diff --git a/examples/post_training_quantization/torch/ssd300_vgg16/main.py b/examples/post_training_quantization/torch/ssd300_vgg16/main.py
index 6d6b9365a34..3bed9cfee45 100644
--- a/examples/post_training_quantization/torch/ssd300_vgg16/main.py
+++ b/examples/post_training_quantization/torch/ssd300_vgg16/main.py
@@ -29,6 +29,7 @@
 from torchvision.models.detection.ssd import SSD
 from torchvision.models.detection.ssd import GeneralizedRCNNTransform
 from nncf.common.logging.track_progress import track
+from functools import partial
 
 ROOT = Path(__file__).parent.resolve()
 DATASET_URL = "https://ultralytics.com/assets/coco128.zip"
@@ -125,10 +126,10 @@ def validate(model: torch.nn.Module, dataset: COCO128Dataset, device: torch.devi
     return computed_metrics["map_50"]
 
 
-def transform_fn(data_item: Tuple[torch.Tensor, Dict]) -> torch.Tensor:
+def transform_fn(data_item: Tuple[torch.Tensor, Dict], device: torch.device) -> torch.Tensor:
     # Skip label and add a batch dimension to an image tensor
     images, _ = data_item
-    return images[None]
+    return images[None].to(device)
 
 
 def main():
@@ -149,7 +150,7 @@ def main():
     disable_tracing(SSD.postprocess_detections)
 
     # Quantize model
-    calibration_dataset = nncf.Dataset(dataset, transform_fn)
+    calibration_dataset = nncf.Dataset(dataset, partial(transform_fn, device=device))
     quantized_model = nncf.quantize(model, calibration_dataset)
 
     # Convert to OpenVINO
diff --git a/nncf/quantization/algorithms/weight_compression/openvino_backend.py b/nncf/quantization/algorithms/weight_compression/openvino_backend.py
index a55ff9c861d..0a0d4f09fa6 100644
--- a/nncf/quantization/algorithms/weight_compression/openvino_backend.py
+++ b/nncf/quantization/algorithms/weight_compression/openvino_backend.py
@@ -77,8 +77,8 @@ def do_compression(
                 if isinstance(reduction_axes, tuple) and len(reduction_axes) != 1:
                     nncf_logger.warning(
                         f"Weight compression expects a single reduction axes, but given {len(reduction_axes)}. "
-                        f"Weight shape: {const_shape}, reduction axes: {reduction_axes}, node name: {nncf_node.name}. "
-                        "The node won't be quantized."
+                        f"Weight shape: {const_shape}, reduction axes: {reduction_axes}, "
+                        f"node name: {nncf_node.node_name}. The node won't be quantized."
                     )
                     continue
                 reduction_axis = reduction_axes[0] if isinstance(reduction_axes, tuple) else reduction_axes
diff --git a/nncf/torch/engine.py b/nncf/torch/engine.py
index 63b4e93f114..44271123d6b 100644
--- a/nncf/torch/engine.py
+++ b/nncf/torch/engine.py
@@ -15,9 +15,6 @@
 from torch import nn
 
 from nncf.common.engine import Engine
-from nncf.torch.nested_objects_traversal import objwalk
-from nncf.torch.utils import get_model_device
-from nncf.torch.utils import is_tensor
 
 
 class PTEngine(Engine):
@@ -34,7 +31,6 @@ def __init__(self, model: nn.Module):
 
         self._model = model
         self._model.eval()
-        self._device = get_model_device(model)
 
     def infer(
         self, input_data: Union[torch.Tensor, Tuple[torch.Tensor], Dict[str, torch.Tensor]]
@@ -46,11 +42,6 @@ def infer(
         :return: Model outputs.
         """
 
-        def send_to_device(tensor):
-            return tensor.to(self._device)
-
-        input_data = objwalk(input_data, is_tensor, send_to_device)
-
         if isinstance(input_data, dict):
             return self._model(**input_data)
         if isinstance(input_data, tuple):
diff --git a/tests/openvino/native/models.py b/tests/openvino/native/models.py
index ca563218df3..860efbdba69 100644
--- a/tests/openvino/native/models.py
+++ b/tests/openvino/native/models.py
@@ -786,3 +786,17 @@ def _create_ov_model(self):
         result.get_output_tensor(0).set_names(set(["Result"]))
         model = ov.Model([result], [input_node])
         return model
+
+
+class GatherWithTwoReductionAxes(OVReferenceModel):
+    def _create_ov_model(self):
+        input_1 = opset.parameter([2, 3], name="Input")
+        convert_1 = opset.convert(input_1, destination_type="i64", name="Convert_1")
+
+        gather_2_data = opset.constant(self._rng.random((3, 2, 1)), dtype=np.float32, name="gather_2_data")
+        gather_2 = opset.gather(gather_2_data, convert_1, axis=0, batch_dims=0)
+        gather_2.set_friendly_name("Gather_2")
+
+        result = opset.result(gather_2, name="Result")
+        model = ov.Model([result], [input_1])
+        return model
diff --git a/tests/openvino/native/quantization/test_weights_compression.py b/tests/openvino/native/quantization/test_weights_compression.py
index 561d1927509..b83cf386462 100644
--- a/tests/openvino/native/quantization/test_weights_compression.py
+++ b/tests/openvino/native/quantization/test_weights_compression.py
@@ -25,6 +25,7 @@
 from nncf.quantization.algorithms.weight_compression.openvino_backend import _reshape_weights_for_grouped_quantization
 from nncf.scopes import IgnoredScope
 from tests.openvino.native.common import get_openvino_version
+from tests.openvino.native.models import GatherWithTwoReductionAxes
 from tests.openvino.native.models import IntegerModel
 from tests.openvino.native.models import SequentialMatmulModel
 from tests.openvino.native.models import WeightsModel
@@ -202,6 +203,14 @@ def test_mixed_precision(ratio, group_size, ref_nf4_nodes):
             assert op.get_element_type() == ov.Type.nf4
 
 
+def test_not_quantize_with_multiple_reduction_axes():
+    model = GatherWithTwoReductionAxes().ov_model
+    compressed_model = compress_weights(model, mode=CompressWeightsMode.INT8)
+    for op in compressed_model.get_ordered_ops():
+        if op.get_type_name() == "Constant" and op.get_friendly_name() == "gather_2_data":
+            assert op.get_element_type() == ov.Type(np.float32)
+
+
 @dataclass
 class QuantErrorDesc:
     weight: List[float]