API Reference

Pair this API map with Implementation Derivations when you need the equations, shape contracts, and solver assumptions behind the public classes. Pair it with Research Citation Audit when you need to cite the methods behind a class, solver, diagnostic, or preset. The global registry starts with the SILVA article [1] and archived package [2].

The API is organized by role. The generated pages show signatures, docstrings, inputs, outputs, and source links.

Module	Main contents
Public API	top-level silva_networks import contract and exported names
Solvers	SolverConfig, SolverResult, fixed_point, solve_equilibrium, picard, anderson, broyden, gmres, implicit, JFB, phantom, and SHINE adjoints
Learned Equilibrium Solvers	learned initialization, residual compression, Anderson control, teacher trajectories, and training losses
Quantum Equilibria	exact compact statevector circuit, external circuit adapter, image filter, QDEQ execution modes, and Jacobian diagnostics
Bayesian, Joint, Dynamic, and Certified	posterior equilibrium samples, joint input/state roots, implicit trajectories, and interval certificates
Evidence	transition equivalence, repeated metrics, evidence records, fingerprints, and lifecycle hooks
Experiment Protocols	three execution tiers, data routes, resource plans, acceptance checks, and JSON export for all 64 families
Source-Aligned Equilibria	fourteen independently implemented multiscale, algorithmic, physical, inverse, robust, and equation-residual families with replaceable internals
Jacobians	full_jacobian, vjp, jvp, spectral radius, stability reports
Diagnostics	residual curves, damped updates, Lyapunov-style energy traces
Layers	SILVALayer, SILVAGraphLayer, silva_generalized_layer, silva_deq_reduction_layer, global/local/self operators
Architectures	stacks, cortex hierarchies, graph networks, image classifiers, pooling, readout heads
Point Architectures	ten shape-preserving vector, token, convolutional, U-Net, attention, and spectral fields
Scientific Operators	finite differences, PDE residuals, boundaries, implicit time steps, reaction-diffusion, Burgers, and Fourier equilibrium operators
Recent Equilibrium Families	input-injected Fourier, physics-guided graph, homotopy-flow, and distributional SILVA equilibria
Recent Equilibrium Datasets	equation-checked fields, transport graphs, homotopy pairs, and variable-size empirical measures
Advanced Equilibria	monotone graph and one-time-injected transformer equilibria
Physics-Informed and DAE	Poisson mirror geometry, implicit ODE derivatives, DAE roots, and residual objectives
Advanced Equilibrium Data	exact chain, teacher-map, Poisson, ODE, and DAE teaching problems
Emerging Equilibria	consistency refinement, mixed-boundary graph PDEs, IFNO materials, forward skinning, mesh inference, mechanics, and guided diffusion
Emerging Equilibrium Data	analytic and source-shaped fixtures for consistency, graph PDE, materials, geometry, mesh, diffusion, and mechanics labs
Structured Equilibria	monotone operators, positive-concave maps, non-Euclidean contractions, infinite graph filters, multiscale graph equilibria, and delta caching
Structured Equilibrium Data	certificate-aware vector, graph, image, and frame-pair fixtures for structured family validation
Implicit Bridge	SILVA-named DEQ transition, fixed-point classifier, Euler flow, quadratic optimization, MDEQ bridge
DEQ Engine	general single-state and multi-state SILVA DEQ engine, variational dropout, state packing
Extensibility	generic conditioned equilibrium, transition reports, contract validation, and custom-family construction
Reproducibility	source relationships, equations, datasets, metrics, evidence paths, constructor signatures, and scale-aware builders
Research Depth	six-stage dossiers, configurable components, experiment acceptance checks, artifacts, and result records for all 64 families
Compact Benchmarks	deterministic same-task vector, graph, and field comparison suites with optimization and solver diagnostics
Optical Flow	RAFT-style correlation, warping, DEQ-flow fixed point, synthetic flow data
Generalized Cases	sequence DEQ, multiscale vision DEQ, IGNN, implicit representations, and diffusion equilibria
Family Selection	available_silva_families, silva_family_description, silva_family_constructor, silva_family_signature, silva_equilibrium_model, family aliases
Optimization	constrained quadratic projections and optional CVXPYlayers bridge
SILVA Presets	SILVA-style graph, vision, convolutional, and molecular presets
Datasets	download helpers, tensor adapters, GraphTensorBatch, validation
Source Data	attributed real-data subsets, reproducibility receipts, verified snapshots, source graph masks, optical flow, and Darcy fields
Training	optional supervised fit/evaluate helpers, seeding, checkpoint/resume
Devices	CPU/CUDA/MPS selection and nested tensor movement
Coverage Registry	implementation families mapped to tutorials, notebooks, examples, and tests
Educational NumPy	hand-sized fixed-point, Jacobian, power-iteration, and adjoint helpers

