API REFERENCE/omnibias-keras

omnibias.keras.fastpath.hermite

0.0.2a1AlphaPython >=3.10Apache-2.0

Keras 3 operator layers and activation paths implemented with keras.ops for TensorFlow, JAX, or Torch.

import omnibias.keras.fastpath.hermite

Module contract & mathematical conventions

Closed-form derivatives of the Gaussian activation via probabilist's Hermite polynomials, evaluated with keras.ops.

Let g(z) = exp(-z^2/2). Then g^(n)(z) = (-1)^n He_n(z) g(z), where He_n obeys He_0 = 1, He_1 = z, He_{n+1} = z He_n - n He_{n-1}. Coefficients come from the shared omnibias.core.polynomials.

Shared formulas do not imply universal floating-point identity. Verify dtype, shape, derivative-order support, and the stated numerical assumptions for the path you use.

Module source ↗Source revision 9a2d73df0573Running reference examples →

Imports & aliases

These names share a definition with another public module. Follow a name for its full contract, parameters, and examples.

Import from this module	Canonical reference
hermite_coeffs	omnibias.core.hermite_coeffs

FUNCTION

gaussian_forward

omnibias.keras.fastpath.gaussian_forwardSource ↗

gaussian_forward(z: Any) -> Any

g(z) = exp(-z^2/2).

Parameters

Name	Type & default	Contract
zpositional-or-keyword	AnyRequired	See the operation contract and implementation below.

ReturnsAny

Executed regression · fastpath order zero is forward

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_fastpath_order_zero_is_forward(fn) -> None:
    z = np.linspace(-2.0, 2.0, 11)
    out0 = _np(fn(_t(z), 0))
    assert out0.shape == z.shape
    assert np.all(np.isfinite(out0))

python -m pytest "packages/omnibias-keras/tests/test_fastpath_correctness.py::test_fastpath_order_zero_is_forward[gaussian_nth_derivative]" -q

Read the implementation

def gaussian_forward(z: Any) -> Any:
    """``g(z) = exp(-z^2/2)``."""
    return ops.exp(-0.5 * z * z)

Other public import paths

• omnibias.keras.fastpath.gaussian_forward
• omnibias.keras.fastpath.hermite.gaussian_forward

FUNCTION

gaussian_nth_derivative

omnibias.keras.fastpath.gaussian_nth_derivativeSource ↗

gaussian_nth_derivative(z: Any, n: int) -> Any

g^(n)(z) via g^(n)(z) = (-1)^n He_n(z) g(z).

Parameters

Name	Type & default	Contract
zpositional-or-keyword	AnyRequired	See the operation contract and implementation below.
npositional-or-keyword	intRequired	See the operation contract and implementation below.

ReturnsAny

Explicit validation & failure cases

• When n < 0, raises ValueError(f'order n must be >= 0, got {n}').

These are explicit source guards. Backend operations may also raise for invalid shapes, dtypes, or unsupported devices.

Executed regression · negative order raises

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_negative_order_raises(fn) -> None:
    with pytest.raises(ValueError):
        fn(_t(np.zeros(3)), -1)

python -m pytest "packages/omnibias-keras/tests/test_fastpath_correctness.py::test_negative_order_raises[gaussian_nth_derivative]" -q

Regression example · fastpath order zero is forward

This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_fastpath_order_zero_is_forward(fn) -> None:
    z = np.linspace(-2.0, 2.0, 11)
    out0 = _np(fn(_t(z), 0))
    assert out0.shape == z.shape
    assert np.all(np.isfinite(out0))

python -m pytest packages/omnibias-keras/tests/test_fastpath_correctness.py -k test_fastpath_order_zero_is_forward -q

Read the implementation

def gaussian_nth_derivative(z: Any, n: int) -> Any:
    """``g^(n)(z)`` via ``g^(n)(z) = (-1)^n He_n(z) g(z)``."""
    if n < 0:
        raise ValueError(f"order n must be >= 0, got {n}")
    g = gaussian_forward(z)
    if n == 0:
        return g
    poly = _horner(hermite_coeffs(n), z)
    sign = -1.0 if (n & 1) else 1.0
    return sign * poly * g

Related APIsomnibias.core.hermite_coeffs↗omnibias.keras.fastpath.gaussian_forward↗

Other public import paths

• omnibias.keras.fastpath.gaussian_nth_derivative
• omnibias.keras.fastpath.hermite.gaussian_nth_derivative

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