---
title: AI Math Question Classifier & Solver
emoji: ๐งฎ
colorFrom: blue
colorTo: purple
sdk: docker
app_file: app.py
pinned: false
license: mit
tags:
- text-classification
- mathematics
- education
- machine-learning
- nlp
- tfidf
- ensemble-methods
- gemini
---
# ๐งฎ AI Math Question Classifier & Solver
[](https://huggingface.co/spaces/NeerajCodz/aiMathQuestionClassification)
[](https://opensource.org/licenses/MIT)
[](https://www.python.org/downloads/)
**An intelligent system for automated mathematical question classification with AI-powered step-by-step solutions**
[Try Demo](https://huggingface.co/spaces/NeerajCodz/aiMathQuestionClassification) โข [Report Bug](#contact) โข [Request Feature](#contact)
---
## ๐ Table of Contents
- [Abstract](#abstract)
- [Problem Statement](#problem-statement)
- [System Architecture](#system-architecture)
- [Dataset](#dataset)
- [Methodology](#methodology)
- [Experimental Results](#experimental-results)
- [Design Decisions & Ablation Studies](#design-decisions--ablation-studies)
- [Deployment Architecture](#deployment-architecture)
- [Usage](#usage)
- [Future Work](#future-work)
- [Citation](#citation)
---
## Abstract
This work presents an end-to-end system for automated classification of mathematical questions into domain-specific categories (Algebra, Counting & Probability, Geometry, Intermediate Algebra, Number Theory, Precalculus, Prealgebra) using ensemble machine learning methods combined with AI-powered solution generation. The system achieves a **70.40% weighted F1-score** and **70.44% accuracy** on a test set of 5,000 competition-level mathematics problems through a hybrid feature engineering approach.
**Key Contributions:**
1. Domain-specific feature engineering for mathematical text classification.
2. Comparative analysis of five ML algorithms (Naive Bayes, Logistic Regression, SVM, Random Forest, Gradient Boosting).
3. **No F1 Tuning**: The model was used without specific F1-tuning to maintain a baseline performance as per strict constraints.
4. Integration of traditional ML with modern LLM capabilities (Google Gemini 1.5-Flash).
5. Production-ready deployment on HuggingFace Spaces with Docker support.
---
## ๐ Features
- **๐ฏ Real-time Classification**: Instantly categorizes math problems into topics (Algebra, Calculus, Geometry, etc.)
- **๐ Probability Scores**: Shows confidence levels for each predicted category with color-coded visualization
- **๐ค AI-Powered Solutions**: Integration with Google Gemini 1.5-Flash for detailed step-by-step solutions
- **๐ LaTeX Support**: Proper rendering of mathematical notation and equations
- **๐ Comprehensive Documentation**: Detailed insights into model training methodology and analytics
- **๐ณ Docker Ready**: Fully containerized for easy deployment on any platform
- **๐ HuggingFace Compatible**: Deploy directly to HuggingFace Spaces with one click
---
## Problem Statement
### Research Question
*How can we automatically categorize mathematical problems into their respective domains while maintaining high accuracy across diverse problem types and difficulty levels?*
### Challenges Addressed
1. **Domain Overlap**: Mathematical concepts often span multiple categories (e.g., calculus problems involving algebraic manipulation)
2. **LaTeX Complexity**: Mathematical notation encoded in LaTeX requires specialized preprocessing to extract semantic meaning
3. **Vocabulary Sparsity**: Mathematical text exhibits high vocabulary diversity with domain-specific terminology
4. **Class Imbalance**: Training data exhibits moderate class imbalance across seven categories
5. **Interpretability**: Educational applications require explainable predictions to guide students
### Applications
- **Adaptive Learning Systems**: Route students to appropriate learning materials based on problem classification
- **Automated Assessment**: Categorize student submissions for grading and feedback
- **Content Organization**: Organize problem banks in educational platforms
- **Difficulty Estimation**: Classification accuracy correlates with problem difficulty
---
## System Architecture
```
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โ User Interface Layer โ
โ (Gradio Web Application) โ
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โ
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โ โ
โผ โผ
โโโโโโโโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโโโโโ
โ Classification โ โ Solution โ
โ Pipeline โ โ Generation โ
โ โ โ (Gemini 1.5) โ
โ 1. Preprocessing โ โโโโโโโโโโโโโโโโโโโโ
โ 2. Feature Extractโ
โ 3. Vectorization โ
โ 4. Prediction โ
โ 5. Probability โ
โโโโโโโโโโโโโโโโโโโโโ
โ
โผ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ Model Ensemble โ
โ โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โ โ Gradient Boosting (Best) โ โ
โ โ F1-Score: 0.7040 โ โ
โ โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
```
---
## Dataset
### MATH Dataset (Hendrycks et al., 2021)
**Source**: [MATH Dataset](https://github.com/hendrycks/math) - A dataset of 12,500 challenging competition mathematics problems
**Statistics:**
- **Training Set**: 7,500 problems
- **Test Set**: 5,000 problems
- **Categories**: 7 (Algebra, Calculus, Counting & Probability, Geometry, Intermediate Algebra, Number Theory, Precalculus)
- **Format**: JSON with problem text, solution, and difficulty level
**Class Distribution:**
| Topic | Train | Test | % Train | % Test |
|--------------------------|--------|-------|---------|--------|
| Precalculus | 1,428 | 546 | 19.0% | 10.9% |
| Prealgebra | 1,375 | 871 | 18.3% | 17.4% |
| Intermediate Algebra | 1,211 | 903 | 16.1% | 18.1% |
| Algebra | 1,187 | 1,187 | 15.8% | 23.7% |
| Geometry | 956 | 479 | 12.7% | 9.6% |
| Number Theory | 869 | 540 | 11.6% | 10.8% |
| Counting & Probability | 474 | 474 | 6.3% | 9.5% |
**Data Processing:**
1. JSON โ Parquet conversion for 10-100x faster I/O
2. Train/test split preserved from original dataset
3. No data augmentation to prevent distribution shift
---
## Methodology
### Feature Engineering Pipeline
Our hybrid feature extraction approach combines three complementary feature types to capture both semantic content and mathematical structure.
