm. The algorithm is stochastic and it uses a “temperature” parameter in a manner similar to that in simulated annealing. A heuristic “annealing schedule” is presented that is effective in finding global minima of error surfaces. In this paper, we report extensive simulation studies illustrating these advantages and show that learning times are comparable to those for standard gradient descent methods. Feedforward networks trained with Alopex are used to solve the MONK's problems and symmetry problems. Recurrent networks trained with the same algorithm are used for solving temporal XOR problems. Scaling properties of the algorithm are demonstrated using encoder problems of different sizes and advantages of appropriate error measures are illustrated using a variety of problems.

Reward-Modulated Hebbian Learning of Decision Making

2010 ◽  
Vol 22 (6) ◽  
pp. 1399-1444 ◽  
Author(s):  
Michael Pfeiffer ◽  
Bernhard Nessler ◽  
Rodney J. Douglas ◽  
Wolfgang Maass
Keyword(s):  
Decision Making ◽  
Hebbian Learning ◽  
Learning Rule ◽  
Final Decision ◽  
Bayesian Decision ◽  
Decision Stage ◽  
Fast Learning ◽  
Hebb Rule ◽  
Adaptive Processes ◽  
Perceptron Learning

We introduce a framework for decision making in which the learning of decision making is reduced to its simplest and biologically most plausible form: Hebbian learning on a linear neuron. We cast our Bayesian-Hebb learning rule as reinforcement learning in which certain decisions are rewarded and prove that each synaptic weight will on average converge exponentially fast to the log-odd of receiving a reward when its pre- and postsynaptic neurons are active. In our simple architecture, a particular action is selected from the set of candidate actions by a winner-take-all operation. The global reward assigned to this action then modulates the update of each synapse. Apart from this global reward signal, our reward-modulated Bayesian Hebb rule is a pure Hebb update that depends only on the coactivation of the pre- and postsynaptic neurons, not on the weighted sum of all presynaptic inputs to the postsynaptic neuron as in the perceptron learning rule or the Rescorla-Wagner rule. This simple approach to action-selection learning requires that information about sensory inputs be presented to the Bayesian decision stage in a suitably preprocessed form resulting from other adaptive processes (acting on a larger timescale) that detect salient dependencies among input features. Hence our proposed framework for fast learning of decisions also provides interesting new hypotheses regarding neural nodes and computational goals of cortical areas that provide input to the final decision stage.

scholarly journals Generalized perceptron learning rule and its implications for photorefractive neural networks

1994 ◽  
Vol 11 (9) ◽  
pp. 1619 ◽  
Author(s):  
Chau-Jern Cheng ◽  
Pochi Yeh ◽  
Ken Yuh Hsu
Keyword(s):  
Neural Networks ◽  
Learning Rule ◽  
Perceptron Learning

A New Supervised Learning Algorithm for Spiking Neurons

2013 ◽  
Vol 25 (6) ◽  
pp. 1472-1511 ◽  
Author(s):  
Yan Xu ◽  
Xiaoqin Zeng ◽  
Shuiming Zhong
Keyword(s):  
Supervised Learning ◽  
Learning Algorithm ◽  
Learning Rule ◽  
Classification Problem ◽  
Higher Learning ◽  
Spiking Neurons ◽  
Spiking Neuron ◽  
Temporal Encoding ◽  
The Times ◽  
Perceptron Learning

The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit a specific spike train encoded by the precise firing times of spikes. If only running time is considered, the supervised learning for a spiking neuron is equivalent to distinguishing the times of desired output spikes and the other time during the running process of the neuron through adjusting synaptic weights, which can be regarded as a classification problem. Based on this idea, this letter proposes a new supervised learning method for spiking neurons with temporal encoding; it first transforms the supervised learning into a classification problem and then solves the problem by using the perceptron learning rule. The experiment results show that the proposed method has higher learning accuracy and efficiency over the existing learning methods, so it is more powerful for solving complex and real-time problems.

Soft Learning Vector Quantization

2003 ◽  
Vol 15 (7) ◽  
pp. 1589-1604 ◽  
Author(s):  
Sambu Seo ◽  
Klaus Obermayer
Keyword(s):  
Vector Quantization ◽  
Gradient Descent ◽  
Distance Measure ◽  
Learning Rule ◽  
Gaussian Mixture ◽  
Classification Performance ◽  
Learning Vector Quantization ◽  
Additional Benefit ◽  
New Approach ◽  
New Methods

Learning vector quantization (LVQ) is a popular class of adaptive nearest prototype classifiers for multiclass classification, but learning algorithms from this family have so far been proposed on heuristic grounds. Here, we take a more principled approach and derive two variants of LVQ using a gaussian mixture ansatz. We propose an objective function based on a likelihood ratio and derive a learning rule using gradient descent. The new approach provides a way to extend the algorithms of the LVQ family to different distance measure and allows for the design of “soft” LVQ algorithms. Benchmark results show that the new methods lead to better classification performance than LVQ 2.1. An additional benefit of the new method is that model assumptions are made explicit, so that the method can be adapted more easily to different kinds of problems.

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