public void SumProductWithSharedHasCorrectGrad()
{
// sequence of input
var xs = T.Matrix <float>("xs");
// accumulator
var z = T.Vector <float>("z");
var b = T.Vector <float>("b");
// sum xs in the accumulator
Func <Tensor <float>, Tensor <float>, IList <Tensor <float> > > rec = (x, a) =>
new List <Tensor <float> >()
{
x + a, x *a + b
};
var loop = T.Scan(rec, xs, new[] { z, null });
// get the last value
var prod = loop[1][-1];
var cost = T.Sum(prod);
//var dz = T.Grad(cost, z);
var db = T.Grad(cost, b);
var reshape = db as Reshaping <float>;
var sum = reshape.x as Sum <float>;
Assert.AreEqual(0, sum.Axis);
var dfor = sum.x as Tensor <float> .For;
var backLoop = dfor.Loop;
Assert.AreEqual(3, backLoop.Sequences.Count);
Assert.AreEqual(4, backLoop.Fors.Count);
Assert.AreEqual(2, dfor.Index);
// TODO: check why a recursive was expected
//var db_ = dfor.RecursiveVariable;
//Assert.AreEqual("db_", db_.Name);
var variables = backLoop.Variables.Cast <Tensor <float> >().ToList();
var x_ = variables[0];
Assert.AreEqual("x_", x_.Name);
var a_ = variables[1];
Assert.AreEqual("a_", a_.Name);
var d_f1_ = variables[2];
Assert.AreEqual("delta_f1_", d_f1_.Name);
var da_ = variables[4];
Assert.AreEqual("da_", da_.Name);
var dx = (Tensor <float>)backLoop.Fors[0].Expression;
var da = (Tensor <float>)backLoop.Fors[1].Expression;
Assert.IsTrue((d_f1_ * a_ + da_).StructuralEquality(dx));
Assert.IsTrue((d_f1_ * x_ + da_).StructuralEquality(da));
Assert.IsTrue((d_f1_).StructuralEquality(dfor.Expression));
}
public void SumProductHasCorrectGrad()
{
// sequence of input
var xs = T.Matrix <float>("xs");
// accumulator
var z = T.Vector <float>("z");
// sum xs in the accumulator
Func <Tensor <float>, Tensor <float>, IList <Tensor <float> > > rec = (x, a) =>
new List <Tensor <float> >()
{
x + a, x *a
};
var loop = T.Scan(rec, xs, new[] { z, null });
// get the last value
var prod = loop[1][-1];
var cost = T.Sum(prod);
var dz = T.Grad(cost, z);
var slicing = dz as Slicing <float>;
Assert.AreEqual(1, slicing.Slices.Count);
Assert.IsTrue(slicing.Slices[0].IsSingleton);
Assert.AreEqual(-1, ((Scalar <int> .Const)slicing.Slices[0].Start).Value);
var dfor = slicing.x as Tensor <float> .For;
var backLoop = dfor.Loop;
Assert.AreEqual(3, backLoop.Sequences.Count);
Assert.AreEqual(3, backLoop.Fors.Count);
Assert.AreEqual(1, dfor.Index);
var variables = backLoop.Variables.Cast <Tensor <float> >().ToList();
var x_ = variables[0];
Assert.AreEqual("x_", x_.Name);
var a_ = variables[1];
Assert.AreEqual("a_", a_.Name);
var d_f1_ = variables[2];
Assert.AreEqual("delta_f1_", d_f1_.Name);
var da_ = variables[4];
Assert.AreEqual("da_", da_.Name);
var dx = (Tensor <float>)backLoop.Fors[0].Expression;
var da = (Tensor <float>)backLoop.Fors[1].Expression;
Assert.IsTrue((d_f1_ * a_ + da_).StructuralEquality(dx));
Assert.IsTrue((d_f1_ * x_ + da_).StructuralEquality(da));
}
public void SumHasCorrectGrad()
{
// sequence of input
var xs = T.Matrix <float>("xs");
// accumulator
var z = T.Vector <float>("z");
// sum xs in the accumulator
