Fix perplexity computation in perplexity.md (huggingface#34387)

fix average NLL in perplexity.md

Author: Framartin

docs/source/en/perplexity.md

@@ -107,7 +107,8 @@ max_length = model.config.n_positions
 stride = 512
 seq_len = encodings.input_ids.size(1)
 
-nlls = []
+nll_sum = 0.0
+n_tokens = 0
 prev_end_loc = 0
 for begin_loc in tqdm(range(0, seq_len, stride)):
     end_loc = min(begin_loc + max_length, seq_len)
@@ -124,13 +125,19 @@ for begin_loc in tqdm(range(0, seq_len, stride)):
         # to the left by 1.
         neg_log_likelihood = outputs.loss
 
-    nlls.append(neg_log_likelihood)
+    # Accumulate the total negative log-likelihood and the total number of tokens
+    num_valid_tokens = (target_ids != -100).sum().item()  # number of valid tokens in target_ids
+    batch_size = target_ids.size(0)
+    num_loss_tokens = num_valid_tokens - batch_size  # subtract batch_size due to internal label shift
+    nll_sum += neg_log_likelihood * num_loss_tokens
+    n_tokens += num_loss_tokens
 
     prev_end_loc = end_loc
     if end_loc == seq_len:
         break
 
-ppl = torch.exp(torch.stack(nlls).mean())
+avg_nll = nll_sum / n_tokens  # average negative log-likelihood per token
+ppl = torch.exp(avg_nll)
 ```
 
 Running this with the stride length equal to the max input length is equivalent to the suboptimal, non-sliding-window
@@ -139,5 +146,5 @@ 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 `19.44`, 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 `16.45`. 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.