omnibias-core

Backend-agnostic mathematical core of the omnibias framework.

This package is the bottom of the dependency graph. It ships the pure-Python polynomial coefficient generators that power every closed-form σ^(n) kernel, plus the generic ActivationSpec protocol that omnibias-torch, omnibias-jax, and omnibias-keras specialise. There is no torch / jax / numpy / tensorflow dependency — both backends import from here, so the Eulerian / Legendre / Hermite recurrences produce bit-identical coefficient sequences by construction.

Install

pip install omnibias-core

Quick start

from omnibias.core.polynomials import (
    sigmoid_polynomial_coeffs,
    tanh_polynomial_coeffs,
    hermite_coeffs,
)

# Coefficients of the degree-(n+1) polynomial P_n such that
#   sigma^(n)(z) = P_n(sigma(z))   (Riccati class)
print(sigmoid_polynomial_coeffs(3))  # 3rd derivative of sigmoid
print(tanh_polynomial_coeffs(4))
print(hermite_coeffs(5))             # probabilist's Hermite (Gaussian)

# ActivationSpec is a frozen dataclass of shared metadata. Backends pin
# TensorT to their array type and fill in forward / fastpath callables.
# Prefer the backend registries rather than constructing one by hand:
#
#   from omnibias.torch import get_activation
#   spec = get_activation("tanh")
#   spec.fastpath(z, n)   # closed-form sigma^(n)

Public surface (highlights)

Why a separate package?

Forking the coefficients per backend would silently break bit-identity. Keeping them in a pure-Python wheel means a JAX-only or torch-only install still shares the same numbers, and the Lean / verified substrate never has to import a framework.

Docs

• Theory primer: docs/theory.md
• Operator surface: docs/operator-surface.md
• Stability matrix: docs/stability.md
• Monorepo overview: README.md

License

Apache-2.0. See LICENSE and ../../LICENSING.md. You never need a commercial licence for this package.