Extensions

Extension experiments are exploratory package examples. They are separate from reference package checks and should be described as extensions, not as reproduction results.

Custom Local Operator

The default graph local branch is

\[ L_j(Z) = \frac{1}{|\mathcal N(j)|} \sum_{i\in\mathcal N(j)}W_\ell z_i. \]

A custom local branch can introduce a different message law, for example

\[ m_i=\tanh(W_c z_i), \qquad L_j(Z)=\sum_{i\in\mathcal N(j)}m_i. \]

Run:

silva-experiment \
  --config custom_operator_experiment

Fully Configurable Stack

The JSON runner also accepts the same per-layer controls as SILVAGraphNetwork. This example uses three equilibrium layers:

{
  "hidden_dims": [14, 12, 10],
  "local": ["graph", "topk", "gat"],
  "local_kwargs": [null, {"k": 3}, {"heads": 2}],
  "global_term": ["mean", "simple", "topk_attention"],
  "global_kwargs": [null, null, {"k": 4}],
  "self_term": ["none", "linear", "identity"],
  "solver": [
    {"solver": "picard", "max_iter": 6, "alpha": 0.5},
    {"solver": "anderson", "max_iter": 6, "alpha": 0.4, "history": 3},
    {"solver": "broyden", "max_iter": 4, "alpha": 0.3}
  ]
}

Run:

silva-experiment \
  --config fully_configurable_graph

The corresponding model recurrence is

\[ z_\ell^\star = f_{\theta_\ell}(z_\ell^\star,h_{\ell-1}), \qquad h_\ell=z_\ell^\star, \]

with \(L_\ell\), \(G_\ell\), \(H_\ell\), and the solver selected independently for each layer.

Notebook

Open:

notebooks/package_api/05_custom_operator_experiment.ipynb

The notebook builds the custom branch, inserts it into a SILVA stack, and runs a small training loop.

Where to Go Next

Question	Page
Where is a custom branch implemented and executed?	Custom Layers Example
What evidence should an extended experiment report?	Reconstructing Paper Experiments
How are research architecture families represented?	Paper Family Adaptations