{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 🎯 Black-Box Uncertainty Quantification\n", "\n", "
\n", "

\n", " Black-box Uncertainty Quantification (UQ) methods treat the LLM as a black box and evaluate \n", " consistency of multiple responses generated from the same prompt to estimate response-level confidence. This demo provides an illustration \n", " of how to use state-of-the-art black-box UQ methods with uqlm. The following scorers are available:\n", "

\n", " \n", "* Non-Contradiction Probability ([Chen & Mueller, 2023](https://arxiv.org/abs/2308.16175); [Lin et al., 2025](https://arxiv.org/abs/2305.19187); [Manakul et al., 2023](https://arxiv.org/abs/2303.08896))\n", "* Semantic Negentropy (based on [Farquhar et al., 2024](https://www.nature.com/articles/s41586-024-07421-0); [Kuhn et al., 2023](https://arxiv.org/pdf/2302.09664))\n", "* Exact Match ([Cole et al., 2023](https://arxiv.org/abs/2305.14613); [Chen & Mueller, 2023](https://arxiv.org/abs/2308.16175))\n", "* BERT-score ([Manakul et al., 2023](https://arxiv.org/abs/2303.08896); [Zheng et al., 2020](https://arxiv.org/abs/1904.09675))\n", "* BLUERT ([Sellam et al., 2020](https://arxiv.org/abs/2004.04696))\n", "* Normalized Cosine Similarity ([Shorinwa et al., 2024](https://arxiv.org/pdf/2412.05563); [HuggingFace](https://huggingface.co/sentence-transformers/all-MiniLM-L6-v2))\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 BlackBoxUQ() 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 black-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 numpy as np\n", "from sklearn.metrics import precision_score, recall_score, f1_score\n", "\n", "from uqlm import BlackBoxUQ\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 [SVAMP benchmark](https://arxiv.org/abs/2103.07191). 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 - svamp...\n", "Processing dataset...\n", "Dataset ready!\n" ] }, { "data": { "text/html": [ "
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questionanswer
0There are 87 oranges and 290 bananas in Philip...145
1Marco and his dad went strawberry picking. Mar...19
2Edward spent $ 6 to buy 2 books each book cost...3
3Frank was reading through his favorite book. T...198
4There were 78 dollars in Olivia's wallet. She ...63
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" ], "text/plain": [ " question answer\n", "0 There are 87 oranges and 290 bananas in Philip... 145\n", "1 Marco and his dad went strawberry picking. Mar... 19\n", "2 Edward spent $ 6 to buy 2 books each book cost... 3\n", "3 Frank was reading through his favorite book. T... 198\n", "4 There were 78 dollars in Olivia's wallet. She ... 63" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Load example dataset (SVAMP)\n", "svamp = load_example_dataset(\"svamp\", n=75)\n", "svamp.head()" ] }, { "cell_type": "code", "execution_count": 4, "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 svamp.question]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we use `ChatVertexAI` 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": 5, "metadata": { "tags": [] }, "outputs": [], "source": [ "# import sys\n", "# !{sys.executable} -m pip install langchain-google-vertexai\n", "from langchain_google_vertexai import ChatVertexAI\n", "\n", "llm = ChatVertexAI(model=\"gemini-pro\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 2. Generate LLM Responses and Confidence Scores" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `BlackBoxUQ()` - Generate LLM responses and compute consistency-based confidence scores for each response.\n", "\n", "![Sample Image](https://raw.githubusercontent.com/cvs-health/uqlm/develop/assets/images/black_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", " \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", " \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 the provided `llm` object.
scorersList[str]
default=None		Specifies which black box (consistency) scorers to include. Must be subset of ['semantic_negentropy', 'noncontradiction', 'exact_match', 'bert_score', 'bleurt', 'cosine_sim']. If None, defaults to [\"semantic_negentropy\", \"noncontradiction\", \"exact_match\", \"cosine_sim\"]. Note that using \"bleurt\" scorer requires installation of bleurt package (pip install pip install --user git+https://github.com/google-research/bleurt.git).
devicestr or torch.device
default=\"cpu\"		Specifies the device that NLI model use for prediction. Only applies to 'semantic_negentropy', 'noncontradiction' scorers. Pass a torch.device to leverage GPU.
use_bestbool
default=True		Specifies whether to swap the original response for the uncertainty-minimized response among all sampled responses based on semantic entropy clusters. Only used if `scorers` includes 'semantic_negentropy' or 'noncontradiction'.
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.
use_n_parambool
default=False		Specifies whether to use n parameter for BaseChatModel. Not compatible with all BaseChatModel classes. If used, it speeds up the generation process substantially when num_responses is large.
postprocessorcallable
default=None		A user-defined function that takes a string input and returns a string. Used for postprocessing outputs.
sampling_temperaturefloat
default=1		The 'temperature' parameter for LLM to use when generating sampled LLM responses. Must be greater than 0.
nli_model_namestr
default=\"microsoft/deberta-large-mnli\"		Specifies which NLI model to use. Must be acceptable input to AutoTokenizer.from_pretrained() and AutoModelForSequenceClassification.from_pretrained().
max_lengthint
default=2000		Specifies the maximum allowed string length for LLM responses for NLI computation. Responses longer than this value will be truncated in NLI computations to avoid OutOfMemoryError.
\n", "\n", "#### 🔍 Parameter Groups\n", "\n", "
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🧠 LLM-Specific

