API REFERENCE/omnibias-keras

omnibias.keras.fastpath.legendre

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.legendre

Module contract & mathematical conventions

Closed-form derivatives of tanh via the Legendre-style recursion, evaluated with keras.ops.

Let t = tanh(z). Then t' = 1 - t^2 and each higher derivative is a polynomial in t:

tanh^(n)(z) = T_n(t), T_0(t) = t, T_{n+1}(t) = (1 - t^2) * T_n'(t).

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
tanh_polynomial_coeffs	omnibias.core.tanh_polynomial_coeffs

FUNCTION

tanh_nth_derivative

omnibias.keras.fastpath.tanh_nth_derivativeSource ↗

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

tanh^(n)(z) evaluated in closed form.

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[tanh_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 tanh_nth_derivative(z: Any, n: int) -> Any:
    """``tanh^(n)(z)`` evaluated in closed form."""
    if n < 0:
        raise ValueError(f"order n must be >= 0, got {n}")
    t = ops.tanh(z)
    if n == 0:
        return t
    return _horner(tanh_polynomial_coeffs(n), t)

Related APIsomnibias.core.tanh_polynomial_coeffs↗

Other public import paths

• omnibias.keras.fastpath.tanh_nth_derivative
• omnibias.keras.fastpath.legendre.tanh_nth_derivative

FUNCTION

tanh_tower

omnibias.keras.fastpath.legendre.tanh_towerSource ↗

tanh_tower(z: Any, max_order: int) -> Any

All derivatives through max_order from one native tanh evaluation.

Parameters

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

ReturnsAny

Explicit validation & failure cases

• When max_order < 0, raises ValueError('max_order must be nonnegative').

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

Executed regression · registered shared tower

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_registered_shared_tower(name: str) -> None:
    spec = get_activation(name)
    assert spec.tower is not None and spec.fastpath is not None
    value = ops.convert_to_tensor([-0.2, 0.0, 0.5])
    tower = spec.tower(value, 6)
    for order in range(7):
        np.testing.assert_array_equal(ops.convert_to_numpy(tower[order]),
                                      ops.convert_to_numpy(spec.fastpath(value, order)))
    with pytest.raises(ValueError, match="nonnegative"):
        spec.tower(value, -1)

python -m pytest "packages/omnibias-keras/tests/test_shared_tower.py::test_registered_shared_tower[tanh]" -q

Read the implementation

def tanh_tower(z: Any, max_order: int) -> Any:
    """All derivatives through max_order from one native tanh evaluation."""
    if max_order < 0:
        raise ValueError("max_order must be nonnegative")
    value = ops.tanh(z)
    rows = [value] + [_horner(tanh_polynomial_coeffs(n), value) for n in range(1, max_order + 1)]
    return ops.stack(rows, axis=0)

Related APIsomnibias.core.tanh_polynomial_coeffs↗

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