From dbb5cbce4354c486559df4342913b29877714222 Mon Sep 17 00:00:00 2001
From: Andy Zhou <andyzhou@4bd094a2-01.cloud.together.ai>
Date: Sun, 18 Aug 2024 18:45:30 -0700
Subject: [PATCH 1/2] Add Language Agent Tree Search (LATS) notebook

---
 notebook/lats_search.ipynb | 1315 ++++++++++++++++++++++++++++++++++++
 1 file changed, 1315 insertions(+)
 create mode 100644 notebook/lats_search.ipynb

diff --git a/notebook/lats_search.ipynb b/notebook/lats_search.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "211913e6",
+   "metadata": {},
+   "source": [
+    "# Language Agent Tree Search\n",
+    "\n",
+    "[Language Agent Tree Search](https://arxiv.org/abs/2310.04406) (LATS), by Zhou, et. al, is a general LLM agent search algorithm that combines reflection/evaluation and search (specifically Monte-Carlo tree search) to achieve stronger overall task performance by leveraging inference-time compute.\n",
+    "\n",
+    "It has four main phases consisting of six steps:\n",
+    "\n",
+    "1. Select: pick the best next state to progress from, based on its aggregate value. \n",
+    "2. Expand and simulate: sample n potential actions to take and execute them in parallel.\n",
+    "3. Reflect + Evaluate: observe the outcomes of these actions and score the decisions based on reflection (and possibly external feedback if available)\n",
+    "4. Backpropagate: update the scores of the root trajectories based on the outcomes.\n",
+    "\n",
+    "![lats](https://i.postimg.cc/NjQScLTv/image.png)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "da705b29",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/andyzhou/venv/lib/python3.10/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
+      "  from .autonotebook import tqdm as notebook_tqdm\n",
+      "2024-08-16 18:36:36,107\tINFO util.py:154 -- Missing packages: ['ipywidgets']. Run `pip install -U ipywidgets`, then restart the notebook server for rich notebook output.\n",
+      "2024-08-16 18:36:36,376\tINFO util.py:154 -- Missing packages: ['ipywidgets']. Run `pip install -U ipywidgets`, then restart the notebook server for rich notebook output.\n"
+     ]
+    }
+   ],
+   "source": [
+    "import json\n",
+    "import logging\n",
+    "import os\n",
+    "import uuid\n",
+    "from typing import Any, Dict, List\n",
+    "\n",
+    "from autogen import AssistantAgent, ConversableAgent, GroupChat, UserProxyAgent, config_list_from_json"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "293fd23b",
+   "metadata": {},
+   "source": [
+    "# Configure logging\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "a02f8a2c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "logging.basicConfig(level=logging.INFO)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1d5ca06b",
+   "metadata": {},
+   "source": [
+    "# Set environment variables\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1566c7df",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "os.environ[\"AUTOGEN_USE_DOCKER\"] = \"0\"  # Disable Docker usage globally for Autogen\n",
+    "os.environ[\"OPENAI_API_KEY\"] = \"YOUR_API_KEY\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "585654ac",
+   "metadata": {},
+   "source": [
+    "## Prerequisites\n",
+    "\n",
+    "Install `autogen` (for the LLM framework and agents)\n",
+    "\n",
+    "Required packages: autogen\n",
+    "\n",
+    "Please ensure these packages are installed before running this script"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "586bcf0f",
+   "metadata": {},
+   "source": [
+    "# Directly create the config_list with the API key"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "9eaf711f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "config_list = [{\"model\": \"gpt-4o-mini\", \"api_key\": \"YOUR_API_KEY\"}]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "79701018",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "if not config_list:\n",
+    "    raise ValueError(\"Failed to create configuration. Please check the API key.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9041e0a3",
+   "metadata": {},
+   "source": [
+    "### Reflection Class\n",
+    "\n",
+    "The reflection chain will score agent outputs based on the decision and the tool responses."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "ce0288e9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "from pydantic import BaseModel, Field\n",
+    "\n",
+    "\n",
+    "class Reflection(BaseModel):\n",
+    "    reflections: str = Field(\n",
+    "        description=\"The critique and reflections on the sufficiency, superfluency,\"\n",
+    "        \" and general quality of the response\"\n",
+    "    )\n",
+    "    score: int = Field(\n",
+    "        description=\"Score from 0-10 on the quality of the candidate response.\",\n",
+    "        gte=0,\n",
+    "        lte=10,\n",
+    "    )\n",
+    "    found_solution: bool = Field(description=\"Whether the response has fully solved the question or task.\")\n",
+    "\n",
+    "    def as_message(self):\n",
+    "        return {\"role\": \"human\", \"content\": f\"Reasoning: {self.reflections}\\nScore: {self.score}\"}\n",
+    "\n",
+    "    @property\n",
+    "    def normalized_score(self) -> float:\n",
+    "        return self.score / 10.0"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1f6d3476",
+   "metadata": {},
+   "source": [
+    "## Tree State\n",
+    "\n",
+    "LATS is based on a (greedy) Monte-Carlo tree search. For each search steps, it picks the node with the highest \"upper confidence bound\", which is a metric that balances exploitation (highest average reward) and exploration (lowest visits). Starting from that node, it generates N (5 in this case) new candidate actions to take, and adds them to the tree. It stops searching either when it has generated a valid solution OR when it has reached the maximum number of rollouts (search tree depth)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "b6d0d7a6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math\n",
+    "import os\n",
+    "from collections import deque\n",
+    "from typing import Optional"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "305a29d6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class Node:\n",
+    "    def __init__(\n",
+    "        self,\n",
+    "        messages: List[Dict[str, str]],\n",
+    "        reflection: Optional[Reflection] = None,\n",
+    "        parent: Optional[\"Node\"] = None,\n",
+    "    ):\n",
+    "        self.messages = messages\n",
+    "        self.parent = parent\n",
+    "        self.children: List[\"Node\"] = []\n",
+    "        self.value = 0.0\n",
+    "        self.visits = 0\n",
+    "        self.reflection = reflection\n",
+    "        self.depth = parent.depth + 1 if parent is not None else 1\n",
+    "        self._is_solved = reflection.found_solution if reflection else False\n",
+    "        if self._is_solved:\n",
+    "            self._mark_tree_as_solved()\n",
+    "        if reflection:\n",
+    "            self.backpropagate(reflection.normalized_score)\n",
+    "\n",
+    "    def __repr__(self) -> str:\n",
+    "        return (\n",
+    "            f\"<Node value={self.value:.2f}, visits={self.visits},\" f\" depth={self.depth}, is_solved={self._is_solved}>\"\n",
+    "        )\n",
+    "\n",
+    "    @property\n",
+    "    def is_solved(self) -> bool:\n",
+    "        \"\"\"If any solutions exist, we can end the search.\"\"\"\n",
+    "        return self._is_solved\n",
+    "\n",
+    "    @property\n",
+    "    def is_terminal(self):\n",
+    "        return not self.children\n",
+    "\n",
+    "    @property\n",
+    "    def best_child(self):\n",
+    "        \"\"\"Select the child with the highest UCT to search next.\"\"\"\n",
+    "        if not self.children:\n",
+    "            return None\n",
+    "        all_nodes = self._get_all_children()\n",
+    "        return max(all_nodes, key=lambda child: child.upper_confidence_bound())\n",
+    "\n",
+    "    @property\n",
+    "    def best_child_score(self):\n",
+    "        \"\"\"Return the child with the highest value.\"\"\"\n",
+    "        if not self.children:\n",
+    "            return None\n",
+    "        return max(self.children, key=lambda child: int(child.is_solved) * child.value)\n",
+    "\n",
+    "    @property\n",
+    "    def height(self) -> int:\n",
+    "        \"\"\"Check for how far we've rolled out the tree.\"\"\"\n",
+    "        if self.children:\n",
+    "            return 1 + max([child.height for child in self.children])\n",
+    "        return 1\n",
+    "\n",
+    "    def upper_confidence_bound(self, exploration_weight=1.0):\n",
+    "        \"\"\"Return the UCT score. This helps balance exploration vs. exploitation of a branch.\"\"\"\n",
+    "        if self.parent is None:\n",
+    "            raise ValueError(\"Cannot obtain UCT from root node\")\n",
+    "        if self.visits == 0:\n",
+    "            return self.value\n",
+    "        # Encourages exploitation of high-value trajectories\n",
+    "        average_reward = self.value / self.visits\n",
+    "        exploration_term = math.sqrt(math.log(self.parent.visits) / self.visits)\n",
+    "        return average_reward + exploration_weight * exploration_term\n",
+    "\n",
+    "    def backpropagate(self, reward: float):\n",
+    "        \"\"\"Update the score of this node and its parents.\"\"\"\n",
+    "        node = self\n",
+    "        while node:\n",
+    "            node.visits += 1\n",
+    "            node.value = (node.value * (node.visits - 1) + reward) / node.visits\n",
+    "            node = node.parent\n",
+    "\n",
+    "    def get_messages(self, include_reflections: bool = True):\n",
+    "        if include_reflections and self.reflection:\n",
+    "            return self.messages + [self.reflection.as_message()]\n",
+    "        return self.messages\n",
+    "\n",
+    "    def get_trajectory(self, include_reflections: bool = True) -> List[Dict[str, str]]:\n",
+    "        \"\"\"Get messages representing this search branch.\"\"\"\n",
+    "        messages = []\n",
+    "        node = self\n",
+    "        while node:\n",
+    "            messages.extend(node.get_messages(include_reflections=include_reflections)[::-1])\n",
+    "            node = node.parent\n",
+    "        # Reverse the final back-tracked trajectory to return in the correct order\n",
+    "        return messages[::-1]  # root solution, reflection, child 1, ...\n",
+    "\n",
+    "    def _get_all_children(self):\n",