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📊 Confidence Scores

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🖥️ Hardware

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⚡ Performance

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\n", "\n", "#### 💻 Usage Examples\n", "\n", "```python\n", "# Basic usage with default parameters\n", "bbuq = BlackBoxUQ(llm=llm)\n", "\n", "# Using GPU acceleration, default scorers\n", "bbuq = BlackBoxUQ(llm=llm, device=torch.device(\"cuda\"))\n", "\n", "# Custom scorer list\n", "bbuq = BlackBoxUQ(llm=llm, scorers=[\"semantic_negentropy\", \"exact_match\", \"cosine_sim\"])\n", "\n", "# High-throughput configuration with rate limiting\n", "bbuq = BlackBoxUQ(llm=llm, max_calls_per_min=200, use_n_param=True) \n", "```" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using cuda device\n" ] } ], "source": [ "import torch\n", "\n", "# Set the torch device\n", "if torch.cuda.is_available(): # NVIDIA GPU\n", " device = torch.device(\"cuda\")\n", "elif torch.backends.mps.is_available(): # macOS\n", " device = torch.device(\"mps\")\n", "else:\n", " device = torch.device(\"cpu\") # CPU\n", "print(f\"Using {device.type} device\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Some weights of the model checkpoint at microsoft/deberta-large-mnli were not used when initializing DebertaForSequenceClassification: ['config']\n", "- This IS expected if you are initializing DebertaForSequenceClassification from the checkpoint of a model trained on another task or with another architecture (e.g. initializing a BertForSequenceClassification model from a BertForPreTraining model).\n", "- This IS NOT expected if you are initializing DebertaForSequenceClassification from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n" ] } ], "source": [ "bbuq = BlackBoxUQ(\n", " llm=llm,\n", " max_calls_per_min=250,\n", " device=device,\n", " scorers=[\"semantic_negentropy\", \"exact_match\", \"cosine_sim\"],\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 🔄 Class Methods\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
MethodDescription & Parameters
BlackBoxUQ.generate_and_score\n", "

Generate LLM responses, sampled LLM (candidate) 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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  • num_responses - (int, default=5) The number of sampled responses used to compute consistency.
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Returns: UQResult containing data (prompts, responses, sampled responses, 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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BlackBoxUQ.score\n", "

Compute confidence scores on provided LLM responses. Should only be used if responses and sampled responses are already generated.

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Parameters:

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  • responses - (list of str) A list of LLM responses for the prompts.
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Returns: UQResult containing data (responses, sampled responses, and confidence scores) and metadata

