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Run in Colab

The package notebooks are Colab-ready. They can run from the published GitHub repository or from an uploaded local folder before release.

Published Repository

Open a notebook from colab/ in Google Colab. The setup cell installs the package from:

https://github.com/jseluis/silva-networks

The installed import is:

import silva_networks

Uploaded Folder

Before the repository is public, upload or clone the suite into Colab as:

/content/silva-networks

The setup cell checks for:

/content/silva-networks/src

and adds it to sys.path. That lets the notebook import the local package without installing from the internet.

Runtime

For CPU:

from silva_networks import resolve_device

device = resolve_device("cpu")

For GPU:

from silva_networks import resolve_device

device = resolve_device("cuda")

Colab GPU availability depends on the selected runtime. The package uses ordinary PyTorch tensors, so the model and all tensors must be on the same device:

model = model.to(device)
x = x.to(device)
edge_index = edge_index.to(device)

Notebook Folder

The Colab copies live in:

colab/

The package API notebooks are at the top level of that folder. The implicit layers bridge notebooks live in:

colab/implicit_bridge/

The same tutorials are rendered in the docs under Notebooks.

The top-level package track includes quickstart, solvers and Jacobians, datasets, public experiments, custom operators, operator options, citation audit, the equation-to-code walkthrough, family-selector/projected-QP and training-helper validation tutorials, the cortex hierarchy, generalized architecture cases, RAFT/DEQ-Flow, and the ten-entry point architecture catalog. The final package notebook derives ODE flow, implicit PDE time stepping, Poisson diagnostics, Fourier operators, and their placement inside a SILVA equilibrium point.

Bridge Notebooks

The bridge track mirrors the five implicit-layer tutorial themes and extends them with SILVA operators:

  1. fixed points as layers;
  2. implicit functions and automatic differentiation;
  3. neural ODE-style repeated operators;
  4. DEQ baselines and SILVA graph layers;
  5. differentiable optimization;
  6. multiscale DEQs and Jacobian regularization;
  7. TorchDEQ-style single-state and multi-state SILVA DEQ systems;
  8. RAFT/DEQ-Flow-style optical-flow fixed points;
  9. method adaptation atlas for source-to-SILVA equations, scope notes, and compact validation checks.

Each notebook starts with a setup cell that looks for /content/silva-networks first. If the folder is not present and the repository is public, the same cell installs from https://github.com/jseluis/silva-networks.

Citation

If you use the package, cite:

Dr. Jose Luis Silva. SILVA Networks. Version 1.2.2. MIT License.
https://github.com/jseluis/silva-networks

If the work is connected to the SILVA Networks paper, cite:

Jose Luis Lima de Jesus Silva. SILVA Networks as Structured Implicit Layers and
Vector Attractors via Dynamic Interaction Fields. 2026. arXiv:2607.28989.
https://arxiv.org/abs/2607.28989

The full BibTeX file is docs/assets/bib/silva-networks.bib.

Where to Go Next

Question Page
Which notebooks and topics are available? Notebooks
Which notebook should I open first? Package Quickstart Notebook
How do I install the same environment locally? Installation