Dataset Quickstart

examples/datasets_quickstart.py loads a public tabular dataset, adapts it to SILVA tensors, and trains a small node-level classifier.

python examples/datasets_quickstart.py

Preprocessing

Rows become entities. Features are standardized:

\[ \tilde X_{ij} = \frac{X_{ij}-\mu_j}{\max(\sigma_j,\varepsilon)}. \]

A kNN graph is built in standardized feature space:

\[ j\in\mathcal N_k(i) \quad\Longleftrightarrow\quad j\text{ is among the }k\text{ smallest values of } \|\tilde x_i-\tilde x_j\|_2. \]

The adapter returns a GraphTensorBatch:

dataset = load_tabular_dataset("iris", root="data", download=True, normalize=True)
graph = tabular_to_silva_graph(dataset, k=8, normalize=True, device=device)
graph.validate()

Model

The graph is passed directly into SILVAGraphNetwork:

logits = model(graph.x, edge_index=graph.edge_index)

The same recipe works for custom tables after replacing the loader with a tensor, NumPy array, pandas frame, or user-defined feature matrix.

The script reports feature and edge shapes, class balance, losses, and accuracy. Before interpreting the task metric, verify graph.validate(), finite standardized features, valid edge bounds, and the residual of every SILVA equilibrium layer. Dataset sources and reporting rules are listed in Paper and References.

Complete Worked Study

The short construction above identifies the main API. A complete study must also distinguish the state equation, task objective, numerical residual, gradient path, and scale transfer. In this example, the equilibrium state is the tensor solved to equilibrium, the condition is the observed input or source tensor, and the repeated map is the state-preserving transition evaluated by the root solver.

Derivation From Transition to Reported Result

The forward solve is defined by

\[ z^\star = T_\theta(z^\star,x). \]

The task output and task objective are separate from convergence:

\[ \widehat y = R_\phi(z^\star), \qquad \mathcal L_{\mathrm{task}}=\ell(\widehat y,y). \]

For a computed state \(z_K\), the normalized fixed-point residual is

\[ r_K = \frac{\lVert T_\theta(z_K,x)-z_K\rVert_2} {\lVert z_K\rVert_2+\varepsilon}. \]

A small task loss does not imply a small \(r_K\), and a small \(r_K\) does not establish task quality. Both belong in the result. For implicit training, the parameter sensitivity follows

\[ \frac{\mathrm d z^\star}{\mathrm d\theta} = \left(I-\partial_z T_\theta(z^\star,x)\right)^{-1} \partial_\theta T_\theta(z^\star,x). \]

This is why the example checks gradients in addition to forward convergence. The reader-facing evidence for this route is dataset identity, tensor shape, and measured classification accuracy. The invariants that must remain true are shape, device, dtype, finiteness, and differentiability.

Run the Complete Example

python examples/datasets_quickstart.py

Measured Compact Output

The following output was produced by the executable program in the current repository. Floating-point values may vary slightly across devices and library builds, while shapes, finite values, invariants, and declared tolerances must remain stable.

dataset iris
shape (150, 4)
accuracy 0.8733333349227905

Interpret the Output

Evidence	What it answers	What would require investigation
Tensor shapes	Did every source, state, branch, and readout preserve its declared contract?	A changed entity, channel, token, or spatial dimension
Task metric	Did the compact task execute and produce finite evidence?	Non-finite loss, a missing mask, or a metric computed on the wrong split
Fixed-point residual	Did the returned state satisfy the repeated transition to the requested tolerance?	A residual plateau, rising trajectory, or convergence flag inconsistent with the value
Iteration or trajectory data	How much numerical work was required?	Solver effort that grows sharply under a small input or resolution change
Gradient evidence	Can the loss reach every trainable component through the selected backward mode?	Missing, non-finite, or implausibly large gradients
Domain invariant	Did the method retain positivity, feasibility, boundary values, permutation behavior, or another structural requirement?	A task metric that looks acceptable while the structural contract fails

The compact output is a mechanism check, not a paper-scale benchmark claim. It shows that data enter the intended construction, the transition executes, the solver returns diagnostics, and differentiation reaches trainable parameters.

Add a Solver and Scale Sweep

The next run should hold model parameters and data fixed while changing one numerical control at a time. A complete experiment record can use this schema:

experiment:
  example: datasets-quickstart
  state: the tensor solved to equilibrium
  condition: the observed input or source tensor
  repeated_transition: the state-preserving transition evaluated by the root solver
  invariant_checks: shape, device, dtype, finiteness, and differentiability
  compact_evidence: dataset identity, tensor shape, and measured classification accuracy
  scale_axes: state width, batch size, and data volume
solver_sweep:
  methods: [picard, anderson, broyden]
  tolerances: [1.0e-4, 1.0e-6, 1.0e-8]
  maximum_iterations: [25, 50, 100]
report:
  - task_metric
  - fixed_point_residual
  - backward_linear_residual
  - iterations
  - wall_time
  - peak_memory
  - gradient_norm

At full scale, move toward the official split with preprocessing fitted only on training data. Increase only one of state width, batch size, and data volume at a time. Retain this compact run as a regression test, preserve the source split and preprocessing receipt, archive the resolved configuration and checkpoint, and report convergence failures rather than discarding them.

Where to Go Next

Question	Page
How should datasets be validated before solving?	Datasets and Preprocessing
Which loaders and tensor objects are public?	Datasets API
Which public dataset experiments are configured?	Dataset Cases