20 projects
omnibias-discrete
Shared differentiable + certified discrete-optimization substrate for omnibias: the DiscreteProblem seam, the annealed temperature-collapse (beta -> inf) sigmoid relaxation solved by unrolled descent (torch + jax twins), a rounding + k-flip local-search decoder with a brute-force oracle, and a rigorous optimality-gap certificate (Lasserre / moment-SOS lower bound over the Boolean hypercube).
omnibias-struct
Certified differentiable dynamic programming: soft Viterbi / shortest-path / CTC layers whose logsumexp_beta relaxation (the beta->inf temperature axis) is differentiated exactly by the closed-form softplus/sigmoid derivative tower (the delta->0 axis) via omnibias.{torch,jax}.jet, with a closed-form logsumexp_beta >= max gap certificate validated against brute-force hard DP; bit-identical torch + jax twins.
omnibias-graph
Differentiable spectral graph operators (Laplacians, spectral embedding, heat kernel) and continuous combinatorial relaxations (Gumbel-Sinkhorn, SoftSort, soft top-k) with torch + jax bit-parity.
omnibias-qcalculus
Quantum / q-calculus: exact q-numbers, q-factorials, Gaussian (q-)binomials and q-Pochhammer symbols, the Jackson q-derivative and q-integral, q-exponentials and q-deformed Bernoulli / Euler numbers, and basic hypergeometric series with certified geometric tails. The q -> 1 limit recovers ordinary calculus (a distinct limit, never conflated with the delta -> 0 founding collapse). Built on omnibias-core and omnibias-difference, with bit-identical torch/jax Jackson-derivative twins.
omnibias-partition
Trainable soft partitions of unity: oblique, axis-aligned and sparse gates, regional expert composition, temperature hardening and scoped membership-gap certificates, with NumPy, PyTorch and JAX implementations.
omnibias-fields
Backend-agnostic field substrate for omnibias: the FieldState value object, the attribute-DSL views, the lazy sigma^(n) cache, and the cross-backend (torch + jax) closed-form differential-operator surface (gradient, divergence, curl, laplacian, hessian, jacobian, integration, inner products, Sobolev norms, tensor divergence, Wirtinger).
omnibias-sos
Certified universal positivity by optimization: sound Sum-of-Squares / Positivstellensatz decompositions. A floating-point SDP proposes a Gram matrix; the proof is a rigorous interval LDL^T positive-definiteness certificate that reuses omnibias.core.verified and the Mathlib-free Lean kernel obligation, so certificates can earn theorem_prover_verified.
omnibias-curvature
Closed-form parameter Hessian / Gauss-Newton Fisher / KFAC factors for one-hidden-layer Riccati fields, built on the omnibias closed-form σ' / σ'' primitives.
omnibias-difference
The founding delta->0 (multi-bias collapse) register: certified finite-difference -> derivative extraction, umbral / Sheffer sequence calculus, and asymptotic-coefficient reading (Stirling / Bernoulli / Euler numbers) read straight off the closed-form omnibias towers. Pure-Python core + rigorous interval-tower certificates from omnibias.core.verified, with bit-identical torch/jax twins for the finite-difference stencil operator.
omnibias-boolean
Differentiable Boolean algebra: exact ANF/Reed-Muller and Walsh spectra, Boolean differential calculus, reproductive equation solving, and a beta-annealed soft-gate system solver built on the omnibias closed-form derivative towers (torch + jax).
omnibias-convex
Differentiable + certified convex optimization (LP/QP) for omnibias: closed-form-Hessian log-barrier interior-point solver, KKT implicit-function gradients (argmin as a differentiable op), and verified optimality enclosures (jax + torch).
omnibias-binary
Closed-form quantization gradients for binary/ternary/k-bit neural-network training via the omnibias tanh-beta Riccati derivative (torch + jax).
omnibias-torch
PyTorch backend for omnibias: trainable scalar operators (OMBU), operator-typed blocks, closed-form activation derivative kernels, and reference PINN / CmbNet / CvxLayer architectures.
omnibias-jax
JAX backend for omnibias: closed-form n-th derivative activation kernels (sigmoid via Eulerian polynomials, tanh via Legendre, Gaussian via Hermite), neural-field Laplacian / Hessian primitives, and Born-Oppenheimer derivative tools for variational quantum Monte Carlo.
omnibias-keras
Keras 3 unified backend for omnibias: closed-form n-th derivative scalar operators (OMBU), operator-typed blocks, and drop-in cmbDense / cmbConv layers that run on TensorFlow, JAX, or PyTorch via keras.ops.
omnibias-core
Numerically-stable closed-form n-th derivative forward-pass framework: pure-Python core with polynomial coefficient generators (Eulerian / Legendre / Hermite) and the backend-agnostic ActivationSpec protocol.
omnibias-geometry
Differential geometry on manifolds for omnibias: metric tensor, Christoffel symbols, covariant derivative, the Laplace-Beltrami operator, Riemann/Ricci/scalar curvature, geodesics, exterior calculus (d, wedge, Hodge star, codifferential), and the pullback metric of a learned chart (g = J^T h J) for learned manifolds. Built on the omnibias-fields substrate with cross-backend (torch + jax) parity.
omnibias-pinn
Physics-informed neural networks with closed-form n-th derivative operators on top of omnibias-core. Cross-backend (torch + jax) typed fields, ops, hard-conservation cages, prebuilt PDE residuals, and diagnostics.
omnibias-ferminet
FermiNet bridge for omnibias: folx-compatible Laplacian adapters, restricted-depth Tier-2 FermiNet ansatz with closed-form Laplacian, and multiblock primitives for analytic nuclear Hessian / Born-Oppenheimer derivative work.
vardang-distributions
Gaussian distributions
