fix tutorials

tutorials/doc-search/metadata.md

@@ -1,7 +1,7 @@
 
 
 ## Document Search by Metadata
-<Callout>PageIndex with metadata support is in closed beta. Fill out this form to request early access to this feature.</Callout>
+<callout>PageIndex with metadata support is in closed beta. Fill out this form to request early access to this feature.</callout>
 
 For documents that can be easily distinguished by metadata, we recommend using metadata to search the documents.
 This method is ideal for the following document types:

tutorials/doc-search/semantics.md

@@ -18,7 +18,9 @@ For each query, conduct a vector-based search to get top-K chunks with their cor
 For each document, calculate a relevance score. Let N be the number of content chunks associated with each document, and let **ChunkScore**(n) be the relevance score of chunk n. The document score is computed as:
 
 
-$\text{DocScore}=\frac{1}{\sqrt{N+1}}\sum_{n=1}^N \text{ChunkScore}(n)$
+$$
+\text{DocScore}=\frac{1}{\sqrt{N+1}}\sum_{n=1}^N \text{ChunkScore}(n)
+$$
 
 - The sum aggregates relevance from all related chunks.
 - The +1 inside the square root ensures the formula handles nodes with zero chunks.

tutorials/tree-search/README.md

@@ -0,0 +1,70 @@
+## Tree Search Examples
+This tutorial provides a basic example of how to perform retrieval using the PageIndex tree.
+
+### Basic LLM Tree Search Example
+A simple strategy is to use an LLM agent to conduct tree search. Here is a basic tree search prompt.
+
+```python
+prompt = f"""
+You are given a query and the tree structure of a document.
+You need to find all nodes that are likely to contain the answer.
+
+Query: {query}
+
+Document tree structure: {PageIndex_Tree}
+
+Reply in the following JSON format:
+{{
+  "thinking": <your reasoning about which nodes are relevant>,
+  "node_list": [node_id1, node_id2, ...]
+}}
+"""
+```
+<callout>
+In our dashboard and retrieval API, we use a combination of LLM tree search and value function-based Monte Carlo Tree Search ([MCTS](https://en.wikipedia.org/wiki/Monte_Carlo_tree_search)). More details will be released soon.
+</callout>
+
+### Integrating User Preference or Expert Knowledge
+Unlike vector-based RAG where integrating expert knowledge or user preference requires fine-tuning the embedding model, in PageIndex, you can incorporate user preferences or expert knowledge by simply adding knowledge to the LLM tree search prompt. Here is an example pipeline.
+
+
+#### 1. Preference Retrieval
+
+When a query is received, the system selects the most relevant user preference or expert knowledge snippets from a database or a set of domain-specific rules. This can be done using keyword matching, semantic similarity, or LLM-based relevance search.
+
+#### 2. Tree Search with Preference
+Integrating preference into the tree search prompt.
+
+**Enhanced Tree Search with Expert Preference Example**
+
+```python
+prompt = f"""
+You are given a question and a tree structure of a document.
+You need to find all nodes that are likely to contain the answer.
+
+Query: {query}
+
+Document tree structure:  {PageIndex_Tree}
+
+Expert Knowledge of relevant sections: {Preference}
+
+Reply in the following JSON format:
+{{
+  "thinking": <reasoning about which nodes are relevant>,
+  "node_list": [node_id1, node_id2, ...]
+}}
+"""
+```
+
+**Example Expert Preference**
+> If the query mentions EBITDA adjustments, prioritize Item 7 (MD&A) and footnotes in Item 8 (Financial Statements) in 10-K reports.
+
+
+
+By integrating user or expert preferences, node search becomes more targeted and effective, leveraging both the document structure and domain-specific insights.
+
+## 💬 Help & Community
+Contact us if you need any advice on conducting document searches for your use case.
+
+- 🤝 [Join our Discord](https://discord.gg/VuXuf29EUj)  
+- 📨 [Leave us a message](https://ii2abc2jejf.typeform.com/to/tK3AXl8T)