Update app.py

app.py

@@ -38,6 +38,11 @@ with gr.Blocks() as demo:
     with gr.Column():
         gr.Markdown(
             """<h1>The Optimal Vocabulary Size Predictor</h1>
+
+            This repo is the offical demo space for [Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabularies](https://huggingface.co/papers/2407.13623). In summary, we show that when scaling up model size, increase vocabulary size too, but at a slower rate than other parameters.
+            
+            ![Vocabulary Demo](figure/vocabulary_demo.png)
+
             This tool is used to predict the optimal vocabulary size given the non-vocabulary parameters. We provide 3 ways for prediction:
             
             - **Approach 1: Build the relationship between studied attributes and FLOPs**: Build the relationship between the optimal data points (the points that reach the lowest loss under the same FLOPs budget) and the FLOPs.
@@ -51,7 +56,7 @@ with gr.Blocks() as demo:
         
 
         with gr.Row():
-            Nnv = gr.Textbox(label="Non-vocabulary Parameters", value=str(7*10**9))
+            Nnv = gr.Textbox(label="Non-vocabulary Parameters", value=str(7e9))
             flops = gr.Textbox(label="FLOPs", placeholder="Optional (e.g. 7.05e21)")
             output_text = gr.Textbox(label="Prediction")
         with gr.Row():