+    "        all_nodes = []\n",
+    "        nodes = deque()\n",
+    "        nodes.append(self)\n",
+    "        while nodes:\n",
+    "            node = nodes.popleft()\n",
+    "            all_nodes.extend(node.children)\n",
+    "            for n in node.children:\n",
+    "                nodes.append(n)\n",
+    "        return all_nodes\n",
+    "\n",
+    "    def get_best_solution(self):\n",
+    "        \"\"\"Return the best solution from within the current sub-tree.\"\"\"\n",
+    "        all_nodes = [self] + self._get_all_children()\n",
+    "        best_node = max(\n",
+    "            all_nodes,\n",
+    "            # We filter out all non-terminal, non-solution trajectories\n",
+    "            key=lambda node: int(node.is_terminal and node.is_solved) * node.value,\n",
+    "        )\n",
+    "        return best_node\n",
+    "\n",
+    "    def _mark_tree_as_solved(self):\n",
+    "        parent = self.parent\n",
+    "        while parent:\n",
+    "            parent._is_solved = True\n",
+    "            parent = parent.parent"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98b719d9",
+   "metadata": {},
+   "source": [
+    "The main component is the tree, represented by the root node."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "586d953a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing_extensions import TypedDict\n",
+    "\n",
+    "\n",
+    "class TreeState(TypedDict):\n",
+    "    # The full tree\n",
+    "    root: Node\n",
+    "    # The original input\n",
+    "    input: str"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3a61a6ee",
+   "metadata": {},
+   "source": [
+    "## Define Language Agent\n",
+    "\n",
+    "Our agent will have three primary LLM-powered processes:\n",
+    "\n",
+    "1. Reflect: score the action based on the tool response.\n",
+    "2. Initial response: to create the root node and start the search.\n",
+    "3. Expand: generate 5 candidate \"next steps\" from the best spot in the current tree\n",
+    "\n",
+    "For more \"Grounded\" tool applications (such as code synthesis), you could integrate code execution into the reflection/reward step. This type of external feedback is very useful."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9e6c27f",
+   "metadata": {},
+   "source": [
+    "#### Tools\n",
+    "For our example, we will give the language agent a search engine."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ffb10a00",
+   "metadata": {},
+   "source": [
+    "Define the UserProxyAgent with web search / tool-use capability\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "e467f73e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "user_proxy = UserProxyAgent(\n",
+    "    name=\"user\",\n",
+    "    human_input_mode=\"NEVER\",\n",
+    "    max_consecutive_auto_reply=10,\n",
+    "    code_execution_config={\n",
+    "        \"work_dir\": \"web\",\n",
+    "        \"use_docker\": False,\n",
+    "    },\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5c2b96b2",
+   "metadata": {},
+   "source": [
+    "Create a ConversableAgent without tools\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "212daaef",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "assistant_agent = ConversableAgent(\n",
+    "    name=\"assistant_agent\",\n",
+    "    system_message=\"You are an AI assistant capable of helping with various tasks.\",\n",
+    "    human_input_mode=\"NEVER\",\n",
+    "    code_execution_config=False,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "527c1a39",
+   "metadata": {},
+   "source": [
+    "### Reflection\n",
+    "\n",
+    "Self-reflection allows the agent to boostrap, improving its future responses based on the outcome of previous ones. In agents this is more powerful since it can use external feedback to improve."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "3bdd8a23",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reflection_prompt = \"\"\"\n",
+    "Reflect and grade the assistant response to the user question below.\n",
+    "User question: {input}\n",
+    "Assistant response: {candidate}\n",
+    "\n",
+    "Provide your reflection in the following format:\n",
+    "Reflections: [Your detailed critique and reflections]\n",
+    "Score: [A score from 0-10]\n",
+    "Found Solution: [true/false]\n",
+    "\"\"\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "7750d32f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reflection_agent = AssistantAgent(\n",
+    "    name=\"reflection_agent\",\n",
+    "    system_message=\"You are an AI assistant that reflects on and grades responses.\",\n",
+    "    llm_config={\n",
+    "        \"config_list\": config_list,\n",
+    "        \"temperature\": 0.2,\n",
+    "    },\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "23f26bf0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def reflection_chain(inputs: Dict[str, Any]) -> Reflection:\n",
+    "    try:\n",
+    "        candidate_content = \"\"\n",
+    "        if \"candidate\" in inputs:\n",
+    "            candidate = inputs[\"candidate\"]\n",
+    "            if isinstance(candidate, list):\n",
+    "                candidate_content = (\n",
+    "                    candidate[-1][\"content\"]\n",
+    "                    if isinstance(candidate[-1], dict) and \"content\" in candidate[-1]\n",
+    "                    else str(candidate[-1])\n",
+    "                )\n",
+    "            elif isinstance(candidate, dict):\n",
+    "                candidate_content = candidate.get(\"content\", str(candidate))\n",
+    "            elif isinstance(candidate, str):\n",
+    "                candidate_content = candidate\n",
+    "            else:\n",
+    "                candidate_content = str(candidate)\n",
+    "\n",
+    "        formatted_prompt = [\n",
+    "            {\"role\": \"system\", \"content\": \"You are an AI assistant that reflects on and grades responses.\"},\n",
+    "            {\n",
+    "                \"role\": \"user\",\n",
+    "                \"content\": reflection_prompt.format(input=inputs.get(\"input\", \"\"), candidate=candidate_content),\n",
+    "            },\n",
+    "        ]\n",
+    "        response = reflection_agent.generate_reply(formatted_prompt)\n",
+    "\n",
+    "        # Parse the response\n",
+    "        response_str = str(response)\n",
+    "        lines = response_str.split(\"\\n\")\n",
+    "        reflections = next((line.split(\": \", 1)[1] for line in lines if line.startswith(\"Reflections:\")), \"\")\n",
+    "        score_str = next((line.split(\": \", 1)[1] for line in lines if line.startswith(\"Score:\")), \"0\")\n",
+    "        try:\n",
+    "            if \"/\" in score_str:\n",
+    "                numerator, denominator = map(int, score_str.split(\"/\"))\n",
+    "                score = int((numerator / denominator) * 10)\n",
+    "            else:\n",
+    "                score = int(score_str)\n",
+    "        except ValueError:\n",
+    "            logging.warning(f\"Invalid score value: {score_str}. Defaulting to 0.\")\n",
+    "        score = 0\n",
+    "\n",
+    "        found_solution = next(\n",
+    "            (line.split(\": \", 1)[1].lower() == \"true\" for line in lines if line.startswith(\"Found Solution:\")), False\n",
+    "        )\n",
+    "\n",
+    "        if not reflections:\n",
+    "            logging.warning(\"No reflections found in the response. Using default values.\")\n",
+    "            reflections = \"No reflections provided.\"\n",
+    "\n",
+    "        return Reflection(reflections=reflections, score=score, found_solution=found_solution)\n",
+    "    except Exception as e:\n",
+    "        logging.error(f\"Error in reflection_chain: {str(e)}\", exc_info=True)\n",
+    "        return Reflection(reflections=f\"Error in reflection: {str(e)}\", score=0, found_solution=False)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc4b9911",
+   "metadata": {},
+   "source": [
+    "### Initial Response\n",
+    "\n",
+    "We start with a single root node, generated by this first step. It responds to the user input either with a tool invocation or a response."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60675131",
+   "metadata": {},
+   "source": [
+    "# Create Autogen agents\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "fd743ab5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "assistant = AssistantAgent(name=\"assistant\", llm_config={\"config_list\": config_list}, code_execution_config=False)\n",
+    "user = UserProxyAgent(\n",
+    "    name=\"user\",\n",
+    "    human_input_mode=\"NEVER\",\n",
+    "    max_consecutive_auto_reply=10,\n",
+    "    code_execution_config={\"work_dir\": \"web\", \"use_docker\": False},\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1f93b734",
+   "metadata": {},
+   "source": [
+    "# Define a function to create the initial prompt\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "b7e00575",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def create_initial_prompt(input_text):\n",
+    "    return [\n",
+    "        {\"role\": \"system\", \"content\": \"You are an AI assistant.\"},\n",
+    "        {\"role\": \"user\", \"content\": input_text},\n",
+    "    ]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b8442317",
+   "metadata": {},
+   "source": [
+    "# Function to generate initial response\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "b7afcd1b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def generate_initial_response(state: TreeState) -> TreeState:\n",
+    "    chat_messages = create_initial_prompt(state[\"input\"])\n",
+    "    try:\n",
+    "        # Ensure chat_messages is a list of dictionaries\n",
+    "        if not isinstance(chat_messages, list):\n",
+    "            chat_messages = [{\"role\": \"user\", \"content\": chat_messages}]\n",
+    "\n",
+    "        logging.info(f\"Generating initial response for input: {state['input']}\")\n",
+    "        logging.debug(f\"Chat messages: {chat_messages}\")\n",
+    "\n",
+    "        response = assistant.generate_reply(chat_messages)\n",
+    "        logging.debug(f\"Raw response from assistant: {response}\")\n",
+    "\n",
+    "        # Ensure response is properly formatted as a string\n",
+    "        if isinstance(response, str):\n",
+    "            content = response\n",
+    "        elif isinstance(response, dict) and \"content\" in response:\n",
+    "            content = response[\"content\"]\n",