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\n", " 💡 Best For: Computing uncertainty scores when responses are already generated elsewhere.\n", "
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" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generating responses...\n", "Generating candidate responses...\n", "Computing confidence scores...\n" ] } ], "source": [ "results = await bbuq.generate_and_score(\n", " prompts=prompts, \n", " num_responses=10, # for lower cost and latency, use smaller value of num_responses\n", ")\n", "\n", "# # alternative approach: directly score if responses already generated\n", "# results = bbuq.score(responses=responses, sampled_responses=sampled_responses)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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responsesampled_responsespromptexact_matchcosine_simsemantic_negentropy
0145[145 \\n, 145 Each group should contain 145 ban...When you solve this math problem only return t...0.80.9723151.000000
119 pounds[19 pounds, 19, 19 pounds, 19 pounds, 19, 19, ...When you solve this math problem only return t...0.50.9090831.000000
2$3[$4, $4\\n, $3, $ 3.00, $3, $3, $ 3.00, $3.00, ...When you solve this math problem only return t...0.30.9151180.802269
3198[198, ```\\n198\\n```, 198, 198, 198, 198, 198, ...When you solve this math problem only return t...0.90.9904221.000000
463[63, 63, 63, 63, 63, 63, 63, 63, 63, 63]When you solve this math problem only return t...1.01.0000001.000000
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" ], "text/plain": [ " response sampled_responses \\\n", "0 145 [145 \\n, 145 Each group should contain 145 ban... \n", "1 19 pounds [19 pounds, 19, 19 pounds, 19 pounds, 19, 19, ... \n", "2 $3 [$4, $4\\n, $3, $ 3.00, $3, $3, $ 3.00, $3.00, ... \n", "3 198 [198, ```\\n198\\n```, 198, 198, 198, 198, 198, ... \n", "4 63 [63, 63, 63, 63, 63, 63, 63, 63, 63, 63] \n", "\n", " prompt exact_match cosine_sim \\\n", "0 When you solve this math problem only return t... 0.8 0.972315 \n", "1 When you solve this math problem only return t... 0.5 0.909083 \n", "2 When you solve this math problem only return t... 0.3 0.915118 \n", "3 When you solve this math problem only return t... 0.9 0.990422 \n", "4 When you solve this math problem only return t... 1.0 1.000000 \n", "\n", " semantic_negentropy \n", "0 1.000000 \n", "1 1.000000 \n", "2 0.802269 \n", "3 1.000000 \n", "4 1.000000 " ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_df = results.to_df()\n", "result_df.head(5)" ] }, { "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": 11, "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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responsesampled_responsespromptexact_matchcosine_simsemantic_negentropyanswerresponse_correct
0145[145 \\n, 145 Each group should contain 145 ban...When you solve this math problem only return t...0.80.9723151.000000145True
119 pounds[19 pounds, 19, 19 pounds, 19 pounds, 19, 19, ...When you solve this math problem only return t...0.50.9090831.00000019True
2$3[$4, $4\\n, $3, $ 3.00, $3, $3, $ 3.00, $3.00, ...When you solve this math problem only return t...0.30.9151180.8022693True
3198[198, ```\\n198\\n```, 198, 198, 198, 198, 198, ...When you solve this math problem only return t...0.90.9904221.000000198True
463[63, 63, 63, 63, 63, 63, 63, 63, 63, 63]When you solve this math problem only return t...1.01.0000001.00000063True
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" ], "text/plain": [ " response sampled_responses \\\n", "0 145 [145 \\n, 145 Each group should contain 145 ban... \n", "1 19 pounds [19 pounds, 19, 19 pounds, 19 pounds, 19, 19, ... \n", "2 $3 [$4, $4\\n, $3, $ 3.00, $3, $3, $ 3.00, $3.00, ... \n", "3 198 [198, ```\\n198\\n```, 198, 198, 198, 198, 198, ... \n", "4 63 [63, 63, 63, 63, 63, 63, 63, 63, 63, 63] \n", "\n", " prompt exact_match cosine_sim \\\n", "0 When you solve this math problem only return t... 0.8 0.972315 \n", "1 When you solve this math problem only return t... 0.5 0.909083 \n", "2 When you solve this math problem only return t... 0.3 0.915118 \n", "3 When you solve this math problem only return t... 0.9 0.990422 \n", "4 When you solve this math problem only return t... 1.0 1.000000 \n", "\n", " semantic_negentropy answer response_correct \n", "0 1.000000 145 True \n", "1 1.000000 19 True \n", "2 0.802269 3 True \n", "3 1.000000 198 True \n", "4 1.000000 63 True " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Populate correct answers \n", "result_df[\"answer\"] = svamp.