Class: TensorStream::MathGradients

Inherits:
Object
  • Object
show all
Extended by:
OpHelper
Defined in:
lib/tensor_stream/math_gradients.rb

Overview

Class that provides auto-differentiation Most gradients are ported over from tensorflow’s math_grad.py

Class Method Summary collapse

Methods included from OpHelper

_op, cons, format_source, fp_type?, i_cons, i_op, i_var, int_type?, reduced_shape, shape_eval, shape_full_specified, shapes_fully_specified_and_equal

Class Method Details

._broadcast_gradient_args(input_a, input_b) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 178

def self._broadcast_gradient_args(input_a, input_b)
  res = _op(:broadcast_gradient_args, input_a, input_b)
  [res[0], res[1]]
end

._broadcast_mul(vec, mat) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 224

def self._broadcast_mul(vec, mat)
  vec = ts.expand_dims(vec, -1)
  vec * mat
end

._broadcast_transform(input_a, input_b) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 183

def self._broadcast_transform(input_a, input_b)
  _op(:broadcast_transform, input_a, input_b)
end

._compute_derivative(node, grad) ⇒ Object

TODO: refactor and implement registerGradient



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# File 'lib/tensor_stream/math_gradients.rb', line 52

def self._compute_derivative(node, grad)
  node.graph.name_scope("#{node.name}_grad") do
    x = node.inputs[0] if node.inputs[0]
    y = node.inputs[1] if node.inputs[1]
    z = node.inputs[2] if node.inputs[2]

    case node.operation
    when :add_n
      return [grad] * node.inputs.size
    when :asin
      ts.control_dependencies([grad]) do
        x2 = ts.square(x)
        one = ts.constant(1, dtype: grad.data_type)
        den = ts.sqrt(ts.subtract(one, x2))
        inv = ts.reciprocal(den)
        grad * inv
      end
    when :acos
      ts.control_dependencies([grad]) do
        x2 = ts.square(x)
        one = ts.constant(1, dtype: grad.data_type)
        den = ts.sqrt(ts.subtract(one, x2))
        inv = ts.reciprocal(den)
        -grad * inv
      end
    when :atan
      ts.control_dependencies([grad]) do
        x2 = ts.square(x)
        one = ts.constant(1, dtype: grad.data_type)
        inv = ts.reciprocal(ts.add(one, x2))
        grad * inv
      end
    when :squared_difference
      sx = i_op(:shape, x)
      sy = i_op(:shape, y)
      rx, ry = _broadcast_gradient_args(sx, sy)

      x_grad = ts.mul(2.0, grad) * (x - y)

      [ts.reshape(ts.reduce_sum(x_grad, rx), sx),
       ts.reshape(-ts.reduce_sum(x_grad, ry), sy),]
    when :abs
      grad * ts.sign(x)
    when :exp
      grad * node
    when :identity, :print
      grad
    when :tile
      input_shape = ts.shape(x)
      split_shape = ts.reshape(ts.transpose(ts.stack([y, input_shape])), [-1])
      axes = ts.range(0, ts.size(split_shape), 2)
      input_grad = ts.reduce_sum(ts.reshape(grad, split_shape), axes)