+    "        elif isinstance(response, list) and len(response) > 0:\n",
+    "            content = response[-1].get(\"content\", str(response[-1]))\n",
+    "        else:\n",
+    "            content = str(response)\n",
+    "\n",
+    "        content = content.strip()\n",
+    "        if not content:\n",
+    "            raise ValueError(\"Generated content is empty after processing\")\n",
+    "\n",
+    "        logging.debug(f\"Processed content: {content[:100]}...\")  # Log first 100 chars\n",
+    "\n",
+    "        # Generate reflection\n",
+    "        reflection_input = {\"input\": state[\"input\"], \"candidate\": content}\n",
+    "        logging.info(\"Generating reflection on the initial response\")\n",
+    "        reflection = reflection_chain(reflection_input)\n",
+    "        logging.debug(f\"Reflection generated: {reflection}\")\n",
+    "\n",
+    "        # Create Node with messages as a list containing a single dict\n",
+    "        messages = [{\"role\": \"assistant\", \"content\": content}]\n",
+    "        root = Node(messages=messages, reflection=reflection)\n",
+    "\n",
+    "        logging.info(\"Initial response and reflection generated successfully\")\n",
+    "        return TreeState(root=root, input=state[\"input\"])\n",
+    "\n",
+    "    except Exception as e:\n",
+    "        logging.error(f\"Error in generate_initial_response: {str(e)}\", exc_info=True)\n",
+    "        return TreeState(root=None, input=state[\"input\"])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87ef17ca",
+   "metadata": {},
+   "source": [
+    "# Example usage of the generate_initial_response function\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "7ab75669",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO:root:Generating initial response for input: Why is the sky blue?\n",
+      "INFO:root:Generating reflection on the initial response\n",
+      "INFO:root:Initial response and reflection generated successfully\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The sky appears blue due to a phenomenon called Rayleigh scattering. Here's a simplified explanation:\n",
+      "\n",
+      "1. **Sunlight Composition**: Sunlight, or white light, is made up of multiple colors (red, orange, yellow, green, blue, indigo, violet), which can be seen when light is passed through a prism.\n",
+      "\n",
+      "2. **Atmospheric Interaction**: As sunlight passes through the Earth's atmosphere, it interacts with air molecules and small particles. Blue light waves are shorter and scatter more than other colors when they hit these particles.\n",
+      "\n",
+      "3. **Direction of Sunlight**: During the day, when the sun is higher in the sky, the blue light is scattered in all directions. As a result, regardless of where you look in the sky, you see more of the scattered blue light than any other color.\n",
+      "\n",
+      "4. **Effects of Angle**: During sunrise and sunset, the sun's light has to pass through more atmosphere, scattering short wavelengths (like blue) out even more and allowing longer wavelengths (like red and orange) to dominate, which is why you see those colors during those times.\n",
+      "\n",
+      "In summary, the blue appearance of the sky is due to the scattering of blue light by the gases and particles in the atmosphere, which makes it the most visible color to human eyes from all angles. \n",
+      "\n",
+      "TERMINATE\n"
+     ]
+    }
+   ],
+   "source": [
+    "initial_prompt = \"Why is the sky blue?\"\n",
+    "initial_state = TreeState(input=initial_prompt, root=None)\n",
+    "result_state = generate_initial_response(initial_state)\n",
+    "if result_state[\"root\"] is not None:\n",
+    "    print(result_state[\"root\"].messages[0][\"content\"])\n",
+    "else:\n",
+    "    print(\"Failed to generate initial response.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e619223f",
+   "metadata": {},
+   "source": [
+    "#### Starting Node\n",
+    "\n",
+    "We will package up the candidate generation and reflection in a single node of our graph. This is represented by the following function:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24c052e0",
+   "metadata": {},
+   "source": [
+    "\n",
+    "# Define the function to generate the initial response"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "94c92498",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "# Define the function to generate the initial response\n",
+    "\n",
+    "\n",
+    "def generate_initial_response(state: TreeState) -> TreeState:\n",
+    "    \"\"\"Generate the initial candidate response using Autogen components.\"\"\"\n",
+    "    assistant = AssistantAgent(name=\"assistant\", llm_config={\"config_list\": config_list}, code_execution_config=False)\n",
+    "\n",
+    "    # Generate initial response\n",
+    "    initial_message = [\n",
+    "        {\"role\": \"system\", \"content\": \"You are an AI assistant.\"},\n",
+    "        {\"role\": \"user\", \"content\": state[\"input\"]},\n",
+    "    ]\n",
+    "\n",
+    "    try:\n",
+    "        logging.info(f\"Generating initial response for input: {state['input']}\")\n",
+    "        response = assistant.generate_reply(initial_message)\n",
+    "        logging.debug(f\"Raw response from assistant: {response}\")\n",
+    "\n",
+    "        # Ensure response is properly formatted as a string\n",
+    "        if isinstance(response, str):\n",
+    "            content = response\n",
+    "        elif isinstance(response, dict):\n",
+    "            content = response.get(\"content\", \"\")\n",
+    "            if not content:\n",
+    "                content = json.dumps(response)\n",
+    "        elif isinstance(response, list):\n",
+    "            content = \" \".join(str(item) for item in response)\n",
+    "        else:\n",
+    "            content = str(response)\n",
+    "\n",
+    "        # Ensure content is always a string and not empty\n",
+    "        content = content.strip()\n",
+    "        if not content:\n",
+    "            raise ValueError(\"Generated content is empty after processing\")\n",
+    "\n",
+    "        logging.debug(f\"Final processed content (first 100 chars): {content[:100]}...\")\n",
+    "\n",
+    "        # Generate reflection\n",
+    "        logging.info(\"Generating reflection on the initial response\")\n",
+    "        reflection_input = {\"input\": state[\"input\"], \"candidate\": content}\n",
+    "        reflection = reflection_chain(reflection_input)\n",
+    "        logging.debug(f\"Reflection generated: {reflection}\")\n",
+    "\n",
+    "        if not isinstance(reflection, Reflection):\n",
+    "            raise TypeError(f\"Invalid reflection type: {type(reflection)}. Expected Reflection, got {type(reflection)}\")\n",
+    "\n",
+    "        # Create Node with messages as a list containing a single dict\n",
+    "        messages = [{\"role\": \"assistant\", \"content\": content}]\n",
+    "        logging.debug(f\"Creating Node with messages: {messages}\")\n",
+    "        root = Node(messages=messages, reflection=reflection)\n",
+    "        logging.info(\"Initial response and reflection generated successfully\")\n",
+    "        logging.debug(f\"Created root node: {root}\")\n",
+    "        return TreeState(root=root, input=state[\"input\"])\n",
+    "\n",
+    "    except Exception as e:\n",
+    "        logging.error(f\"Error in generate_initial_response: {str(e)}\", exc_info=True)\n",
+    "        return TreeState(root=None, input=state[\"input\"])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c58a4074",
+   "metadata": {},
+   "source": [
+    "### Candidate Generation\n",
+    "The following code prompts the same LLM to generate N additional candidates to check.\n",
+    "\n",
+    "This generates N candidate values for a single input to sample actions from the environment"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "27a3a1db",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def generate_candidates(messages: list, config: dict):\n",
+    "    n = config.get(\"N\", 5)\n",
+    "    assistant = AssistantAgent(name=\"assistant\", llm_config={\"config_list\": config_list}, code_execution_config=False)\n",
+    "\n",
+    "    candidates = []\n",
+    "    for _ in range(n):\n",
+    "        try:\n",
+    "            # Use the assistant to generate a response\n",
+    "            last_message = messages[-1][\"content\"] if messages and isinstance(messages[-1], dict) else str(messages[-1])\n",
+    "            response = assistant.generate_reply([{\"role\": \"user\", \"content\": last_message}])\n",
+    "            if isinstance(response, str):\n",
+    "                candidates.append(response)\n",
+    "            elif isinstance(response, dict) and \"content\" in response:\n",
+    "                candidates.append(response[\"content\"])\n",
+    "            elif (\n",
+    "                isinstance(response, list) and response and isinstance(response[-1], dict) and \"content\" in response[-1]\n",
+    "            ):\n",
+    "                candidates.append(response[-1][\"content\"])\n",
+    "            else:\n",
+    "                candidates.append(str(response))\n",
+    "        except Exception as e:\n",
+    "            logging.error(f\"Error generating candidate: {str(e)}\")\n",
+    "            candidates.append(\"Failed to generate candidate.\")\n",
+    "\n",
+    "    if not candidates:\n",
+    "        logging.warning(\"No candidates were generated.\")\n",
+    "\n",
+    "    return candidates\n",
+    "\n",
+    "\n",
+    "expansion_chain = generate_candidates"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a47c8161",
+   "metadata": {},
+   "source": [
+    "#### Candidate generation node\n",
+    "\n",
+    "We will package the candidate generation and reflection steps in the following \"expand\" node.\n",
+    "We do all the operations as a batch process to speed up execution."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "175afca7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def expand(state: TreeState, config: Dict[str, Any]) -> dict:\n",
+    "    root = state[\"root\"]\n",
+    "    best_candidate: Node = root.best_child if root.children else root\n",
+    "    messages = best_candidate.get_trajectory()\n",
+    "\n",
+    "    # Generate N candidates using Autogen's generate_candidates function\n",
+    "    new_candidates = generate_candidates(messages, config)\n",
+    "\n",
+    "    # Reflect on each candidate using Autogen's AssistantAgent\n",
