// Forward Propagation
public void Forward(ManagedArray training)
{
// add bias column to input layer
var InputBias = new ManagedArray(1, training.y);
ManagedOps.Set(InputBias, 1.0);
// x = cbind(array(1, c(nrow(training_set), 1)), training_set)
var x = ManagedMatrix.CBind(InputBias, training);
// compute hidden layer activation
// z_2 = x %*% t(w_ji)
var tWji = new ManagedArray(Wji.y, Wji.x);
ManagedMatrix.Transpose(tWji, Wji);
Z2 = new ManagedArray(tWji.x, x.y);
ManagedMatrix.Multiply(Z2, x, tWji);
// z_j = nnet_sigmoid(z_2)
var Zj = ManagedMatrix.Sigm(Z2);
// add bias column to hidden layer output
var HiddenBias = new ManagedArray(1, Zj.y);
ManagedOps.Set(HiddenBias, 1.0);
// a_2 = cbind(array(1, c(nrow(z_j), 1)), z_j)
A2 = ManagedMatrix.CBind(HiddenBias, Zj);
// compute output layer
var tWkj = new ManagedArray(Wkj.y, Wkj.x);
ManagedMatrix.Transpose(tWkj, Wkj);
// y_k = nnet_sigmoid(a_2 %*% t(w_kj))
var A2Wkj = new ManagedArray(tWkj.x, A2.y);
ManagedMatrix.Multiply(A2Wkj, A2, tWkj);
Yk = ManagedMatrix.Sigm(A2Wkj);
// cleanup
ManagedOps.Free(A2Wkj, HiddenBias, InputBias);
ManagedOps.Free(tWkj, tWji, x, Zj);
}
// Forward Propagation
public void Forward(ManagedArray input)
{
// create bias column
var InputBias = new ManagedArray(1, input.y, false);
ManagedOps.Set(InputBias, 1.0);
// Compute input activations
var last = Weights.GetLength(0) - 1;
for (var layer = 0; layer < Weights.GetLength(0); layer++)
{
var XX = layer == 0 ? ManagedMatrix.CBind(InputBias, input) : ManagedMatrix.CBind(InputBias, Activations[layer - 1]);
var tW = ManagedMatrix.Transpose(Weights[layer]);
var ZZ = ManagedMatrix.Multiply(XX, tW);
X[layer] = XX;
Z[layer] = ZZ;
if (layer != last)
{
var SS = ManagedMatrix.Sigm(ZZ);
Activations[layer] = SS;
}
else
{
ManagedOps.Free(Y);
Y = ManagedMatrix.Sigm(ZZ);
}
ManagedOps.Free(tW);
}
// Cleanup
for (var layer = 0; layer < Activations.GetLength(0); layer++)
{
ManagedOps.Free(Activations[layer]);
}
ManagedOps.Free(InputBias);
}
// Backward propagation
public void BackPropagation(ManagedArray training)
{
// add bias column to input layer
var InputBias = new ManagedArray(1, training.y);
ManagedOps.Set(InputBias, 1.0);
// x = cbind(array(1, c(nrow(training_set), 1)), training_set)
var x = ManagedMatrix.CBind(InputBias, training);
// compute intermediate delta values per layer
// d3 = y_k - y_matrix
var D3 = ManagedMatrix.Diff(Yk, Y_output);
// d2 = d3 %*% w_kj[, 2:ncol(w_kj)] * nnet_dsigmoid(z_2)
var sWkj = new ManagedArray(Wkj.x - 1, Wkj.y);
ManagedOps.Copy2D(sWkj, Wkj, 1, 0);
var D2 = new ManagedArray(sWkj.x, D3.y);
ManagedMatrix.Multiply(D2, D3, sWkj);
var DZ2 = ManagedMatrix.DSigm(Z2);
ManagedMatrix.Product(D2, DZ2);
// dWji = (t(d2) %*% x)
// dWkj = (t(d3) % *% a_2)
var tD2 = new ManagedArray(D2.y, D2.x);
var tD3 = new ManagedArray(D3.y, D3.x);
ManagedMatrix.Transpose(tD2, D2);
ManagedMatrix.Transpose(tD3, D3);
DeltaWji = new ManagedArray(Wji.x, Wji.y);
DeltaWkj = new ManagedArray(Wkj.x, Wkj.y);
ManagedMatrix.Multiply(DeltaWji, tD2, x);
ManagedMatrix.Multiply(DeltaWkj, tD3, A2);
// cost = sum(-y_matrix * log(y_k) - (1 - y_matrix) * log(1 - y_k))
Cost = 0.0;
L2 = 0.0;
for (var i = 0; i < Y_output.Length(); i++)
{
L2 += 0.5 * (D3[i] * D3[i]);
Cost += (-Y_output[i] * Math.Log(Yk[i]) - (1 - Y_output[i]) * Math.Log(1 - Yk[i]));
}
// cost = cost / m
// dWji = dWji / m
// dWkj = dWkj / m
Cost /= training.y;
L2 /= training.y;
ManagedMatrix.Multiply(DeltaWji, 1.0 / training.y);
