silva_non_euclidean_equilibrium Reproduction Dossier

weighted-infinity non-Euclidean monotone equilibrium. This dossier connects the source mechanism to its SILVA implementation, compact evidence, replaceable components, and source-scale route. Existing tests and notebooks remain the executable authority.

Evidence boundary

The mechanism is compact-verified in the package suite. The final source-scale stage remains planned until the cited data, complete optimization budget, checkpoints, and evaluation protocol have actually run.

Identity and Sources

Field	Value
Domain	optimization and certified equilibria
Task contract	B,D input -> certified B,H equilibrium and task readout
Source relation	paper-adaptation
References	[77]
Repositories	https://github.com/davydovalexander/Non-Euclidean_Mon_Op_Net
Editable scale plan	experiments/reproduction/configs/silva_non_euclidean_equilibrium.json

Governing Equation

The domain-level state contract is

\[ 0\in\mathcal A_\theta(z^\star;x)+\mathcal B(z^\star),\qquad y=Q_\psi(z^\star). \]

The implementation registry specializes it operationally as

z_star=phi(A z_star+B x+b); mu_infinity,D(A)<1

Define the root residual

\[ R_\theta(z;x)=z-T_\theta(z;x). \]

At a regular equilibrium, differentiating \(R_\theta(z^\star;x)=0\) gives

\[ \frac{\partial z^\star}{\partial x} = \left(I-\frac{\partial T_\theta}{\partial z}\right)^{-1} \frac{\partial T_\theta}{\partial x}. \]

This identity explains why the forward residual, the conditioning derivative, and the adjoint linear solve must be diagnosed separately from the task metric.

What Is Preserved

• weighted-infinity matrix-measure contraction certificate
• diagonally weighted parameterization and averaged fixed-point iteration
• input-output sensitivity bound in the learned non-Euclidean metric

What Can Be Replaced

Each item below is an explicit control rather than an undocumented modification:

• replace the certified operator, source, activation, metric, or readout
• evaluate input-output sensitivity in the learned weighted norm
• state width
• learned metric
• one-sided bound
• averaging coefficient

Constructor and Shape Contract

silva_non_euclidean_equilibrium(in_dim: 'int', state_dim: 'int', out_dim: 'int', *, operator: 'nn.Module | None' = None, source: 'nn.Module | None' = None, activation: 'Callable[[Tensor], Tensor]' = <function relu>, readout: 'nn.Module | None' = None, one_sided_bound: 'float' = 0.05, averaging: 'float | None' = None, config: 'SolverConfig | None' = None) -> 'None'

The transition must preserve the declared equilibrium-state shape even when the encoder, branch operators, constraints, solver, and readout are replaced. Test the transition by itself before testing the complete root solve.

Progressive Experiment Ladder

1. Equation and tensor contract

Objective: Make the state, conditioning variables, operator, and readout explicit.

Procedure:

• Write and evaluate the family equation: z_star=phi(A z_star+B x+b); mu_infinity,D(A)<1
• Declare every tensor axis, boundary, mask, graph, or physical unit.
• Check the transition output has exactly the same shape as the equilibrium state.

Acceptance checks:

• finite transition values
• shape-preserving state update
• all conditioning variables affect the intended branch

Evidence target: contract-verified.

2. Primitive mechanism reconstruction

Objective: Build the retained source mechanism from replaceable modules.

Procedure:

• weighted-infinity matrix-measure contraction certificate
• diagonally weighted parameterization and averaged fixed-point iteration
• input-output sensitivity bound in the learned non-Euclidean metric

Acceptance checks:

• primitive modules expose trainable parameters and gradients
• mechanism-specific invariance or constraint check passes
• direct transition evaluation is deterministic under a fixed seed

Evidence target: compact-verified.

3. Public abstraction equivalence

Objective: Verify that the assembled family evaluates the same transition as its primitives.

Procedure:

• Copy the primitive module parameters into the public family constructor.
• Evaluate one transition and one complete equilibrium with identical inputs.
• Compare outputs, residuals, and parameter gradients with declared tolerances.

Acceptance checks:

• transition outputs agree
• equilibrium residual is finite and decreases
• primitive and assembled gradients agree on the compact case

Evidence target: compact-verified.

4. Compact real or analytic task

Objective: Exercise training, evaluation, diagnostics, and serialization end to end.

Procedure:

• make_non_euclidean_robustness_dataset gives clean/perturbed inputs and known weighted-infinity equilibria.

Acceptance checks:

• record clean and perturbed task metric
• record one-sided Lipschitz certificate
• record empirical sensitivity
• record fixed-point residual
• checkpoint reload reproduces the recorded prediction
• result record contains data and configuration fingerprints

Evidence target: compact-verified.

5. Official-data subset

Objective: Validate the complete source data path before spending the full budget.

Procedure:

• Acquire one declared benchmark and reproduce clean and perturbed evaluation preprocessing.
• Freeze preprocessing, split logic, metric code, and checkpoint format.
• Run a deterministic subset large enough to expose batching and memory failures.

Acceptance checks:

• dataset receipt and checksum are stored
• resume and evaluation paths reproduce the same subset metric
• memory and runtime are measured rather than estimated

Evidence target: subset-verified.