      [input_grad, nil]
    when :reciprocal
      -grad * (ts.constant(1, dtype: x.dtype) / x**2)
    when :sqrt
      ts.constant(1, dtype: x.dtype) / (ts.constant(2, dtype: x.dtype) * ts.sqrt(x)) * grad
    when :stop_gradient
      ts.zeros_like(grad)
    when :square
      y = ts.constant(2.0, dtype: x.dtype)
      ts.multiply(grad, ts.multiply(x, y))
    when :where
      x_mask = i_op(:where, x, i_op(:ones_like, y), i_op(:zeros_like, z))
      y_mask = i_op(:where, x, i_op(:zeros_like, y), i_op(:ones_like, z))
      [nil, x_mask * grad, y_mask * grad]
    when :mean
      sum_grad = _sum_grad(x, y, grad)[0]
      input_shape = ts.shape(x)
      output_shape = ts.shape(node)
      factor = _safe_shape_div(ts.reduce_prod(input_shape), ts.reduce_prod(output_shape))
      [ts.div(sum_grad, ts.cast(factor, sum_grad.data_type)), nil]
    when :log1p
      grad * ts.reciprocal(i_cons(1, dtype: grad.data_type) + x)
    when :sigmoid_grad
      gb = grad * y
      [gb - 2.0 * gb * x, i_op(:sigmoid_grad, x, grad)]
    when :softmax
      i_op(:softmax_grad, x, grad)
    when :softmax_cross_entropy_with_logits_v2
      output = node
      logits = node.inputs[0]
      [_broadcast_mul(grad, output[1]), -ts.nn.log_softmax(logits)]
    when :sparse_softmax_cross_entropy_with_logits
      output = node
      [_broadcast_mul(grad, output[1]), nil]
     when :zeros_like
      # non differentiable
      nil
    when :transpose
      return [ts.transpose(grad, ts.invert_permutation(y)), nil]
    when :index
      # hack!! not sure how to fix this yet
      return grad if i[softmax_cross_entropy_with_logits_v2 sparse_softmax_cross_entropy_with_logits].include?(node.inputs[0].operation)

      if node.inputs[0].shape.known? && node.inputs[1].const_value
        multiplier = node.inputs[0].shape.shape[0]
        filler = ts.zeros_like(grad)

        res = Array.new(multiplier) { |index|
          index == node.inputs[1].const_value ? grad : filler
        }
        [res]
      end
    when :squeeze
      _reshape_to_input(node, grad)
    when :concat
      _concat_grad_helper(node, grad, 1, node.inputs.size, 0)
    when :stack
      res = ts.unstack(grad, num: node.inputs.size, axis: node.options[:axis])
      Array.new(node.inputs.size) { |i| res[i] }
    when :unstack
      ts.stack(grad, axis: node.options[:axis])
    when :conv2d
      _Conv2DGrad(node, grad)
    else
      TensorStream::OpMaker.gradient_op(self, node, grad)
    end
  end
end

._concat_grad_helper(op, grad, start_value_index, end_value_index, dim_index) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 253

def self._concat_grad_helper(op, grad, start_value_index, end_value_index, dim_index)
  # Degenerate concatenation, just return grad.
  if op.inputs.size == 2
    return end_value_index <= dim_index ? [grad] + [nil] : [nil] + [grad]
  end
  concat_dim = op.inputs[dim_index]
  input_values = op.inputs[start_value_index..end_value_index]
  non_neg_concat_dim = concat_dim % ts.rank(input_values[0])
  sizes = _extract_input_shapes(input_values)

  slicer = ts.slice(ts.stack(sizes, axis: 1), [non_neg_concat_dim, 0], [1, -1])
  sizes = ts.squeeze(slicer)

  out_grads = ts.split(grad, sizes, axis: non_neg_concat_dim, num: op.inputs.size - 1)
  end_value_index <= dim_index ? out_grads + [nil] : [nil] + out_grads
end

._Conv2DGrad(op, grad) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 270

def self._Conv2DGrad(op, grad)
  # dilations = op.get_attr("dilations")
  strides = op.options[:strides]
  padding = op.options[:padding]
  use_cudnn_on_gpu = op.options[:use_cudnn_on_gpu]
  data_format = op.options[:data_format]

  shape_0, shape_1 = ts.shape_n([op.inputs[0], op.inputs[1]])
  [
    _op(:conv2d_backprop_input,
      shape_0,
      op.inputs[1],
      grad,
      strides: strides,
        padding: padding,
        use_cudnn_on_gpu: use_cudnn_on_gpu,
        data_format: data_format),
    _op(:conv2d_backprop_filter,
      op.inputs[0],
      shape_1,
      grad,
      strides: strides,
      padding: padding,
      use_cudnn_on_gpu: use_cudnn_on_gpu,
      data_format: data_format),
  ]
end

._extract_input_shapes(inputs) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 234

def self._extract_input_shapes(inputs)
  sizes = []
  fully_known = true
  inputs.each do |x|
    input_shape = ts.shape(x)
    unless input_shape.is_const
      fully_known = false
      break
    end
    sizes << input_shape.value
  end

  if fully_known
    sizes
  else
    ts.shape_n(inputs)
  end
end

._include?(arr, obj) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/tensor_stream/math_gradients.rb', line 229

def self._include?(arr, obj)
  arr.each { |a| return true if a.equal?(obj) }
  false
end

