Functional nominal metrics fail for non-zero-based category labels

Bug description

The functional nominal association metrics infer the number of categories from the count of unique values, but pass the original category IDs directly to the confusion-matrix implementation. As a result, valid categorical labels that are not zero-based and contiguous can raise a reshape error.

Nominal association should be invariant to renaming categories.

Reproduction

import torch

from torchmetrics.functional.nominal import (
    cramers_v,
    pearsons_contingency_coefficient,
    theils_u,
    tschuprows_t,
)

base = torch.tensor([0, 0, 1, 1])
shifted = base + 1

metrics = [
    (cramers_v, {"bias_correction": False}),
    (pearsons_contingency_coefficient, {}),
    (theils_u, {}),
    (tschuprows_t, {"bias_correction": False}),
]

for metric, kwargs in metrics:
    print(metric(base, base, **kwargs))
    print(metric(shifted, shifted, **kwargs))

The first call succeeds for each metric. The relabeled input raises:

RuntimeError: shape '[2, 2]' is invalid for input of size 7

The corresponding matrix APIs are affected as well when columns contain sparse or independently labeled categories.

Expected behavior

The shifted input describes the same two categories and should produce the same association value as the zero-based input. For example, Cramer's V should be tensor(1.) in both cases.

Root cause

The functional paths derive num_classes using the number of unique values, while the classification confusion-matrix updater uses the raw label values as bin indices. With labels 1 and 2, the inferred class count is two, but label 2 creates a bin outside the expected 2 x 2 range.

Normalizing the observed categories to contiguous IDs after logits and NaN preprocessing avoids that mismatch. Stateful metrics that receive an explicit num_classes should keep their existing stable encoding behavior across updates.

Environment

• TorchMetrics: 1.9.0 / current master at 37a80809
• PyTorch: 2.13.0+cpu
• Python: 3.11.9
• OS: Windows

AI disclosure: I used Codex to help identify and reproduce the behavior, search for existing reports, and draft this issue. I reviewed the reproduction and diagnosis.

Start with the functional nominal entry points in torchmetrics.functional.nominal and the corresponding classification confusion-matrix APIs. Reproduce the shifted-label example, then add regression coverage for sparse or independently labeled categories. Done means relabeled inputs return the same association values without reshape errors while explicit stateful class encodings remain unchanged.