tfp.experimental.substrates.jax.math.round_exponential_bump_function

Function supported on [-1, 1], smooth on the real line, with a round top.

Define

f(x) := exp(-1 / (1 - x**2)) * exp(1), for x in (-1, 1)
f(x) := 0, for |x| >= 1.

One can show that f(x)...

  • is C^\infty on the real line.
  • is supported on [-1, 1].
  • is equal to 1 at x = 0.
  • is strictly increasing on (-1, 0).
  • is strictly decreasing on (0, 1).
  • has gradient = 0 at 0.

See Bump Function

x Floating-point Tensor.
name Optional Python str naming the operation.

y Tensor of same shape and dtype as x.