BinaryMatthewsCorrCoef behaves inconsistently when denominator = 0

Bug: BinaryMatthewsCorrCoef behaves inconsistently when denominator = 0

Hi, I came across an inconsistency in BinaryMatthewsCorrCoef while testing edge cases and wanted to check whether this is intended behavior.

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Minimal Example

import torch
from torchmetrics.classification import BinaryMatthewsCorrCoef
from sklearn.metrics import matthews_corrcoef

metric = BinaryMatthewsCorrCoef()

def test_case(preds, targets):
    tm = metric(preds, targets).item()
    sk = matthews_corrcoef(targets.numpy(), preds.numpy())
    return tm, sk

# Case 1: all negatives
preds = torch.zeros(10)
targets = torch.zeros(10)
print(test_case(preds, targets))
# TorchMetrics: 1.0, sklearn: 0.0

# Case 2: degenerate mixed
preds = torch.zeros(10)
targets = torch.tensor([0,0,0,1,1,1,1,1,1,1])
print(test_case(preds, targets))
# TorchMetrics: -0.276..., sklearn: 0.0

# Case 3: near-trivial
preds = torch.tensor([1] + [0]*9)
targets = torch.tensor([0]*10)
print(test_case(preds, targets))
# TorchMetrics: ~0.84, sklearn: 0.0

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Observation

The discrepancy appears specifically when the MCC denominator is zero (i.e., degenerate confusion matrices).

In these cases:

• sklearn returns 0.0
• torchmetrics returns values such as 1.0 or other non-zero floats depending on the configuration

I observed this consistently across randomized tests; all mismatches traced back to these zero-denominator cases.

For context, this was identified during differential testing against a reference implementation based on a formally specified definition of these metrics, which helped isolate the behavior.

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Question

Since MCC is mathematically undefined when the denominator is zero, different conventions are possible.

However, the current behavior does not seem to clearly align with:

• the common convention used by sklearn (0), or
• a rule-based alternative (e.g., mapping to {1, 0, -1} depending on the case)

Is this behavior intentional? If so, could you clarify the convention being followed here?

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Options

• Align with sklearn (return 0 when denominator = 0), or
• Clearly document the intended behavior for these cases
• Optionally expose a zero_division-style parameter for flexibility

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Happy to provide additional test cases or help explore a fix if useful. Thanks!

Start by reproducing the three minimal examples with BinaryMatthewsCorrCoef and compare their zero-denominator results with sklearn's matthews_corrcoef. Trace the metric's denominator-zero behavior and determine whether the intended outcome is a fix or documentation; done means the convention is implemented consistently and covered for the shown degenerate cases.