ManagedMatrix.Multiply(DeltaWkj, 1.0 / training.y);
// cleanup
ManagedOps.Free(D2, D3, DZ2, InputBias);
ManagedOps.Free(sWkj, tD2, tD3, x);
// cleanup of arrays allocated in Forward
ManagedOps.Free(A2, Yk, Z2);
}
// Update Network Weights based on computed errors
public void BackPropagation(ManagedArray batch)
{
var n = Layers.Count;
var last = n - 1;
var batchz = Layers[last].Activation.z;
// backprop deltas
ManagedOps.Free(OutputDelta, OutputError);
OutputDelta = new ManagedArray(Output, false);
OutputError = new ManagedArray(Output, false);
for (var x = 0; x < Output.Length(); x++)
{
// error
OutputError[x] = Output[x] - batch[x];
// output delta
OutputDelta[x] = OutputError[x] * (Output[x] * (1 - Output[x]));
}
// Loss Function
L = 0.5 * ManagedMatrix.SquareSum(OutputError) / batch.x;
ManagedOps.Free(WeightsTransposed, FeatureVectorDelta);
FeatureVectorDelta = new ManagedArray(FeatureVector, false);
WeightsTransposed = new ManagedArray(Weights, false);
// feature vector delta
ManagedMatrix.Transpose(WeightsTransposed, Weights);
ManagedMatrix.Multiply(FeatureVectorDelta, WeightsTransposed, OutputDelta);
// only conv layers has sigm function
if (Layers[last].Type == LayerTypes.Convolution)
{
for (var x = 0; x < FeatureVectorDelta.Length(); x++)
{
FeatureVectorDelta[x] = FeatureVectorDelta[x] * FeatureVector[x] * (1 - FeatureVector[x]);
}
}
// reshape feature vector deltas into output map style
var MapSize = Layers[last].Activation.x * Layers[last].Activation.y;
var temp1D = new ManagedArray(1, MapSize, false);
var temp2D = new ManagedArray(Layers[last].Activation.x, Layers[last].Activation.y, false);
ManagedOps.Free(Layers[last].Delta);
Layers[last].Delta = new ManagedArray(Layers[last].Activation, false);
for (var j = 0; j < Layers[last].Activation.i; j++)
{
for (var ii = 0; ii < batchz; ii++)
{
ManagedOps.Copy2D(temp1D, FeatureVectorDelta, ii, j * MapSize);
temp1D.Reshape(Layers[last].Activation.x, Layers[last].Activation.y);
ManagedMatrix.Transpose(temp2D, temp1D);
ManagedOps.Copy2D4D(Layers[last].Delta, temp2D, ii, j);
temp1D.Reshape(1, MapSize);
}
}
ManagedOps.Free(temp1D, temp2D);
for (var l = n - 2; l >= 0; l--)
{
var next = l + 1;
if (Layers[l].Type == LayerTypes.Convolution)
{
ManagedOps.Free(Layers[l].Delta);
Layers[l].Delta = new ManagedArray(Layers[l].Activation, false);
var xx = Layers[next].Scale * Layers[next].Activation.x;
var yy = Layers[next].Scale * Layers[next].Activation.y;
var FeatureMap = new ManagedArray(Layers[next].Activation.x, Layers[next].Activation.y, false);
var FeatureMapExpanded = new ManagedArray(xx, yy, false);
var Activation = new ManagedArray(xx, yy, false);
var Delta = new ManagedArray(xx, yy, false);
var Scale = (1.0 / (Layers[next].Scale * Layers[next].Scale));
for (var j = 0; j < Layers[l].Activation.i; j++)
{
for (var z = 0; z < batchz; z++)
{
ManagedOps.Copy4D2D(FeatureMap, Layers[next].Delta, z, j);
ManagedMatrix.Expand(FeatureMap, Layers[next].Scale, Layers[next].Scale, FeatureMapExpanded);
ManagedOps.Copy4D2D(Activation, Layers[l].Activation, z, j);
for (var x = 0; x < Delta.Length(); x++)
{
Delta[x] = Activation[x] * (1 - Activation[x]) * FeatureMapExpanded[x] * Scale;
}
ManagedOps.Copy2D4D(Layers[l].Delta, Delta, z, j);
}
}
ManagedOps.Free(FeatureMap, FeatureMapExpanded, Activation, Delta);
}
else if (Layers[l].Type == LayerTypes.Subsampling)
{
ManagedOps.Free(Layers[l].Delta);
