Initial Control Points

By default, fit() generates random initial control points for the Bézier simplex. You can override this by supplying your own initial control points via the init argument, which may help the optimizer converge faster or to a better solution when you have prior knowledge about the shape of the target manifold.

The init argument accepts a dictionary mapping multi-index tuples to value vectors, or an already-constructed object (such as a BezierSimplex or control-points data) that you have loaded in Python. Each key is a multi-index \(\mathbf{d} \in \mathbb{N}_D^M\) and each value is the corresponding control point \(\mathbf{p}_{\mathbf{d}} \in \mathbb{R}^N\).

When working from a file in Python, load the control points or Bézier simplex first (for example, via torch_bsf.bezier_simplex.load(path)()) and then pass the resulting object as init. The command-line interface instead accepts a file path directly via --init.

Supported file formats for saving and loading control points (and for use with the CLI --init option) are described below. In every format the key is the string representation of the multi-index tuple (e.g., "(2, 0)" for the control point at index \((2, 0)\)) and the value is a list of floats.

Pickled PyTorch

See PyTorch documentation for details:

• https://pytorch.org/docs/stable/generated/torch.save.html#torch.save

• https://pytorch.org/docs/stable/generated/torch.load.html#torch.load

CSV

"(2, 0)", 0.0, 0.1
"(1, 1)", 1.0, 1.1
"(0, 2)", 2.0, 2.1

TSV

"(2, 0)"     0.0     0.1
"(1, 1)"     1.0     1.1
"(0, 2)"     2.0     2.1

JSON

{
  "(2, 0)": [0.0, 0.1],
  "(1, 1)": [1.0, 1.1],
  "(0, 2)": [2.0, 2.1]
}

YAML

(2, 0): [0.0, 0.1]
(1, 1): [1.0, 1.1]
(0, 2): [2.0, 2.1]