{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 🎯 White-Box Uncertainty Quantification\n", "\n", "
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\n", " White-box Uncertainty Quantification (UQ) methods leverage token probabilities to estimate uncertainty. They are significantly faster and cheaper than black-box methods, but require access to the LLM's internal probabilities, meaning they are not necessarily compatible with all LLMs/APIs. This demo provides an illustration of how to use state-of-the-art white-box UQ methods with uqlm. The following scorers are available:\n", "

\n", " \n", "* Minimum token probability ([Manakul et al., 2023](https://arxiv.org/abs/2303.08896))\n", "* Length-Normalized Joint Token Probability ([Malinin & Gales, 2021](https://arxiv.org/pdf/2002.07650))\n", "
\n", "\n", "## 📊 What You'll Do in This Demo\n", "\n", "
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1
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Set up LLM and prompts.

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Set up LLM instance and load example data prompts.

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2
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Generate LLM Responses and Confidence Scores

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Generate and score LLM responses to the example questions using the WhiteBoxUQ() class.

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3
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Evaluate Hallucination Detection Performance

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Visualize model accuracy at different thresholds of the various white-box UQ confidence scores. Compute precision, recall, and F1-score of hallucination detection.

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\n", "\n", "## ⚖️ Advantages & Limitations\n", "\n", "
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Pros

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Cons

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" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [] }, "outputs": [], "source": [ "import os\n", "\n", "import numpy as np\n", "from sklearn.metrics import precision_score, recall_score, f1_score\n", "\n", "from uqlm import WhiteBoxUQ\n", "from uqlm.utils import load_example_dataset, math_postprocessor, plot_model_accuracies, Tuner" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 1. Set up LLM and Prompts" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this demo, we will illustrate this approach using a set of math questions from the [GSM8K benchmark](https://github.com/openai/grade-school-math). To implement with your use case, simply **replace the example prompts with your data**. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loading dataset - gsm8k...\n", "Processing dataset...\n", "Dataset ready!\n" ] }, { "data": { "text/html": [ "
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questionanswer
0Natalia sold clips to 48 of her friends in Apr...72
1Weng earns $12 an hour for babysitting. Yester...10
2Betty is saving money for a new wallet which c...5
3Julie is reading a 120-page book. Yesterday, s...42
4James writes a 3-page letter to 2 different fr...624
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" ], "text/plain": [ " question answer\n", "0 Natalia sold clips to 48 of her friends in Apr... 72\n", "1 Weng earns $12 an hour for babysitting. Yester... 10\n", "2 Betty is saving money for a new wallet which c... 5\n", "3 Julie is reading a 120-page book. Yesterday, s... 42\n", "4 James writes a 3-page letter to 2 different fr... 624" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Load example dataset (gsm8k)\n", "gsm8k = load_example_dataset(\"gsm8k\", n=100)\n", "gsm8k.head()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [] }, "outputs": [], "source": [ "# Define prompts\n", "MATH_INSTRUCTION = (\n", " \"When you solve this math problem only return the answer with no additional text.\\n\"\n", ")\n", "prompts = [MATH_INSTRUCTION + prompt for prompt in gsm8k.question]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we use `AzureChatOpenAI` to instantiate our LLM, but any [LangChain Chat Model](https://js.langchain.com/docs/integrations/chat/) may be used. Be sure to **replace with your LLM of choice.**" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [] }, "outputs": [], "source": [ "# import sys\n", "# !{sys.executable} -m pip install python-dotenv\n", "# !{sys.executable} -m pip install langchain-openai\n", "\n", "# # User to populate .env file with API credentials\n", "from dotenv import load_dotenv, find_dotenv\n", "from langchain_openai import AzureChatOpenAI\n", "\n", "load_dotenv(find_dotenv())\n", "llm = AzureChatOpenAI(\n", " deployment_name=os.getenv(\"DEPLOYMENT_NAME\"),\n", " openai_api_key=os.getenv(\"API_KEY\"),\n", " azure_endpoint=os.getenv(\"API_BASE\"),\n", " openai_api_type=os.getenv(\"API_TYPE\"),\n", " openai_api_version=os.getenv(\"API_VERSION\"),\n", " temperature=1, # User to set temperature\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 2. Generate responses and confidence scores" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `WhiteBoxUQ()` - Generate LLM responses and compute token-probability-based confidence scores for each response.\n", "\n", "![Sample Image](https://raw.githubusercontent.com/cvs-health/uqlm/develop/assets/images/white_box_graphic.png)\n", "\n", "#### 📋 Class Attributes\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ParameterType & DefaultDescription
llmBaseChatModel
default=None		A langchain llm `BaseChatModel`. User is responsible for specifying temperature and other relevant parameters to the constructor of their `llm` object.
scorersList[str]
default=None		Specifies which white-box (token-probability-based) scorers to include. Must be subset of {\"normalized_probability\", \"min_probability\"}. If None, defaults to all.
system_promptstr or None
default=\"You are a helpful assistant.\"		Optional argument for user to provide custom system prompt for the LLM.
max_calls_per_minint
default=None		Specifies how many API calls to make per minute to avoid rate limit errors. By default, no limit is specified.
\n", "\n", "#### 🔍 Parameter Groups\n", "\n", "
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🧠 Model-Specific

