add figure for tuning & enrich the tuning section in doc

README.md

@@ -273,7 +273,7 @@ or refer to `example/librispeech/run_test.sh`.
 
 ## Hyper-parameters Tuning
 
-The hyper-parameters $\alpha$ (coefficient for language model scorer) and $\beta$ (coefficient for word count scorer) for the [*CTC beam search decoder*](https://arxiv.org/abs/1408.2873) often have a significant impact on the decoder's performance. It would be better to re-tune them on a validation set when the acoustic model is renewed.
+The hyper-parameters $\alpha$ (language model weight) and $\beta$ (word insertion weight) for the [*CTC beam search decoder*](https://arxiv.org/abs/1408.2873) often have a significant impact on the decoder's performance. It would be better to re-tune them on the validation set when the acoustic model is renewed.
 
 `tools/tune.py` performs a 2-D grid search over the hyper-parameter $\alpha$ and $\beta$. You must provide the range of $\alpha$ and $\beta$, as well as the number of their attempts.
 
@@ -283,12 +283,12 @@ The hyper-parameters $\alpha$ (coefficient for language model scorer) and $\beta
     CUDA_VISIBLE_DEVICES=0,1,2,3,4,5,6,7 \
     python tools/tune.py \
     --trainer_count 8 \
-    --alpha_from 0.1 \
+    --alpha_from 1.0 \
-    --alpha_to 0.36 \
+    --alpha_to 3.2 \
-    --num_alphas 14 \
+    --num_alphas 45 \
-    --beta_from 0.05 \
+    --beta_from 0.1 \
-    --beta_to 1.0 \
+    --beta_to 0.45 \
-    --num_betas 20
+    --num_betas 8
     ```
 
 - Tuning with CPU:
@@ -296,15 +296,23 @@ The hyper-parameters $\alpha$ (coefficient for language model scorer) and $\beta
     ```bash
     python tools/tune.py --use_gpu False
     ```
+ The grid search will log the WER (word error rate) or CER (character error rate) at each point in the hyper-parameter space and their minima, and draw the error surface optionally. A proper hyper-parameters range should include the global minima of the error surface for WER/CER, as illustrated in the following figure.  
 
-After tuning, you can reset $\alpha$ and $\beta$ in the inference and evaluation modules to see if they really help improve the ASR performance.
+<p align="center">
+<img src="docs/images/tuning_error_surface.png" width=450>
+<br/>An example error surface for tuning on the dev-clean set of LibriSpeech
+</p>
+
+Usually, as the figure shows the variation of language model weight ($alpha$) mainly affect the performance of CTC beam search decoder. And a better procedure is first tuning on serveral data batches (the number can be specified) to find out the proper range of hyper-parameters, then change to the whole validataion set to carray out an accurate tuning.
+
+After tuning, you can reset $\alpha$ and $\beta$ in the inference and evaluation modules to see if they really help improve the ASR performance. For more help
 
 ```bash
 python tune.py --help
 ```
 or refer to `example/librispeech/run_tune.sh`.
 
-TODO: add figure.
+
 
 ## Distributed Cloud Training