tf.contrib.bayesflow.custom_grad.custom_gradient

tf.contrib.bayesflow.custom_grad.custom_gradient(
    fx,
    gx,
    x,
    axis=(),
    fx_gx_manually_stopped=False,
    name=None
)

Defined in tensorflow/contrib/bayesflow/python/ops/custom_grad_impl.py.

Enables specifying a custom gradient.

This function works by clever application of stop_gradient. I.e., observe that:

h(x) = x * stop_gradient(g(x)) + stop_gradient(f(x) - x * g(x))

is such that h(x) = stop_gradient(f(x)) and grad[h(x), x] = stop_gradient(g(x)).

In addition to scalar-domain/scalar-range functions, this function also supports tensor-domain/scalar-range functions. However, in the latter case it is necessary to reduce x to a scalar. This can be done by indicating the axis over which f operates or by appropriately reduce_sum-ing x, prior to calling this function.

Partial Custom Gradient:

Suppose h(x) = htilde(x, y). Note that dh/dx = stop(g(x)) but dh/dy = None. This is because a Tensor cannot have only a portion of its gradient stopped. To circumvent this issue, one must manually stop_gradient the relevant portions of f, g. For example see the unit-test, test_works_correctly_fx_gx_manually_stopped.

Args:

  • fx: Tensor. Output of function evaluated at x.
  • gx: Tensor. Gradient of function evaluated at x.
  • x: Tensor. Point of evaluation for f, g.
  • axis: 1D int Tensor representing dimensions of x which are the domain of f. If () (the default), f is assumed scalar-domain/scalar-range. If None f is assumed to render one scalar given all of x. Otherwise f is assumed to output one scalar for each of axis dimensions of x.
  • fx_gx_manually_stopped: Python bool indicating that fx, gx manually have stop_gradient applied.
  • name: Python str name prefixed to Ops created by this function.

Returns:

  • fx: Floating-type Tensor equal to f(x) but which has gradient stop_gradient(g(x)).