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\"], svamp[\"answer\"])\n", "]\n", "result_df.head(5)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Baseline LLM accuracy: 0.72\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": 13, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for confidence_score in [\"semantic_negentropy\", \"exact_match\", \"cosine_sim\"]:\n", " plot_model_accuracies(\n", " scores=result_df[confidence_score],\n", " correct_indicators=result_df.response_correct,\n", " title=f\"LLM Accuracy by {confidence_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": 14, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "semantic_negentropy F1-optimal threshold: 0.59\n", " \n", "semantic_negentropy precision: 0.8333333333333334\n", "semantic_negentropy recall: 0.9259259259259259\n", "semantic_negentropy f1-score: 0.8771929824561403\n", " \n", " \n", "exact_match F1-optimal threshold: 0.2\n", " \n", "exact_match precision: 0.7910447761194029\n", "exact_match recall: 0.9814814814814815\n", "exact_match f1-score: 0.8760330578512396\n", " \n", " \n", "cosine_sim F1-optimal threshold: 0.88\n", " \n", "cosine_sim precision: 0.8305084745762712\n", "cosine_sim recall: 0.9074074074074074\n", "cosine_sim f1-score: 0.8672566371681416\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 confidence_score in [\"semantic_negentropy\", \"exact_match\", \"cosine_sim\"]:\n", " y_scores = result_df[confidence_score] # 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\"{confidence_score} F1-optimal threshold: {best_threshold}\")\n", " print(\" \")\n", "\n", " # evaluate precision, recall, and f1-score of predictions of correctness\n", " print(\n", " f\"{confidence_score} precision: {precision_score(y_true=correct_indicators, y_pred=y_pred)}\"\n", " )\n", " print(\n", " f\"{confidence_score} recall: {recall_score(y_true=correct_indicators, y_pred=y_pred)}\"\n", " )\n", " print(\n", " f\"{confidence_score} f1-score: {f1_score(y_true=correct_indicators, y_pred=y_pred)}\"\n", " )\n", " print(\" \")\n", " print(\" \")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Scorer Definitions\n", "Below we define the scorers offered by the `BlackBoxUQ` class. These scorers exploit variation in LLM responses to the same prompt to measure semantic consistency. All scorers have outputs ranging from 0 to 1, with higher values indicating higher confidence. \n", "\n", "For a given prompt $x_i$, these approaches involves generating $m$ responses $\\tilde{\\mathbf{y}}_i = \\{ \\tilde{y}_{i1},...,\\tilde{y}_{im}\\}$, using a non-zero temperature, from the same prompt and comparing these responses to the original response $y_{i}$. We provide detailed descriptions of each below.\n", "\n", "### Exact Match Rate (`exact_match`)\n", "Exact Match Rate (EMR) computes the proportion of candidate responses that are identical to the original response.\n", "$$ EMR(y_i; \\tilde{\\mathbf{y}}_i) = \\frac{1}{m} \\sum_{j=1}^m \\mathbb{I}(y_i=\\tilde{y}_{ij}). $$\n", "\n", "For more on this scorer, refer to [Cole et al., 2023](https://arxiv.org/abs/2305.14613).\n", "\n", "### Non-Contradiction Probability (`noncontradiction`)\n", "Non-contradiction probability (NCP) computes the mean non-contradiction probability estimated by a natural language inference (NLI) model. This score is formally defined as follows:\n", "\n", "\\begin{equation}\n", " NCP(y_i; \\tilde{\\mathbf{y}}_i) = \\frac{1}{m} \\sum_{j=1}^m(1 - p_j)\n", "\\end{equation}\n", "where\n", "\n", "\\begin{equation}\n", " p_j = \\frac{\\eta(y_{i}, \\tilde{y}_{ij}) + \\eta(\\tilde{y}_{ij},y_i)}{2}.\n", "\\end{equation}\n", "\n", "Above, $\\eta(\\tilde{y}_{ij},y_i)$ denotes the contradiction probability estimated by the NLI model for response $y_i$ and candidate $\\tilde{y}_{ij}$. For more on this scorer, refer to [Chen & Mueller, 2023](https://arxiv.org/abs/2308.16175), [Lin et al., 2025](https://arxiv.org/abs/2305.19187), or [Manakul et al., 2023](https://arxiv.org/abs/2303.08896).