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📊 Confidence Scores

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⚡ Performance

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" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [] }, "outputs": [], "source": [ "wbuq = WhiteBoxUQ(llm=llm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 🔄 Class Methods\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MethodDescription & Parameters
WhiteBoxUQ.generate_and_score\n", "

Generate LLM responses and compute confidence scores for the provided prompts.

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Parameters:

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  • prompts - (list of str) A list of input prompts for the model.
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Returns: UQResult containing data (prompts, responses, log probabilities, and confidence scores) and metadata

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\n", " 💡 Best For: Complete end-to-end uncertainty quantification when starting with prompts.\n", "
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" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generating responses...\n" ] } ], "source": [ "results = await wbuq.generate_and_score(prompts=prompts)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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promptresponselogprobnormalized_probabilitymin_probability
0When you solve this math problem only return t...72[{'token': '72', 'bytes': [55, 50], 'logprob':...0.9999490.999949
1When you solve this math problem only return t...$10[{'token': '$', 'bytes': [36], 'logprob': -0.0...0.9993980.998797
2When you solve this math problem only return t...$20[{'token': '$', 'bytes': [36], 'logprob': -0.0...0.9453830.900076
3When you solve this math problem only return t...48[{'token': '48', 'bytes': [52, 56], 'logprob':...0.9966840.996684
4When you solve this math problem only return t...624[{'token': '624', 'bytes': [54, 50, 52], 'logp...0.9999260.999926
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" ], "text/plain": [ " prompt response \\\n", "0 When you solve this math problem only return t... 72 \n", "1 When you solve this math problem only return t... $10 \n", "2 When you solve this math problem only return t... $20 \n", "3 When you solve this math problem only return t... 48 \n", "4 When you solve this math problem only return t... 624 \n", "\n", " logprob normalized_probability \\\n", "0 [{'token': '72', 'bytes': [55, 50], 'logprob':... 0.999949 \n", "1 [{'token': '$', 'bytes': [36], 'logprob': -0.0... 0.999398 \n", "2 [{'token': '$', 'bytes': [36], 'logprob': -0.0... 0.945383 \n", "3 [{'token': '48', 'bytes': [52, 56], 'logprob':... 0.996684 \n", "4 [{'token': '624', 'bytes': [54, 50, 52], 'logp... 0.999926 \n", "\n", " min_probability \n", "0 0.999949 \n", "1 0.998797 \n", "2 0.900076 \n", "3 0.996684 \n", "4 0.999926 " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_df = results.to_df()\n", "result_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 3. Evaluate Hallucination Detection Performance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To evaluate hallucination detection performance, we 'grade' the responses against an answer key. Note the `math_postprocessor` is specific to our use case (math questions). **If you are using your own prompts/questions, update the grading method accordingly**." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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promptresponselogprobnormalized_probabilitymin_probabilityanswerresponse_correct
