/// <summary>
/// Execute Backpropagation through time
/// </summary>
/// <returns></returns>
public (float loss, Array <FloatArray2D> dwy, Array <FloatArray> dby, Array <Array <FloatArray2D> > dwh, Array <FloatArray> dbh, Array <FloatArray> hs) BPTT(int[] inputs, int[] targets, Array <FloatArray> hprev)
{
float loss = 0f;
//Feedforward
var xs = new Array <FloatArray>(inputs.Length); // Inputs
var hs = new Array <Array <FloatArray> >(inputs.Length); // Hidden Result
var ps = new Array <Array <FloatArray> >(inputs.Length); // Softmax probabilit
var tg = new Array <FloatArray>(inputs.Length); // Targets
hs[-1] = hprev;
//Backward
var dwy = new Array <FloatArray2D>(1);
var dby = new Array <FloatArray>(1);
var dwh = new Array <Array <FloatArray2D> >(recurrentUnits);
var dbh = new Array <FloatArray>(recurrentUnits);
var dhnext = new Array <FloatArray>(recurrentUnits);
for (int t = 0; t < inputs.Length; t++)
{
xs[t] = new FloatArray(input_size);
xs[t][inputs[t]] = 1;
tg[t] = new FloatArray(output_size);
tg[t][targets[t]] = 1;
(hs[t], ps[t]) = FeedForward(xs[t], hs[t - 1]);
}
for (int t = inputs.Length - 1; t >= 0; t--)
{
// Sequencial
(var l, var dy) = decoder.ComputeErrorNBackward(tg[t], ps[t]);
(dhnext, _) = encoder.Backward(dy, dhnext, hs[t]);
// Parallel
(var wy, var by) = decoder.ComputeGradient(hs[t][-1]);
(var wh, var bh) = encoder.ComputeGradient(xs[t], hs[t - 1]);
// Parallel
dwy = dwy.Sum(wy);
dby = dby.Sum(by);
dwh = dwh.Sum(wh);
dbh = dbh.Sum(bh);
loss += l;
}
// Parallel
dwy = NumMath.Normalize(-5, 5, dwy);
dby = NumMath.Normalize(-5, 5, dby);
dwh = NumMath.Normalize(-5, 5, dwh);
dbh = NumMath.Normalize(-5, 5, dbh);
return(loss, dwy, dby, dwh, dbh, hs[-1]);
FloatArray hs, FloatArray cs) BPTT(Array <FloatArray> inputs, FloatArray error, FloatArray hprev, FloatArray cprev)
{
// store states
var z_s = new Array <FloatArray>(inputs.Length);
var f_s = new Array <FloatArray>(inputs.Length);
var i_s = new Array <FloatArray>(inputs.Length);
var c_s_s = new Array <FloatArray>(inputs.Length);
var c_s = new Array <FloatArray>(inputs.Length);
var o_s = new Array <FloatArray>(inputs.Length);
var h_s = new Array <FloatArray>(inputs.Length);
// init timing
h_s[-1] = hprev.Clone();
c_s[-1] = cprev.Clone();
// forward
for (var t = 0; t < inputs.Length; t++)
{
(z_s[t], f_s[t], i_s[t], c_s_s[t], c_s[t], o_s[t], h_s[t]) =
FeedForward(inputs[t], h_s[t - 1], c_s[t - 1]);
}
// gradients
var dWf = NumMath.Array(Wf.W, Wf.H);
var dWi = NumMath.Array(Wi.W, Wi.H);
var dWc = NumMath.Array(Wc.W, Wc.H);
var dWo = NumMath.Array(Wo.W, Wo.H);
var dBf = NumMath.Array(Bf.Length);
var dBi = NumMath.Array(Bi.Length);
var dBc = NumMath.Array(Bc.Length);
var dBo = NumMath.Array(Bo.Length);
var dhnext = error;
var dcnext = NumMath.Array(hidden_size);
// backward
for (var t = inputs.Length - 1; t >= 0; t--)
{
