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API REFERENCE/omnibias-core

omnibias.core

0.5.0rc1Release candidatePython >=3.10Apache-2.0

Coefficient recurrences, activation contracts, jet algebra, and verified arithmetic shared by the numerical backends.

import omnibias.core

Use core when you need backend-independent coefficients, mathematical specifications, or verified arithmetic. It does not replace a tensor backend for a training loop. Activation specifications describe available value, derivative, integral, and transform paths; availability is explicit and varies by specification.

The jet modules distinguish Taylor coefficients from raw derivative towers. Order-n Taylor coefficients include the factorial normalization; converting between representations is part of the contract. Multivariate expansions also carry a multi-index convention and an explicit combinatorial budget.

Verified arithmetic has separate assumptions from ordinary floating-point evaluation. Represent exact rationals and floating-point data deliberately, preserve enclosure endpoints, and inspect the outcome of every supported checker. A digest is integrity evidence, not a mathematical proof. Start with the polynomial example and the verified-arithmetic guide before integrating a specialized enclosure algorithm.

Module contract & mathematical conventions

Shared activation specifications, derivative coefficients, and jet algebra.

Numerical implementations live in explicit submodules; this package has no tensor-framework dependency.

Shared formulas do not imply universal floating-point identity. Verify dtype, shape, derivative-order support, and the stated numerical assumptions for the path you use.

Module source ↗Source revision 9a2d73df0573Running reference examples →
band_embedModule ↗bellModule ↗block_searchModule ↗composed_curvatureModule ↗confluenceModule ↗contractionModule ↗cubatureModule ↗framesModule ↗ftcModule ↗implicitModule ↗integral_kernelModule ↗jetsModule ↗line_searchModule ↗locusModule ↗mollifierModule ↗multi_indexModule ↗multipackModule ↗parameter_jetsModule ↗polynomialsModule ↗proofModule ↗realizationModule ↗refineModule ↗scaleModule ↗scanModule ↗specModule ↗spectral_designModule ↗tanh_methodModule ↗transferModule ↗transforms_pdeModule ↗uncertaintyModule ↗verifiedModule ↗weight_loss_jetModule ↗

Imports & aliases​

These names share a definition with another public module. Follow a name for its full contract, parameters, and examples.

