diff --git a/tests/classification/__init__.py b/tests/classification/__init__.py
index e69de29bb2d..6acfc5730db 100644
--- a/tests/classification/__init__.py
+++ b/tests/classification/__init__.py
@@ -0,0 +1,13 @@
+from torchmetrics import Metric
+
+
+class MetricWrapper(Metric):
+    def __init__(self, metric):
+        super().__init__()
+        self.metric = metric
+
+    def update(self, *args, **kwargs):
+        self.metric.update(*args, **kwargs)
+
+    def compute(self, *args, **kwargs):
+        return self.metric.compute(*args, **kwargs)
diff --git a/tests/classification/inputs.py b/tests/classification/inputs.py
index df7cfe4b496..635f99957f1 100644
--- a/tests/classification/inputs.py
+++ b/tests/classification/inputs.py
@@ -126,3 +126,13 @@ def generate_plausible_inputs_binary(num_batches=NUM_BATCHES, batch_size=BATCH_S
 _temp[_temp == _class_remove] = _class_replace
 
 _input_multiclass_with_missing_class = Input(_temp.clone(), _temp.clone())
+
+
+_negmetric_noneavg = {
+    "pred1": torch.tensor([[0.0, 1.0, 0.0], [1.0, 0.0, 0.0]]),
+    "target1": torch.tensor([0, 1]),
+    "res1": torch.tensor([0.0, 0.0, float("nan")]),
+    "pred2": torch.tensor([[0.0, 1.0, 0.0], [1.0, 0.0, 0.0]]),
+    "target2": torch.tensor([0, 2]),
+    "res2": torch.tensor([0.0, 0.0, 0.0]),
+}
diff --git a/tests/classification/test_accuracy.py b/tests/classification/test_accuracy.py
index 20b857feaec..40c27f20368 100644
--- a/tests/classification/test_accuracy.py
+++ b/tests/classification/test_accuracy.py
@@ -20,6 +20,7 @@
 from sklearn.metrics import accuracy_score as sk_accuracy
 from torch import tensor
 
+from tests.classification import MetricWrapper
 from tests.classification.inputs import _input_binary, _input_binary_logits, _input_binary_prob
 from tests.classification.inputs import _input_multiclass as _input_mcls
 from tests.classification.inputs import _input_multiclass_logits as _input_mcls_logits
@@ -32,6 +33,7 @@
 from tests.classification.inputs import _input_multilabel_multidim as _input_mlmd
 from tests.classification.inputs import _input_multilabel_multidim_prob as _input_mlmd_prob
 from tests.classification.inputs import _input_multilabel_prob as _input_mlb_prob
+from tests.classification.inputs import _negmetric_noneavg
 from tests.helpers import seed_all
 from tests.helpers.testers import NUM_BATCHES, NUM_CLASSES, THRESHOLD, MetricTester
 from torchmetrics import Accuracy
@@ -438,3 +440,11 @@ def test_negative_ignore_index(preds, target, ignore_index, result):
     # Test functional
     with pytest.raises(ValueError, match="^[The `target` has to be a non-negative tensor.]"):
         acc_score = accuracy(preds, target, num_classes=num_classes, ignore_index=ignore_index)
+
+
+def test_negmetric_noneavg(noneavg=_negmetric_noneavg):
+    acc = MetricWrapper(Accuracy(average="none", num_classes=noneavg["pred1"].shape[1]))
+    result1 = acc(noneavg["pred1"], noneavg["target1"])
+    assert torch.allclose(noneavg["res1"], result1, equal_nan=True)
+    result2 = acc(noneavg["pred2"], noneavg["target2"])
+    assert torch.allclose(noneavg["res2"], result2, equal_nan=True)
diff --git a/tests/classification/test_precision_recall.py b/tests/classification/test_precision_recall.py
index ebdbfe393f9..1c117d70591 100644
--- a/tests/classification/test_precision_recall.py
+++ b/tests/classification/test_precision_recall.py
@@ -20,6 +20,7 @@
 from sklearn.metrics import precision_score, recall_score
 from torch import Tensor, tensor
 
