Choose the quantity.
Then the computation.
Mathematical infrastructure for derivative-heavy models. A public library that runs in your own Python environment.
Activation identities
Shared Riccati, Eulerian, and Hermite recurrences evaluate supported activation derivatives. One base activation evaluation is reused; polynomial arithmetic still grows with order.
Read the API ↗02 / TORCHForward Taylor composition
Directional jets carry selected directions; mixed jets carry mixed partials. Taylor coefficients use factorial normalization. Their parameter gradients stay available for learning.
Read the API ↗03 / FIELDSDirect operator contractions
Laplacians can be propagated without a full Hessian. For fixed widths and depth, the deep path grows with input dimension; it has no fixed dimension ceiling.
Read the API ↗04 / PARTITIONTrainable decisions
Smooth partition gates and structured relaxations put routing inside the training loop. Temperature hardening approaches discrete decisions under the documented conditions.
Read the API ↗Explicit backends.
Shared mathematics.
PyTorch and JAX expose network jets and operator contractions. Keras 3 exposes activation and operator layers on its supported backends. These surfaces have different contracts.
Numerical agreement depends on dtype, operation ordering, and the workload. Shared coefficients do not imply universal floating-point identity.
PyTorch
Trainable operators, directional and mixed jets, and optimizer interfaces.
JAX
Functional derivatives, jets, contractions, and explicit precision configuration.
Keras 3
Activation and operator layers for TensorFlow, JAX, or PyTorch.
Nearby shifts. An exact derivative.
Move the bias gap toward zero. The normalized difference approaches the first derivative. omnibias evaluates the analytic limit directly, avoiding subtraction of nearby samples.
Workload by workload.
Measured evaluation times, accuracy checks, and explicit baselines.
Order 8 · 20,000 tanh inputs · Torch eager
Recorded derivative evaluation, not end-to-end training.
Know what
your result means.
Closed-form expressions are evaluated in floating point. Numerical integration and stochastic estimates retain their own limitations. Certificates apply to a stated quantity, domain, and set of assumptions.
Read the guarantees ↗Package-specific licensing
Apache-2.0 covers core, torch, jax, keras, fields, binary, boolean, difference, and qcalculus. Convex, curvature, discrete, graph, partition, sos, and struct offer AGPL-3.0-or-later or a commercial agreement.
Previously distributed Apache versions retain their grants. Check the version you install, including external consumer dependencies.
License & version details ↗