seemps.analysis.sketching.tt_rss#

seemps.analysis.sketching.tt_rss(black_box: BlackBoxLoadMPS, samples: ndarray[tuple[Any, ...], dtype[_ScalarT]], max_bond_dimensions: TypeAliasForwardRef('~seemps.typing.Vector') | None = None, strategy: Strategy = DEFAULT_STRATEGY) MPS[source]#

Tensor Train via Recursive Sketching from Samples (TT-RSS).

Implements the TT-RSS algorithm that computes the MPS representation of a black-box function from a set of pivot samples defining the region of interest through randomized recursive sketching. Source: https://arxiv.org/abs/2501.06300v1

Parameters:
black_boxBlackBoxLoadMPS

A real-valued black-box function f(x_1,…,x_m), together with quantization parameters map_matrix and physical_dimensions representing MPS structure. Evaluates arrays of MPS indices, of shape (D, n), returning a vector of size D.

samplesMatrix

Array of shape (D, m), containing D samples xᵢ ∈ ℝ^m of the function. These are automatically quantized from m dimensions to n bits, to match the MPS dimensions defined on black_box.

max_bond_dimensionsVector, optional

Vector of maximal bond dimensions χ_k allowed during the sketching procedure. If given, random Haar unitaries of size (t, t) are replaced by random isometries of size (t, χ_k), enhancing efficiency.

strategyStrategy, optional

SVD rank-revealing strategy, determining the complexity of the target MPS. Defaults to DEFAULT_STRATEGY.

Returns:
MPS

The MPS representation encoding the approximation of the target function.