Welcome to PyTorch-BSF!

Fit smooth, high-dimensional manifolds to your data — from a single GPU to a multi-node cluster.

PyTorch-BSF brings Bézier simplex fitting to PyTorch. A Bézier simplex is a high-dimensional generalization of the Bézier curve: it can model an arbitrarily complex point cloud as a smooth parametric hyper-surface in any number of dimensions. This makes it a natural tool for representing Pareto fronts in multi-objective optimization, interpolating scattered observations, and fitting geometric structures in high-dimensional spaces.

The project is on GitHub.

User guide

• Quickstart
  • Run as an MLflow project
  • Run as a Python package
  • Run as Python code
• Advanced Topics
  • Initial control points
  • Partial training
• What is Bézier simplex fitting?
  • Bezier simplex
  • Fitting a Bezier simplex to a dataset
  • Why does Bézier simplex fitting matter?
  • Application 1: Elastic net
  • Application 2: Deep neural networks
  • References
• Frequently asked questions
  • There are already many tools for hyperparameter search in ML. Why propose yet another one?
  • Are approximation results always reliable?
  • Are there any applications other than multiobjective optimization?
  • How do I choose the degree of the Bézier simplex?
  • How many training samples do I need?
  • What if my input parameters do not lie on a simplex?
  • Can I train on a GPU?
  • What should I do if fitting does not converge or the accuracy is poor?
  • When should I use partial training (the fix argument)?
  • Can I verify whether my problem is weakly simplicial before fitting?
  • What kinds of shapes can a Bézier simplex represent beyond Pareto fronts?

API reference

• torch_bsf
  • torch_bsf package

Indices and tables

• Index

• Module Index

• Search Page