Case-to-API Map

Case	Classes/functions
Scalar DEQ	fixed_point, DEQLayer, np_picard
New conditioned family	SILVAConditionedEquilibrium, SILVAZeroInitializer, validate_silva_transition
Generic SILVA layer	SILVALayer, silva_generalized_layer, make_local_operator, make_global_operator, make_self_operator
Cortex hierarchy	SILVACortexLayer, SILVACortexNetwork, SILVAImageCortexClassifier, silva_cortex_layer, silva_cortex_network
Internal point architectures	available_silva_point_architectures, silva_point_architecture, and ten SILVA...PointArchitecture modules
ODE, PDE, and learned operators	SILVAImplicitTimeStep, SILVAOperatorModel, SILVAFourierNeuralOperator, numerical derivatives, PDE and boundary residuals
Recent equilibrium mechanisms	SILVAFNODEQ, SILVAPhysicsGuidedGraphDEQ, SILVAHomotopyEquilibrium, SILVADistributionalDEQ
Advanced equilibrium mechanisms	SILVAMonotoneGraphEquilibrium, SILVAGenerativeEquilibriumTransformer, SILVAPoissonMirrorEquilibrium
Physics-informed and DAE mechanisms	SILVAPhysicsInformedEquilibrium, SILVAImplicitDAEStep, SILVAResidualDiscriminator
SILVA reductions to baseline implicit models	silva_deq_reduction_layer, silva_message_passing_reduction_layer, SILVAFixedPointBlock, SILVADEQEngine
Graph node or graph prediction	SILVAGraphLayer, SILVAGraphNetwork, SILVAGraphPresetNetwork, pool_entities
Vision vectors	SILVAVisionVectorLayer, SILVAVisionVectorClassifier, DynamicChannelLocal, ChannelSelfAttentionGlobal
Convolutional vision	SILVAConvStem, SILVAConvVisionClassifier, SILVAImageLayer, SILVAImageClassifier
Molecules	SILVAMolecularLayer, SILVAMolecularRegressor, molecular_to_silva_graph
Implicit-layer tutorials	silva_fixed_point_block, silva_fixed_point_classifier, silva_euler_flow_block, silva_quadratic_optimization_layer, silva_multiscale_deq_block
General DEQ systems	SILVADEQEngine, SILVADEQConfig, silva_deq, SILVAVariationalDropout
SILVA DEQ flow	SILVADEQFlow, silva_deq_flow, silva_all_pairs_correlation, silva_flow_warp, silva_endpoint_error
Sequence DEQ	SILVASequenceDEQ, SILVASequenceTransition, SILVARelativeSelfAttention
Multiscale vision DEQ	SILVAMultiscaleDEQ, SILVAMultiscaleClassifier, SILVAMultiscaleSegmenter
Implicit graph and coordinate fields	SILVAImplicitGraphNetwork, SILVAImplicitNeuralRepresentation, SILVACoordinateInjection
Diffusion trajectory equilibrium	SILVADiffusionEquilibrium with a user denoiser and schedule
Learned equilibrium solver	SILVAHyperDEQ, SILVAHyperInitializer, SILVAResidualCompressor, SILVAHyperAndersonController, silva_hyper_deq_loss
Approximate implicit backward paths	SolverConfig(backward_mode="jfb"), BroydenInverseEstimate, SolverConfig(backward_mode="shine"), shine_adjoint_solve
Quantum-circuit equilibrium	SILVAQuantumDEQ, SILVAStatevectorQuantumCircuit, SILVAQuantumCircuitAdapter, SILVAQuantumImageFilter
Bayesian equilibrium	SILVABayesianDEQ, posterior transition protocol, sample states, predictive variance, and KL term
Joint input/state inference	SILVAJointInferenceEquilibrium, replaceable representation transition and projected input update
Implicit spatiotemporal dynamics	SILVAImplicitSpatiotemporalEquilibrium, known and learned dynamics, projector, and per-step solver records
Certified equilibrium	SILVACertifiedEquilibrium, interval bounds, class certificates, and semialgebraic export
Evidence and equivalence	compare_silva_transitions, run_silva_evidence, metric summaries, and staged lifecycle hooks
Three-tier experiment protocol	silva_family_experiment_protocol, protocol audit, resource routes, and JSON export
Sequence DEQ	SILVASequenceDEQ, relative attention, adaptive embedding/projected softmax, custom module hooks
Multiscale DEQ	SILVAMultiscaleDEQ, learned fusion, weight norm, material classification and segmentation heads
Coupled RAFT/DEQ-Flow	SILVARAFTDEQ, residual encoders, SILVACorrelationPyramid, SILVARAFTUpdateBlock, correction loss and cached state
Optical-flow compatibility names	SILVAOpticalFlowDEQ, silva_optical_flow_deq
Projected QP	SILVAProjectedQPLayer, silva_projected_qp_layer, projection helpers
Constrained optimization compatibility	SILVAConstrainedQuadraticLayer, silva_constrained_quadratic_layer, silva_cvxpy_layer
Family selection	available_silva_families, silva_equilibrium_model, silva_family_description, silva_family_constructor, silva_family_signature; see Family Selection
Reproduction	silva_reproduction_spec, all_silva_reproduction_specs, audit_silva_reproduction_specs, build_silva_reproduction; see Reproducibility
Experiment dossiers	silva_experiment_dossier, all_silva_experiment_dossiers, audit_silva_experiment_dossiers, SILVAResultRecord; see Research Depth
Common compact comparisons	run_vector_comparison, run_graph_comparison, run_field_comparison, run_compact_comparisons; see Compact Benchmarks
Dataset conversion	GraphTensorBatch, tabular_to_silva_graph, images_to_silva_vectors, images_to_silva_pixel_graph, pyg_data_to_silva_graph
Source-data reproduction	load_source_snapshot, load_vision_source_subset, load_planetoid_source_subset, load_optical_flow_source_subset, load_darcy_source_subset; see Source Data
Custom training objectives	BatchStep, fit_supervised(..., step_fn=...), evaluate(..., step_fn=...)
Optional training loop	TrainConfig, fit_supervised, evaluate, seed_everything
Diagnostics	residual_curve, stability_report, damped_spectral_radius, solve_with_energy

