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silva_efficient_infinite_graph Reproduction Dossier

efficient infinite-depth graph 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 graphs and distributed systems
Task contract N,D node features and symmetric or sparse graph operator -> node output
Source relation paper-adaptation
References [78]
Repositories https://github.com/liu-jc/EIGNN
Editable scale plan experiments/reproduction/configs/silva_efficient_infinite_graph.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_star=gamma S^T Z_star g(F)^T+X; g(F)=F^T F/||F^T F||_F

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

  • Frobenius-normalized positive-semidefinite channel Gram map
  • graph/channel eigendecomposition for an exact dense symmetric solve
  • the same equilibrium equation through iterative sparse or directed propagation

What Can Be Replaced

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

  • replace source/readout maps and normalized channel Gram factor
  • switch between differentiable closed-form and iterative SILVA solves
  • nodes
  • sparse edges
  • channel width
  • spectral cache

Constructor and Shape Contract

silva_efficient_infinite_graph(in_dim: 'int', state_dim: 'int', out_dim: 'int', *, gamma: 'float' = 0.8, learnable_gamma: 'bool' = False, source: 'nn.Module | None' = None, readout: 'nn.Module | None' = None, solve_mode: 'GraphSolveMode' = 'auto', gram_epsilon: 'float' = 1e-12, 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=gamma S^T Z_star g(F)^T+X; g(F)=F^T F/||F^T F||_F
  • 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:

  • Frobenius-normalized positive-semidefinite channel Gram map
  • graph/channel eigendecomposition for an exact dense symmetric solve
  • the same equilibrium equation through iterative sparse or directed propagation

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_eignn_chain_dataset gives a normalized graph, injected signals, and a known infinite-depth equilibrium.

Acceptance checks:

  • record node accuracy
  • record closed-form/iterative agreement
  • record denominator margin
  • 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 its official features, labels, split, and normalization.
  • 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 its official features, labels, split, and normalization.
  • Use the normalized channel Gram map and match gamma, width, optimizer, early stopping, and either spectral or iterative solve route.
  • Check closed-form/iterative agreement on a compact graph before reporting source-scale node accuracy, denominator margin, runtime, and memory.
  • source graph split, features, graph normalization, labels, and transductive protocol
  • hidden width, gamma, optimizer, weight decay, early stopping, and seeds
  • node accuracy, closed-form agreement, denominator margin, 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 co-purchase graphs
  • compact chain graphs

Authoritative routes:

  • https://arxiv.org/abs/2202.10720
  • https://github.com/liu-jc/EIGNN

Access obligations:

  • Citation and co-purchase graph datasets are publicly distributed through their respective benchmark providers.
  • Retain the exact split, feature normalization, self-loop convention, graph normalization, and source revision.

Storage planning:

  • Sparse iterative storage is proportional to edges plus node states; the dense closed form additionally stores graph eigenvectors with quadratic node cost.
  • Precompute dense spectra only when they fit comfortably; shard features and use sparse propagation for large graphs.

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
  • closed-form/iterative agreement
  • denominator margin
  • 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 0.401511
Final loss 0.0134108
Fractional loss reduction 0.967
Residual or final increment norm 0.00533069
Iterations or tied increments 28
Parameter count 52
Final gradient norm 0.210812

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/39_silva_efficient_infinite_graph.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 its official features, labels, split, and normalization.
  • Use the normalized channel Gram map and match gamma, width, optimizer, early stopping, and either spectral or iterative solve route.
  • Check closed-form/iterative agreement on a compact graph before reporting source-scale node accuracy, denominator margin, runtime, and memory.

Benchmark-specific requirements:

  • source graph split, features, graph normalization, labels, and transductive protocol
  • hidden width, gamma, optimizer, weight decay, early stopping, and seeds
  • node accuracy, closed-form agreement, denominator margin, 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