+    "    reflections = []\n",
+    "    for candidate in new_candidates:\n",
+    "        reflection = reflection_chain({\"input\": state[\"input\"], \"candidate\": candidate})\n",
+    "        reflections.append(reflection)\n",
+    "\n",
+    "    # Grow tree\n",
+    "    child_nodes = [\n",
+    "        Node([{\"role\": \"assistant\", \"content\": candidate}], parent=best_candidate, reflection=reflection)\n",
+    "        for candidate, reflection in zip(new_candidates, reflections)\n",
+    "    ]\n",
+    "    best_candidate.children.extend(child_nodes)\n",
+    "\n",
+    "    # We have already extended the tree directly, so we just return the state\n",
+    "    return state"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "717b7b93",
+   "metadata": {},
+   "source": [
+    "## Create Tree\n",
+    "\n",
+    "With those two nodes defined, we are ready to define the tree. After each agent step, we have the option of finishing."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "e309ea9f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing import Any, Dict, Literal\n",
+    "\n",
+    "\n",
+    "def should_loop(state: Dict[str, Any]) -> Literal[\"expand\", \"end\"]:\n",
+    "    \"\"\"Determine whether to continue the tree search.\"\"\"\n",
+    "    root = state[\"root\"]\n",
+    "    if root.is_solved:\n",
+    "        return \"end\"\n",
+    "    if root.height > 5:\n",
+    "        return \"end\"\n",
+    "    return \"expand\"\n",
+    "\n",
+    "\n",
+    "def run_lats(input_query: str, max_iterations: int = 10):\n",
+    "    import logging\n",
+    "\n",
+    "    logging.basicConfig(level=logging.INFO)\n",
+    "    logger = logging.getLogger(__name__)\n",
+    "\n",
+    "    try:\n",
+    "\n",
+    "        state = {\"input\": input_query, \"root\": None}\n",
+    "        try:\n",
+    "            state = generate_initial_response(state)\n",
+    "            if not isinstance(state, dict) or \"root\" not in state or state[\"root\"] is None:\n",
+    "                logger.error(\"Initial response generation failed or returned invalid state\")\n",
+    "                return \"Failed to generate initial response.\"\n",
+    "            logger.info(\"Initial response generated successfully\")\n",
+    "        except Exception as e:\n",
+    "            logger.error(f\"Error generating initial response: {str(e)}\", exc_info=True)\n",
+    "            return \"Failed to generate initial response due to an unexpected error.\"\n",
+    "\n",
+    "        for iteration in range(max_iterations):\n",
+    "            action = should_loop(state)\n",
+    "            if action == \"end\":\n",
+    "                logger.info(f\"Search ended after {iteration + 1} iterations\")\n",
+    "                break\n",
+    "            try:\n",
+    "                state = expand(\n",
+    "                    state,\n",
+    "                    {\n",
+    "                        \"N\": 5,\n",
+    "                        \"input_query\": input_query,\n",
+    "                    },\n",
+    "                )\n",
+    "                logger.info(f\"Completed iteration {iteration + 1}\")\n",
+    "            except Exception as e:\n",
+    "                logger.error(f\"Error during iteration {iteration + 1}: {str(e)}\", exc_info=True)\n",
+    "                continue\n",
+    "\n",
+    "        if not isinstance(state, dict) or \"root\" not in state or state[\"root\"] is None:\n",
+    "            return \"No valid solution found due to an error in the search process.\"\n",
+    "\n",
+    "        solution_node = state[\"root\"].get_best_solution()\n",
+    "        best_trajectory = solution_node.get_trajectory(include_reflections=False)\n",
+    "        if not best_trajectory:\n",
+    "            return \"No solution found in the search process.\"\n",
+    "\n",
+    "        result = (\n",
+    "            best_trajectory[-1].get(\"content\") if isinstance(best_trajectory[-1], dict) else str(best_trajectory[-1])\n",
+    "        )\n",
+    "        logger.info(\"LATS search completed successfully\")\n",
+    "        return result\n",
+    "    except Exception as e:\n",
+    "        logger.error(f\"An unexpected error occurred during LATS execution: {str(e)}\", exc_info=True)\n",
+    "        return f\"An unexpected error occurred: {str(e)}\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e274e373",
+   "metadata": {},
+   "source": [
+    "Example usage:\n",
+    "\n",
+    "result = run_lats(\"Write a research report on deep learning.\")\n",
+    "\n",
+    "print(result)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aa719ff2",
+   "metadata": {},
+   "source": [
+    "\n",
+    "# Example usage of the LATS algorithm with Autogen"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "683c0f2c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import logging\n",
+    "\n",
+    "logging.basicConfig(level=logging.INFO, format=\"%(asctime)s - %(levelname)s - %(message)s\")\n",
+    "logger = logging.getLogger(__name__)\n",
+    "\n",
+    "\n",
+    "def run_lats_example(question):\n",
+    "    try:\n",
+    "        logger.info(f\"Processing question: {question}\")\n",
+    "        result = run_lats(question)\n",
+    "        logger.info(f\"LATS algorithm completed. Result: {result[:100]}...\")  # Log first 100 chars of result\n",
+    "        print(f\"Question: {question}\")\n",
+    "        print(f\"Answer: {result}\")\n",
+    "    except Exception as e:\n",
+    "        logger.error(f\"An error occurred while processing the question: {str(e)}\", exc_info=True)\n",
+    "        print(f\"An error occurred: {str(e)}\")\n",
+    "    finally:\n",
+    "        print(\"---\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a4ce778e",
+   "metadata": {},
+   "source": [
+    "# List of example questions\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "60fa1f07",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "questions = [\n",
+    "    \"Explain how epigenetic modifications can influence gene expression across generations and the implications for evolution.\",\n",
+    "    \"Discuss the challenges of grounding ethical theories in moral realism, especially in light of the is-ought problem introduced by Hume.\",\n",
+    "    \"How does the Riemann Hypothesis relate to the distribution of prime numbers, and why is it significant in number theory?\",\n",
+    "    \"Describe the challenges and theoretical underpinnings of unifying general relativity with quantum mechanics, particularly focusing on string theory and loop quantum gravity.\",\n",
+    "]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0fed5fe",
+   "metadata": {},
+   "source": [
+    "# Run LATS algorithm for each question\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "5d1e5754",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO:__main__:Processing question: Explain how epigenetic modifications can influence gene expression across generations and the implications for evolution.\n",
+      "INFO:root:Generating initial response for input: Explain how epigenetic modifications can influence gene expression across generations and the implications for evolution.\n",
+      "INFO:root:Generating reflection on the initial response\n",
+      "INFO:root:Initial response and reflection generated successfully\n",
+      "INFO:__main__:Initial response generated successfully\n",
+      "INFO:__main__:Search ended after 1 iterations\n",
+      "INFO:__main__:LATS search completed successfully\n",
+      "INFO:__main__:LATS algorithm completed. Result: Epigenetic modifications refer to changes in gene expression that do not involve alterations to the ...\n",
+      "INFO:__main__:Processing question: Discuss the challenges of grounding ethical theories in moral realism, especially in light of the is-ought problem introduced by Hume.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Example 1:\n",
+      "Question: Explain how epigenetic modifications can influence gene expression across generations and the implications for evolution.\n",
+      "Answer: Epigenetic modifications refer to changes in gene expression that do not involve alterations to the underlying DNA sequence. These modifications can influence how genes are expressed, leading to varied phenotypic outcomes. Here’s an explanation of how these modifications can influence gene expression across generations and their implications for evolution:\n",
+      "\n",
+      "### Mechanisms of Epigenetic Modifications\n",
+      "\n",
+      "1. **DNA Methylation**: The addition of a methyl group to DNA, usually at cytosine bases, can silence gene expression. For example, if a gene is heavily methylated, it may be turned off, preventing its transcription into RNA.\n",
+      "\n",
+      "2. **Histone Modification**: Histones are proteins around which DNA is wrapped. Modifications such as acetylation, methylation, and phosphorylation can change the accessibility of the DNA for transcription. Acetylation generally leads to a more relaxed chromatin structure and increases gene expression, while methylation can either activate or repress gene expression depending on the context.\n",
+      "\n",
+      "3. **Non-coding RNA**: Small non-coding RNAs can regulate gene expression by interacting with mRNA to prevent its translation or enhance degradation.\n",
+      "\n",
+      "### Influence Across Generations\n",
+      "\n",
+      "Epigenetic modifications can be stable and heritable, meaning they can be passed from one generation to the next without changes to the DNA sequence itself. For example:\n",
+      "\n",
+      "- **Environmental Influences**: Factors such as diet, stress, and toxins can induce epigenetic changes which might be inherited. For instance, certain stressors experienced by parents can lead to modifications that affect how offspring respond to similar stressors.\n",
+      "\n",
+      "- **Transgenerational Epigenetic Inheritance**: Research suggests that some epigenetic changes can be transmitted through germ cells (sperm and eggs), meaning that traits acquired in response to environmental pressures can affect not only the individual but also subsequent generations.\n",
+      "\n",
+      "### Implications for Evolution\n",
+      "\n",
+      "1. **Rapid Adaptation**: Epigenetic changes can provide a rapid means of adapting to environmental changes, as they can occur without the lengthy process of genetic mutation. This allows populations to adapt in real-time to shifting environmental parameters.\n",
+      "\n",
+      "2. **Phenotypic Variation**: Epigenetic mechanisms contribute to phenotypic diversity within a population, which is crucial for natural selection. If certain traits become beneficial due to environmental changes, individuals expressing these traits may have higher reproductive success.\n",
+      "\n",
+      "3. **Ecosystem Dynamics**: As epigenetic traits can influence population dynamics and interactions within ecosystems, they can affect broader ecological and evolutionary processes.\n",
+      "\n",
+      "4. **Potential for Speciation**: Epigenetic changes can sometimes lead to reproductive isolation if they affect mating behaviors or other compatibility factors, potentially leading to the emergence of new species.\n",
+      "\n",
+      "### Conclusion\n",
+      "\n",
+      "Overall, epigenetic modifications represent a complex layer that adds to our understanding of genetics and evolution. They demonstrate that evolution is not solely dictated by DNA sequence variations, but also by how genes are expressed and regulated. This insight reshapes our understanding of heritability, adaptation, and the dynamics of evolutionary processes.\n",
+      "\n",
+      "TERMINATE\n",
+      "---\n",
+      "\n",
+      "Example 2:\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO:root:Generating initial response for input: Discuss the challenges of grounding ethical theories in moral realism, especially in light of the is-ought problem introduced by Hume.\n",
+      "INFO:root:Generating reflection on the initial response\n",
+      "INFO:root:Initial response and reflection generated successfully\n",
+      "INFO:__main__:Initial response generated successfully\n",
+      "INFO:__main__:Completed iteration 1\n",
+      "INFO:__main__:Completed iteration 2\n",
+      "INFO:__main__:Completed iteration 3\n",
+      "INFO:__main__:Completed iteration 4\n",
+      "INFO:__main__:Completed iteration 5\n",
+      "INFO:__main__:Completed iteration 6\n",
+      "INFO:__main__:Completed iteration 7\n",
+      "INFO:__main__:Completed iteration 8\n",
+      "INFO:__main__:Completed iteration 9\n",
+      "INFO:__main__:Completed iteration 10\n",
+      "INFO:__main__:LATS search completed successfully\n",
+      "INFO:__main__:LATS algorithm completed. Result: Grounding ethical theories in moral realism presents several challenges, particularly when consideri...\n",
+      "INFO:__main__:Processing question: How does the Riemann Hypothesis relate to the distribution of prime numbers, and why is it significant in number theory?\n",
+      "INFO:root:Generating initial response for input: How does the Riemann Hypothesis relate to the distribution of prime numbers, and why is it significant in number theory?\n",
+      "INFO:root:Generating reflection on the initial response\n",
+      "INFO:root:Initial response and reflection generated successfully\n",
+      "INFO:__main__:Initial response generated successfully\n",
+      "INFO:__main__:Search ended after 1 iterations\n",
+      "INFO:__main__:LATS search completed successfully\n",
+      "INFO:__main__:LATS algorithm completed. Result: The Riemann Hypothesis is one of the most important and famous unsolved problems in mathematics, par...\n",
+      "INFO:__main__:Processing question: Describe the challenges and theoretical underpinnings of unifying general relativity with quantum mechanics, particularly focusing on string theory and loop quantum gravity.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Question: Discuss the challenges of grounding ethical theories in moral realism, especially in light of the is-ought problem introduced by Hume.\n",
+      "Answer: Grounding ethical theories in moral realism presents several challenges, particularly when considering the is-ought problem introduced by philosopher David Hume. Here’s a discussion of the key challenges:\n",
+      "\n",
+      "### 1. **The Is-Ought Problem**\n",
+      "Hume famously argued that one cannot derive prescriptive statements (what ought to be) directly from descriptive statements (what is). This poses a significant challenge for moral realism, which posits that there are objective moral truths or facts. If moral realists claim that moral statements can be objectively true in the same way that descriptive statements can, they need to address how these moral facts can be derived from non-moral facts without violating Hume’s separation of is and ought.\n",
+      "\n",
+      "### 2. **The Nature of Moral Facts**\n",
+      "Another challenge is defining what is meant by \"moral facts.\" Moral realists must explain the nature of these facts. Are they objective, mind-independent entities? If so, this raises questions about their existence and accessibility. Critics argue that the existence of such facts is difficult to substantiate and that moral discourse often relies on subjective or culturally influenced perspectives.\n",
+      "\n",
+      "### 3. **Moral Disagreement**\n",
+      "Moral realism must confront the issue of widespread moral disagreement. If there are objective moral truths, why do reasonable people often disagree vehemently on moral issues? This challenge leads to the question of whether moral disagreements indicate that moral realism is flawed or incomplete. \n",
+      "\n",
+      "### 4. **Moral Motivation**\n",
+      "There is also a challenge regarding moral motivation. If moral facts exist independently, how do they motivate individuals to act? Hume argued that reason alone cannot motivate action; rather, it is the passions that drive behavior. This raises questions for moral realism: if moral truths exist, how do they translate into motivation for individuals who may not recognize or accept these truths?\n",
+      "\n",
+      "### 5. **Epistemological concerns**\n",
+      "Lastly, moral realists face significant epistemological challenges. How do we come to know these moral facts? Critics often point to the difficulty of attaining certainty about moral claims compared to empirical claims about the world. This issue leads to skepticism about the possibility of moral knowledge, further complicating the grounding of ethical theories in moral realism.\n",
+      "\n",
+      "### Conclusion\n",
+      "In summary, the effort to ground ethical theories in moral realism is fraught with challenges. The is-ought problem presents a fundamental barrier to deriving moral principles from empirical observations. Furthermore, issues of the nature and existence of moral facts, the prevalence of moral disagreement, the mechanisms of moral motivation, and epistemological concerns all create a complex landscape for moral realists to navigate. Addressing these challenges requires robust philosophical arguments and possible reexamination of either the nature of ethics or the framework of moral realism itself.\n",
+      "\n",
+      "TERMINATE\n",
+      "---\n",
+      "\n",
+      "Example 3:\n",
+      "Question: How does the Riemann Hypothesis relate to the distribution of prime numbers, and why is it significant in number theory?\n",
+      "Answer: The Riemann Hypothesis is one of the most important and famous unsolved problems in mathematics, particularly in number theory. To understand its significance and relationship to the distribution of prime numbers, let's break it down:\n",
+      "\n",
+      "1. **Prime Numbers and Their Distribution**: Prime numbers are the building blocks of the integers, defined as numbers greater than 1 that have no positive divisors other than 1 and themselves. The distribution of prime numbers is somewhat irregular, and mathematicians have been studying the patterns in which primes appear.\n",
+      "\n",
+      "2. **The Riemann Zeta Function**: The connection between prime numbers and the Riemann Hypothesis comes through the Riemann zeta function, defined as:\n",
+      "   \\[\n",
+      "   \\zeta(s) = \\sum_{n=1}^{\\infty} \\frac{1}{n^s} \\quad \\text{for } \\text{Re}(s) > 1.\n",
+      "   \\]\n",
+      "   This function can be analytically continued to other values of \\( s \\) (except for \\( s = 1 \\)), where it becomes crucial in studying the distribution of primes.\n",
+      "\n",
+      "3. **Non-Trivial Zeros of the Zeta Function**: The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function, typically denoted as \\( \\rho \\), have their real part equal to \\( \\frac{1}{2} \\). That is, they lie on the so-called \"critical line\" in the complex plane, \\( \\text{Re}(s) = \\frac{1}{2} \\).\n",
+      "\n",
+      "4. **Implications for Prime Distribution**: The distribution of prime numbers is closely related to the behavior of the zeta function. Specifically, if the Riemann Hypothesis is true, it would lead to very precise estimates on the distribution of primes, particularly through results like the Prime Number Theorem, which originally gives an asymptotic form for the number of primes less than a certain number \\( x \\).\n",
+      "\n",
+      "5. **Significance in Number Theory**: The Riemann Hypothesis has significant implications not only for number theory but also for fields like cryptography, numerical analysis, and mathematical physics. Proving or disproving it would affect many established results in these areas. It is considered foundational because it relates number theory to complex analysis in profound ways.\n",
+      "\n",
+      "In conclusion, the Riemann Hypothesis is significant because of its deep connections to the distribution of prime numbers, the Riemann zeta function, and the fundamental structure of number theory. Its resolution could enhance our understanding of primes and likelihoods, impacting various scientific and mathematical domains.\n",
+      "\n",
+      "TERMINATE\n",
+      "---\n",
+      "\n",
+      "Example 4:\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO:root:Generating initial response for input: Describe the challenges and theoretical underpinnings of unifying general relativity with quantum mechanics, particularly focusing on string theory and loop quantum gravity.\n",
+      "INFO:root:Generating reflection on the initial response\n",
+      "INFO:root:Initial response and reflection generated successfully\n",
+      "INFO:__main__:Initial response generated successfully\n",
+      "INFO:__main__:Completed iteration 1\n",
+      "INFO:__main__:Completed iteration 2\n",
+      "INFO:__main__:Completed iteration 3\n",
+      "INFO:__main__:Completed iteration 4\n",
+      "INFO:__main__:Completed iteration 5\n",
