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 337

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 383

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 342

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 :add
      return [grad, grad] if shapes_fully_specified_and_equal(x, y)
      sx = ts.shape(x, name: 'add/shape_x')
      sy = ts.shape(y, name: 'add/shape_y')
      rx, ry = _broadcast_gradient_args(sx, sy)

      [ts.reshape(ts.reduce_sum(grad, rx, name: 'add/reduce_sum_x'), sx),
       ts.reshape(ts.reduce_sum(grad, ry, name: 'add/reduce_sum_y'), sy)]
    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 :fill
      [nil, ts.reduce_sum(grad)]
    when :sub
      return [grad, -grad] if shapes_fully_specified_and_equal(x, y)

      sx = ts.shape(x, name: 'sub/shape_x')
      sy = ts.shape(y, name: 'sub/shape_y')
      rx, ry = _broadcast_gradient_args(sx, sy)

      [ts.reshape(ts.reduce_sum(grad, rx, name: 'add/reduce_sub_x'), sx),
       -ts.reshape(ts.reduce_sum(grad, ry, name: 'add/reduce_sub_y'), sy)]
    when :mul
      sx = ts.shape(x)
      sy = ts.shape(y)
      rx, ry = _broadcast_gradient_args(sx, sy)

      [ts.reshape(ts.reduce_sum(ts.mul(grad, y), rx), sx),
       ts.reshape(ts.reduce_sum(ts.mul(x, grad), ry), sy)]
    when :div
      sx = i_op(:shape, x)
      sy = i_op(:shape, y)
      rx, ry = _broadcast_gradient_args(sx, sy)

      [ts.reshape(ts.reduce_sum(ts.div(grad, y), rx), sx),
       ts.reshape(ts.reduce_sum(grad * ts.div(ts.div(-x, y), y), ry), sy)]
    when :mod
      sx = ts.shape(x)
      sy = ts.shape(y)
      rx, ry = _broadcast_gradient_args(sx, sy)
      floor_xy = ts.floor_div(x, y)
      gx = ts.reshape(ts.reduce_sum(grad, rx), sx)
      gy = ts.reshape(ts.reduce_sum(grad * ts.negative(floor_xy), ry), sy)

      [gx, gy]
    when :prod
      input_shape = ts.shape(x)
      y = ts.range(0, ts.rank(x)) if y.nil?
      reduction_indices = ts.reshape(y, [-1])

      output_shape_kept_dims = ts.reduced_shape(input_shape, y)
      tile_scaling = _safe_shape_div(input_shape, output_shape_kept_dims)
      grad = ts.reshape(grad, output_shape_kept_dims)
      grad = ts.tile(grad, tile_scaling)

      perm, reduced_num, other_num = ts.device("/cpu:0") do
        rank = ts.rank(x)
        reduction_indices = (reduction_indices + rank) % rank
        reduced = ts.cast(reduction_indices, :int32)
        idx = ts.range(0, rank)
        other, = ts.setdiff1d(idx, reduced)
        [ts.concat([reduced, other], 0),
         ts.reduce_prod(ts.gather(input_shape, reduced)),
         ts.reduce_prod(ts.gather(input_shape, other))]
      end

      permuted = ts.transpose(x, perm)
      permuted_shape = ts.shape(permuted)

      reshaped = ts.reshape(permuted, [reduced_num, other_num])

      # Calculate product, leaving out the current entry
      left = ts.cumprod(reshaped, axis: 0, exclusive: true)
      right = ts.cumprod(reshaped, axis: 0, exclusive: true, reverse: true)
      y = ts.reshape(left * right, permuted_shape)

      # Invert the transpose and reshape operations.
      # Make sure to set the statically known shape information through a reshape.
      out = grad * ts.transpose(y, ts.invert_permutation(perm))
      [ts.reshape(out, input_shape, name: 'prod'), nil]
    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 :mat_mul
      t_a = node.options[:transpose_a]
      t_b = node.options[:transpose_b]

      if !t_a && !t_b
        grad_a = ts.matmul(grad, y, transpose_b: true)
        grad_b = ts.matmul(x, grad, transpose_a: true)
      elsif !ta && tb
        grad_a = ts.matmul(grad, y)
        grad_b = ts.matmul(grad, x, transpose_a: true)
      elsif t_a && !t_b
        grad_a = ts.matmul(y, grad, transpose_b: true)
        grad_b = ts.matmul(x, grad)
      elsif t_a && t_b
        grad_a = ts.matmul(y, grad, transpose_a: true, transpose_b: true)
        grad_b = ts.matmul(grad, x, transpose_a: true, transpose_b: true)
      end

      [grad_a, grad_b]
    when :sin
      grad * ts.cos(x)
    when :tanh
      grad * i_op(:tanh_grad, x)
    when :pow
      z = node
      sx = ts.shape(x)
      sy = ts.shape(y)
      rx, ry = _broadcast_gradient_args(sx, sy)
      gx = ts.reduce_sum(grad * y * ts.pow(x, y - 1), rx)

      log_x = ts.where(x > 0, ts.log(x), ts.zeros_like(x))
      gy = ts.reduce_sum(grad * z * log_x, ry)

      [gx, gy]
    when :abs
      grad * ts.sign(x)
    when :log
      grad * ts.reciprocal(x)
    when :cos
      -grad * ts.sin(x)
    when :max
      _min_or_max_grad(node.inputs, grad, ->(a, b) { ts.greater_equal(a, b) })
    when :min
      _min_or_max_grad(node.inputs, grad, ->(a, b) { ts.less_equal(a, b) })
    when :tan
      secx = ts.reciprocal(ts.cos(x))
      secx2 = ts.square(secx)
      grad * secx2
    when :negate
      -grad
    when :exp
      grad * node
    when :identity, :print
      grad
    when :sign
      ts.zeros(ts.shape(x), dtype: x.data_type)
    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 :sum
      _sum_grad(x, y, grad)
    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 :case
      n_preds = node.inputs.size - 2

      case_grads = Array.new(n_preds) do |index|
        i_op(:case_grad, index, node.inputs[0], node.inputs[2 + index], grad)
      end

      [nil, i_op(:case_grad, -1, node.inputs[0], node.inputs[1], grad)] + case_grads
    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
      i_op(:sigmoid_grad, x, grad)
    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 :floor, :ceil, :round
      # non differentiable
      nil
    when :zeros_like
      # non differentiable
      nil
    when :argmin, :argmax, :floor_div
      # non differentiable
      [nil, 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) do |index|
          index == node.inputs[1].const_value ? grad : filler
        end
        [res]
      end
    when :squeeze
      _reshape_to_input(node, grad)
    when :expand_dims
      [_reshape_to_input(node, grad), nil]
    when :concat
      _concat_grad_helper(node, grad, 1, node.inputs.size, 0)
    when :reshape
      [ts.reshape(grad, ts.shape(node.inputs[0])), nil]
    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)
    when :cast
      t = %i[float16 float32 float64]
      src_type = node.inputs[0].data_type
      dst_type = grad.data_type

      if t.key?(src_type) && t.key?(dst_type)
        ts.cast(grad, src_type)
      end

      nil
    else
      raise "no derivative op for #{node.operation}"
    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 412

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 429

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 393

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 388

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 366

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 361

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 do |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)
    end.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 333

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 346

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 350

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 do |t|
    node = tensor.graph.nodes[t]
    node.consumers.include?(tensor.name) || node.equal?(tensor)
  end.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