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API REFERENCE/omnibias-keras

omnibias.keras.activations.trigonometric

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.activations.trigonometric
Module contract & mathematical conventions

Trigonometric & hyperbolic activations for physics-class wavefunctions.

Mirrors omnibias.torch.activations.trigonometric on keras.ops. sin / cos / sinh / cosh are closed form for every order; tan / cot / coth for n in {0, 1, 2, 3}; sech for n in {0, 1, 2, 3}.

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 →
CONSTANT

COS​

omnibias.keras.activations.trigonometric.COSSource ↗
COS = register_activation(ActivationSpec(name='cos', forward=_cos_forward, derivative=lambda z: -ops.sin(z), fastpath=_cos_fastpath, integral=lambda z: ops.sin(z), riccati_polynomial=None, noise_model='none', operator_role='Plane-wave / Bloch embedding (real part); cos(z + n*pi/2) gives every order in closed form.'))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
COS = register_activation(
    ActivationSpec(
        name="cos",
        forward=_cos_forward,
        derivative=lambda z: -ops.sin(z),
        fastpath=_cos_fastpath,
        integral=lambda z: ops.sin(z),
        riccati_polynomial=None,
        noise_model="none",
        operator_role=(
            "Plane-wave / Bloch embedding (real part); cos(z + n*pi/2) "
            "gives every order in closed form."
        ),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
CONSTANT

COSH​

omnibias.keras.activations.trigonometric.COSHSource ↗
COSH = register_activation(ActivationSpec(name='cosh', forward=_cosh_forward, derivative=lambda z: ops.sinh(z), fastpath=_cosh_fastpath, integral=lambda z: ops.sinh(z), riccati_polynomial=None, noise_model='none', operator_role='Hyperbolic even primitive; eigenfunction of d^2/dz^2 with eigenvalue +1; alternates with sinh under differentiation.'))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
COSH = register_activation(
    ActivationSpec(
        name="cosh",
        forward=_cosh_forward,
        derivative=lambda z: ops.sinh(z),
        fastpath=_cosh_fastpath,
        integral=lambda z: ops.sinh(z),
        riccati_polynomial=None,
        noise_model="none",
        operator_role=(
            "Hyperbolic even primitive; eigenfunction of d^2/dz^2 with "
            "eigenvalue +1; alternates with sinh under differentiation."
        ),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
CONSTANT

COT​

omnibias.keras.activations.trigonometric.COTSource ↗
COT = register_activation(ActivationSpec(name='cot', forward=_cot_forward, derivative=lambda z: -(1.0 + (1.0 / ops.tan(z)) ** 2), fastpath=_cot_fastpath, integral=lambda z: ops.log(ops.abs(ops.sin(z))), riccati_polynomial=(-1.0, 0.0, -1.0), noise_model='none', operator_role="Riccati-class periodic activation; cot'(z) = -(1 + cot^2(z)); complementary to tan in phase-only ansatze.", aliases=('ctg', 'ctan')))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
COT = register_activation(
    ActivationSpec(
        name="cot",
        forward=_cot_forward,
        derivative=lambda z: -(1.0 + (1.0 / ops.tan(z)) ** 2),
        fastpath=_cot_fastpath,
        integral=lambda z: ops.log(ops.abs(ops.sin(z))),
        riccati_polynomial=(-1.0, 0.0, -1.0),
        noise_model="none",
        operator_role=(
            "Riccati-class periodic activation; cot'(z) = -(1 + cot^2(z)); "
            "complementary to tan in phase-only ansatze."
        ),
        aliases=("ctg", "ctan"),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
CONSTANT

COTH​

omnibias.keras.activations.trigonometric.COTHSource ↗
COTH = register_activation(ActivationSpec(name='coth', forward=_coth_forward, derivative=lambda z: 1.0 - (1.0 / ops.tanh(z)) ** 2, fastpath=_coth_fastpath, integral=lambda z: ops.log(ops.abs(ops.sinh(z))), riccati_polynomial=(1.0, 0.0, -1.0), noise_model='none', operator_role="Hyperbolic Riccati: coth'(z) = 1 - coth^2(z); Langevin-like saturation, finite-T NQS amplitude."))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
COTH = register_activation(
    ActivationSpec(
        name="coth",
        forward=_coth_forward,
        derivative=lambda z: 1.0 - (1.0 / ops.tanh(z)) ** 2,
        fastpath=_coth_fastpath,
        integral=lambda z: ops.log(ops.abs(ops.sinh(z))),
        riccati_polynomial=(1.0, 0.0, -1.0),
        noise_model="none",
        operator_role=(
            "Hyperbolic Riccati: coth'(z) = 1 - coth^2(z); Langevin-like "
            "saturation, finite-T NQS amplitude."
        ),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
CONSTANT

