func (_ SigmoidCECost) Cost(x linalg.Vector, a autofunc.Result) autofunc.Result {
logsig := autofunc.LogSigmoid{}
log := logsig.Apply(a)
invLog := logsig.Apply(autofunc.Scale(a, -1))
xVar := &autofunc.Variable{x}
oneMinusX := autofunc.AddScaler(autofunc.Scale(xVar, -1), 1)
sums := autofunc.Add(autofunc.Mul(xVar, log), autofunc.Mul(oneMinusX, invLog))
return autofunc.Scale(autofunc.SumAll(sums), -1)
}
func (_ CrossEntropyCost) Cost(x linalg.Vector, a autofunc.Result) autofunc.Result {
return autofunc.Pool(a, func(a autofunc.Result) autofunc.Result {
xVar := &autofunc.Variable{x}
logA := autofunc.Log{}.Apply(a)
oneMinusA := autofunc.AddScaler(autofunc.Scale(a, -1), 1)
oneMinusX := autofunc.AddScaler(autofunc.Scale(xVar, -1), 1)
log1A := autofunc.Log{}.Apply(oneMinusA)
errorVec := autofunc.Add(autofunc.Mul(xVar, logA),
autofunc.Mul(oneMinusX, log1A))
return autofunc.Scale(autofunc.SumAll(errorVec), -1)
})
}
func (s *LogSoftmaxLayer) Apply(in autofunc.Result) autofunc.Result {
return autofunc.Pool(in, func(in autofunc.Result) autofunc.Result {
// Compute the log of the sum of the exponents by
// factoring out the largest exponent so that all
// the exponentials fit nicely inside floats.
maxIdx := maxVecIdx(in.Output())
maxValue := autofunc.Slice(in, maxIdx, maxIdx+1)
exponents := autofunc.AddFirst(in, autofunc.Scale(maxValue, -1))
expSum := autofunc.SumAll(autofunc.Exp{}.Apply(exponents))
expLog := autofunc.Log{}.Apply(expSum)
denomLog := autofunc.Add(expLog, maxValue)
return autofunc.AddFirst(in, autofunc.Scale(denomLog, -1))
})
}
// Loss returns the weighted exponential loss.
// It determines which samples are positive vs. negative
// by checking the sign of the element in the expected
// vector.
func (w *WeightedExpLoss) Loss(actual autofunc.Result, expected linalg.Vector) autofunc.Result {
expVar := &autofunc.Variable{Vector: expected.Copy().Scale(-1)}
dots := autofunc.Mul(actual, expVar)
exps := autofunc.Exp{}.Apply(dots)
weightVec := &autofunc.Variable{Vector: make(linalg.Vector, len(expected))}
for i, x := range expected {
if x > 0 {
weightVec.Vector[i] = w.PosWeight
} else {
weightVec.Vector[i] = 1
}
}
return autofunc.SumAll(autofunc.Mul(exps, weightVec))
}
// Loss returns the exponential loss, as given by
// exp(-actual*expected).
func (_ ExpLoss) Loss(actual autofunc.Result, expected linalg.Vector) autofunc.Result {
expVar := &autofunc.Variable{Vector: expected.Copy().Scale(-1)}
dots := autofunc.Mul(actual, expVar)
exps := autofunc.Exp{}.Apply(dots)
return autofunc.SumAll(exps)
}
// Loss returns the squared magnitude of the difference
// between actual and expected.
func (_ SquareLoss) Loss(actual autofunc.Result, expected linalg.Vector) autofunc.Result {
expVar := &autofunc.Variable{Vector: expected.Copy().Scale(-1)}
return autofunc.SumAll(autofunc.Square(autofunc.Add(actual, expVar)))
}
func (_ DotCost) Cost(x linalg.Vector, a autofunc.Result) autofunc.Result {
xVar := &autofunc.Variable{x}
return autofunc.Scale(autofunc.SumAll(autofunc.Mul(xVar, a)), -1)
}