var partialSums = T.Scan((x, a) => x + a, xs, z);
// get the last value
var sum = partialSums[-1];
var cost = T.Sum(sum * sum);
var dz = T.Grad(cost, z);
var slicing = dz as Slicing <float>;
Assert.AreEqual(1, slicing.Slices.Count);
Assert.IsTrue(slicing.Slices[0].IsSingleton);
Assert.AreEqual(-1, ((Scalar <int> .Const)slicing.Slices[0].Start).Value);
var dfor = slicing.x as Tensor <float> .For;
var backLoop = dfor.Loop;
Assert.AreEqual(3, backLoop.Sequences.Count);
Assert.AreEqual(3, backLoop.Fors.Count);
Assert.AreEqual(1, dfor.Index);
var variables = backLoop.Variables.Cast <Tensor <float> >().ToList();
var x_ = variables[0];
Assert.AreEqual("x_", x_.Name);
var a_ = variables[1];
Assert.AreEqual("a_", a_.Name);
var delta_a_ = variables[2];
Assert.AreEqual("delta_a_", delta_a_.Name);
var dx_ = variables[3];
Assert.AreEqual("dx_", dx_.Name);
var da_ = variables[4];
Assert.AreEqual("da_", da_.Name);
var dx = (Tensor <float>)backLoop.Fors[0].Expression;
var da = (Tensor <float>)backLoop.Fors[1].Expression;
Assert.IsTrue((delta_a_ + da_).StructuralEquality(dx));
Assert.IsTrue((delta_a_ + da_).StructuralEquality(da));
}
public void SumProductWithSharedCanTrain()
{
var n = 2;
// sequence of input
var xs = T.Matrix <float>("xs");
// accumulator
var z = T.Vector <float>("z");
var b = T.Shared(NN.Ones(n), "b");
// sum xs in the accumulator
Func <Tensor <float>, Tensor <float>, IList <Tensor <float> > > rec = (x, a) =>
new List <Tensor <float> >()
{
x + a, x *a + b
};
var loop = T.Scan(rec, xs, new[] { z, null });
// get the last value
var prod = loop[1][-1];
// compute the cost and the gradient for the shared b.
var cost = T.Sum(prod);
var db = T.Grad(cost, b);
var costFunction = T.Function(input: (xs, z), output: cost);
var xs_ = NN.Array(new float[, ] {
{ 1, -1 },
{ 0, -2 }
});
var z_ = NN.Zeros(n);
var cost_xs_z = costFunction(xs_, z_);
Assert.AreEqual(4, cost_xs_z);
var updates = new OrderedDictionary {
{ b, b - 0.05f * db }
};
var train = T.Function(input: (xs, z), output: cost, updates: updates);
var cost_xs_z2 = train(xs_, z_);
AssertArray.AreAlmostEqual(NN.Array(new[] { 0.95f, 0.95f }), b.Value);
}
public void RnnXorHasCorrectGradient()
{
NN.Random.Seed(12345);
int nh = 10; // hidden layer
var Wbit = T.Shared(0.2f * NN.Random.Uniform(-1.0f, 1.0f, nh, 1).As <float>(), "Wbit");
var Wstate = T.Shared(NN.Eye <float>(nh), "Wstate");
var Wout = T.Shared(0.2f * NN.Random.Uniform(-1.0f, 1.0f, 1, nh).As <float>(), "Wout");
var b = T.Shared(0.2f * NN.Random.Uniform(-1.0f, 1.0f, nh, 1).As <float>(), "b");
var state0 = T.Shared(NN.Zeros <float>(nh, 1), "state0");
var bits = T.Tensor3 <float>("bits"); // n x 1
var expected = T.Matrix <float>("expected"); // 1 x 1
Func <Tensor <float>, Tensor <float>, Tensor <float> > recurrence = (bit, oldState) =>
{
return(T.Tanh(T.Dot(Wbit, bit) + T.Dot(Wstate, oldState) + b));
};
var states = T.Scan(fn: recurrence, sequence: bits, outputsInfo: state0);
var output = T.Tanh(T.Dot(Wout, states[(Slice)(-1)]));
var error = 0.5f * T.Norm2(output - expected);