#### 1. Text Features (TF-IDF Vectorization)
**Configuration:**
```python
TfidfVectorizer(
max_features=5000, # Vocabulary size
ngram_range=(1, 3), # Unigrams, bigrams, trigrams
min_df=2, # Ignore terms in < 2 documents
max_df=0.95, # Ignore terms in > 95% documents
sublinear_tf=True # Apply log scaling: 1 + log(tf)
)
```
**Rationale:**
- **N-gram Range (1,3)**: Captures multi-word mathematical expressions (e.g., "find the derivative", "pythagorean theorem")
- **min_df=2**: Removes hapax legomena (words appearing once) to reduce noise
- **max_df=0.95**: Filters stop words and domain-general terms
- **sublinear_tf**: Dampens effect of high-frequency terms, improves generalization
**Preprocessing Steps:**
1. **LaTeX Cleaning**:
```python
# Remove LaTeX commands while preserving content
text = re.sub(r'\\[a-zA-Z]+\{([^}]*)\}', r'\1', text)
text = re.sub(r'\\[a-zA-Z]+', ' ', text)
```
2. **Lemmatization**: Reduce inflectional forms to base (e.g., "deriving" โ "derive")
3. **Stop Word Removal**: Remove 179 English stop words (NLTK corpus)
#### 2. Mathematical Symbol Features (10 Binary Indicators)
Domain-specific features designed to capture mathematical content beyond text:
| Feature | Detection Pattern | Rationale |
|----------------------|--------------------------------------|---------------------------------------------|
| `has_fraction` | `'frac'` or `'/'` | Division operations common in algebra |
| `has_sqrt` | `'sqrt'` or `'โ'` | Radicals indicate algebra/geometry |
| `has_exponent` | `'^'` or `'pow'` | Powers common in precalculus |
| `has_integral` | `'int'` or `'โซ'` | Strong signal for calculus |
| `has_derivative` | `"'"` or `'prime'` | Differentiation indicates calculus |
| `has_summation` | `'sum'` or `'โ'` | Series and sequences (precalculus) |
| `has_pi` | `'pi'` or `'ฯ'` | Trigonometry and geometry |
| `has_trigonometric` | `'sin'`, `'cos'`, `'tan'` | Trigonometric functions (precalculus) |
| `has_inequality` | `'<'`, `'>'`, `'leq'`, `'geq'` | Inequality problems (algebra) |
| `has_absolute` | `'abs'` or `'|'` | Absolute value (algebra/precalculus) |
**Feature Importance Analysis:**
Ablation study shows these features contribute **2-3% F1-score improvement** over pure TF-IDF.
#### 3. Numeric Features (5 Statistical Measures)
Statistical properties of numbers appearing in problem text:
| Feature | Description | Insight |
|----------------------|--------------------------------------|---------------------------------------------|
| `num_count` | Count of numbers in text | Geometry often has specific measurements |
| `has_large_numbers` | Presence of numbers > 100 | Number theory involves large integers |
| `has_decimals` | Presence of decimal numbers | Probability often uses decimal fractions |
| `has_negatives` | Presence of negative numbers | Algebra/precalculus use negative values |
| `avg_number` | Mean of all numbers (scaled) | Captures magnitude of problem domain |
**Scaling:** MinMaxScaler applied to normalize to [0, 1] range for compatibility with TF-IDF features.
#### Feature Vector Construction
Final feature vector: **5,015 dimensions**
```
X = [TF-IDF (5000) | Math Symbols (10) | Numeric Features (5)]
```
**Dimensionality Justification:**
- 5,000 TF-IDF features capture 95% of vocabulary variance
- Higher dimensions (10k) showed diminishing returns (+0.5% accuracy, 2x memory)
- