Transparent AI for Mathematics: Transformer-Based Large Language Models for Mathematical Entity Relationship Extraction with XAI

This paper proposes a transparent AI framework for Mathematical Entity Relation Extraction (MERE) that utilizes BERT to achieve 99.39% accuracy in identifying mathematical relationships and incorporates SHAP-based explainability to enhance model trust and interpretability for applications in automated problem solving and education.

The Gist

Imagine you have a robot that is incredibly smart at reading books, but when you hand it a math word problem, it gets confused. It sees words like "mangoes," "children," and "divided," but it doesn't quite understand that these words are actually hiding a secret math equation waiting to be solved.

This paper is about teaching that robot to not only read the words but to understand the math story behind them, and then to show us exactly how it figured it out.

Here is the breakdown of their work, explained simply:

1. The Big Idea: Math as a Relationship Game

Usually, when we read a sentence like "A man bought ten mangoes and divided them equally among five children," we see a story.
The researchers decided to treat this sentence like a relationship game.

• The Characters (Entities): The "ten mangoes" and the "five children" are the players.
• The Action (Relationship): The word "divided" is the action connecting them.

Their goal was to build a computer program that can automatically spot the characters and figure out what action is happening between them, turning a messy paragraph of text into a clean math equation.

2. The Star Player: BERT (The Super-Reader)

To do this, they used a famous AI model called BERT. Think of BERT as a super-advanced librarian who has read almost every book in the English language.

• Because BERT has read so much, it understands context. It knows that "bank" means something different in a river vs. a money bank.
• The researchers took this super-reader and gave it a specific training course on math problems. They taught it to look for numbers and action words (like "plus," "minus," "root," "factorial") and predict the relationship.

The Result: This trained BERT model was a superstar. It got 99.39% of the answers right. That's like getting 99 out of 100 questions correct on a math test!

3. The Problem: The "Black Box" Mystery

Here is the tricky part. Even though the robot got the answer right, we didn't know why.
Imagine a student gets a math problem right. If they just say "I got it!" but refuse to show their work, you might not trust them. You'd wonder, "Did they guess? Did they cheat?"
In AI, this is called a "Black Box." We see the input (the question) and the output (the answer), but the thinking process inside is hidden.

4. The Solution: XAI and SHAP (The Flashlight)

To fix the "Black Box" problem, the researchers used a tool called SHAP (which stands for Shapley Additive Explanations).

• The Analogy: Imagine SHAP is a magnifying glass or a flashlight that shines on the robot's brain.
• When the robot makes a prediction, SHAP highlights the specific words that made the robot say "Yes, this is Division!" or "No, this is Addition!"
• Red highlights mean a word helped the robot make the right choice.
• Blue highlights mean a word made the robot less sure.

What they found:

• For the word "Square Root," the robot relied heavily on the words "root" and "square." It was very confident.
• For "Addition," the robot looked at a mix of words like "total," "sum," and "plus." It had to gather clues from many places to be sure.

This proves the robot isn't just guessing; it's actually reading the math story and understanding the clues, just like a human would.

5. Why This Matters

Why should we care about a robot that solves math word problems?

• Smart Tutors: Imagine an app that doesn't just give you the answer, but explains why it's the answer, helping students learn better.
• Research Assistants: Scientists could use this to scan thousands of research papers and automatically pull out all the math formulas and relationships, saving hours of work.
• Trust: Because they used the "flashlight" (SHAP), we can trust the robot. We know it's not making up answers; it's following the logic of the text.

Summary

In short, the researchers built a math-savvy robot (using BERT) that can read word problems and find the hidden math equations. They then built a flashlight (using SHAP) to show us exactly which words the robot used to solve the puzzle. This makes the robot not only smart but also trustworthy and transparent, paving the way for better educational tools and automated math systems in the future.

Technical Summary

Here is a detailed technical summary of the paper "Transparent AI for Mathematics: Transformer-Based Large Language Models for Mathematical Entity Relationship Extraction with XAI."

1. Problem Statement

Mathematical text understanding is a complex task due to the presence of specialized entities (operands) and intricate relationships (operators) between them. Traditional Natural Language Processing (NLP) often struggles to bridge the gap between natural language descriptions and mathematical notation.

• Core Challenge: The paper addresses Mathematical Entity Relation Extraction (MERE), defined as identifying mathematical entities within text and determining the specific relationship (operator) connecting them.
• Gap: While Large Language Models (LLMs) like BERT have shown success in general NLP, their application to mathematical texts often lacks transparency. These models function as "black boxes," making it difficult for educators and researchers to trust automated extraction systems or understand why a specific mathematical operation was predicted.

2. Methodology

The proposed framework integrates deep learning with Explainable Artificial Intelligence (XAI) to create a transparent MERE system.

