fix implementation

Author: SkafteNicki

src/lightning/pytorch/callbacks/model_checkpoint.py

@@ -380,7 +380,10 @@ def on_train_epoch_end(self, trainer: "pl.Trainer", pl_module: "pl.LightningModu
             monitor_candidates = self._monitor_candidates(trainer)
             if self._every_n_epochs >= 1 and (trainer.current_epoch + 1) % self._every_n_epochs == 0:
                 self._save_topk_checkpoint(trainer, monitor_candidates)
-            self._save_last_checkpoint(trainer, monitor_candidates)
+            # Only save last checkpoint if a checkpoint was actually saved in this step or if save_last="link"
+            if (self._last_global_step_saved == trainer.global_step or 
+                (self.save_last == "link" and self._last_checkpoint_saved)):
+                self._save_last_checkpoint(trainer, monitor_candidates)
 
     @override
     def on_validation_end(self, trainer: "pl.Trainer", pl_module: "pl.LightningModule") -> None:
@@ -397,7 +400,10 @@ def on_validation_end(self, trainer: "pl.Trainer", pl_module: "pl.LightningModul
 
             if self._every_n_epochs >= 1 and (trainer.current_epoch + 1) % self._every_n_epochs == 0:
                 self._save_topk_checkpoint(trainer, monitor_candidates)
-            self._save_last_checkpoint(trainer, monitor_candidates)
+            # Only save last checkpoint if a checkpoint was actually saved in this step or if save_last="link"
+            if (self._last_global_step_saved == trainer.global_step or 
+                (self.save_last == "link" and self._last_checkpoint_saved)):
+                self._save_last_checkpoint(trainer, monitor_candidates)
 
     @override
     def on_exception(self, trainer: "pl.Trainer", pl_module: "pl.LightningModule", exception: BaseException) -> None:
@@ -902,3 +908,5 @@ def _should_remove_checkpoint(self, trainer: "pl.Trainer", previous: str, curren
     def _remove_checkpoint(self, trainer: "pl.Trainer", filepath: str) -> None:
         """Calls the strategy to remove the checkpoint file."""
         trainer.strategy.remove_checkpoint(filepath)
+
+