public Tensor categorical_crossentropy(Tensor target, Tensor output, bool from_logits = false)
{
// https://github.com/fchollet/keras/blob/f65a56fb65062c8d14d215c9f4b1015b97cc5bf3/keras/backend/cntk_backend.py#L1480
var _output = In(output);
var _target = In(target);
if (from_logits)
{
var result = C.CrossEntropyWithSoftmax(_output, _target);
// cntk's result shape is (batch, 1), while keras expect (batch, )
CNTK.Function r = C.Reshape(result, NDShape.CreateNDShape(new int[] { }));
return(Out(r));
}
else
{
// scale preds so that the class probas of each sample sum to 1
var o = C.ElementDivide(_output.function, C.ReduceSum(_output, Axis.EndStaticAxis()));
var eps = Constant.Scalar(epsilon(), DeviceDescriptor.CPUDevice);
var omeps = Constant.Scalar(1.0 - epsilon(), DeviceDescriptor.CPUDevice);
// avoid numerical instability with _EPSILON clipping
o = C.Clip(o, eps, omeps);
CNTK.Function r = C.Negate(C.ReduceSum(C.ElementTimes(_target, C.Log(_output)), Axis.EndStaticAxis()));
return(Out(r));
}
}
C.Function get_length_and_remove_last_dimension(C.Function x, string name)
{
var number_dimensions = x.Output.Shape.Dimensions.Count;
x = CC.Square(x);
var sum_entries = CC.ReduceSum(x, new C.Axis(number_dimensions - 1));
var epsilon = C.Constant.Scalar(C.DataType.Float, 1e-7, computeDevice);
x = CC.Sqrt(CC.Plus(sum_entries, epsilon));
x = CC.Squeeze(x);
return(x);
}
C.Function squash(C.Function vectors, string name, int axis)
{
var squared_values = CC.Square(vectors);
var s_squared_sum = CC.ReduceSum(squared_values, new C.AxisVector(new C.Axis[] { new C.Axis(axis) }), keepDims: true);
var epsilon = C.Constant.Scalar(C.DataType.Float, 1e-7, computeDevice);
var one = C.Constant.Scalar(C.DataType.Float, 1.0, computeDevice);
var normalize_factor = CC.Plus(CC.Sqrt(s_squared_sum), epsilon);
var one_plus_s_squared_sum = CC.Plus(s_squared_sum, one);
var scale = CC.ElementDivide(s_squared_sum, one_plus_s_squared_sum);
scale = CC.ElementDivide(scale, normalize_factor);
var result = CC.ElementTimes(scale, vectors, name);
return(result);
}
C.Function create_capsule_layer(C.Function inputs, int num_capsule, int dim_capsule, int routings, string name)
{
var inputs_shape = inputs.Output.Shape.Dimensions;
var input_num_capsule = inputs_shape[0];
var input_dim_capsule = inputs_shape[1];
var W = new C.Parameter(
new int[] { num_capsule, dim_capsule, input_num_capsule, input_dim_capsule },
C.DataType.Float,
CC.GlorotUniformInitializer(),
computeDevice,
name: "W");
inputs = CC.Reshape(inputs, new int[] { 1, 1, input_num_capsule, input_dim_capsule }); // [1, 1, 1152, 8])
var inputs_hat = CC.ElementTimes(W, inputs);
inputs_hat = CC.ReduceSum(inputs_hat, new C.Axis(3));
inputs_hat = CC.Squeeze(inputs_hat);
C.Function outputs = null;
var zeros = new C.Constant(new int[] { num_capsule, 1, input_num_capsule }, C.DataType.Float, 0, computeDevice);
var b = CC.Combine(new C.VariableVector()
{
zeros
});
for (int i = 0; i < routings; i++)
{
var c = CC.Softmax(b, new C.Axis(0));
var batch_dot_result = CC.ElementTimes(c, inputs_hat);
batch_dot_result = CC.ReduceSum(batch_dot_result, new C.Axis(2));
batch_dot_result = CC.Squeeze(batch_dot_result);
outputs = squash(batch_dot_result, name: $"squashed_{i}", axis: 1);
if (i < (routings - 1))
{
outputs = CC.Reshape(outputs, new int[] { num_capsule, dim_capsule, 1 });
batch_dot_result = CC.ElementTimes(outputs, inputs_hat);
batch_dot_result = CC.ReduceSum(batch_dot_result, new C.Axis(1));
b = CC.Plus(b, batch_dot_result);
}
}
outputs = CC.Combine(new C.VariableVector()
{
outputs