Layers[l].Delta = new ManagedArray(Layers[l].Activation, false);
var Delta = new ManagedArray(Layers[next].Activation.x, Layers[next].Activation.y, batchz);
var FeatureMap = new ManagedArray(Layers[next].KernelSize, Layers[next].KernelSize, false);
var rot180 = new ManagedArray(Layers[next].KernelSize, Layers[next].KernelSize, false);
var z = new ManagedArray(Layers[l].Activation.x, Layers[l].Activation.y, batchz);
var ztemp = new ManagedArray(Layers[l].Activation.x, Layers[l].Activation.y, batchz, false);
for (var i = 0; i < Layers[l].Activation.i; i++)
{
ManagedOps.Set(z, 0.0);
for (var j = 0; j < Layers[next].Activation.i; j++)
{
ManagedOps.Copy4DIJ2D(FeatureMap, Layers[next].FeatureMap, i, j);
ManagedMatrix.Rotate180(rot180, FeatureMap);
ManagedOps.Copy4D3D(Delta, Layers[next].Delta, j);
ManagedConvolution.Full(Delta, rot180, ztemp);
ManagedMatrix.Add(z, ztemp);
}
ManagedOps.Copy3D4D(Layers[l].Delta, z, i);
}
ManagedOps.Free(Delta, FeatureMap, rot180, z, ztemp);
}
}
// calc gradients
for (var l = 1; l < n; l++)
{
var prev = l - 1;
if (Layers[l].Type == LayerTypes.Convolution)
{
ManagedOps.Free(Layers[l].DeltaFeatureMap, Layers[l].DeltaBias);
Layers[l].DeltaFeatureMap = new ManagedArray(Layers[l].FeatureMap, false);
Layers[l].DeltaBias = new ManagedArray(Layers[l].OutputMaps, false);
var FeatureMapDelta = new ManagedArray(Layers[l].FeatureMap.x, Layers[l].FeatureMap.y, Layers[l].FeatureMap.z, false);
// d[j]
var dtemp = new ManagedArray(Layers[l].Activation.x, Layers[l].Activation.y, batchz, false);
// a[i] and flipped
var atemp = new ManagedArray(Layers[prev].Activation.x, Layers[prev].Activation.y, batchz, false);
var ftemp = new ManagedArray(Layers[prev].Activation.x, Layers[prev].Activation.y, batchz, false);
for (var j = 0; j < Layers[l].Activation.i; j++)
{
ManagedOps.Copy4D3D(dtemp, Layers[l].Delta, j);
for (var i = 0; i < Layers[prev].Activation.i; i++)
{
ManagedOps.Copy4D3D(atemp, Layers[prev].Activation, i);
ManagedMatrix.FlipAll(ftemp, atemp);
ManagedConvolution.Valid(ftemp, dtemp, FeatureMapDelta);
ManagedMatrix.Multiply(FeatureMapDelta, 1.0 / batchz);
ManagedOps.Copy2D4DIJ(Layers[l].DeltaFeatureMap, FeatureMapDelta, i, j);
}
Layers[l].DeltaBias[j] = ManagedMatrix.Sum(dtemp) / batchz;
}
ManagedOps.Free(FeatureMapDelta, dtemp, atemp, ftemp);
}
}
var FeatureVectorTransposed = new ManagedArray(FeatureVector, false);
ManagedMatrix.Transpose(FeatureVectorTransposed, FeatureVector);
ManagedOps.Free(WeightsDelta, BiasDelta);
WeightsDelta = new ManagedArray(Weights, false);
BiasDelta = new ManagedArray(Bias, false);
ManagedMatrix.Multiply(WeightsDelta, OutputDelta, FeatureVectorTransposed);
ManagedMatrix.Multiply(WeightsDelta, 1.0 / batchz);
ManagedMatrix.Mean(BiasDelta, OutputDelta, 0);
ManagedOps.Free(FeatureVectorTransposed);
}
// Compute Forward Transform on 3D Input
public void FeedForward(ManagedArray batch, bool pool = false)
{
var n = Layers.Count;
var last = n - 1;
var InputMaps = 1;
ManagedOps.Free(Layers[0].Activation);
Layers[0].Activation = new ManagedArray(batch, false);
ManagedOps.Copy4D3D(Layers[0].Activation, batch, 0);
for (var l = 1; l < n; l++)
{
var prev = l - 1;
if (Layers[l].Type == LayerTypes.Convolution)
{
var zx = Layers[prev].Activation.x - Layers[l].KernelSize + 1;
var zy = Layers[prev].Activation.y - Layers[l].KernelSize + 1;
var zz = batch.z;
ManagedOps.Free(Layers[l].Activation);
Layers[l].Activation = new ManagedArray(zx, zy, zz, Layers[l].OutputMaps, 1, false);