var classify = T.Function(bits, output);
var gradients = T.Grad(error);
var gradWstate = gradients[Wstate];
Assert.IsNotNull(gradWstate);
var gradWstateIsReshape = gradWstate as Reshaping <float>;
Assert.IsNotNull(gradWstateIsReshape);
var gradWstateIsSum = gradWstateIsReshape.x as Sum <float>;
Assert.IsNotNull(gradWstateIsSum);
var dfor = gradWstateIsSum.x as Tensor <float> .For;
var backLoop = dfor.Loop;
Assert.AreEqual(3, backLoop.Sequences.Count); // bit, states, delta
Assert.AreEqual(6, backLoop.Fors.Count); // dbit, dstate, dWstate, db, dWbit, dstate_p1
Assert.AreEqual(3, dfor.Index);
// TODO: check why a recursive was expected
//var dWstate_ = dfor.RecursiveVariable;
//Assert.AreEqual("dWstate_", dWstate_.Name);
var variables = backLoop.Variables.Cast <Tensor <float> >().ToList();
var bit_ = variables[0];
Assert.AreEqual("bit_", bit_.Name);
var oldState_ = variables[1];
Assert.AreEqual("oldState_", oldState_.Name);
var delta_oldState_ = variables[2];
Assert.AreEqual("delta_oldState_", delta_oldState_.Name);
var dbit_ = variables[3];
Assert.AreEqual("dbit_", dbit_.Name);
var doldState_ = variables[4];
Assert.AreEqual("doldState_", doldState_.Name);
var oldState_tp1_ = variables[5];
Assert.AreEqual("oldState_tp1", oldState_tp1_.Name);
var d = T.Sum((delta_oldState_ + doldState_) * (1f - T.Square(oldState_tp1_)), axis: 1, keepDims: true);
var doldState = (Tensor <float>)backLoop.Fors[1].Expression;
(T.Dot(Wstate, d, transposeX: true)).AssertEqual(doldState);
var dWstate = (Tensor <float>)backLoop.Fors[3].Expression;
var dWstateExp = T.Dot(d, oldState_, transposeY: true);
dWstateExp.AssertEqual(dWstate);
var dbit = (Tensor <float>)backLoop.Fors[0].Expression;
(T.Dot(Wbit, d, transposeX: true)).StructuralEquality(dbit);
var oldState_tp1 = (Tensor <float>)backLoop.Fors[5].Expression;
oldState_tp1.AssertEqual(oldState_);
}
/// <summary></summary>
/// <param name="inputDim">dimension of the input vectors</param>
/// <param name="hiddenDim">dimension of the hidden layer</param>
/// <param name="outputDim">dimension of the output vector</param>
/// <param name="scale">scaling factor to initialize weights</param>
public GRU(int inputDim, int hiddenDim, int outputDim, float scale = 0.2f)
{
// initial hidden state
h0 = T.Shared(NN.Zeros <float>(hiddenDim), "h0");
// reset gate layers
Wr = T.Shared(NN.Random.Uniform(-scale, scale, inputDim, hiddenDim), "Wr");
Ur = T.Shared(NN.Eye <float>(hiddenDim), "Ur");
br = T.Shared(NN.Zeros <float>(/*1,*/ hiddenDim), "br");
// update gate layers
Wz = T.Shared(NN.Random.Uniform(-scale, scale, inputDim, hiddenDim), "Wz");
Uz = T.Shared(NN.Eye <float>(hiddenDim), "Uz");
bz = T.Shared(NN.Zeros <float>(/*1,*/ hiddenDim), "bz");
// layers
W = T.Shared(NN.Random.Uniform(-scale, scale, inputDim, hiddenDim), "W");
U = T.Shared(NN.Eye <float>(hiddenDim), "U");
b = T.Shared(NN.Zeros <float>(/*1,*/ hiddenDim), "b");
// prediction layer
S = T.Shared(NN.Random.Uniform(-scale, scale, hiddenDim, outputDim), "S");
Sb = T.Shared(NN.Zeros <float>(/*1,*/ outputDim), "Sb");
