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 



192
193
194
195
 
# File 'lib/tensor_stream/math_gradients.rb', line 192

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 



238
239
240
241
 
# File 'lib/tensor_stream/math_gradients.rb', line 238

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

._broadcast_transform(input_a, input_b) ⇒ Object 



197
198
199
 
# File 'lib/tensor_stream/math_gradients.rb', line 197

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



52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
 
# 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)
    when :flow_dynamic_stitch
      num_values = node.inputs.size / 2
      indices_grad = [nil] * num_values

      inputs = (0...num_values).map { |i| _int32(node, node.inputs[i]) }

      values_grad = inputs.map { |inp| TensorStream.gather(grad, inp) }
      indices_grad + values_grad
    when :gather
      [_op(:gather_grad, grad, node.inputs[1], TensorStream.shape(node.inputs[0])), nil]
    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 



267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
 
# File 'lib/tensor_stream/math_gradients.rb', line 267

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 



284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
 
# File 'lib/tensor_stream/math_gradients.rb', line 284

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 



248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
 
# File 'lib/tensor_stream/math_gradients.rb', line 248

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) 


243
244
245
246
 
# File 'lib/tensor_stream/math_gradients.rb', line 243

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

._int32(node, x) ⇒ Object 



184
185
186
 
# File 'lib/tensor_stream/math_gradients.rb', line 184

def self._int32(node, x)
  (node.inputs[0].data_type == :int32 ? x : TensorStream.cast(x, :int32))
end

._min_or_max_grad(inputs, grad, selector_op) ⇒ Object 



221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
 
# File 'lib/tensor_stream/math_gradients.rb', line 221

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) 


216
217
218
219
 
# File 'lib/tensor_stream/math_gradients.rb', line 216

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 



25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
 
# 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 



188
189
190
 
# File 'lib/tensor_stream/math_gradients.rb', line 188

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

._safe_shape_div(arg_x, arg_y) ⇒ Object 



201
202
203
 
# File 'lib/tensor_stream/math_gradients.rb', line 201

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 



205
206
207
208
209
210
211
212
213
214
 
# File 'lib/tensor_stream/math_gradients.rb', line 205

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 



11
12
13
14
15
16
17
18
19
20
21
22
23
 
# 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 



7
8
9
 
# File 'lib/tensor_stream/math_gradients.rb', line 7

def self.ts
  TensorStream
end