Import from this moduleCanonical reference
ActivationSpecomnibias.core.ActivationSpec
AffineSetomnibias.core.AffineSet
BandPlanomnibias.core.BandPlan
BankSpecomnibias.core.BankSpec
BlockKindomnibias.core.BlockKind
BlockSpecomnibias.core.BlockSpec
ComposedCurvatureConfigomnibias.core.ComposedCurvatureConfig
ComposedCurvatureReportomnibias.core.ComposedCurvatureReport
DEQConfigomnibias.core.DEQConfig
DEQNotContractiveomnibias.core.DEQNotContractive
DEQSolverUnknownomnibias.core.DEQSolverUnknown
EffectiveOperatoromnibias.core.EffectiveOperator
EqualitySystemomnibias.core.EqualitySystem
FlowSystemomnibias.core.FlowSystem
FrameSpecomnibias.core.FrameSpec
GradientSecantomnibias.core.GradientSecant
Indicatoromnibias.core.Indicator
JetLineSearchConfigomnibias.core.JetLineSearchConfig
Layeromnibias.core.Layer
LineSearchResultomnibias.core.LineSearchResult
LinearizingTransformomnibias.core.LinearizingTransform
MollifierSpecomnibias.core.MollifierSpec
MomentSystemomnibias.core.MomentSystem
MultiPackSpecomnibias.core.MultiPackSpec
NewtonResultomnibias.core.NewtonResult
NthDerivativeFnomnibias.core.NthDerivativeFn
PackSpecomnibias.core.PackSpec
QuadratureRuleomnibias.core.QuadratureRule
RefinePolicyomnibias.core.RefinePolicy
RefineReportomnibias.core.RefineReport
RefinedPackomnibias.core.RefinedPack
ScaleBandomnibias.core.ScaleBand
ScaledPackomnibias.core.ScaledPack
TensorFnomnibias.core.TensorFn
TensorTomnibias.core.TensorT
TransformKernelsomnibias.core.TransformKernels
TravellingWaveAnsatzomnibias.core.TravellingWaveAnsatz
UnitTermomnibias.core.UnitTerm
WeightLossJetSpecomnibias.core.WeightLossJetSpec
admissibility_constantomnibias.core.admissibility_constant
affine_locusomnibias.core.affine_locus
alpha_for_peakomnibias.core.alpha_for_peak
apply_block_stepomnibias.core.apply_block_step
apply_ruleomnibias.core.apply_rule
arrangement_w_blockomnibias.core.arrangement_w_block
assert_zero_perturbationomnibias.core.assert_zero_perturbation
bell_completeomnibias.core.bell_complete
bell_numberomnibias.core.bell_number
bell_partialomnibias.core.bell_partial
central_stencil_weightsomnibias.core.central_stencil_weights
certified_band_gapomnibias.core.certified_band_gap
certified_erroromnibias.core.certified_error
certified_truncation_radiusomnibias.core.certified_truncation_radius
certify_locus_pointomnibias.core.certify_locus_point
chain_rule_mse_blocksomnibias.core.chain_rule_mse_blocks
coarse_grain_linearomnibias.core.coarse_grain_linear
cole_hopf_jetomnibias.core.cole_hopf_jet
cole_hopf_uomnibias.core.cole_hopf_u
compile_bankomnibias.core.compile_bank
contact_residualomnibias.core.contact_residual
default_block_configomnibias.core.default_block_config
design_band_planomnibias.core.design_band_plan
design_orderomnibias.core.design_order
design_ruleomnibias.core.design_rule
dilated_sigma_nomnibias.core.dilated_sigma_n
eigh_symmetricomnibias.core.eigh_symmetric
eval_gaussian_derivativeomnibias.core.eval_gaussian_derivative
eval_sigma_derivativeomnibias.core.eval_sigma_derivative
eval_tanh_derivativeomnibias.core.eval_tanh_derivative
factorial_jet_multiplyomnibias.core.factorial_jet_multiply
factorial_jet_reciprocalomnibias.core.factorial_jet_reciprocal
flow_coefficientsomnibias.core.flow_coefficients
gram_matrixomnibias.core.gram_matrix
hermite_coeffsomnibias.core.hermite_coeffs
honesty_payloadomnibias.core.honesty_payload
hp_decisionomnibias.core.hp_decision
incidence_matrixomnibias.core.incidence_matrix
index_positionomnibias.core.index_position
is_admissibleomnibias.core.is_admissible
is_holonomicomnibias.core.is_holonomic
is_poisedomnibias.core.is_poised
last_linear_blockomnibias.core.last_linear_block
local_scale_from_derivativesomnibias.core.local_scale_from_derivatives
make_tempered_fastpathomnibias.core.make_tempered_fastpath
make_tempered_transformsomnibias.core.make_tempered_transforms
mish_inner_coeffsomnibias.core.mish_inner_coeffs
momentsomnibias.core.moments
multi_index_factorialomnibias.core.multi_index_factorial
multi_indicesomnibias.core.multi_indices
multiply_tableomnibias.core.multiply_table
num_multi_indicesomnibias.core.num_multi_indices
ombu_bias_blockomnibias.core.ombu_bias_block
one_layer_lossomnibias.core.one_layer_loss
one_layer_loss_gradomnibias.core.one_layer_loss_grad
one_layer_loss_hessianomnibias.core.one_layer_loss_hessian
one_layer_loss_jetomnibias.core.one_layer_loss_jet
one_layer_newton_directionomnibias.core.one_layer_newton_direction
one_layer_output_jetomnibias.core.one_layer_output_jet
one_layer_param_countomnibias.core.one_layer_param_count
overlapomnibias.core.overlap
pack_momentomnibias.core.pack_moment
pack_one_layer_paramsomnibias.core.pack_one_layer_params
peak_frequencyomnibias.core.peak_frequency
peano_kernelomnibias.core.peano_kernel
polya_conditionomnibias.core.polya_condition
polynomial_wolfeomnibias.core.polynomial_wolfe
refine_bankomnibias.core.refine_bank
reject_andersonomnibias.core.reject_anderson
reject_deq_contractionomnibias.core.reject_deq_contraction
reject_full_parameter_jacobianomnibias.core.reject_full_parameter_jacobian
relative_bandwidthomnibias.core.relative_bandwidth
report_exponentsomnibias.core.report_exponents
rescale_packomnibias.core.rescale_pack
resolve_block_maskomnibias.core.resolve_block_mask
response_profileomnibias.core.response_profile
run_model_line_searchomnibias.core.run_model_line_search
scalar_nest_hessianomnibias.core.scalar_nest_hessian
select_composed_stepomnibias.core.select_composed_step
select_model_stepomnibias.core.select_model_step
sigmoid_polynomial_coeffsomnibias.core.sigmoid_polynomial_coeffs
solve_denseomnibias.core.solve_dense
solve_ruleomnibias.core.solve_rule
spectral_radius_inf_boundomnibias.core.spectral_radius_inf_bound
stiffness_matrixomnibias.core.stiffness_matrix
symmetrizeomnibias.core.symmetrize
tail_boundomnibias.core.tail_bound
tanh_polynomial_coeffsomnibias.core.tanh_polynomial_coeffs
target_momentsomnibias.core.target_moments
taylor_coeffs_from_derivativesomnibias.core.taylor_coeffs_from_derivatives
temperedomnibias.core.tempered
unit_direction_from_maskomnibias.core.unit_direction_from_mask
unpack_one_layer_paramsomnibias.core.unpack_one_layer_params
vanishing_momentsomnibias.core.vanishing_moments
verify_cole_hopf_burgers_jetomnibias.core.verify_cole_hopf_burgers_jet
verify_exactomnibias.core.verify_exact
verify_transformomnibias.core.verify_transform
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