A. Data Collection and Preprocessing

• Datasets: The authors constructed a custom dataset by combining two sources:
  1. Bangla MER: An existing dataset for Mathematical Entity Recognition (English subset used).
  2. Somikoron: A dataset containing mathematical statements.
• Labeling: The combined dataset contains 3,284 unique mathematical statements. The task was framed as a classification problem where the "relationship" is the target label.
• Target Classes: Six fundamental mathematical operations: Addition, Subtraction, Multiplication, Division, Square Root, and Factorial.
• Preprocessing Pipeline:
  • Removal of non-alphabetic characters (e.g., $, %, #).
  • Stop-word removal (using NLTK).
  • Lemmatization and Stemming: To reduce token size and model complexity.
  • Entity Handling: Multi-word number phrases (e.g., "five thousand and forty") were treated as single entities.

B. Model Architecture

• Base Model: BERT (Bidirectional Encoder Representations from Transformers), specifically bert-base-uncased.
• Training Strategy:
  • Pre-training: Utilized standard BERT pre-training (Masked Language Modeling and Next Sentence Prediction) on Wikipedia and BooksCorpus.
  • Fine-tuning: The model was fine-tuned on the custom MERE dataset.
  • Input Processing: Text is tokenized, and positional/segment embeddings are added. The output of the [CLS] token is passed through a fully connected layer followed by a Softmax activation to predict the relationship class.
• Hyperparameters:
  • Learning Rate: $2 \times 10^{-4}$ (AdamW)
  • Max Sequence Length: 50 tokens
  • Batch Size: 12
  • Epochs: 40

C. Explainability (XAI)

To address the "black box" nature of BERT, the study integrates SHAP (SHapley Additive exPlanations):

• Mechanism: SHAP uses cooperative game theory to assign an importance value to each input token (word) for a specific prediction.
• Implementation: A model-agnostic explainer was used on the Hugging Face pipeline. It perturbs input tokens to observe changes in output probabilities, generating SHAP values.
• Visualization:
  • Text Plots: Highlight words in red (positive contribution) or blue (negative contribution) to show how specific tokens influence the prediction of a specific class (e.g., "divided" positively influencing "Division").
  • Bar Plots: Show mean SHAP values across the dataset to identify globally important features for each operation.

3. Key Contributions

1. Task Formulation: Successfully reframed mathematical word problems as an Entity-Relation Extraction task, treating operands as entities and operators as relationships.
2. Dataset Creation: Developed a specialized, labeled dataset combining Bangla MER and Somikoron resources, filling a gap in available resources for mathematical relation extraction.
3. Transparent AI Framework: Unlike previous works that focus solely on accuracy, this study integrates SHAP to provide interpretability, allowing users to verify which words drove the model's decision.
4. State-of-the-Art Performance: Demonstrated that Transformer-based models, specifically BERT, significantly outperform traditional methods and other transformer variants (RoBERTa, XLNet, etc.) in this specific domain.

4. Results

The model was evaluated against other transformer architectures (Electra, RoBERTa, AlBERT, DistilBERT, XLNet) using Accuracy, Micro-F1, and Macro-F1 scores.

• Performance Metrics (BERT):
  • Accuracy: 99.39%
  • Micro-F1 Score: 99.36%
  • Macro-F1 Score: 99.27%
  • Comparison: BERT outperformed all other models (e.g., RoBERTa achieved ~97.56% accuracy).
• Confusion Matrix Analysis:
  • The model achieved near-perfect scores for Factorial, Square Root, and Subtraction (100% Precision/Recall).
  • Minor misclassifications occurred primarily between Addition and Subtraction (8 errors) and Division and Multiplication (4 errors), likely due to contextual ambiguity in natural language.
• SHAP Analysis Insights:
  • Operation-Specific Keywords: The model relies heavily on semantic cues. For example, "Square Root" is driven by "root" and "square"; "Division" by "divided," "equally," and "each."
  • Contextual Understanding: For ambiguous operations like Addition and Multiplication, the model aggregates evidence from multiple contextual words (e.g., "total," "contains," "how many") rather than relying on a single trigger word.
  • Confidence: The SHAP plots confirmed that high-confidence predictions (>80%) correlate with strong positive contributions from operation-specific keywords.

5. Significance and Future Work

• Significance:
  • Trust and Transparency: By using SHAP, the study moves beyond simple accuracy metrics, providing a mechanism to audit model decisions, which is critical for educational and scientific applications.
  • Educational Applications: The framework supports the development of intelligent tutoring systems, automated theorem provers, and knowledge graph construction for mathematical content.
  • Robustness: The model demonstrates an ability to generalize mathematical intent from linguistic structures rather than memorizing specific numbers.
• Limitations:
  • The current dataset is limited to six basic operations and short text sequences.
  • The computational cost is high due to the simultaneous use of BERT and SHAP.
• Future Directions:
  • Expanding to complex mathematical domains (Algebra, Calculus, Geometry).
  • Optimizing model efficiency for real-time deployment.
  • Integrating the system with automated theorem proving and advanced knowledge graph generation.

In conclusion, this paper establishes a highly accurate and interpretable framework for understanding mathematical text, proving that combining Transformer-based learning with XAI is essential for the reliable deployment of AI in STEM education and research.