0When you solve this math problem only return t...72[{'token': '72', 'bytes': [55, 50], 'logprob':...0.9999490.99994972True
1When you solve this math problem only return t...$10[{'token': '$', 'bytes': [36], 'logprob': -0.0...0.9993980.99879710True
2When you solve this math problem only return t...$20[{'token': '$', 'bytes': [36], 'logprob': -0.0...0.9453830.9000765False
3When you solve this math problem only return t...48[{'token': '48', 'bytes': [52, 56], 'logprob':...0.9966840.99668442False
4When you solve this math problem only return t...624[{'token': '624', 'bytes': [54, 50, 52], 'logp...0.9999260.999926624True
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" ], "text/plain": [ " prompt response \\\n", "0 When you solve this math problem only return t... 72 \n", "1 When you solve this math problem only return t... $10 \n", "2 When you solve this math problem only return t... $20 \n", "3 When you solve this math problem only return t... 48 \n", "4 When you solve this math problem only return t... 624 \n", "\n", " logprob normalized_probability \\\n", "0 [{'token': '72', 'bytes': [55, 50], 'logprob':... 0.999949 \n", "1 [{'token': '$', 'bytes': [36], 'logprob': -0.0... 0.999398 \n", "2 [{'token': '$', 'bytes': [36], 'logprob': -0.0... 0.945383 \n", "3 [{'token': '48', 'bytes': [52, 56], 'logprob':... 0.996684 \n", "4 [{'token': '624', 'bytes': [54, 50, 52], 'logp... 0.999926 \n", "\n", " min_probability answer response_correct \n", "0 0.999949 72 True \n", "1 0.998797 10 True \n", "2 0.900076 5 False \n", "3 0.996684 42 False \n", "4 0.999926 624 True " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Populate correct answers\n", "result_df[\"answer\"] = gsm8k.answer\n", "\n", "# Grade responses against correct answers\n", "result_df[\"response_correct\"] = [\n", " math_postprocessor(r) == a for r, a in zip(result_df[\"response\"], gsm8k[\"answer\"])\n", "]\n", "result_df.head(5)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Baseline LLM accuracy: 0.51\n" ] } ], "source": [ "print(f\"\"\"Baseline LLM accuracy: {np.mean(result_df[\"response_correct\"])}\"\"\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.1 Filtered LLM Accuracy Evaluation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we explore ‘filtered accuracy’ as a metric for evaluating the performance of our confidence scores. Filtered accuracy measures the change in LLM performance when responses with confidence scores below a specified threshold are excluded. By adjusting the confidence score threshold, we can observe how the accuracy of the LLM improves as less certain responses are filtered out.\n", "\n", "We will plot the filtered accuracy across various confidence score thresholds to visualize the relationship between confidence and LLM accuracy. This analysis helps in understanding the trade-off between response coverage (measured by sample size below) and LLM accuracy, providing insights into the reliability of the LLM’s outputs. We conduct this analysis separately for each of our scorers. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for scorer in [\"normalized_probability\", \"min_probability\"]:\n", " plot_model_accuracies(\n", " scores=result_df[scorer],\n", " correct_indicators=result_df.response_correct,\n", " title=f\"LLM Accuracy by {scorer} Score Threshold\",\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2 Precision, Recall, F1-Score of Hallucination Detection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lastly, we compute the optimal threshold for binarizing confidence scores, using F1-score as the objective. Using this threshold, we compute precision, recall, and F1-score for black box scorer predictions of whether responses are correct." