API REFERENCE/omnibias-torch

omnibias.torch.activations.trigonometric

0.5.0rc1Release candidatePython >=3.10Apache-2.0

PyTorch activation derivatives, trainable operator layers, network jets, and direct differential-operator contractions.

import omnibias.torch.activations.trigonometric

Module contract & mathematical conventions

Trigonometric & hyperbolic activations for physics-class wavefunctions.

These activations target physics-class wavefunctions and periodic / lattice-Bloch neural-VMC. Every spec exposes a closed-form n-th derivative; the supported orders depend on the activation:

================== ========================================= =================== Activation n-th derivative formula Max fastpath order ================== ========================================= =================== sin(z) sin(z + n * pi/2) every n cos(z) cos(z + n * pi/2) every n sinh(z) alternating sinh / cosh every n cosh(z) alternating cosh / sinh every n tan(z) Riccati P(t) = 1 + t^2 n in {0, 1, 2, 3} cot(z) Riccati P(c) = -(1 + c^2) n in {0, 1, 2, 3} sech(z) sech * (1 - 2 sech^2) etc. n in {0, 1, 2, 3} coth(z) Riccati P(c) = 1 - c^2 (tanh-like) n in {0, 1, 2, 3} ================== ========================================= ===================

All four hyperbolic activations are closed-form for arbitrarily many orders; the support cap on tan / cot / sech is purely a development cost choice — the recursions are well known and can be extended on demand.

Physical motivation

• sin / cos — plane-wave embeddings for periodic systems (Bloch wavefunctions on a lattice; k-point sampling for crystalline Hamiltonians).
• sinh / cosh — anti-Bragg / evanescent states; logarithmic derivatives of Slater determinants in 1D models with linear backbone symmetry.
• sech — soliton wavefunctions (sine-Gordon, KdV, NLS); Pöschl-Teller potential bound states; the canonical sech^2 reflectionless potential.
• tan / cot — phase-only activations for unitary RNN-style amplitude/phase factorisations, and as raw building blocks for the envelope-modulator branch of period-aware ansatze.
• coth — Langevin-function-like saturation; thermal-state amplitude in finite-T NQS. Riccati-class (same polynomial shape as tanh).

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.torch.activations.trigonometric.COSSource ↗

COS = register_activation(ActivationSpec(name='cos', forward=_cos_forward, derivative=_cos_derivative, fastpath=_cos_fastpath, integral=_cos_integral, 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=_cos_derivative,
        fastpath=_cos_fastpath,
        integral=_cos_integral,
        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.torch.register_activation↗

CONSTANT

COSH

omnibias.torch.activations.trigonometric.COSHSource ↗

COSH = register_activation(ActivationSpec(name='cosh', forward=_cosh_forward, derivative=_cosh_derivative, fastpath=_cosh_fastpath, integral=_cosh_integral, 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=_cosh_derivative,
        fastpath=_cosh_fastpath,
        integral=_cosh_integral,
        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.torch.register_activation↗

CONSTANT

COT

omnibias.torch.activations.trigonometric.COTSource ↗

COT = register_activation(ActivationSpec(name='cot', forward=_cot_forward, derivative=_cot_derivative, fastpath=_cot_fastpath, integral=_cot_integral, 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=_cot_derivative,
        fastpath=_cot_fastpath,
        integral=_cot_integral,
        riccati_polynomial=(-1.0, 0.0, -1.0),  # P(c) = -(1 + c^2)
        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.torch.register_activation↗

CONSTANT

COTH

omnibias.torch.activations.trigonometric.COTHSource ↗

COTH = register_activation(ActivationSpec(name='coth', forward=_coth_forward, derivative=_coth_derivative, fastpath=_coth_fastpath, integral=_coth_integral, 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=_coth_derivative,
        fastpath=_coth_fastpath,
        integral=_coth_integral,
        riccati_polynomial=(1.0, 0.0, -1.0),  # P(c) = 1 - c^2 (same shape as tanh)
        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.torch.register_activation↗

CONSTANT

SECH

omnibias.torch.activations.trigonometric.SECHSource ↗

SECH = register_activation(ActivationSpec(name='sech', forward=_sech_forward, derivative=_sech_derivative, fastpath=_sech_fastpath, integral=_sech_integral, 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=_sech_derivative,
        fastpath=_sech_fastpath,
        integral=_sech_integral,
        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.torch.register_activation↗

CONSTANT

SIN

omnibias.torch.activations.trigonometric.SINSource ↗

SIN = register_activation(ActivationSpec(name='sin', forward=_sin_forward, derivative=_sin_derivative, fastpath=_sin_fastpath, integral=_sin_integral, 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=_sin_derivative,
        fastpath=_sin_fastpath,
        integral=_sin_integral,
        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.torch.register_activation↗

CONSTANT

SINH

omnibias.torch.activations.trigonometric.SINHSource ↗

SINH = register_activation(ActivationSpec(name='sinh', forward=_sinh_forward, derivative=_sinh_derivative, fastpath=_sinh_fastpath, integral=_sinh_integral, 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=_sinh_derivative,
        fastpath=_sinh_fastpath,
        integral=_sinh_integral,
        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.torch.register_activation↗

CONSTANT

TAN

omnibias.torch.activations.trigonometric.TANSource ↗

TAN = register_activation(ActivationSpec(name='tan', forward=_tan_forward, derivative=_tan_derivative, fastpath=_tan_fastpath, integral=_tan_integral, 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=_tan_derivative,
        fastpath=_tan_fastpath,
        integral=_tan_integral,
        riccati_polynomial=(1.0, 0.0, 1.0),  # P(t) = 1 + t^2
        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.torch.register_activation↗

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