Minor fixes

README.md

@@ -3,15 +3,11 @@ This project implements a method for faster and more memory-efficient RNN-T comp
 
 ## How does the pruned-rnnt work ?
 
-We first obtain pruning bounds for the RNN-T recursion using
-a simple joiner network that is just an addition of the encoder and decoder,
-then we use those pruning bounds to evaluate the full, non-linear joiner network.
+We first obtain pruning bounds for the RNN-T recursion using a simple joiner network that is just an addition of the encoder and decoder, then we use those pruning bounds to evaluate the full, non-linear joiner network.
 
-The picture below display the gradients (obtained by rnnt_loss_simple with return_grad equals to true)
-of transducer lattice node, at each time frame, only a small set of nodes have a non-zero gradient,
-which justifies the pruned RNN-T loss, i.e., putting a limit on the number of symbols per frame.
+The picture below display the gradients (obtained by `rnnt_loss_simple` with `return_grad=true`) of lattice nodes, at each time frame, only a small set of nodes have a non-zero gradient, which justifies the pruned RNN-T loss, i.e., putting a limit on the number of symbols per frame.
 
-<img src="https://user-images.githubusercontent.com/5284924/158116784-4dcf1107-2b84-4c0c-90c3-cb4a02f027c9.png" width="500" height="125" />
+<img src="https://user-images.githubusercontent.com/5284924/158116784-4dcf1107-2b84-4c0c-90c3-cb4a02f027c9.png" width="900" height="250" />
 
 > This picture is taken from [here](https://github.com/k2-fsa/icefall/pull/251)
 
@@ -89,7 +85,7 @@ and describe your problem there.
 
 ### For rnnt_loss_simple
 
-This is a simple case of the RNN-T loss, where the 'joiner' network is just
+This is a simple case of the RNN-T loss, where the joiner network is just
 addition.
 
 ```python
@@ -114,14 +110,14 @@ loss = fast_rnnt.rnnt_loss_simple(
 
 ### For rnnt_loss_smoothed
 
-The same as `rnnt_loss_simple`, except that it supports am_only & lm_only smoothing
-that allows you to make the loss-function one of the form::
+The same as `rnnt_loss_simple`, except that it supports `am_only` & `lm_only` smoothing
+that allows you to make the loss-function one of the form:
 
           lm_only_scale * lm_probs +
           am_only_scale * am_probs +
           (1-lm_only_scale-am_only_scale) * combined_probs
 
-where lm_probs and am_probs are the probabilities given the lm and acoustic model independently.
+where `lm_probs` and `am_probs` are the probabilities given the lm and acoustic model independently.
 
 ```python
 am = torch.randn((B, T, C), dtype=torch.float32)
@@ -147,8 +143,7 @@ loss = fast_rnnt.rnnt_loss_simple(
 
 ### For rnnt_loss_pruned
 
-`rnnt_loss_pruned` can not be used alone, it needs the gradients returned by
-`rnnt_loss_simple/rnnt_loss_smoothed` to get pruning bounds.
+`rnnt_loss_pruned` can not be used alone, it needs the gradients returned by `rnnt_loss_simple/rnnt_loss_smoothed` to get pruning bounds.
 
 ```python
 am = torch.randn((B, T, C), dtype=torch.float32)
@@ -196,8 +191,7 @@ You can also find recipes [here](https://github.com/k2-fsa/icefall/tree/master/e
 
 ### For rnnt_loss
 
-The unprund rnnt_loss is the same as torchaudio rnnt_loss, it produces same output as
-torchaudio for the same input.
+The `unprund rnnt_loss` is the same as `torchaudio rnnt_loss`, it produces same output as torchaudio for the same input.
 
 ```python
 logits = torch.randn((B, S, T, C), dtype=torch.float32)