}, name);
return(outputs);
}
C.Function get_mask_and_infer_from_last_dimension(C.Function inputs, C.Function mask)
{
if (mask == null)
{
var inputs_shape = inputs.Output.Shape.Dimensions.ToArray();
var ndims = inputs_shape.Length - 1;
var x = CC.Sqrt(CC.ReduceSum(CC.Square(inputs), new C.Axis(ndims - 1)));
x = CC.Squeeze(x);
System.Diagnostics.Debug.Assert(x.Output.Shape.Dimensions.Count == 1);
x = CC.Argmax(x, new C.Axis(0));
mask = CC.OneHotOp(x, numClass: (uint)inputs_shape[0], outputSparse: false, axis: new C.Axis(0));
}
mask = CC.Reshape(mask, mask.Output.Shape.AppendShape(new int[] { 1 }));
var masked = CC.ElementTimes(inputs, mask);
masked = CC.Flatten(masked);
masked = CC.Squeeze(masked);
return(masked);
}
public Tensor Sum(Tensor x, int dim)
{
dim = dim < 0 ? x.DimCount + dim : dim;
return(Out(C.ReduceSum(In(x), new Axis(dim))));
}
public float Sum(Tensor x)
{
return(Out(C.ReduceSum(In(x), Axis.AllAxes())).ToScalar());
}
void create_network()
{
imageVariable = Util.inputVariable(input_shape, "image");
var conv1 = Layers.Convolution2D(
imageVariable, 256, new int[] { 9, 9 }, computeDevice,
use_padding: false, activation: CC.ReLU, name: "conv1");
var primarycaps = create_primary_cap(
conv1, dim_capsule: 8, n_channels: 32,
kernel_size: new int[] { 9, 9 }, strides: new int[] { 2, 2 }, pad: false);
var digitcaps = create_capsule_layer(
primarycaps, num_capsule: 10, dim_capsule: 16,
routings: routings, name: "digitcaps");
var out_caps = get_length_and_remove_last_dimension(digitcaps, name: "capsnet");
categoricalLabel = Util.inputVariable(new int[] { 10 }, "label");
var masked_by_y = get_mask_and_infer_from_last_dimension(digitcaps, CC.Combine(new C.VariableVector()
{
categoricalLabel
}));
var masked = get_mask_and_infer_from_last_dimension(digitcaps, null);
var decoder = create_decoder(masked.Output.Shape.Dimensions.ToArray());
var decoder_output_training = Model.invoke_model(decoder, new C.Variable[] { masked_by_y });
var decoder_output_evaluation = Model.invoke_model(decoder, new C.Variable[] { masked });
network = CC.Combine(new C.VariableVector()
{
out_caps, decoder_output_training
}, "overall_training_network");
Logging.log_number_of_parameters(network);
// first component of the loss
var y_true = categoricalLabel;
var y_pred = out_caps;
var digit_loss = CC.Plus(
CC.ElementTimes(y_true, CC.Square(CC.ElementMax(DC(0), CC.Minus(DC(0.9), y_pred), ""))),
CC.ElementTimes(DC(0.5),
CC.ElementTimes(CC.Minus(DC(1), y_true), CC.Square(CC.ElementMax(DC(0), CC.Minus(y_pred, DC(0.1)), "")))));
digit_loss = CC.ReduceSum(digit_loss, C.Axis.AllStaticAxes());
// second component of the loss
var num_pixels_at_output = Util.np_prod(decoder_output_training.Output.Shape.Dimensions.ToArray());
var squared_error = CC.SquaredError(decoder_output_training, imageVariable);
var image_mse = CC.ElementDivide(squared_error, DC(num_pixels_at_output));
loss_function = CC.Plus(digit_loss, CC.ElementTimes(DC(0.35), image_mse));
eval_function = CC.ClassificationError(y_pred, y_true);
learner = CC.AdamLearner(
new C.ParameterVector(network.Parameters().ToArray()),
new C.TrainingParameterScheduleDouble(0.001 * batch_size, (uint)batch_size),
new C.TrainingParameterScheduleDouble(0.9),
true,
new C.TrainingParameterScheduleDouble(0.99));
trainer = CC.CreateTrainer(network, loss_function, eval_function, new C.LearnerVector(new C.Learner[] { learner }));
evaluator = CC.CreateEvaluator(eval_function);
}
public Tensor Sum(Tensor x, int dim)
{
dim = CorrDim(x.DimCount, dim);
return(Out(C.ReduceSum(In(x), new Axis(dim))));
}
