AI462

 Switch Net Switch Net. Switch Net is a neural network based on using the fast Walsh Hadamard tranform (WHT) as a fixed set of layer weights with a parametric switching based activation function. The cost of the WHT is nlog2(n) add subtracts as opposed to n squared fused multiply adds for a conventional dense neural layer's weight calculations. A fixed random pattern of sign flips is applied to the input data so that the first WHT fairly distributes information with a Gaussian distribution across its outputs. Then a switching decision is applied to each output of the WHT and the output is multiplied by one weight or another.  The section between the red lines is basically a layer and can be repeated a number of times. A final WHT is done to combine the last lot of switched weight outputs. Some example code is here: https://editor.p5js.org/congchuatocmaydangyeu7/sketches/7ekZTwQMF One slight issue is if the switching weights for a particular output have opposite signs then the ...

Associative Memory using a Locality Sensitive Hash Hashing and Associative Memory Suppose you have a hash algorithm with d (+1,-1) binary outputs and you apply a weighted sum to those d binary outputs. Then you can store up to d <input,scalar> associations. Where the input goes to the hash function and the scalar value is the output of the weighted sum.  Only if by chance the hash algorithm outputs 2 binary patterns (for particular inputs) that are not linearly seperable will the storage capacity be less than d. As d increases the probability of such a collision decreases. The training algorithm simply involves adding or subtracting the recall error (divided by d) to the weights according to whether the hash bit for the particular weight is valued -1 or +1.  The training algorithm is applied to the training data a number of times to drive the recall error to a low value solving a set of d linear simultaneous equations. An input that was not in the training set results in...

Random Projections for Neural Networks  Variance and the CLT For Linear Combinations of Random Variables a negative sign before a particular variable has no effect on variance. And of course the Central Limit Theorem is in operation. The Walsh Hadamard transform (WHT) is a set of orthogonal weighted sums (where the weights are +1 or -1 or some constant multiple of those.)  And so the variance equation for linear combinations of random variables applies (minus signs not invalidating that), as does the Central Limit Theorem. 8-Point Walsh Hadamard transform. Therefore applying the WHT to a sequence of random numbers from the Uniform random number distribution results in a sequence of numbers from the Gaussian (Normal) distribution. Example code is here: https://editor.p5js.org/siobhan.491/sketches/WhoxMA7pH If you want to use that behavior to generate Gaussians you should remember that the WHT leaves vector magnitued (length) unchanged (except by a constant c.)  The result ...

 Switch Net 4 The layers in a fully connected artificial neural network don't scale nicely with width. Width of a neural network. For width n the number of multiply add operations required per layer is n squared. For a layer of width 256 the number multiply adds would be 65536 (256*256.) Even with modern hardward layers cannot be made much wider than that. Or can they?  A layer of width 2 only requires 4 operations, width 4 only 16 operations, width 8 only 64 operations. If you could combine k width n (n being small) layers into a new much wider layer you'd end up with a computational advantage. For example 64 width 4 layers combined into a width 256 layer would cost 64*16=1024 multiply add operations plus the combining cost.  A combining algorithm. The fast Walsh Hadmard transform can be used as a combiner because a change in a single input causes all the outputs to vary. The combining cost is n*log2(n) add subtract operations. For a layer of width 256 the combining cost...