Real-Dataset Reproduction

SILVA separates three questions that are easy to conflate:

1. Is the mathematical mechanism correct? Known-solution generators test fixed points, certificates, gradients, and solver residuals.
2. Does the implementation accept the source data representation? Compact, attributed source snapshots test real images, graph masks, fields, or video frames through the public constructors.
3. Does a complete experiment reproduce a published result? That requires the full dataset, source split, architecture, training schedule, seeds, stopping rules, and metrics.

A compact run answers the first two questions. It is not evidence for the third.

Source Receipts

Every source adapter returns a SourceDataReceipt. If the selected tensors are \(T_1,\ldots,T_m\), the recorded content identifier is

\[ h=\operatorname{SHA256}\left( \operatorname{encode}(T_1)\Vert\cdots\Vert\operatorname{encode}(T_m) \right). \]

The encoding includes each tensor's dtype, shape, and contiguous bytes. The receipt also records source indices, split, adapter version, preprocessing, dataset page, citation, and access statement. A reader can therefore distinguish two runs that used the same dataset name but different examples or transforms.

from silva_networks import load_source_snapshot

sample = load_source_snapshot(
    "docs/assets/source-data/cifar10-balanced-10.pt"
)
print(sample.receipt.as_dict())
images = sample.tensors["images"]
labels = sample.tensors["labels"]

load_source_snapshot recomputes the tensor hash by default and rejects altered content.

Included Compact Sources

All three records are present both under docs/assets/source-data/ and inside the installed package. load_bundled_source_snapshot("cifar10"), load_bundled_source_snapshot("cora"), and load_bundled_source_snapshot("motion") therefore reproduce the compact teaching inputs without a repository checkout.

Snapshot	Contents	Size in the source collection	Purpose
CIFAR-10	one indexed image per class, resized to \(16\times16\)	about 170 MB compressed	vision shape, loss, gradient, and certificate checks
Cora	connected 96-node induced graph with source node ids and all split-mask kinds	less than 20 MB	graph propagation, masked loss, and scale-fusion checks
public motion	consecutive real-video frames 100 and 101 at \(96\times160\)	about 3.5 MB	qualitative cache-activity check

CIFAR-10 is cited at [81], the Planetoid protocol at [82], and the public motion source at [86]. The generated manifest.json records archive and tensor checksums.

Regenerate the snapshots from locally available source data with:

python scripts/prepare_source_snapshots.py

The script does not enable network access unless --download is supplied.

Live Dataset Adapters

The snapshots keep every notebook executable from a repository checkout. The same public functions open complete local datasets:

from silva_networks import (
    load_optical_flow_source_subset,
    load_planetoid_source_subset,
    load_vision_source_subset,
)

cifar = load_vision_source_subset(
    "CIFAR10",
    root="data",
    samples_per_class=50,
    seed=0,
    normalization="source",
    download=False,
)

cora = load_planetoid_source_subset(
    "Cora",
    root="data/planetoid",
    subset_nodes=None,  # complete transductive graph
    download=False,
)

sintel = load_optical_flow_source_subset(
    "Sintel",
    root="data/flow",
    split="train",
    pass_name="clean",
    index=0,
)

subset_nodes=None is essential for a Planetoid benchmark. An induced Cora snapshot changes the graph and is only a teaching task.

Six Structured Families

Monotone Operator Equilibrium

For flattened image \(x\in\mathbb{R}^{3HW}\), the equilibrium is the monotone inclusion

\[ 0\in(I-W)z^\star-Ux-b+\partial f(z^\star). \]

The compact CIFAR-10 section in notebook 36 trains the public constructor and verifies both residual and monotonicity certificate. To scale, replace the dense operator with a convolutional monotone module implementing forward, resolvent, and monotonicity_certificate; preserve the source monDEQ splitting and data schedule [75].

Positive-Concave Equilibrium

Unit-valued image tensors enter

\[ z^\star=\phi(W_+z^\star+S_\theta(x)),\qquad W_+\geq0. \]

Notebook 37 keeps the state spatial, pools only the class field, and applies project_nonnegative_() after optimizer steps. Full pcDEQ experiments must preserve the chosen variant, positive parameterization, and source preprocessing [76].

Non-Euclidean Equilibrium

NEMON constrains a weighted matrix measure rather than only an Euclidean norm:

\[ \mu_{\infty,D}(W)<1,\qquad \lVert z^\star(x+\delta)-z^\star(x)\rVert_{\infty,D} \leq \frac{\lVert U\delta\rVert_{\infty,D}} {1-\mu_{\infty,D}(W)}. \]

Notebook 38 reports the certificate, bounded perturbation, observed logit displacement, and latent bound separately. A complete robustness claim also needs the source attack or certification protocol [77].