SECH​

omnibias.keras.activations.trigonometric.SECHSource ↗
SECH = register_activation(ActivationSpec(name='sech', forward=_sech_forward, derivative=lambda z: -(1.0 / ops.cosh(z)) * ops.tanh(z), fastpath=_sech_fastpath, integral=lambda z: 2.0 * ops.arctan(ops.tanh(0.5 * z)), riccati_polynomial=None, noise_model='none', operator_role='Soliton bound-state amplitude: sech(z) is the Poschl-Teller ground state and the sine-Gordon / KdV / NLS soliton profile.'))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
SECH = register_activation(
    ActivationSpec(
        name="sech",
        forward=_sech_forward,
        derivative=lambda z: -(1.0 / ops.cosh(z)) * ops.tanh(z),
        fastpath=_sech_fastpath,
        integral=lambda z: 2.0 * ops.arctan(ops.tanh(0.5 * z)),
        riccati_polynomial=None,
        noise_model="none",
        operator_role=(
            "Soliton bound-state amplitude: sech(z) is the Poschl-Teller "
            "ground state and the sine-Gordon / KdV / NLS soliton profile."
        ),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
CONSTANT

SIN​

omnibias.keras.activations.trigonometric.SINSource ↗
SIN = register_activation(ActivationSpec(name='sin', forward=_sin_forward, derivative=lambda z: ops.cos(z), fastpath=_sin_fastpath, integral=lambda z: -ops.cos(z), riccati_polynomial=None, noise_model='none', operator_role='Plane-wave / Bloch embedding; eigenfunction of d^2/dz^2 with eigenvalue -1; sin(z + n*pi/2) gives every order in closed form.'))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
SIN = register_activation(
    ActivationSpec(
        name="sin",
        forward=_sin_forward,
        derivative=lambda z: ops.cos(z),
        fastpath=_sin_fastpath,
        integral=lambda z: -ops.cos(z),
        riccati_polynomial=None,
        noise_model="none",
        operator_role=(
            "Plane-wave / Bloch embedding; eigenfunction of d^2/dz^2 with "
            "eigenvalue -1; sin(z + n*pi/2) gives every order in closed form."
        ),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
CONSTANT

SINH​

omnibias.keras.activations.trigonometric.SINHSource ↗
SINH = register_activation(ActivationSpec(name='sinh', forward=_sinh_forward, derivative=lambda z: ops.cosh(z), fastpath=_sinh_fastpath, integral=lambda z: ops.cosh(z), riccati_polynomial=None, noise_model='none', operator_role='Hyperbolic odd primitive; eigenfunction of d^2/dz^2 with eigenvalue +1; alternates with cosh under differentiation.'))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
SINH = register_activation(
    ActivationSpec(
        name="sinh",
        forward=_sinh_forward,
        derivative=lambda z: ops.cosh(z),
        fastpath=_sinh_fastpath,
        integral=lambda z: ops.cosh(z),
        riccati_polynomial=None,
        noise_model="none",
        operator_role=(
            "Hyperbolic odd primitive; eigenfunction of d^2/dz^2 with "
            "eigenvalue +1; alternates with cosh under differentiation."
        ),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
CONSTANT

TAN​

omnibias.keras.activations.trigonometric.TANSource ↗
TAN = register_activation(ActivationSpec(name='tan', forward=_tan_forward, derivative=lambda z: 1.0 + ops.tan(z) ** 2, fastpath=_tan_fastpath, integral=lambda z: -ops.log(ops.abs(ops.cos(z))), riccati_polynomial=(1.0, 0.0, 1.0), noise_model='none', operator_role="Riccati-class periodic activation; tan'(z) = 1 + tan^2(z); phase factor in unitary-RNN amplitude/phase factorisations."))

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation
TAN = register_activation(
    ActivationSpec(
        name="tan",
        forward=_tan_forward,
        derivative=lambda z: 1.0 + ops.tan(z) ** 2,
        fastpath=_tan_fastpath,
        integral=lambda z: -ops.log(ops.abs(ops.cos(z))),
        riccati_polynomial=(1.0, 0.0, 1.0),
        noise_model="none",
        operator_role=(
            "Riccati-class periodic activation; tan'(z) = 1 + tan^2(z); "
            "phase factor in unitary-RNN amplitude/phase factorisations."
        ),
    )
)
Related APIsomnibias.core.ActivationSpec↗omnibias.keras.register_activation↗
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