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# File 'lib/tensor_stream/math_gradients.rb', line 6
def self.derivative(tensor, dx, options = {})
gradient_program_name = "_grad_#{tensor.name}_#{dx.name}"
return options[:graph].get_node(gradient_program_name) if options[:graph] && options[:graph].node_added?(gradient_program_name)
constant_options = { dtype: options[:dtype] }
constant_options_1 = { dtype: options[:dtype] || tensor.data_type }
return i_op(:ones_like, dx, constant_options_1) if tensor.equal?(dx)
return i_cons(0, constant_options) if options[:stop_gradients] && _include?(options[:stop_gradients], tensor)
if tensor.is_a?(Operation)
grad = derivative(tensor.items[0], dx, options) if tensor.items[0]
grad2 = derivative(tensor.items[1], dx, options) if tensor.items[1]
case tensor.operation
when :max
x_mask = i_op(:where, i_op(:ones_like, tensor.items[0]), i_op(:zeros_like, tensor.items[1]), pred: tensor.items[0] > tensor.items[1])
y_mask = i_op(:where, i_op(:zeros_like, tensor.items[0]), i_op(:ones_like, tensor.items[1]), pred: tensor.items[0] < tensor.items[1])
x_mask * grad + y_mask * grad2
when :where
x_mask = i_op(:where, i_op(:ones_like, tensor.items[0]), i_op(:zeros_like, tensor.items[1]), pred: tensor.options[:pred])
y_mask = i_op(:where, i_op(:zeros_like, tensor.items[0]), i_op(:ones_like, tensor.items[1]), pred: tensor.options[:pred])
x_mask * grad + y_mask * grad2
when :cond
i_op(:cond, grad, grad2, pred: tensor.options[:pred])
when :identity, :print, :pad
grad
when :negate
i_cons(-1, constant_options_1) * grad
when :abs
grad * i_op(:sign, _ds(tensor.items[0]))
when :square
i_cons(2, constant_options_1) * _ds(tensor.items[0]) * grad
when :exp
i_op(:exp, tensor.items[0]) * grad
when :log
(i_cons(1, constant_options_1) / _ds(tensor.items[0])) * grad
when :tanh
(i_cons(1, constant_options_1) - (i_op(:tanh, _ds(tensor.items[0]))**2)) * grad
when :tan
(i_cons(1, constant_options_1) / (i_op(:cos, _ds(tensor.items[0]))**2)) * grad
when :sin
i_op(:cos, tensor.items[0]) * grad
when :sqrt
i_cons(1, constant_options_1) / (i_cons(2, constant_options_1) * i_op(:sqrt, _ds(tensor.items[0]))) * grad
when :cos
-i_op(:sin, tensor.items[0]) * grad
when :add
grad_with_broadcast(tensor, dx, ->(a,b) { i_op(:add, a, b, name: 'grad_sum') } , options)
when :sub
grad_with_broadcast(tensor, dx, ->(a,b) { i_op(:sub, a, b, name: 'grad_sub') } , options)
when :pow
gx = _ds(tensor.items[1])*( _ds(tensor.items[0])**(_ds(tensor.items[1]) - 1)) * grad
log_x = i_op(:where, i_op(:log, tensor.items[0], nil, name: 'log_pow_grad'), i_op(:zeros_like, tensor.items[0]), pred: tensor.items[0] > 0)
gy = _ds(tensor.items[0])**_ds(tensor.items[1]) * log_x * grad2
gx + gy
when :div
gx = i_op(:div, grad, _ds(tensor.items[1]))
gy = grad2 * i_op(:div, i_op(:div, -_ds(tensor.items[0]), _ds(tensor.items[1])), _ds(tensor.items[1]))
gx + gy
when :mul
grad * _ds(tensor.items[1]) + _ds(tensor.items[0]) * grad2
when :reduce_mean
input_size = i_op(:reduce_prod, i_op(:shape, tensor.items[0]))
output_size = i_op(:reduce_prod, i_op(:shape, tensor))
factor = input_size / output_size
(grad / i_op(:cast, factor, data_type: grad.dtype))
when :reduce_sum
grad
when :stop_gradient
return i_cons(0, constant_options)
when :matmul
tensor_shape1 = tensor.items[1].shape ? tensor.items[1].shape.shape : nil
tensor_shape0 = tensor.items[0].shape ? tensor.items[0].shape.shape : nil
derivative_a = derivative(tensor.items[0], dx)
derivative_b = derivative(tensor.items[1], dx)
s0 = i_op(:shape, tensor.items[0])
s1 = i_op(:shape, tensor.items[1])
identity_0 = i_op(:ones, [s0[0], s1[1]], nil, data_type: tensor.items[0].data_type)
identity_1 = i_op(:ones, [s0[0], s1[1]], nil, data_type: tensor.items[1].data_type)
matmul_da = i_op(:matmul, identity_0, tensor.items[1], transpose_b: true,
pad_zeros: true,
name: 'matrix_dx')
matmul_db = i_op(:matmul, tensor.items[0], identity_1, transpose_a: true,
pad_zeros: true,
name: 'matrix_dy')
zero_vect = i_op(:zeros_like, dx, nil, name: 'zero_vect')
matmul_da = i_op(:cond, matmul_da[0], matmul_da, pred: op(:rank, derivative_a) > 0)
norm_a = i_op(:mul, derivative_a, matmul_da, name: 'grad_a_norm_mul_da')
norm_b = i_op(:mul, derivative_b, matmul_db, name: 'grad_b_norm_mul_db')
i_op(:cond, norm_a, zero_vect, pred: i_op(:reduce_sum, norm_a) != 0) + i_op(:cond, norm_b, zero_vect, pred: i_op(:reduce_sum, norm_b) != 0)
else
raise "no derivative implementation found for op #{tensor.operation}"
end
elsif tensor.is_a?(TensorStream::Variable)
i_cons(0, constant_options)
elsif tensor.is_a?(TensorStream::Placeholder)
i_cons(0, constant_options)
else
i_cons(0, constant_options)
end.tap do |ops|
options[:graph].add_node!(gradient_program_name, ops) if options[:graph]
end
end
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