Add doc for TBPTT (#20422)

* Add doc for TBPTT

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* add tbptt.rst file

* adjust doc:

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* Update docs/source-pytorch/common/tbptt.rst

---------

Co-authored-by: Alan Chu <alanchu@Alans-Air.lan>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Luca Antiga <luca.antiga@gmail.com>
Co-authored-by: Alan Chu <alanchu@Alans-Air.Home>
Co-authored-by: Luca Antiga <luca@lightning.ai>

docs/source-pytorch/common/index.rst

@@ -202,6 +202,13 @@ How-to Guides
     :col_css: col-md-4
     :height: 180
 
+.. displayitem::
+    :header: Truncated Back-Propagation Through Time
+    :description: Efficiently step through time when training recurrent models
+    :button_link: ../common/tbtt.html
+    :col_css: col-md-4
+    :height: 180
+
 .. raw:: html
 
         </div>

docs/source-pytorch/common/tbptt.rst

@@ -0,0 +1,59 @@
+##############################################
+Truncated Backpropagation Through Time (TBPTT)
+##############################################
+
+Truncated Backpropagation Through Time (TBPTT) performs backpropogation every k steps of
+a much longer sequence. This is made possible by passing training batches
+split along the time-dimensions into splits of size k to the
+``training_step``. In order to keep the same forward propagation behavior, all
+hidden states should be kept in-between each time-dimension split.
+
+
+.. code-block:: python
+
+    import torch
+    import torch.optim as optim
+    import pytorch_lightning as pl
+    from pytorch_lightning import LightningModule
+
+    class LitModel(LightningModule):
+
+        def __init__(self):
+            super().__init__()
+
+            # 1. Switch to manual optimization
+            self.automatic_optimization = False
+
+            self.truncated_bptt_steps = 10
+            self.my_rnn = ParityModuleRNN() # Define RNN model using ParityModuleRNN
+
+        # 2. Remove the `hiddens` argument
+        def training_step(self, batch, batch_idx):
+
+            # 3. Split the batch in chunks along the time dimension
+            split_batches = split_batch(batch, self.truncated_bptt_steps)
+
+            batch_size = 10
+            hidden_dim = 20
+            hiddens = torch.zeros(1, batch_size, hidden_dim, device=self.device)
+            for split_batch in range(split_batches):
+                # 4. Perform the optimization in a loop
+                loss, hiddens = self.my_rnn(split_batch, hiddens)
+                self.backward(loss)
+                self.optimizer.step()
+                self.optimizer.zero_grad()
+
+                # 5. "Truncate"
+                hiddens = hiddens.detach()
+
+            # 6. Remove the return of `hiddens`
+            # Returning loss in manual optimization is not needed
+            return None
+
+        def configure_optimizers(self):
+            return optim.Adam(self.my_rnn.parameters(), lr=0.001)
+
+    if __name__ == "__main__":
+        model = LitModel()
+        trainer = pl.Trainer(max_epochs=5)
+        trainer.fit(model, train_dataloader) # Define your own dataloader