Efficient Infinite Graph

For normalized graph operator \(S\) and normalized channel Gram map \(g(F)\),

\[ Z^\star=\gamma S Z^\star g(F)^\mathsf{T}+X_\theta. \]

Notebook 39 runs the iterative route on real Cora tensors. Full Cora, CiteSeer, or PubMed experiments use the complete graph, fixed Planetoid masks, and either the closed-form eigensystem or iterative route declared before evaluation [78].

Multiscale Graph Implicit Network

Each scale solves

\[ Z_m^\star=\gamma S^m Z_m^\star g(F_m)^\mathsf{T}+X_\theta, \]

then nodewise weights fuse the states:

\[ \bar Z_i=\sum_m\alpha_{im}Z_{m,i}^\star,\qquad \sum_m\alpha_{im}=1. \]

Notebook 40 plots the full node-by-scale allocation. Paper-level work must preserve the complete graph, scale set, fusion rule, and split protocol [79].

Delta-Cached Equilibrium

For a linear or convolutional recurrent block \(L\),

\[ c_{k+1}=c_k+L(\Delta_\tau z_{k+1})-L(0), \qquad \Delta_\tau z=\mathbf 1(|\Delta z|>\tau)\odot\Delta z. \]

Notebook 41 measures activity and exact-convolution disagreement on real consecutive frames. It does not report endpoint error because the public clip has no flow labels. Use MPI Sintel [83], KITTI Flow [84], or FlyingChairs [85] for supervised evaluation, and measure latency on the target hardware instead of inferring it from activity alone.

Neural-Operator Fields

load_darcy_source_subset accepts local .pt or .npz archives with x/y, inputs/targets, coeff/solution, or a/u arrays:

from silva_networks import load_darcy_source_subset, silva_fno_deq

darcy = load_darcy_source_subset(
    "data/darcy/darcy_small.npz",
    samples=64,
    seed=0,
)
model = silva_fno_deq(
    in_channels=darcy.inputs.shape[1],
    hidden_channels=64,
    out_channels=darcy.targets.shape[1],
    modes=(16, 16),
)

The adapter boundary is intentionally independent of one storage package. Source-scale FNO-DEQ work must preserve the Darcy or Navier-Stokes resolutions, normalization, relative-\(L^2\) metric, noise protocol, and solver budget [31] [43].

Storage and Access

Dataset	Approximate local allowance	Access action
CIFAR-10	170 MB compressed	loader-supported
Cora / CiteSeer	below 20 MB each	loader-supported
PubMed	below 100 MB	loader-supported
MPI Sintel complete	about 5.3 GB	accept and retrieve from the benchmark site
KITTI Flow archives	about 2 GB	accept and retrieve from the benchmark site
FlyingChairs	about 22 GB	retrieve data and split assignment from the source site
Darcy multi-resolution cache	reserve at least 1 GB	use the official operator-data loader or a local mirror

SILVA does not silently retrieve datasets whose providers require a separate access step.

Complete Experiment Checklist

Before calling a run a reproduction:

1. Record the paper, repository revision, dataset receipt, and access page.
2. Preserve official train, validation, and test definitions.
3. Match architecture width, depth or equilibrium transition, normalization, augmentation, optimizer, schedule, and regularization.
4. Record forward and backward solver configurations separately.
5. Run every declared seed and report dispersion, convergence failures, wall time, memory, and parameter count.
6. Use the source metric implementation and evaluation resolution.
7. Compare against a source-aligned baseline under the same data and compute budget.

The packaged profiles structured_real_subset_suite.json and structured_source_scale_suite.json make these choices explicit. They are starting records, not hidden claims that the complete published runs have already been executed.

Extending to Another Paper

A new family does not need a new data system. Implement an adapter that returns tensors plus SourceDataReceipt, then expose the family through the same five boundaries:

1. source encoder \(S_\theta(x)\);
2. state-preserving transition \(T_\theta(z,x)\);
3. initializer;
4. readout;
5. SolverConfig.

First test one transition step against an independent reference function. Then test the equilibrium, gradients, compact source subset, and complete-data configuration. This keeps the new method inside SILVA while leaving every internal operator replaceable.

The six executed structured-family labs and their retained plots are indexed in the Notebook Overview.

Where to Go Next

Question	Page
Which functions load and verify source data?	Source Data API
Where is the complete runnable code?	Source-Data Family Example
How are all paper adaptations registered?	Reproducing SILVA and Source Methods
How are large runs configured?	Full-Scale SILVA