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silva_multiscale_graph_implicit Reproduction Dossier

multiscale graph implicit network with nodewise fusion. 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 graphs and distributed systems
Task contract N,D node features and graph operator -> per-scale equilibria and fused node output
Source relation paper-adaptation
References [79]
Repositories https://github.com/liu-jc/MGNNI
Editable scale plan experiments/reproduction/configs/silva_multiscale_graph_implicit.json

Governing Equation

The domain-level state contract is

\[ Z^\star=T_\theta(Z^\star;X,A,E,b),\qquad \widehat Y=Q_\psi(Z^\star). \]

The implementation registry specializes it operationally as

Z_m_star=gamma S^m Z_m_star g(F_m)^T+X; Z=sum_m beta_m(Z_m_star)Z_m_star

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

  • one infinite graph equilibrium for each declared graph-power scale
  • independent normalized channel factors across scales
  • nodewise softmax attention over converged scale states

What Can Be Replaced

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

  • replace each scale factor, source, fusion attention, readout, or solver
  • add graph powers while retaining separately inspectable equilibria
  • graph-power scales
  • per-scale widths
  • sparse edges
  • solver budgets

Constructor and Shape Contract

silva_multiscale_graph_implicit(in_dim: 'int', state_dim: 'int', out_dim: 'int', *, scales: 'Sequence[int]' = (1, 2), gamma: 'float' = 0.8, source: 'nn.Module | None' = None, graph_source: 'nn.Module | None' = None, readout: 'nn.Module | None' = None, fusion: 'ScaleFusion' = 'attention', attention_dim: 'int | None' = None, gram_epsilon: 'float' = 1e-12, config: 'SolverConfig | Sequence[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_m_star=gamma S^m Z_m_star g(F_m)^T+X; Z=sum_m beta_m(Z_m_star)Z_m_star
  • 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:

  • one infinite graph equilibrium for each declared graph-power scale
  • independent normalized channel factors across scales
  • nodewise softmax attention over converged scale states

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_mgnni_multiscale_dataset gives per-scale graph equilibria and node-dependent target fusion weights.

Acceptance checks:

  • record node accuracy
  • record per-scale residual
  • record attention entropy and scale usage
  • record runtime and memory
  • 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 a declared graph benchmark and preserve the official split, graph normalization, and feature 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 a declared graph benchmark and preserve the official split, graph normalization, and feature preprocessing.
  • Match graph-power scales, per-scale channel factors, equilibrium budgets, and nodewise attention fusion.
  • Validate per-scale states and normalized attention on the compact case, then report task accuracy, residuals, fusion statistics, runtime, and memory.
  • source graph split, features, graph normalization, labels, and scale list
  • per-scale widths, gamma, attention dimension, optimizer, early stopping, and seeds
  • node accuracy, per-scale residuals, attention statistics, runtime, and memory

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:

  • Cora
  • Citeseer
  • Pubmed
  • Amazon
  • Coauthor
  • compact multiscale chain graphs

Authoritative routes:

  • https://arxiv.org/abs/2210.08353
  • https://github.com/liu-jc/MGNNI

Access obligations:

  • Use the benchmark provider's original graph, labels, and declared transductive split.
  • Cache graph powers or sparse propagation plans by dataset checksum, normalization, and scale list.

Storage planning:

  • State storage scales with nodes times state width times the number of graph scales, plus per-scale solver history.
  • Cache sparse graph powers or repeated sparse propagation plans rather than materializing dense matrices.

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:

  • node accuracy
  • per-scale residual
  • attention entropy and scale usage
  • runtime and memory

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

Measure Recorded value
Initial loss 0.628229
Final loss 0.0291975
Fractional loss reduction 0.954
Residual or final increment norm 0.00382243
Iterations or tied increments 56
Parameter count 111
Final gradient norm 0.259409

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/40_silva_multiscale_graph_implicit.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=0, 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=0, 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 a declared graph benchmark and preserve the official split, graph normalization, and feature preprocessing.
  • Match graph-power scales, per-scale channel factors, equilibrium budgets, and nodewise attention fusion.
  • Validate per-scale states and normalized attention on the compact case, then report task accuracy, residuals, fusion statistics, runtime, and memory.

Benchmark-specific requirements:

  • source graph split, features, graph normalization, labels, and scale list
  • per-scale widths, gamma, attention dimension, optimizer, early stopping, and seeds
  • node accuracy, per-scale residuals, attention statistics, runtime, and memory

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