// bundle
this.@params = new[] { h0, Wr, Ur, br, Wz, Uz, bz, W, U, b, S, Sb };
// Adagrad shared variables
this.grads = new Dictionary <string, Tensor <float> .Shared>();
foreach (var param in @params)
{
var name = param.Name + "Grad";
this.grads[name] = T.Shared(NN.Zeros <float>(param.Value.Shape), name);
}
this.hists = new Dictionary <string, Tensor <float> .Shared>();
foreach (var param in @params)
{
var name = param.Name + "Hist";
this.hists[name] = T.Shared(NN.Zeros <float>(param.Value.Shape), name);
}
// Adadelta shared variables
var hists2 = new Dictionary <string, Tensor <float> .Shared>();
foreach (var param in @params)
{
var name = param.Name + "Hist2";
hists2[name] = T.Shared(NN.Zeros <float>(param.Value.Shape), name);
}
var x = T.Matrix <float>("x"); // [sentence, inputDim]
var expected = T.Vector <float>("expected");
Func <Tensor <float>, Tensor <float>, Tensor <float>[]> recurrence = (x_t, h_tm1) =>
{
// reset gate
var r_t = T.Sigmoid(T.Dot(x_t, Wr) + T.Dot(h_tm1, Ur) + br);
// update gate
var z_t = T.Sigmoid(T.Dot(x_t, Wz) + T.Dot(h_tm1, Uz) + bz);
// proposed hidden state
var _h_t = T.Tanh(T.Dot(x_t, W) + T.Dot(r_t * h_tm1, U) + b);
// actual hidden state
var h_t = z_t * h_tm1 + (1 - z_t) * _h_t;
// return all the intermediate variables because they may be reused by T.Grad to optimize gradient computation
return(new[] { h_t, r_t, z_t, _h_t });
};
var h = T.Scan(recurrence, x, new[] { h0, null, null, null })[0][-1];
// cost and gradients
var output = T.Dot(h, S) + Sb;
var error = 0.5f * T.Norm2(output - expected);
var gradients = T.Grad(error);
var updatesTrain = new OrderedDictionary();
foreach (var param in @params)
{
var grad = gradients[param];
//var grad = T.Clip(update.Item2, -10, 10);
// Adagrad
//const float eps = 1e-5f;
var g = grads[param.Name + "Grad"];
updatesTrain[g] = g + grad;
//updates[param] = param - lr * grad / T.Sqrt(hist + eps);
// Adadelta
//const float rho = 0.95f;
//const float eps = 1e-5f;
//var hist = hists[param.Name + "Hist"];
//var hist2 = hists2[param.Name + "Hist2"];
//var newHist = rho * hist + (1 - rho) * (grad * grad);
//updates[hist] = newHist;
//var newGrad = grad * T.Sqrt((hist2 + eps) / (newHist + eps));
//updates[param] = param - newGrad;
//updates[hist2] = rho * hist2 + (1 - rho) * (newGrad * newGrad);
// Regular
//updates[param] = param - lr * grad;
}
var batchSize = T.Scalar <float>("batchSize");
var lr = T.Scalar <float>("lr");
const float eps = 1e-5f;
var updates = new OrderedDictionary();
foreach (var param in this.@params)
{
var grad = this.grads[param.Name + "Grad"];
var meanGrad = grad / batchSize;
var hist = this.hists[param.Name + "Hist"];
updates[hist] = hist + meanGrad * meanGrad;
updates[param] = param - lr * meanGrad / T.Sqrt(hist + eps);
updates[grad] = T.ZerosLike(grad);
}
// theano functions
this.Classify = T.Function(input: x, output: output);
this.Train = T.Function(input: (x, expected),
output: error,
updates: updatesTrain);
this.Update = T.Function(input: (lr, batchSize), updates: updates);
}