Fix incorrect size of input for 1st strided window length in `Perplexity of...

Fix incorrect size of input for 1st strided window length in `Perplexity of fixed-length models` (#18906)

* update the PPL for stride 512

* fix 1st strided window size

* linting

* fix typo

* styling

docs/source/en/perplexity.mdx

@@ -101,22 +101,32 @@ from tqdm import tqdm
 
 max_length = model.config.n_positions
 stride = 512
+seq_len = encodings.input_ids.size(1)
 
 nlls = []
-for i in tqdm(range(0, encodings.input_ids.size(1), stride)):
-    begin_loc = max(i + stride - max_length, 0)
-    end_loc = min(i + stride, encodings.input_ids.size(1))
-    trg_len = end_loc - i  # may be different from stride on last loop
+prev_end_loc = 0
+for begin_loc in tqdm(range(0, seq_len, stride)):
+    end_loc = min(begin_loc + max_length, seq_len)
+    trg_len = end_loc - prev_end_loc  # may be different from stride on last loop
     input_ids = encodings.input_ids[:, begin_loc:end_loc].to(device)
     target_ids = input_ids.clone()
     target_ids[:, :-trg_len] = -100
 
     with torch.no_grad():
         outputs = model(input_ids, labels=target_ids)
-        neg_log_likelihood = outputs[0] * trg_len
+
+        # loss is calculated using CrossEntropyLoss which averages over input tokens.
+        # Multiply it with trg_len to get the summation instead of average.
+        # We will take average over all the tokens to get the true average
+        # in the last step of this example.
+        neg_log_likelihood = outputs.loss * trg_len
 
     nlls.append(neg_log_likelihood)
 
+    prev_end_loc = end_loc
+    if end_loc == seq_len:
+        break
+
 ppl = torch.exp(torch.stack(nlls).sum() / end_loc)
 ```
 
@@ -126,5 +136,5 @@ and the better the reported perplexity will typically be.
 
 When we run the above with `stride = 1024`, i.e. no overlap, the resulting PPL is `19.64`, which is about the same
 as the `19.93` reported in the GPT-2 paper. By using `stride = 512` and thereby employing our striding window
-strategy, this jumps down to `16.53`. This is not only a more favorable score, but is calculated in a way that is
+strategy, this jumps down to `16.44`. This is not only a more favorable score, but is calculated in a way that is
 closer to the true autoregressive decomposition of a sequence likelihood.