diff --git a/pytorch_lightning/plugins/training_type/tpu_spawn.py b/pytorch_lightning/plugins/training_type/tpu_spawn.py
index 44422cc49cddc..0f55100bf1ab9 100644
--- a/pytorch_lightning/plugins/training_type/tpu_spawn.py
+++ b/pytorch_lightning/plugins/training_type/tpu_spawn.py
@@ -203,12 +203,14 @@ def test_step(self, *args, **kwargs):
     def predict(self, *args, **kwargs):
         return self.lightning_module.predict(*args, **kwargs)
 
-    def save_checkpoint(self, checkpoint: Dict[str, Any], filepath: str) -> None:
+    def save_checkpoint(self, filepath: str, weights_only: bool = False) -> None:
         """Save model/training states as a checkpoint file through state-dump and file-write.
         Args:
-            checkpoint: dict containing model and trainer state
             filepath: write-target file's path
+            weights_only: saving model weights only
         """
+        # dump states as a checkpoint dictionary object
+        checkpoint = self.lightning_module.trainer.checkpoint_connector.dump_checkpoint(weights_only)
         # Todo: TypeError: 'mappingproxy' object does not support item assignment
         if _OMEGACONF_AVAILABLE:
             checkpoint = apply_to_collection(checkpoint, (DictConfig, ListConfig), OmegaConf.to_container)
diff --git a/tests/models/test_tpu.py b/tests/models/test_tpu.py
index b64b22c66caa7..24c0b615b95bb 100644
--- a/tests/models/test_tpu.py
+++ b/tests/models/test_tpu.py
@@ -122,7 +122,7 @@ def test_model_16bit_tpu_cores_1(tmpdir):
         progress_bar_refresh_rate=0,
         max_epochs=2,
         tpu_cores=1,
-        limit_train_batches=8,
+        limit_train_batches=0.7,
         limit_val_batches=2,
     )
 
@@ -210,8 +210,8 @@ def test_tpu_grad_norm(tmpdir):
         progress_bar_refresh_rate=0,
         max_epochs=4,
         tpu_cores=1,
-        limit_train_batches=0.4,
-        limit_val_batches=0.4,
+        limit_train_batches=10,
+        limit_val_batches=10,
         gradient_clip_val=0.5,
     )
 
diff --git a/tests/test_profiler.py b/tests/test_profiler.py
index 667e153a9edd4..6abcf17a04893 100644
--- a/tests/test_profiler.py
+++ b/tests/test_profiler.py
@@ -20,6 +20,7 @@
 import pytest
 
 from pytorch_lightning.profiler import AdvancedProfiler, SimpleProfiler
+from tests.helpers.runif import RunIf
 
 PROFILER_OVERHEAD_MAX_TOLERANCE = 0.0005
 
@@ -165,6 +166,7 @@ def test_advanced_profiler_overhead(advanced_profiler, n_iter=5):
     assert average_duration < PROFILER_OVERHEAD_MAX_TOLERANCE
 
 
+@RunIf(max_torch="1.8.1")
 def test_advanced_profiler_describe(tmpdir, advanced_profiler):
     """
     ensure the profiler won't fail when reporting the summary
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index fd2b48a3fa140..306d38d2d651b 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -42,6 +42,7 @@
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 from tests.base import EvalModelTemplate
 from tests.helpers import BoringModel, RandomDataset
+from tests.helpers.runif import RunIf
 
 
 @pytest.fixture
@@ -1499,6 +1500,7 @@ def test_trainer_predict_ddp_cpu(tmpdir):
     predict(tmpdir, "ddp_cpu", 0, 2)
 
 
+@RunIf(max_torch="1.8.1")
 def test_pytorch_profiler_describe(pytorch_profiler):
     """Ensure the profiler won't fail when reporting the summary."""
     with pytorch_profiler.profile("test_step"):