6. Source-scale reproduction or declared extension

Objective: Run the cited protocol, or change it explicitly as a SILVA extension.

Procedure:

• Acquire one declared benchmark and reproduce clean and perturbed evaluation preprocessing.
• Match the weighted metric, one-sided matrix-measure target, averaging rule, architecture, and solver settings.
• Verify the compact certificate and empirical sensitivity, then report clean/robust task metrics, residuals, runtime, and memory.
• source architecture, metric initialization, one-sided target, data perturbations, and preprocessing
• averaging rule, solver tolerance, optimizer, robustness protocol, and seeds
• task accuracy, certified bound, empirical sensitivity, residual, and source baselines

Acceptance checks:

• all required artifacts are archived
• reported metrics use the cited evaluation protocol
• every architectural or training deviation is listed
• claims match the achieved evidence status

Evidence target: planned.

Data, Access, and Storage

Candidate datasets:

• MNIST
• CIFAR-10
• compact weighted-infinity perturbation pairs

Authoritative routes:

• https://arxiv.org/abs/2106.03194
• https://github.com/davydovalexander/Non-Euclidean_Mon_Op_Net

Access obligations:

• Acquire the declared vision benchmark through its stated public route and preserve train/test preprocessing.
• Archive clean and perturbed evaluation indices, perturbation norm, metric weights, and checkpoint revision together.

Storage planning:

• Budget the base checkpoint, learned metric, clean/perturbed batches, solver traces, and certificate tables independently.
• For large dense states, prefer structured operators because the unconstrained matrix and its optimizer state scale quadratically.

Preprocessing record:

• record dataset version, split, normalization, shape convention, and seed
• preserve masks, graph indices, boundaries, or physical units required by the domain

Metrics and Current Evidence

Required metrics:

• clean and perturbed task metric
• one-sided Lipschitz certificate
• empirical sensitivity
• fixed-point residual

The vector compact suite ran this family on the same task and data as the other compatible families in that suite.

Measure	Recorded value
Initial loss	0.130369
Final loss	0.00584279
Fractional loss reduction	0.955
Residual or final increment norm	9.74717e-07
Iterations or tied increments	16
Parameter count	73
Final gradient norm	0.070943

These values are compact-verified evidence. They establish finite optimization, gradient flow, and diagnostic reporting; they are not a publication ranking.

Executed notebook paths:

• notebooks/package_api/38_silva_non_euclidean_equilibrium.ipynb

Mechanism tests:

• tests/test_structured_equilibria.py

Compact Defaults

Option	Value
tier	'smoke'
config	SolverConfig(solver='anderson', max_iter=12, tol=1e-05, alpha=1.0, history=3, ridge=0.0001, beta=1.0, stop_mode='relative', relative_eps=1e-08, anderson_batch_dims=1, track_residuals=True, reengage=True, backward_mode='implicit', backward_solver='gmres', backward_max_iter=20, backward_tol=1e-05, backward_stop_mode='relative', backward_relative_eps=1e-08, phantom_steps=1, phantom_tau=1.0, neumann_terms=5, shine_refine_steps=0, indexing=(), return_best=True)

Full Defaults

Option	Value
tier	'full'
config	SolverConfig(solver='anderson', max_iter=60, tol=1e-05, alpha=1.0, history=6, ridge=0.0001, beta=1.0, stop_mode='relative', relative_eps=1e-08, anderson_batch_dims=1, track_residuals=True, reengage=True, backward_mode='implicit', backward_solver='gmres', backward_max_iter=80, backward_tol=1e-05, backward_stop_mode='relative', backward_relative_eps=1e-08, phantom_steps=1, phantom_tau=1.0, neumann_terms=5, shine_refine_steps=0, indexing=(), return_best=True)

Defaults establish a starting budget; the cited source protocol takes precedence whenever reproduction is the claim.

Source-Scale Checklist

• Acquire one declared benchmark and reproduce clean and perturbed evaluation preprocessing.
• Match the weighted metric, one-sided matrix-measure target, averaging rule, architecture, and solver settings.
• Verify the compact certificate and empirical sensitivity, then report clean/robust task metrics, residuals, runtime, and memory.

Benchmark-specific requirements:

• source architecture, metric initialization, one-sided target, data perturbations, and preprocessing
• averaging rule, solver tolerance, optimizer, robustness protocol, and seeds
• task accuracy, certified bound, empirical sensitivity, residual, and source baselines

Required archived artifacts:

• machine-readable model and solver configuration
• dataset receipt with source revision, split, license, and checksum
• preprocessing and normalization record
• seeded training and evaluation log
• checkpoint and optimizer-resume state for trained experiments
• task metrics and equilibrium diagnostics in a machine-readable result
• runtime, peak-memory, device, precision, and dependency record
• declared deviations from the cited protocol

Reporting Rule

Report the achieved evidence status, not the intended one. A compact or subset run may validate the implementation and data path, but only a completed cited protocol supports a source-scale reproduction statement. Modified operators are valuable SILVA extensions when every deviation is named and measured.

Where to Go Next

Question	Page
Where are all family dossiers?	Family Dossier Index
How is a custom family assembled?	Advanced Extension Handbook
How are experiment stages represented in the API?	Research-Depth API
Which lab inspects every dossier?	Family Dossier Lab