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We present some novel, straightforward methods for training the connectiongraph of a randomly initialized neural network without training the weights.These methods do not use hyperparameters defining cutoff thresholds andtherefore remove the need for iteratively searching optimal values of suchhyperparameters. We can achieve similar or higher performances than in the caseof training all weights, with a similar computational cost as for standardtraining techniques. Besides switching connections on and off, we introduce anovel way of training a network by flipping the signs of the weights. If we tryto minimize the number of changed connections, by changing less than 10% of thetotal it is already possible to reach more than 90% of the accuracy achieved bystandard training. We obtain good results even with weights of constantmagnitude or even when weights are drawn from highly asymmetric distributions.These results shed light on the over-parameterization of neural networks and onhow they may be reduced to their effective size.

Training highly effective connectivities within neural networks with randomly initialized, fixed weights