+      "INFO:__main__:Completed iteration 6\n",
+      "INFO:__main__:Completed iteration 7\n",
+      "WARNING:root:No reflections found in the response. Using default values.\n",
+      "INFO:__main__:Completed iteration 8\n",
+      "INFO:__main__:Completed iteration 9\n",
+      "INFO:__main__:Completed iteration 10\n",
+      "INFO:__main__:LATS search completed successfully\n",
+      "INFO:__main__:LATS algorithm completed. Result: Unifying general relativity (GR) and quantum mechanics (QM) has been one of the most significant cha...\n",
+      "INFO:__main__:All examples processed.\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Question: Describe the challenges and theoretical underpinnings of unifying general relativity with quantum mechanics, particularly focusing on string theory and loop quantum gravity.\n",
+      "Answer: Unifying general relativity (GR) and quantum mechanics (QM) has been one of the most significant challenges in modern theoretical physics. Both frameworks are incredibly successful in their respective domains, but they fundamentally differ in their principles and predictions. Below are the challenges and theoretical underpinnings, with a particular focus on string theory and loop quantum gravity.\n",
+      "\n",
+      "### Challenges in Unification\n",
+      "\n",
+      "1. **Different Mathematical Frameworks**:\n",
+      "   - General Relativity is a classical theory that describes gravity as a curvature of spacetime, represented by a smooth manifold. It relies on differential geometry.\n",
+      "   - Quantum Mechanics, on the other hand, uses a probabilistic framework and is based on the principles of quantum states and operators in a Hilbert space.\n",
+      "\n",
+      "2. **Non-Renormalizability of Gravity**:\n",
+      "   - Attempts to quantize GR using methods analogous to those in particle physics lead to non-renormalizable theories, meaning that the infinite quantities cannot be systematically resolved.\n",
+      "\n",
+      "3. **Nature of Singularities**:\n",
+      "   - GR predicts singularities (like those at the center of black holes) where the laws of physics as we know them break down. A unified theory must address what happens at these singularities.\n",
+      "\n",
+      "4. **Concept of Time**:\n",
+      "   - In GR, time is treated as a dimension of spacetime, while in QM, time is an external parameter. This leads to complications in formulating a theory that encompasses both views.\n",
+      "\n",
+      "5. **Emergence of Spacetime**:\n",
+      "   - Some approaches suggest that spacetime itself may emerge from more fundamental quantum processes, complicating the integration of gravitational effects with quantum mechanics.\n",
+      "\n",
+      "### Theoretical Underpinnings\n",
+      "\n",
+      "#### String Theory\n",
+      "- **Basic Concept**: String theory posits that the fundamental constituents of the universe are one-dimensional strings rather than point particles. The vibrational modes of these strings correspond to different particles.\n",
+      "- **Unification of Forces**: String theory aims to unify all fundamental forces (including gravity) in a single framework. It often requires additional spatial dimensions (10 or 11 total) beyond the familiar four dimensions of spacetime.\n",
+      "- **Type I, Type IIA, Type IIB, Heterotic**: Different string theories exist, and they can be connected through dualities, suggesting that they are various limits of a more fundamental theory known as \"M-theory.\"\n",
+      "- **Quantum Gravity**: In string theory, gravitational interactions emerge naturally due to the properties of strings, offering a potential pathway to a consistent theory of quantum gravity.\n",
+      "\n",
+      "#### Loop Quantum Gravity\n",
+      "- **Basic Concept**: Loop quantum gravity (LQG) is a non-perturbative and background-independent approach to quantizing gravity. It suggests that spacetime has a discrete structure at the smallest scales, with the geometry being quantized.\n",
+      "- **Spin Networks and Spin Foams**: LQG uses entities known as spin networks to represent quantum states of geometry. These are complemented by spin foams, which serve as a way to visualize the evolution of these states over time.\n",
+      "- **No Extra Dimensions**: Unlike string theory, LQG does not require additional dimensions; it builds directly on the structures of GR and quantum principles, making it appealing for those desiring a more geometric perspective.\n",
+      "- **Black Hole Entropy**: LQG has provided insights into black hole entropy, suggesting that black hole areas are quantized, consistent with certain thermodynamic properties.\n",
+      "\n",
+      "### Summary\n",
+      "While string theory aims to unify all forces in a mathematically rigorous framework with additional dimensions, loop quantum gravity focuses on quantizing spacetime itself without invoking extra dimensions. Both approaches face significant challenges, including the need for experimental evidence, the conceptual implications regarding time and singularities, and the mathematical compatibility with established theories. Despite these challenges, they represent the forefront of efforts to reconcile the discrepancies between general relativity and quantum mechanics.\n",
+      "\n",
+      "TERMINATE\n",
+      "---\n"
+     ]
+    }
+   ],
+   "source": [
+    "for i, question in enumerate(questions, 1):\n",
+    "    print(f\"\\nExample {i}:\")\n",
+    "    run_lats_example(question)\n",
+    "\n",
+    "logger.info(\"All examples processed.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "af7254a5",
+   "metadata": {},
+   "source": [
+    "## Conclusion\n",
+    "\n",
+    "Congrats on implementing LATS! This is a technique that can be reasonably fast and effective at solving complex agent tasks. A few notes that you probably observed above:\n",
+    "\n",
+    "1. While LATS is effective, the tree rollout process can require additional inference compute time. If you plan to integrate this into a production application, consider streaming intermediate steps to allow users to see the thought process and access intermediate results. Alternatively, you could use it to generate fine-tuning data to enhance single-shot accuracy and avoid lengthy rollouts. The cost of using LATS has significantly decreased since its initial proposal and is expected to continue decreasing.\n",
+    "\n",
+    "2. The effectiveness of the candidate selection process depends on the quality of the rewards generated. In this example, we exclusively use self-reflection as feedback, but if you have access to external feedback sources (such as code test execution), those should be incorporated as suggested above."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "be01ff1e",
+   "metadata": {},
+   "source": [
+    "# \n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "venv",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From 2111230548854e4e952cadcd93be07e49d3e3c6a Mon Sep 17 00:00:00 2001
From: Andy Zhou <andyzhou@4bd094a2-01.cloud.together.ai>
Date: Mon, 19 Aug 2024 19:22:47 -0700
Subject: [PATCH 2/2] removed outputs

---
 notebook/lats_search.ipynb | 310 ++++---------------------------------
 1 file changed, 27 insertions(+), 283 deletions(-)

diff --git a/notebook/lats_search.ipynb b/notebook/lats_search.ipynb
index a0eb89ac9f1..01b4449890e 100644
--- a/notebook/lats_search.ipynb
+++ b/notebook/lats_search.ipynb
@@ -21,21 +21,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "id": "da705b29",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/andyzhou/venv/lib/python3.10/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
-      "  from .autonotebook import tqdm as notebook_tqdm\n",
-      "2024-08-16 18:36:36,107\tINFO util.py:154 -- Missing packages: ['ipywidgets']. Run `pip install -U ipywidgets`, then restart the notebook server for rich notebook output.\n",
-      "2024-08-16 18:36:36,376\tINFO util.py:154 -- Missing packages: ['ipywidgets']. Run `pip install -U ipywidgets`, then restart the notebook server for rich notebook output.\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import json\n",
     "import logging\n",
@@ -56,7 +45,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "id": "a02f8a2c",
    "metadata": {},
    "outputs": [],
@@ -107,7 +96,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "9eaf711f",
    "metadata": {},
    "outputs": [],
@@ -117,7 +106,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "79701018",
    "metadata": {},
    "outputs": [],
@@ -138,7 +127,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "id": "ce0288e9",
    "metadata": {},
    "outputs": [],
@@ -179,7 +168,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "id": "b6d0d7a6",
    "metadata": {},
    "outputs": [],
@@ -192,7 +181,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "id": "305a29d6",
    "metadata": {},
    "outputs": [],
@@ -325,7 +314,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "id": "586d953a",
    "metadata": {},
    "outputs": [],
@@ -375,7 +364,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": null,
    "id": "e467f73e",
    "metadata": {},
    "outputs": [],
@@ -401,7 +390,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "id": "212daaef",
    "metadata": {},
    "outputs": [],
@@ -426,7 +415,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "id": "3bdd8a23",
    "metadata": {},
    "outputs": [],
@@ -445,7 +434,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "id": "7750d32f",
    "metadata": {},
    "outputs": [],
@@ -462,7 +451,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "id": "23f26bf0",
    "metadata": {},
    "outputs": [],
@@ -543,7 +532,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "id": "fd743ab5",
    "metadata": {},
    "outputs": [],
@@ -567,7 +556,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "id": "b7e00575",
    "metadata": {},
    "outputs": [],
@@ -589,7 +578,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": null,
    "id": "b7afcd1b",
    "metadata": {},
    "outputs": [],
@@ -651,39 +640,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": null,
    "id": "7ab75669",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "INFO:root:Generating initial response for input: Why is the sky blue?\n",
-      "INFO:root:Generating reflection on the initial response\n",
-      "INFO:root:Initial response and reflection generated successfully\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The sky appears blue due to a phenomenon called Rayleigh scattering. Here's a simplified explanation:\n",
