AI462

 Switch Net 4  Switch Net 4. Random sign flipping before a fast Walsh Hadamard transform results in a Random Projection. For almost any input the result is a Gaussian distributed output vector where each output element contains knowledge of all the input elements. With Switch Net 4 the output elements are 2-way switched using (x<0?) as a switching predicate. Where x is the input to the switch.  The switches are grouped together in units of 4 which together form a small width 4 neural. When a particualr x>=0, the pattern in the selected pattern of weights is forward projected with intensity x. When x<0 a different pattern of forward selected weights is again projected with intensity x (x being negative this time.) If nothing was projected when x<0 then the situation would be identical to using a ReLU. You could view the situation in Switch Net 4 as using 2 ReLUs one with input x and one with input -x.  The reason to 2-way switch (or +- ReLU) is to avoid ea...

 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 ...

 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...

2 Siding ReLU via Forward Projections The ReLU acivation function in neural networks has special properties that allow it to be considered in a different way to other activation functions. The Switching Viewpoint You can view ReLU as being non-conducting when x<=0 and fully conducting when x>0.  It is a switch which is automatically turned on when x>0 and automatically turned off when x<=0. Which is an ideal rectifier in electrical engineering terms.  Hence the term  Rectified Linear Unit. A switch isn't there when it is on from the point of view of the flowing electricity (or analogous thing.)  Electricity flows through pushed together switch contacts the same as through the wires to the switch.  All the ReLUs in a neural network that are conducting, wire together various sub-components of the network. The wiring being complete the ReLUs become essentially invisible, until one or more ReLUs change state. Since neural networks are computed in a ...