._min_or_max_grad(inputs, grad, selector_op) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 207

def self._min_or_max_grad(inputs, grad, selector_op)
  x = inputs[0]
  y = inputs[1]
  gdtype = grad.data_type
  sx = ts.shape(x)
  sy = ts.shape(y)
  gradshape = ts.shape(grad)
  zeros = ts.zeros(gradshape, dtype: gdtype)
  xmask = selector_op.call(x, y)
  rx, ry = _broadcast_gradient_args(sx, sy)
  xgrad = ts.where(xmask, grad, zeros, name: "x")
  ygrad = ts.where(xmask, zeros, grad, name: "y")
  gx = ts.reshape(ts.reduce_sum(xgrad, rx), sx)
  gy = ts.reshape(ts.reduce_sum(ygrad, ry), sy)
  [gx, gy]
end

._op_supports_broadcast?(node) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/tensor_stream/math_gradients.rb', line 202

def self._op_supports_broadcast?(node)
  return true if i[add sub div mul pow].include?(node.operation)
  false
end

._propagate(grad, tensor, stop_tensor, nodes_to_compute, stop_gradients = []) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 25

def self._propagate(grad, tensor, stop_tensor, nodes_to_compute, stop_gradients = [])
  return grad if stop_tensor.equal?(tensor)
  return nil if stop_gradients && _include?(stop_gradients, tensor)
  return nil unless tensor.is_a?(Operation)

  computed_op = _compute_derivative(tensor, grad)

  if computed_op.is_a?(Array)
    grads = computed_op.each_with_index.collect { |op_grad, index|
      next if op_grad.nil?
      next unless nodes_to_compute.include?(tensor.inputs[index].name)

      _propagate(op_grad, tensor.inputs[index], stop_tensor, nodes_to_compute, stop_gradients)
    }.compact

    return nil if grads.empty?
    grads.size > 1 ? ts.add_n(grads) : grads[0]
  else

    if computed_op.nil?
      return nil
    end
    _propagate(computed_op, tensor.inputs[0], stop_tensor, nodes_to_compute, stop_gradients)
  end
end

._reshape_to_input(node, grad) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 174

def self._reshape_to_input(node, grad)
  ts.reshape(grad, ts.shape(node.inputs[0]))
end

._safe_shape_div(arg_x, arg_y) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 187

def self._safe_shape_div(arg_x, arg_y)
  _op(:floor_div, arg_x, ts.maximum(arg_y, 1))
end

._sum_grad(arg_x, arg_y, grad) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 191

def self._sum_grad(arg_x, arg_y, grad)
  input_shape = _op(:shape, arg_x)
  output_shape_kept_dims = ts.reduced_shape(input_shape, arg_y)
  tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
  new_grad = _op(:reshape, grad, output_shape_kept_dims)

  grad = _op(:case, [_op(:rank, grad).zero?], _op(:tile, new_grad, tile_scaling), _op(:fill, input_shape, grad))

  [grad, nil]
end

.derivative(tensor, wrt_dx, options = {}) ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 11

def self.derivative(tensor, wrt_dx, options = {})
  return i_op(:ones_like, tensor) if tensor.equal?(wrt_dx)
  return i_op(:zeros_like, wrt_dx) unless wrt_dx.consumers.include?(tensor.name)

  nodes_to_compute = wrt_dx.consumers.select { |t|
    node = tensor.graph.nodes[t]
    node.consumers.include?(tensor.name) || node.equal?(tensor)
  }.compact + [wrt_dx.name]

  grad = i_op(:fill, ts.shape(tensor), ts.constant(1, dtype: wrt_dx.data_type))

  _propagate(grad, tensor, wrt_dx, nodes_to_compute, options[:stop_gradients] || []) || i_op(:zeros_like, wrt_dx)
end

.ts ⇒ Object 



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# File 'lib/tensor_stream/math_gradients.rb', line 7

def self.ts
  TensorStream
end