\n", "\n", "### Normalized Semantic Negentropy (`semantic_negentropy`)\n", "Normalized Semantic Negentropy (NSN) normalizes the standard computation of discrete semantic entropy to be increasing with higher confidence and have [0,1] support. In contrast to the EMR and NCP, semantic entropy does not distinguish between an original response and candidate responses. Instead, this approach computes a single metric value on a list of responses generated from the same prompt. Under this approach, responses are clustered using an NLI model based on mutual entailment. We consider the discrete version of SE, where the final set of clusters is defined as follows:\n", "\n", "\\begin{equation}\n", " SE(y_i; \\tilde{\\mathbf{y}}_i) = - \\sum_{C \\in \\mathcal{C}} P(C|y_i, \\tilde{\\mathbf{y}}_i)\\log P(C|y_i, \\tilde{\\mathbf{y}}_i),\n", "\\end{equation}\n", "where $P(C|y_i, \\tilde{\\mathbf{y}}_i)$ denotes the probability a randomly selected response $y \\in \\{y_i\\} \\cup \\tilde{\\mathbf{y}}_i $ belongs to cluster $C$, and $\\mathcal{C}$ denotes the full set of clusters of $\\{y_i\\} \\cup \\tilde{\\mathbf{y}}_i$.\n", "\n", "To ensure that we have a normalized confidence score with $[0,1]$ support and with higher values corresponding to higher confidence, we implement the following normalization to arrive at *ormalized Semantic Negentropy* (NSN):\n", "\\begin{equation}\n", " NSN(y_i; \\tilde{\\mathbf{y}}_i) = 1 - \\frac{SE(y_i; \\tilde{\\mathbf{y}}_i)}{\\log m},\n", "\\end{equation}\n", "where $\\log m$ is included to normalize the support.\n", "\n", "### BERTScore (`bert_score`)\n", "Let a tokenized text sequence be denoted as $\\textbf{t} = \\{t_1,...t_L\\}$ and the corresponding contextualized word embeddings as $\\textbf{E} = \\{\\textbf{e}_1,...,\\textbf{e}_L\\}$, where $L$ is the number of tokens in the text. The BERTScore precision, recall, and F1-scores between two tokenized texts $\\textbf{t}, \\textbf{t}'$ are respectively defined as follows:\n", "\n", "\\begin{equation}\n", " BertP(\\textbf{t}, \\textbf{t}') = \\frac{1}{| \\textbf{t}|} \\sum_{t \\in \\textbf{t}} \\max_{t' \\in \\textbf{t}'} \\textbf{e} \\cdot \\textbf{e}'\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", " BertR(\\textbf{t}, \\textbf{t}') = \\frac{1}{| \\textbf{t}'|} \\sum_{t' \\in \\textbf{t}'} \\max_{t \\in \\textbf{t}} \\textbf{e} \\cdot \\textbf{e}'\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", " BertF(\\textbf{t}, \\textbf{t}') = 2\\frac{ BertP(\\textbf{t}, \\textbf{t}') BertR(\\textbf{t}, \\textbf{t}')}{BertP(\\textbf{t}, \\textbf{t}') + BertRec(\\textbf{t}, \\textbf{t}')},\n", "\\end{equation}\n", "where $e, e'$ respectively correspond to $t, t'$. We compute our BERTScore-based confidence scores as follows:\n", "\\begin{equation}\n", " BertConf(y_i; \\tilde{\\mathbf{y}}_i) = \\frac{1}{m} \\sum_{j=1}^m BertF(y_i, \\tilde{y}_{ij}),\n", "\\end{equation}\n", "i.e. the average BERTScore F1 across pairings of the original response with all candidate responses. For more on BERTScore, refer to [Zheng et al., 2020](https://arxiv.org/abs/1904.09675).\n", "\n", "### BLEURT (`bleurt`)\n", "In contrast to the aforementioned scorers, BLEURT is specifically pre-trained and fine-tuned to learn human judgments of text similarity. Our BLEURT confidence score is the average BLEURT value across pairings of the original response with all candidate responses:\n", "\n", "\\begin{equation}\n", " BLEURTConf(y_i; \\tilde{\\mathbf{y}}_i) = \\frac{1}{m} \\sum_{j=1}^m BLEURT(y_i, \\tilde{y}_{ij}).\n", "\\end{equation}\n", "\n", "For more on this scorer, refer to [Sellam et al., 2020](https://arxiv.org/abs/2004.04696).\n", "\n", "\n", "### Normalized Cosine Similarity (`cosine_sim`)\n", "This scorer leverages a sentence transformer to map LLM outputs to an embedding space and measure similarity using those sentence embeddings. Let $V: \\mathcal{Y} \\xrightarrow{} \\mathbb{R}^d$ denote the sentence transformer, where $d$ is the dimension of the embedding space. The average cosine similarity across pairings of the original response with all candidate responses is given as follows:\n", "\n", "\\begin{equation}\n", " CS(y_i; \\tilde{\\mathbf{y}}_i) = \\frac{1}{m} \\sum_{i=1}^m \\frac{\\mathbf{V}(y_i) \\cdot \\mathbf{V}(\\tilde{y}_{ij}) }{ \\lVert \\mathbf{V}(y_i) \\rVert \\lVert \\mathbf{V}(\\tilde{y}_{ij}) \\rVert}.\n", "\\end{equation}\n", "\n", "To ensure a standardized support of $[0, 1]$, we normalize cosine similarity to obtain confidence scores as follows:\n", "\n", "\\begin{equation}\n", " NCS(y_i; \\tilde{\\mathbf{y}}_i) = \\frac{CS(y_i; \\tilde{\\mathbf{y}}_i) + 1}{2}.\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "© 2025 CVS Health and/or one of its affiliates. 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