Core computation contracts

This page collects the interpretation rules shared by the dense, exact blockwise, and optional CuPy-backed fuzzy-rough execution paths. These contracts apply to ITFRS, VQRS, and OWAFRS unless a model-specific section states otherwise.

Relation orientation

A dense or precomputed relation uses the orientation:

similarity_matrix[i, j] = R(x_i, x_j)

Row i is the query row whose approximation value is returned for sample x_i. Column j contributes evidence from sample x_j. Symmetric similarity matrices are unaffected by this distinction; transposing an asymmetric relation can change the result.

The core model attribute is:

model.relation_orientation == "rows_are_queries"

Self-comparisons

The current model implementations exclude diagonal self-comparisons from the reported sample scores:

• ITFRS sets diagonal lower evidence to the neutral minimum value 1 and diagonal upper evidence to the neutral maximum value 0.
• VQRS excludes the diagonal from both supporting mass and total similarity mass.
• OWAFRS removes one diagonal evidence value from each sorted row before OWA aggregation.

Dense and blockwise implementations use the same rule. This is a fixed model contract in the current release, not a public configuration parameter.

VQRS defaults

The default VQRS lower and upper quantifiers are intentionally different:

lower: quadratic Q(alpha=0.2, beta=1.0)
upper: quadratic Q(alpha=0.0, beta=0.6)

The defaults represent a stricter lower quantifier and a more permissive upper quantifier. Flat and nested configuration can replace either quantifier explicitly.

Boundary and positive-region outputs

FRsutils reports:

signed_boundary = upper - lower
positive_region = lower

The boundary is not clipped. Custom component combinations can therefore produce negative signed-boundary values when they do not guarantee lower <= upper.

The public aliases result.boundary, boundary_region(), and compute_boundary_region() are retained for backward compatibility and expose the same signed difference. signed_boundary and compute_signed_boundary() are the explicit names for new code.

The positive-region output retains the current lower-score contract. Its name and meaning are unchanged in this release.

Dense, blockwise, and CuPy equivalence

For the same model, data, and component configuration, exact blockwise NumPy execution is expected to agree numerically with the dense NumPy reference path. Optional CuPy-backed blockwise execution is tested against the same dense reference within floating-point tolerance.

Backend residency differs by model:

Model	CuPy similarity blocks	CuPy approximation accumulators
ITFRS	supported	supported
VQRS	supported	supported
OWAFRS	supported	not claimed; OWA sorting and aggregation remain NumPy-resident

All public result arrays are converted to NumPy arrays.

Input validity

Feature matrices and precomputed relations must be finite numeric arrays. Public and direct core paths reject NaN, positive infinity, and negative infinity. Precomputed relations must be square, labels must be one-dimensional and aligned, and fuzzy-rough approximation models require at least two samples.