PyTorch-BSF

Fit smooth manifolds with explicit geometry, observations and numerical evidence.

PyTorch-BSF fits Bézier simplices, products of simplices, and cells glued along shared faces. A single model type and regression API cover all three.

import torch
from torch_bsf import BezierSpace, Samples, fit

space = BezierSpace.simplex(dimension=1, degree=2)
t = torch.tensor([[1.0, 0.0], [0.5, 0.5], [0.0, 1.0]])
result = fit(space, Samples(t, [[0.0], [1.0], [4.0]]))
result.require_success()
predictions = result.model(t)
print(result.metrics, result.diagnostics)

• BezierSpace holds immutable geometry and shared coefficient ordering.
• BezierModel is a differentiable PyTorch module containing coefficients.
• fit(space, samples) always returns FitResult: model, metrics, diagnostics and stopping state.
• Dense SVD and optional sparse LSMR solve the same weighted, penalized objective in CPU float64.
• Objective minimization uses minimize with explicit PreconditionedSGD settings.
• Cross-validation, degree search and ensembles retain explicit evidence and ownership.
• Sampling, plotting, subdivision and versioned persistence use the same model types.

Install with Python 3.10 or later:

pip install pytorch-bsf
# Optional: sparse solving, plotting, scikit-learn, execution or recording
pip install 'pytorch-bsf[sparse,plot,sklearn,lightning,mlflow]'

Conda is an optional environment manager. Lightning and MLflow are optional adapters and are never imported by core fitting. Random/Sobol sampling needs no extra dependency. Tracking is opt-in.

python -m torch_bsf fit --params params.csv --values values.csv --degree 3 --save model.bsf
python -m torch_bsf predict --model model.bsf --params params.csv --save predictions.csv
bash examples/quickstart/run.sh

Save and load any model, including glued geometry, with torch_bsf.io.save_model / load_model. The format is versioned and does not pickle Python classes. CSV coefficient export is a separate operation.

This v0 release deliberately consolidates previous APIs without compatibility aliases. See the migration guide, documentation and contributing guide.

Research foundations:

• Kobayashi et al. (AAAI 2019), Bézier simplex fitting.
• Tanaka et al. (AAAI 2020), asymptotic risk.