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "normalized_probability score F1-optimal threshold: 0.5700000000000001\n", " \n", "normalized_probability precision: 0.8070175438596491\n", "normalized_probability recall: 0.9019607843137255\n", "normalized_probability f1-score: 0.8518518518518519\n", " \n", " \n", "min_probability score F1-optimal threshold: 0.51\n", " \n", "min_probability precision: 0.8076923076923077\n", "min_probability recall: 0.8235294117647058\n", "min_probability f1-score: 0.8155339805825242\n", " \n", " \n" ] } ], "source": [ "# instantiate UQLM tuner object for threshold selection\n", "t = Tuner()\n", "\n", "correct_indicators = (\n", " result_df.response_correct\n", ") * 1 # Whether responses is actually correct\n", "for scorer in [\"normalized_probability\", \"min_probability\"]:\n", " y_scores = result_df[scorer] # confidence score\n", "\n", " # Solve for threshold that maximizes F1-score\n", " best_threshold = t.tune_threshold(\n", " y_scores=y_scores,\n", " correct_indicators=correct_indicators,\n", " thresh_objective=\"fbeta_score\",\n", " )\n", " y_pred = [\n", " (s > best_threshold) * 1 for s in y_scores\n", " ] # predicts whether response is correct based on confidence score\n", " print(f\"{scorer} score F1-optimal threshold: {best_threshold}\")\n", " print(\" \")\n", "\n", " # evaluate precision, recall, and f1-score of predictions of correctness\n", " print(\n", " f\"{scorer} precision: {precision_score(y_true=correct_indicators, y_pred=y_pred)}\"\n", " )\n", " print(f\"{scorer} recall: {recall_score(y_true=correct_indicators, y_pred=y_pred)}\")\n", " print(f\"{scorer} f1-score: {f1_score(y_true=correct_indicators, y_pred=y_pred)}\")\n", " print(\" \")\n", " print(\" \")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 4. Scorer Definitions\n", "White-box UQ scorers leverage token probabilities of the LLM's generated response to quantify uncertainty. All scorers have outputs ranging from 0 to 1, with higher values indicating higher confidence. We define two white-box UQ scorers below.\n", "\n", "### Length-Normalized Token Probability (`normalized_probability`)\n", "Let the tokenization LLM response $y_i$ be denoted as $\\{t_1,...,t_{L_i}\\}$, where $L_i$ denotes the number of tokens the response. Length-normalized token probability (LNTP) computes a length-normalized analog of joint token probability:\n", "\n", "\\begin{equation}\n", " LNTP(y_i) = \\prod_{t \\in y_i} p_t^{\\frac{1}{L_i}},\n", "\\end{equation}\n", "where $p_t$ denotes the token probability for token $t$. Note that this score is equivalent to the geometric mean of token probabilities for response $y_i$. For more on this scorer, refer to [Malinin & Gales, 2021](https://arxiv.org/pdf/2002.07650).\n", "\n", "\n", "### Minimum Token Probability (`min_probability`)\n", "Minimum token probability (MTP) uses the minimum among token probabilities for a given responses as a confidence score:\n", "\n", "\\begin{equation}\n", " MTP(y_i) = \\min_{t \\in y_i} p_t,\n", "\\end{equation}\n", "where $t$ and $p_t$ follow the same definitions as above. For more on this scorer, refer to [Manakul et al., 2023](https://arxiv.org/abs/2303.08896)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "© 2025 CVS Health and/or one of its affiliates. All rights reserved." ] } ], "metadata": { "environment": { "kernel": "uqlm", "name": "workbench-notebooks.m126", "type": "gcloud", "uri": "us-docker.pkg.dev/deeplearning-platform-release/gcr.io/workbench-notebooks:m126" }, "kernelspec": { "display_name": "uqlm", "language": "python", "name": "uqlm" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.21" } }, "nbformat": 4, "nbformat_minor": 4 }