Headline figures are float64 on a single data-center GPU (H=256, B=4096). Every method agrees to ≤ 1e-15 — speedups are bit-for-bit. See benchmark methodology.
One primitive, a full operator surface
omnibias turns the closed-form activation derivative tower into every differential operator scientific ML needs.
Closed-form n-th derivative
Call σⁿ(z) for arbitrary n with one activation evaluation — polynomial recurrences from the Riccati / Eulerian / Hermite identities.
O(1) Laplacian in dimension
The closed-form Laplacian overhead is independent of input dimension D. Grow D 80x and the wall-clock barely moves.
Bit-identical backends
PyTorch, JAX, and Keras 3 import the same pure-Python coefficients, so every (activation, order) pair is float64-ULP-equal.
Certified register
Interval / Taylor-model arithmetic produces provable enclosures, sealed in tamper-evident certificates with a Lean-kernel gate.
Iterated operators stay flat
Poly-Laplacians Δᵏ for biharmonic and beyond cost one tower per order — no nested-autodiff blow-up or OOM.
Full operator surface
Gradient, divergence, curl, Hessian, Jacobian, Laplace-Beltrami, exterior derivative, and multivariate jets.
A 30-second tour
Drop a typed operator into your model and keep your training loop.
import torch
from omnibias.torch import OMBU, OperatorBlock, cmbLinear
# OMBU: trainable K-bias operator, drop-in for an activation.
ombu = OMBU(num_channels=4, K=2, base="tanh")
out = ombu(torch.zeros(8, 4))
# Typed scalar operator (grad / laplacian / integral / identity).
laplacian = OperatorBlock(channels=8, op="laplacian", base="gaussian")
Who is omnibias for?
Make high-order derivatives cheap
Start with the quickstart, then wire the closed-form path into your PINN, VMC, or optimization loop.
Or email info@derivon.ai