The derivative engine for scientific machine learning
A single closed-form primitive, exposed as a full operator surface, with bit-identical backends and a certified register for trust-critical work.
# Most common: PyTorch users
pip install omnibias-torch
# JAX users
pip install omnibias-jax
# FermiNet bridge (pulls in jax + core)
pip install omnibias-ferminet
# Pure math, no backend
pip install omnibias-coreThree layers, one source of truth
From the raw derivative tower up to certified applications - all sharing the same pure-Python coefficients.
Derivative engine
- Closed-form σⁿ(z) for the Riccati class at arbitrary order
- Gradient, Laplacian, Δᵏ poly-Laplacian, Hessian, Jacobian
- Multivariate Faà di Bruno jets - every mixed partial from one pass
- 23+ activations with documented per-order support
Operator surface
- Divergence, curl, tensor divergence, Wirtinger derivatives
- Laplace-Beltrami, Christoffel, curvature on learned manifolds
- Exterior derivative, wedge, Hodge star, codifferential
- Structural cages for incompressibility and conservation
Certified register
- Interval, affine, and Taylor-model arithmetic (outward-rounded)
- Radii-polynomial existence and QR-Lohner validated flow
- Hash-sealed certificates with independent replay twins
- Lean 4 kernel gate for finite, rational obligations
How the platform fits together
The pure-Python core holds every polynomial recurrence. Backends import it unchanged, so the closed-form derivative math is bit-identical across backends by construction.
Works with the stack you already run
PyTorch
OMBU, OperatorBlock, cmbLinear / cmbConv*, growable units
JAX
Closed-form Laplacian / Hessian, complex activations, jets
Keras 3
Unified backend across TensorFlow, JAX, and PyTorch
FermiNet / DeepQMC
folx-compatible local kinetic energy adapter
NumPy
Pure-Python discovery, geometry, and verified arithmetic
Lean 4
Mathlib-free kernel for the formal obligation gate
Run it where your science runs
Open-core library
pip install the backend you need. The derivative tower and everything built on it - 28 of 42 packages, including every backend - is Apache-2.0, free for closed-source and hosted use. Only the certified-decision layer is AGPL-3.0-or-later or commercial.
In your training cluster
Runs wherever your PyTorch/JAX jobs run - CPU or GPU, single node or multi-node. No service to call, no data leaves your environment.
Air-gapped & on-prem
Pure-Python core with no network dependency at runtime. Vendor-neutral and reproducible for regulated environments.
Security & reproducibility by design
Derivon is a library, not a SaaS black box. Your data and models stay in your environment. The numerics are deterministic and reproducible bit-for-bit on a given platform.
- No runtime network dependency - air-gap friendly
- Deterministic seeds: same inputs, same bits
- Tamper-evident, hash-sealed certificates
- Vendor-neutral - no scheduler or host lock-in
- Open-source core you can audit end to end
- Independent replay twins catch forged results
Monitoring
- Forecast-horizon and relative-L2-per-time diagnostics
- Spectral fidelity and energy / enstrophy / palinstrophy tracking
- Norm-drift and probability-current continuity for quantum systems
- Autodiff-vs-closed-form parity benchmarks on every release
Analytics
- Cross-backend bit-parity reports (float64 ULP)
- Per-activation, per-order support matrices
- Reproducible CPU smoke tier plus GPU headline transcriptions
- Coefficient-uncertainty and model-selection scores for discovery
A prove / disprove machine for model statements
Every certificate goes through the same gates: schema validation, independent replay, an honesty gate, and an optional formal kernel pass.
- 1
Define
State the model statement: a residual bound, a robustness margin, a conservation property, a discovered law.
- 2
Enclose
Compute a rigorous interval / Taylor-model enclosure of the quantity with the certified jet.
- 3
Replay
An independent numpy twin regenerates the result with a different algorithm; disagreement blocks the verdict.
- 4
Certify
Seal a hash-stamped certificate; optionally route the finite obligation through the Lean kernel gate.
The machine never manufactures a grand claim - a verdict is always about a precise, certified model statement.
The numbers, on identical answers
float64 on a single data-center GPU at D = 240. Full methodology in the docs.
float64, GPU, H = 256, B = 4096. Lower is faster. All methods agree to <= 1e-15.
MiB, process-isolated per method. Lower is better.
Put closed-form derivatives in your inner loop
Send us one derivative bottleneck. We will benchmark a closed-form, bit-stable replacement against your current autodiff path - on your problem sizes.
Or email info@derivon.ai