(dhnext, dcnext) = Backward(dhnext, dcnext, c_s[t - 1],
z_s[t], f_s[t], i_s[t], c_s_s[t], c_s[t], o_s[t], h_s[t],
ref dWf, ref dWi, ref dWc, ref dWo, ref dBf, ref dBi, ref dBc, ref dBo);
}
dWf = NumMath.Normalize(-5, 5, dWf / inputs.Length);
dWi = NumMath.Normalize(-5, 5, dWi / inputs.Length);
dWc = NumMath.Normalize(-5, 5, dWc / inputs.Length);
dWo = NumMath.Normalize(-5, 5, dWo / inputs.Length);
dBf = NumMath.Normalize(-5, 5, dBf / inputs.Length);
dBi = NumMath.Normalize(-5, 5, dBi / inputs.Length);
dBc = NumMath.Normalize(-5, 5, dBc / inputs.Length);
dBo = NumMath.Normalize(-5, 5, dBo / inputs.Length);
return(dWf, dWi, dWc, dWo, dBf, dBi, dBc, dBo, h_s[inputs.Length - 1], c_s[inputs.Length - 1]);
public (FloatArray2D dWxt, FloatArray2D dWtt, FloatArray dbh, FloatArray hs) BPTT(Array <FloatArray> inputs, FloatArray hprev, FloatArray error)
{
var xs = new Array <FloatArray>(inputs.Length);
var ht = new Array <FloatArray>(inputs.Length);
ht[-1] = hprev;
var dWxt = new FloatArray2D(Wxt.W, Wxt.H);
var dWtt = new FloatArray2D(Wtt.W, Wtt.H);
var dhnext = new FloatArray(hidden_size);
var dbt = new FloatArray(bt.Length);
for (var t = 0; t < inputs.Length; t++)
{
xs[t] = inputs[t];
ht[t] = FeedForward(xs[t], ht[t - 1]);
}
dhnext = error;
for (var t = inputs.Length - 1; t >= 0; t--)
{
var dt = dhnext;
// Compute gradient of T (Derivate of Tanh)
var dtraw = (1 - ht[t] * ht[t]) * dt;
dWtt += ht[t - 1].T * dtraw; // Temporal
dWxt += xs[t].T * dtraw; // Input
dbt += dtraw;
// Acc to next Time
dhnext = (dtraw * Wtt).SumColumn();
}
// Normalize
dWxt = NumMath.Normalize(-5, 5, dWxt);
dWtt = NumMath.Normalize(-5, 5, dWtt);
dbt = NumMath.Normalize(-5, 5, dbt);
return(dWxt, dWtt, dbt, ht[inputs.Length - 1]);
BPTT(int[] inputs, int[] targets, FloatArray hprev)
{
var loss = 0f;
var xs = new Array <FloatArray>(inputs.Length);
var ht = new Array <FloatArray>(inputs.Length);
var ps = new Array <FloatArray>(inputs.Length);
var tg = new Array <FloatArray>(inputs.Length);
ht[-1] = hprev;
var dWxt = new FloatArray2D(Wxt.W, Wxt.H);
var dWtt = new FloatArray2D(Wtt.W, Wtt.H);
var dWhy = new FloatArray2D(Why.W, Why.H);
var dhnext = new FloatArray(hidden_size);
var dbt = new FloatArray(bt.Length);
var dby = new FloatArray(by.Length);
for (var t = 0; t < inputs.Length; t++)
{
xs[t] = new FloatArray(input_size);
xs[t][inputs[t]] = 1;
tg[t] = new FloatArray(output_size);
tg[t][targets[t]] = 1;
(ps[t], ht[t]) = FeedForward(xs[t], ht[t - 1]);
loss += -(tg[t] * ps[t].Log()).Sum();
}
for (var t = inputs.Length - 1; t >= 0; t--)
{
// output probabilities
var dy = ps[t].Clone();
// derive our first gradient
dy[targets[t]] -= 1;
// backpropagate to
var dt = (Why * dy).SumColumn() + dhnext;
// Compute gradient of T (Derivate of Tanh)
var dtraw = (1 - ht[t] * ht[t]) * dt;
dWtt += ht[t - 1].T * dtraw; // Temporal
dWxt += xs[t].T * dtraw; // Input
dbt += dtraw;