Citation Shortcuts

API family	Citation shortcut
solvers	Anderson, Broyden, or GMRES depending on SolverConfig.solver and adjoint method
Jacobian diagnostics	Deep Implicit Layers, Hutchinson, and Jacobian-regularized DEQ when applicable
graph attention	GAT and attention literature
global pooling/context	Deep Sets plus SILVA for the gated/context field
implicit bridge	DEQ, Neural ODEs, OptNet/differentiable optimization, or MDEQ depending on the object
DEQ engine	TorchDEQ, DEQ, and SILVA package
optical flow	RAFT and DEQ-Flow, plus the optical-flow dataset or benchmark
optimization	projected-gradient methods, OptNet, CVXPYlayers depending on the selected layer
presets	SILVA paper/package plus the branch-level citations used by the chosen preset
point architectures	SILVA plus the primary architecture paper when the selected field derives from a named architecture
recent equilibrium families	SILVA plus FNO-DEQ, physics-guided graph DEQ, HomoODE, or DDEQ according to the selected mechanism
advanced equilibrium families	SILVA plus MIGNN, GET, DEQ-MD, or PIDEQ according to the selected mechanism
DAE and residual objectives	DAE-PINN or differential-equation GAN lineage; the latter is not a deep-equilibrium family
learned solver	SILVA plus Neural Deep Equilibrium Solvers; cite the task architecture and dataset separately
approximate backward path	SILVA plus JFB or SHINE according to the selected backward_mode
quantum equilibrium	SILVA plus QDEQ, the circuit/backend method, and the image dataset

Common Imports

from silva_networks import (
    SolverConfig,
    SILVACortexLayer,
    SILVACortexNetwork,
    SILVAConditionedEquilibrium,
    SILVADEQFlow,
    SILVADiffusionEquilibrium,
    SILVAGraphNetwork,
    SILVAGraphPresetNetwork,
    SILVAProjectedQPLayer,
    SILVARAFTDEQ,
    SILVASequenceDEQ,
    SILVAMultiscaleDEQ,
    SILVAImplicitGraphNetwork,
    SILVAImplicitNeuralRepresentation,
    SILVAImageCortexClassifier,
    available_silva_families,
    available_silva_point_architectures,
    load_source_snapshot,
    silva_deq_reduction_layer,
    silva_projected_qp_layer,
    silva_point_architecture,
    silva_equilibrium_model,
    silva_generalized_layer,
    silva_deq,
    solve_equilibrium,
    silva_deq_flow,
    tabular_to_silva_graph,
    fit_supervised,
    TrainConfig,
    stability_report,
    validate_silva_transition,
)

Object Families

The package has three layers of abstraction:

Level	Use when
SILVALayer and operator modules	building a new interaction field directly
SILVAConditionedEquilibrium	wrapping a completely custom conditioned transition, initializer, and readout
SILVACortexLayer and SILVACortexNetwork	putting deep internal modules inside one equilibrium point and linking several points
SILVAStack and SILVAGraphNetwork	stacking equilibrium layers with custom operators
reference presets	reproducing or varying the public SILVA configurations

The tensor adapters are intentionally separate from the model classes. This keeps the engine stable while allowing new datasets to be preprocessed into the same x, edge_index, edge_attr, batch, y structure.

Where to Go Next

Question	Page
Which names form the stable import surface?	Public API
How are objects organized by scientific case?	Case Atlas
Where are complete runnable programs?	Examples