-      "\n",
-      "1. **Sunlight Composition**: Sunlight, or white light, is made up of multiple colors (red, orange, yellow, green, blue, indigo, violet), which can be seen when light is passed through a prism.\n",
-      "\n",
-      "2. **Atmospheric Interaction**: As sunlight passes through the Earth's atmosphere, it interacts with air molecules and small particles. Blue light waves are shorter and scatter more than other colors when they hit these particles.\n",
-      "\n",
-      "3. **Direction of Sunlight**: During the day, when the sun is higher in the sky, the blue light is scattered in all directions. As a result, regardless of where you look in the sky, you see more of the scattered blue light than any other color.\n",
-      "\n",
-      "4. **Effects of Angle**: During sunrise and sunset, the sun's light has to pass through more atmosphere, scattering short wavelengths (like blue) out even more and allowing longer wavelengths (like red and orange) to dominate, which is why you see those colors during those times.\n",
-      "\n",
-      "In summary, the blue appearance of the sky is due to the scattering of blue light by the gases and particles in the atmosphere, which makes it the most visible color to human eyes from all angles. \n",
-      "\n",
-      "TERMINATE\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "initial_prompt = \"Why is the sky blue?\"\n",
     "initial_state = TreeState(input=initial_prompt, root=None)\n",
@@ -715,7 +675,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": null,
    "id": "94c92498",
    "metadata": {},
    "outputs": [],
@@ -793,7 +753,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": null,
    "id": "27a3a1db",
    "metadata": {},
    "outputs": [],
@@ -844,7 +804,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": null,
    "id": "175afca7",
    "metadata": {},
    "outputs": [],
@@ -886,7 +846,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": null,
    "id": "e309ea9f",
    "metadata": {},
    "outputs": [],
@@ -982,7 +942,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": null,
    "id": "683c0f2c",
    "metadata": {},
    "outputs": [],
@@ -1017,7 +977,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": null,
    "id": "60fa1f07",
    "metadata": {},
    "outputs": [],
@@ -1040,226 +1000,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": null,
    "id": "5d1e5754",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "INFO:__main__:Processing question: Explain how epigenetic modifications can influence gene expression across generations and the implications for evolution.\n",
-      "INFO:root:Generating initial response for input: Explain how epigenetic modifications can influence gene expression across generations and the implications for evolution.\n",
-      "INFO:root:Generating reflection on the initial response\n",
-      "INFO:root:Initial response and reflection generated successfully\n",
-      "INFO:__main__:Initial response generated successfully\n",
-      "INFO:__main__:Search ended after 1 iterations\n",
-      "INFO:__main__:LATS search completed successfully\n",
-      "INFO:__main__:LATS algorithm completed. Result: Epigenetic modifications refer to changes in gene expression that do not involve alterations to the ...\n",
-      "INFO:__main__:Processing question: Discuss the challenges of grounding ethical theories in moral realism, especially in light of the is-ought problem introduced by Hume.\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Example 1:\n",
-      "Question: Explain how epigenetic modifications can influence gene expression across generations and the implications for evolution.\n",
-      "Answer: Epigenetic modifications refer to changes in gene expression that do not involve alterations to the underlying DNA sequence. These modifications can influence how genes are expressed, leading to varied phenotypic outcomes. Here’s an explanation of how these modifications can influence gene expression across generations and their implications for evolution:\n",
-      "\n",
-      "### Mechanisms of Epigenetic Modifications\n",
-      "\n",
-      "1. **DNA Methylation**: The addition of a methyl group to DNA, usually at cytosine bases, can silence gene expression. For example, if a gene is heavily methylated, it may be turned off, preventing its transcription into RNA.\n",
-      "\n",
-      "2. **Histone Modification**: Histones are proteins around which DNA is wrapped. Modifications such as acetylation, methylation, and phosphorylation can change the accessibility of the DNA for transcription. Acetylation generally leads to a more relaxed chromatin structure and increases gene expression, while methylation can either activate or repress gene expression depending on the context.\n",
-      "\n",
-      "3. **Non-coding RNA**: Small non-coding RNAs can regulate gene expression by interacting with mRNA to prevent its translation or enhance degradation.\n",
-      "\n",
-      "### Influence Across Generations\n",
-      "\n",
-      "Epigenetic modifications can be stable and heritable, meaning they can be passed from one generation to the next without changes to the DNA sequence itself. For example:\n",
-      "\n",
-      "- **Environmental Influences**: Factors such as diet, stress, and toxins can induce epigenetic changes which might be inherited. For instance, certain stressors experienced by parents can lead to modifications that affect how offspring respond to similar stressors.\n",
-      "\n",
-      "- **Transgenerational Epigenetic Inheritance**: Research suggests that some epigenetic changes can be transmitted through germ cells (sperm and eggs), meaning that traits acquired in response to environmental pressures can affect not only the individual but also subsequent generations.\n",
-      "\n",
-      "### Implications for Evolution\n",
-      "\n",
-      "1. **Rapid Adaptation**: Epigenetic changes can provide a rapid means of adapting to environmental changes, as they can occur without the lengthy process of genetic mutation. This allows populations to adapt in real-time to shifting environmental parameters.\n",
-      "\n",
-      "2. **Phenotypic Variation**: Epigenetic mechanisms contribute to phenotypic diversity within a population, which is crucial for natural selection. If certain traits become beneficial due to environmental changes, individuals expressing these traits may have higher reproductive success.\n",
-      "\n",
-      "3. **Ecosystem Dynamics**: As epigenetic traits can influence population dynamics and interactions within ecosystems, they can affect broader ecological and evolutionary processes.\n",
-      "\n",
-      "4. **Potential for Speciation**: Epigenetic changes can sometimes lead to reproductive isolation if they affect mating behaviors or other compatibility factors, potentially leading to the emergence of new species.\n",
-      "\n",
-      "### Conclusion\n",
-      "\n",
-      "Overall, epigenetic modifications represent a complex layer that adds to our understanding of genetics and evolution. They demonstrate that evolution is not solely dictated by DNA sequence variations, but also by how genes are expressed and regulated. This insight reshapes our understanding of heritability, adaptation, and the dynamics of evolutionary processes.\n",
-      "\n",
-      "TERMINATE\n",
-      "---\n",
-      "\n",
-      "Example 2:\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "INFO:root:Generating initial response for input: Discuss the challenges of grounding ethical theories in moral realism, especially in light of the is-ought problem introduced by Hume.\n",
-      "INFO:root:Generating reflection on the initial response\n",
-      "INFO:root:Initial response and reflection generated successfully\n",
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-      "INFO:__main__:LATS algorithm completed. Result: Grounding ethical theories in moral realism presents several challenges, particularly when consideri...\n",
-      "INFO:__main__:Processing question: How does the Riemann Hypothesis relate to the distribution of prime numbers, and why is it significant in number theory?\n",
-      "INFO:root:Generating initial response for input: How does the Riemann Hypothesis relate to the distribution of prime numbers, and why is it significant in number theory?\n",
-      "INFO:root:Generating reflection on the initial response\n",
-      "INFO:root:Initial response and reflection generated successfully\n",
-      "INFO:__main__:Initial response generated successfully\n",
-      "INFO:__main__:Search ended after 1 iterations\n",
-      "INFO:__main__:LATS search completed successfully\n",
-      "INFO:__main__:LATS algorithm completed. Result: The Riemann Hypothesis is one of the most important and famous unsolved problems in mathematics, par...\n",
-      "INFO:__main__:Processing question: Describe the challenges and theoretical underpinnings of unifying general relativity with quantum mechanics, particularly focusing on string theory and loop quantum gravity.\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Question: Discuss the challenges of grounding ethical theories in moral realism, especially in light of the is-ought problem introduced by Hume.\n",
-      "Answer: Grounding ethical theories in moral realism presents several challenges, particularly when considering the is-ought problem introduced by philosopher David Hume. Here’s a discussion of the key challenges:\n",
-      "\n",
-      "### 1. **The Is-Ought Problem**\n",
-      "Hume famously argued that one cannot derive prescriptive statements (what ought to be) directly from descriptive statements (what is). This poses a significant challenge for moral realism, which posits that there are objective moral truths or facts. If moral realists claim that moral statements can be objectively true in the same way that descriptive statements can, they need to address how these moral facts can be derived from non-moral facts without violating Hume’s separation of is and ought.\n",
-      "\n",
-      "### 2. **The Nature of Moral Facts**\n",
-      "Another challenge is defining what is meant by \"moral facts.\" Moral realists must explain the nature of these facts. Are they objective, mind-independent entities? If so, this raises questions about their existence and accessibility. Critics argue that the existence of such facts is difficult to substantiate and that moral discourse often relies on subjective or culturally influenced perspectives.\n",