// Acc to next Time
dhnext = (dtraw * Wtt).SumColumn();
// Compute Derivates
dWhy += ht[t].T * dy;
dby += dy;
}
// Normalize
dWxt = NumMath.Normalize(-5, 5, dWxt);
dWtt = NumMath.Normalize(-5, 5, dWtt);
dWhy = NumMath.Normalize(-5, 5, dWhy);
dbt = NumMath.Normalize(-5, 5, dbt);
dby = NumMath.Normalize(-5, 5, dby);
return(loss, dWxt, dWtt, dWhy, dbt, dby, ht[inputs.Length - 1]);
FloatArray hs, FloatArray cs) BPTT(int[] inputs, int[] targets, FloatArray hprev, FloatArray cprev)
{
// store states
var x_s = new Array <FloatArray>(inputs.Length);
var z_s = new Array <FloatArray>(inputs.Length);
var f_s = new Array <FloatArray>(inputs.Length);
var i_s = new Array <FloatArray>(inputs.Length);
var c_s_s = new Array <FloatArray>(inputs.Length);
var c_s = new Array <FloatArray>(inputs.Length);
var o_s = new Array <FloatArray>(inputs.Length);
var h_s = new Array <FloatArray>(inputs.Length);
var v_s = new Array <FloatArray>(inputs.Length);
var y_s = new Array <FloatArray>(inputs.Length);
var t_g = new Array <FloatArray>(inputs.Length);
// loss
var loss = 0d;
// init timing
h_s[-1] = hprev.Clone();
c_s[-1] = cprev.Clone();
// forward
for (var t = 0; t < inputs.Length; t++)
{
x_s[t] = new FloatArray(input_size);
x_s[t][inputs[t]] = 1;
t_g[t] = new FloatArray(output_size);
t_g[t][targets[t]] = 1;
(z_s[t], f_s[t], i_s[t], c_s_s[t], c_s[t], o_s[t], h_s[t], v_s[t], y_s[t]) =
FeedForward(x_s[t], h_s[t - 1], c_s[t - 1]);
loss += -(t_g[t] * y_s[t].Log()).Sum();
}
// gradients
var dWf = NumMath.Array(Wf.W, Wf.H);
var dWi = NumMath.Array(Wi.W, Wi.H);
var dWc = NumMath.Array(Wc.W, Wc.H);
var dWo = NumMath.Array(Wo.W, Wo.H);
var dWv = NumMath.Array(Wv.W, Wv.H);
var dBf = NumMath.Array(Bf.Length);
var dBi = NumMath.Array(Bi.Length);
var dBc = NumMath.Array(Bc.Length);
var dBo = NumMath.Array(Bo.Length);
var dBv = NumMath.Array(Bv.Length);
var dhnext = NumMath.Array(hidden_size);
var dcnext = NumMath.Array(hidden_size);
// backward
for (var t = inputs.Length - 1; t >= 0; t--)
{
(dhnext, dcnext) = Backward(targets[t], dhnext, dcnext, c_s[t - 1],
z_s[t], f_s[t], i_s[t], c_s_s[t], c_s[t], o_s[t], h_s[t], v_s[t], y_s[t],
ref dWf, ref dWi, ref dWc, ref dWo, ref dWv, ref dBf, ref dBi, ref dBc, ref dBo, ref dBv);
}
dWf = NumMath.Normalize(-5, 5, dWf / inputs.Length);
dWi = NumMath.Normalize(-5, 5, dWi / inputs.Length);
dWc = NumMath.Normalize(-5, 5, dWc / inputs.Length);
dWo = NumMath.Normalize(-5, 5, dWo / inputs.Length);
dWv = NumMath.Normalize(-5, 5, dWv / inputs.Length);
dBf = NumMath.Normalize(-5, 5, dBf / inputs.Length);
dBi = NumMath.Normalize(-5, 5, dBi / inputs.Length);
dBc = NumMath.Normalize(-5, 5, dBc / inputs.Length);
dBo = NumMath.Normalize(-5, 5, dBo / inputs.Length);
dBv = NumMath.Normalize(-5, 5, dBv / inputs.Length);
return(loss, dWf, dWi, dWc, dWo, dWv, dBf, dBi, dBc, dBo, dBv, h_s[inputs.Length - 1], c_s[inputs.Length - 1]);