Neural net with scalar Boolean output for binary classification

Question

How can I create and train a neural network with a scalar Boolean output for binary classification, and hopefully have it automatically compute the "ErrorRate" property (described here) during training?

Here is an attempt that resulted in errors:

(* create training data *)

rmf = RegionMember[Disk[]];
pts = RandomReal[{-1, 1}, {1000, 2}];
data = Thread[pts -> rmf[pts]];

(* construct net *)

net = NetChain[{100, Ramp, 1}, "Input" -> 2, "Output" -> NetDecoder["Boolean"]]

(* attempt training *)

NetTrain[net, data]

This results in:

First::nofirst: {} has zero length and no first element.

NetTrain::encgenfail1: Could not encode input number 459 for port "Output": input was not a sequence of length 1. Please check the example.

I am not experienced with neutral networks. I am generally confused about how to specify that the output of a net is even a scalar (not a vector). In the example above, this does not seem to be the problem as changing the training data to use size-1 Boolean vectors instead of Boolean scalars does not fix the error.

Answer 1

You can attach a SequenceLastLayer to your chain to get this to work:

net = NetChain[{100, Ramp, 1, SequenceLastLayer[]}, "Input" -> 2, "Output" -> NetDecoder["Boolean"]]

Normally, to get a network to output a scalar, you can do "Output"->"Scalar", but since you're already using a NetDecoder, this doesn't work easily. A SequenceLastLayer always returns a scalar, so this is an easy way to work around this issue.

It does seem to me that the boolean NetDecoder could handle this a little better. You can set the "InputDepth" of the NetDecoder like so: NetDecoder[{"Boolean", "InputDepth"->2}], but you should also be able to specify that the input should be a scalar here.