-      "\n",
-      "### 3. **Moral Disagreement**\n",
-      "Moral realism must confront the issue of widespread moral disagreement. If there are objective moral truths, why do reasonable people often disagree vehemently on moral issues? This challenge leads to the question of whether moral disagreements indicate that moral realism is flawed or incomplete. \n",
-      "\n",
-      "### 4. **Moral Motivation**\n",
-      "There is also a challenge regarding moral motivation. If moral facts exist independently, how do they motivate individuals to act? Hume argued that reason alone cannot motivate action; rather, it is the passions that drive behavior. This raises questions for moral realism: if moral truths exist, how do they translate into motivation for individuals who may not recognize or accept these truths?\n",
-      "\n",
-      "### 5. **Epistemological concerns**\n",
-      "Lastly, moral realists face significant epistemological challenges. How do we come to know these moral facts? Critics often point to the difficulty of attaining certainty about moral claims compared to empirical claims about the world. This issue leads to skepticism about the possibility of moral knowledge, further complicating the grounding of ethical theories in moral realism.\n",
-      "\n",
-      "### Conclusion\n",
-      "In summary, the effort to ground ethical theories in moral realism is fraught with challenges. The is-ought problem presents a fundamental barrier to deriving moral principles from empirical observations. Furthermore, issues of the nature and existence of moral facts, the prevalence of moral disagreement, the mechanisms of moral motivation, and epistemological concerns all create a complex landscape for moral realists to navigate. Addressing these challenges requires robust philosophical arguments and possible reexamination of either the nature of ethics or the framework of moral realism itself.\n",
-      "\n",
-      "TERMINATE\n",
-      "---\n",
-      "\n",
-      "Example 3:\n",
-      "Question: How does the Riemann Hypothesis relate to the distribution of prime numbers, and why is it significant in number theory?\n",
-      "Answer: The Riemann Hypothesis is one of the most important and famous unsolved problems in mathematics, particularly in number theory. To understand its significance and relationship to the distribution of prime numbers, let's break it down:\n",
-      "\n",
-      "1. **Prime Numbers and Their Distribution**: Prime numbers are the building blocks of the integers, defined as numbers greater than 1 that have no positive divisors other than 1 and themselves. The distribution of prime numbers is somewhat irregular, and mathematicians have been studying the patterns in which primes appear.\n",
-      "\n",
-      "2. **The Riemann Zeta Function**: The connection between prime numbers and the Riemann Hypothesis comes through the Riemann zeta function, defined as:\n",
-      "   \\[\n",
-      "   \\zeta(s) = \\sum_{n=1}^{\\infty} \\frac{1}{n^s} \\quad \\text{for } \\text{Re}(s) > 1.\n",
-      "   \\]\n",
-      "   This function can be analytically continued to other values of \\( s \\) (except for \\( s = 1 \\)), where it becomes crucial in studying the distribution of primes.\n",
-      "\n",
-      "3. **Non-Trivial Zeros of the Zeta Function**: The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function, typically denoted as \\( \\rho \\), have their real part equal to \\( \\frac{1}{2} \\). That is, they lie on the so-called \"critical line\" in the complex plane, \\( \\text{Re}(s) = \\frac{1}{2} \\).\n",
-      "\n",
-      "4. **Implications for Prime Distribution**: The distribution of prime numbers is closely related to the behavior of the zeta function. Specifically, if the Riemann Hypothesis is true, it would lead to very precise estimates on the distribution of primes, particularly through results like the Prime Number Theorem, which originally gives an asymptotic form for the number of primes less than a certain number \\( x \\).\n",
-      "\n",
-      "5. **Significance in Number Theory**: The Riemann Hypothesis has significant implications not only for number theory but also for fields like cryptography, numerical analysis, and mathematical physics. Proving or disproving it would affect many established results in these areas. It is considered foundational because it relates number theory to complex analysis in profound ways.\n",
-      "\n",
-      "In conclusion, the Riemann Hypothesis is significant because of its deep connections to the distribution of prime numbers, the Riemann zeta function, and the fundamental structure of number theory. Its resolution could enhance our understanding of primes and likelihoods, impacting various scientific and mathematical domains.\n",
-      "\n",
-      "TERMINATE\n",
-      "---\n",
-      "\n",
-      "Example 4:\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
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-      "INFO:root:Generating initial response for input: Describe the challenges and theoretical underpinnings of unifying general relativity with quantum mechanics, particularly focusing on string theory and loop quantum gravity.\n",
-      "INFO:root:Generating reflection on the initial response\n",
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-      "INFO:__main__:LATS search completed successfully\n",
-      "INFO:__main__:LATS algorithm completed. Result: Unifying general relativity (GR) and quantum mechanics (QM) has been one of the most significant cha...\n",
-      "INFO:__main__:All examples processed.\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Question: Describe the challenges and theoretical underpinnings of unifying general relativity with quantum mechanics, particularly focusing on string theory and loop quantum gravity.\n",
-      "Answer: Unifying general relativity (GR) and quantum mechanics (QM) has been one of the most significant challenges in modern theoretical physics. Both frameworks are incredibly successful in their respective domains, but they fundamentally differ in their principles and predictions. Below are the challenges and theoretical underpinnings, with a particular focus on string theory and loop quantum gravity.\n",
-      "\n",
-      "### Challenges in Unification\n",
-      "\n",
-      "1. **Different Mathematical Frameworks**:\n",
-      "   - General Relativity is a classical theory that describes gravity as a curvature of spacetime, represented by a smooth manifold. It relies on differential geometry.\n",
-      "   - Quantum Mechanics, on the other hand, uses a probabilistic framework and is based on the principles of quantum states and operators in a Hilbert space.\n",
-      "\n",
-      "2. **Non-Renormalizability of Gravity**:\n",
-      "   - Attempts to quantize GR using methods analogous to those in particle physics lead to non-renormalizable theories, meaning that the infinite quantities cannot be systematically resolved.\n",
-      "\n",
-      "3. **Nature of Singularities**:\n",
-      "   - GR predicts singularities (like those at the center of black holes) where the laws of physics as we know them break down. A unified theory must address what happens at these singularities.\n",
-      "\n",
-      "4. **Concept of Time**:\n",
-      "   - In GR, time is treated as a dimension of spacetime, while in QM, time is an external parameter. This leads to complications in formulating a theory that encompasses both views.\n",
-      "\n",
-      "5. **Emergence of Spacetime**:\n",
-      "   - Some approaches suggest that spacetime itself may emerge from more fundamental quantum processes, complicating the integration of gravitational effects with quantum mechanics.\n",
-      "\n",
-      "### Theoretical Underpinnings\n",
-      "\n",
-      "#### String Theory\n",
-      "- **Basic Concept**: String theory posits that the fundamental constituents of the universe are one-dimensional strings rather than point particles. The vibrational modes of these strings correspond to different particles.\n",
-      "- **Unification of Forces**: String theory aims to unify all fundamental forces (including gravity) in a single framework. It often requires additional spatial dimensions (10 or 11 total) beyond the familiar four dimensions of spacetime.\n",
-      "- **Type I, Type IIA, Type IIB, Heterotic**: Different string theories exist, and they can be connected through dualities, suggesting that they are various limits of a more fundamental theory known as \"M-theory.\"\n",
-      "- **Quantum Gravity**: In string theory, gravitational interactions emerge naturally due to the properties of strings, offering a potential pathway to a consistent theory of quantum gravity.\n",
-      "\n",
-      "#### Loop Quantum Gravity\n",
-      "- **Basic Concept**: Loop quantum gravity (LQG) is a non-perturbative and background-independent approach to quantizing gravity. It suggests that spacetime has a discrete structure at the smallest scales, with the geometry being quantized.\n",
-      "- **Spin Networks and Spin Foams**: LQG uses entities known as spin networks to represent quantum states of geometry. These are complemented by spin foams, which serve as a way to visualize the evolution of these states over time.\n",
-      "- **No Extra Dimensions**: Unlike string theory, LQG does not require additional dimensions; it builds directly on the structures of GR and quantum principles, making it appealing for those desiring a more geometric perspective.\n",
-      "- **Black Hole Entropy**: LQG has provided insights into black hole entropy, suggesting that black hole areas are quantized, consistent with certain thermodynamic properties.\n",
-      "\n",
-      "### Summary\n",
-      "While string theory aims to unify all forces in a mathematically rigorous framework with additional dimensions, loop quantum gravity focuses on quantizing spacetime itself without invoking extra dimensions. Both approaches face significant challenges, including the need for experimental evidence, the conceptual implications regarding time and singularities, and the mathematical compatibility with established theories. Despite these challenges, they represent the forefront of efforts to reconcile the discrepancies between general relativity and quantum mechanics.\n",
-      "\n",
-      "TERMINATE\n",
-      "---\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "for i, question in enumerate(questions, 1):\n",
     "    print(f\"\\nExample {i}:\")\n",