+from tests.classification import MetricWrapper
 from tests.classification.inputs import _input_binary, _input_binary_logits, _input_binary_prob
 from tests.classification.inputs import _input_multiclass as _input_mcls
 from tests.classification.inputs import _input_multiclass_logits as _input_mcls_logits
@@ -30,6 +31,7 @@
 from tests.classification.inputs import _input_multilabel as _input_mlb
 from tests.classification.inputs import _input_multilabel_logits as _input_mlb_logits
 from tests.classification.inputs import _input_multilabel_prob as _input_mlb_prob
+from tests.classification.inputs import _negmetric_noneavg
 from tests.helpers import seed_all
 from tests.helpers.testers import NUM_BATCHES, NUM_CLASSES, THRESHOLD, MetricTester
 from torchmetrics import Metric, Precision, Recall
@@ -457,3 +459,12 @@ def test_same_input(metric_class, metric_functional, sk_fn, average):
 
     assert torch.allclose(class_res, torch.tensor(sk_res).float())
     assert torch.allclose(func_res, torch.tensor(sk_res).float())
+
+
+@pytest.mark.parametrize("metric_cls", [Precision, Recall])
+def test_noneavg(metric_cls, noneavg=_negmetric_noneavg):
+    prec = MetricWrapper(metric_cls(average="none", num_classes=noneavg["pred1"].shape[1]))
+    result1 = prec(noneavg["pred1"], noneavg["target1"])
+    assert torch.allclose(noneavg["res1"], result1, equal_nan=True)
+    result2 = prec(noneavg["pred2"], noneavg["target2"])
+    assert torch.allclose(noneavg["res2"], result2, equal_nan=True)
diff --git a/torchmetrics/functional/classification/accuracy.py b/torchmetrics/functional/classification/accuracy.py
index 29580ee4047..9ae4febcee6 100644
--- a/torchmetrics/functional/classification/accuracy.py
+++ b/torchmetrics/functional/classification/accuracy.py
@@ -178,7 +178,7 @@ def _accuracy_compute(
         numerator = tp + tn
         denominator = tp + tn + fp + fn
     else:
-        numerator = tp
+        numerator = tp.clone()
         denominator = tp + fn
 
     if mdmc_average != MDMCAverageMethod.SAMPLEWISE:
diff --git a/torchmetrics/functional/classification/precision_recall.py b/torchmetrics/functional/classification/precision_recall.py
index 3d0d7f0376c..5640477ad74 100644
--- a/torchmetrics/functional/classification/precision_recall.py
+++ b/torchmetrics/functional/classification/precision_recall.py
@@ -49,7 +49,7 @@ def _precision_compute(
         tensor(0.2500)
     """
 
-    numerator = tp
+    numerator = tp.clone()
     denominator = tp + fp
 
     if average == AverageMethod.MACRO and mdmc_average != MDMCAverageMethod.SAMPLEWISE:
@@ -241,7 +241,7 @@ def _recall_compute(
         >>> _recall_compute(tp, fp, fn, average='micro', mdmc_average=None)
         tensor(0.2500)
     """
-    numerator = tp
+    numerator = tp.clone()
     denominator = tp + fn
 
     if average == AverageMethod.MACRO and mdmc_average != MDMCAverageMethod.SAMPLEWISE:
diff --git a/torchmetrics/functional/classification/specificity.py b/torchmetrics/functional/classification/specificity.py
index 85d0180162c..3e0097842f2 100644
--- a/torchmetrics/functional/classification/specificity.py
+++ b/torchmetrics/functional/classification/specificity.py
@@ -51,7 +51,7 @@ def _specificity_compute(
         tensor(0.6250)
     """
 
-    numerator = tn
+    numerator = tn.clone()
     denominator = tn + fp
     if average == AverageMethod.NONE and mdmc_average != MDMCAverageMethod.SAMPLEWISE:
         # a class is not present if there exists no TPs, no FPs, and no FNs