var Activation = new ManagedArray(Layers[prev].Activation.x, Layers[prev].Activation.y, batch.z, false);
var FeatureMap = new ManagedArray(Layers[l].KernelSize, Layers[l].KernelSize, false);
// create temp output map
var z = new ManagedArray(zx, zy, zz);
var ztemp = new ManagedArray(zx, zy, zz, false);
// !!below can probably be handled by insane matrix operations
for (var j = 0; j < Layers[l].OutputMaps; j++) // for each output map
{
ManagedOps.Set(z, 0.0);
for (var i = 0; i < InputMaps; i++)
{
// copy Layers
ManagedOps.Copy4D3D(Activation, Layers[prev].Activation, i);
ManagedOps.Copy4DIJ2D(FeatureMap, Layers[l].FeatureMap, i, j);
// convolve with corresponding kernel and add to temp output map
ManagedConvolution.Valid(Activation, FeatureMap, ztemp);
ManagedMatrix.Add(z, ztemp);
}
// add bias, pass through nonlinearity
ManagedMatrix.Add(z, Layers[l].Bias[j]);
var sigm = ManagedMatrix.Sigm(z);
ManagedOps.Copy3D4D(Layers[l].Activation, sigm, j);
ManagedOps.Free(sigm);
}
ManagedOps.Free(Activation, FeatureMap, z, ztemp);
InputMaps = Layers[l].OutputMaps;
}
else if (Layers[l].Type == LayerTypes.Subsampling)
{
// downsample
// generate downsampling kernel
var scale = (double)(Layers[l].Scale * Layers[l].Scale);
var FeatureMap = new ManagedArray(Layers[l].Scale, Layers[l].Scale, false);
ManagedOps.Set(FeatureMap, 1.0 / scale);
ManagedOps.Free(Layers[l].Activation);
Layers[l].Activation = new ManagedArray(Layers[prev].Activation.x / Layers[l].Scale, Layers[prev].Activation.y / Layers[l].Scale, batch.z, InputMaps, 1);
var Activation = new ManagedArray(Layers[prev].Activation.x, Layers[prev].Activation.y, batch.z, false);
var z = new ManagedArray(Layers[prev].Activation.x - Layers[l].Scale + 1, Layers[prev].Activation.y - Layers[l].Scale + 1, batch.z, false);
for (var j = 0; j < InputMaps; j++)
{
// copy Layers
ManagedOps.Copy4D3D(Activation, Layers[prev].Activation, j);
// Subsample
ManagedConvolution.Valid(Activation, FeatureMap, z);
if (pool)
{
ManagedOps.Pool3D4D(Layers[l].Activation, z, j, Layers[l].Scale);
}
else
{
ManagedOps.Copy3D4D(Layers[l].Activation, z, j, Layers[l].Scale);
}
}
ManagedOps.Free(Activation, FeatureMap, z);
}
}
var MapSize = Layers[last].Activation.x * Layers[last].Activation.y;
ManagedOps.Free(FeatureVector);
FeatureVector = new ManagedArray(batch.z, MapSize * Layers[last].Activation.i);
var temp1D = new ManagedArray(Layers[last].Activation.y, Layers[last].Activation.x, false);
var temp2D = new ManagedArray(Layers[last].Activation.x, Layers[last].Activation.y, false);
// concatenate all end layer feature maps into vector
for (var j = 0; j < Layers[last].Activation.i; j++)
{
for (var ii = 0; ii < batch.z; ii++)
{
// Use Row-major in flattening the feature map
ManagedOps.Copy4D2D(temp2D, Layers[last].Activation, ii, j);
ManagedMatrix.Transpose(temp1D, temp2D);
temp1D.Reshape(1, MapSize);
ManagedOps.Copy2DOffset(FeatureVector, temp1D, ii, j * MapSize);
}
}
var WeightsFeatureVector = new ManagedArray(FeatureVector.x, Weights.y, false);
ManagedMatrix.Multiply(WeightsFeatureVector, Weights, FeatureVector);
var repmat = new ManagedArray(batch.z, Bias.Length(), false);
ManagedMatrix.Expand(Bias, batch.z, 1, repmat);
ManagedMatrix.Add(WeightsFeatureVector, repmat);
// feedforward into output perceptrons
ManagedOps.Free(Output);
Output = ManagedMatrix.Sigm(WeightsFeatureVector);
ManagedOps.Free(WeightsFeatureVector, repmat, temp1D, temp2D);
}