Merge branch 'main' of https://github.com/toshiaki1729/stable-diffusion-webui-text2prompt

README.md

@@ -26,7 +26,7 @@ git clone https://github.com/toshiaki1729/stable-diffusion-webui-text2prompt.git
  It's doing nothing special;
  
  1. Danbooru tags and it's descriptions are in the `data` folder
-    - descriptions are generated from wiki and already tokenised
+    - descriptions are generated from wiki and already tokenized
     - [all-mpnet-base-v2](https://huggingface.co/sentence-transformers/all-mpnet-base-v2) model is used to tokenize the text
     - for now, some tags (such as <1k tagged or containing title of the work) are deleted to prevent from "noisy" result
  1. Tokenize your input text and calculate cosine similarity with all tag descriptions
@@ -39,13 +39,16 @@ git clone https://github.com/toshiaki1729/stable-diffusion-webui-text2prompt.git
  ### More detailed
  $i \in N = \\{1, 2, ..., n\\}$ for index number of the tag  
  cosine similarity between tag description $d_i$ and your text $t$ : $S_C(d_i, t) = s_i$  
- probablity for the tag to be chosen : $P_i$
+ probability for the tag to be chosen : $P_i$
 
- ### "Method to convert similarity into probablity"
+ ### "Method to convert similarity into probability"
  #### "Cutoff and Power"
- - $p_i = \text{clamp}(s_i, 0, 1)^{\text{Power}} = \text{max}(s_i, 0)^{\text{Power}}$
+ 
+ $$p_i = \text{clamp}(s_i, 0, 1)^{\text{Power}} = \text{max}(s_i, 0)^{\text{Power}}$$
+
  #### "Softmax"
- - $p_i = \text{softmax}(s_i)$
+ 
+ $$p_i = \sigma(\\{s_n|n \in N\\})_i = \dfrac{e^{s_i}}{ \Sigma_{j \in N}\ e^{s_j} }$$
 
  ### "Sampling method"
  #### "NONE"
@@ -56,18 +59,18 @@ git clone https://github.com/toshiaki1729/stable-diffusion-webui-text2prompt.git
 
  $$
  P_i = \begin{cases} 
- \frac{p_i}{\Sigma p_j \text{ for all top-}k} & \text{if } p_i \text{ is top-}k \text{ largest in } \\{p_n | n \in N \\} \\
+ \dfrac{p_i}{\Sigma p_j \text{ for all top-}k} & \text{if } p_i \text{ is top-}k \text{ largest in } \\{p_n | n \in N \\} \\
  0 & \text{otherwise} \\
  \end{cases}
  $$
 
  #### "Top-p (Nucleus)"
- - $N_p \subset N$ such that $\Sigma_{i \in N_p}\ p_i\ \geq p$
-   - set $N_p=\emptyset$ at first, and add $k$ into $N_p$ where $p_k$ is the $k$-th largest in $\\{p_n | n \in N \\}$, while the equation holds.
-            
+ - Find smallest $N_p \subset N$ such that $\Sigma_{i \in N_p}\ p_i\ \geq p$
+   - set $N_p=\emptyset$ at first, and add index of $p_{(k)}$ into $N_p$ where $p_{(k)}$ is the $k$-th largest in $\\{p_n | n \in N \\}$ for $k = 1, 2, ..., N$, until the equation holds.
+
 $$
 P_i = \begin{cases} 
-\frac{p_i}{\Sigma p_j \text{ for all }j \in N_p} & \text{if } i \in N_p \\
+\dfrac{p_i}{\Sigma p_j \text{ for all }j \in N_p} & \text{if } i \in N_p \\
 0 & \text{otherwise} \\
 \end{cases}
 $$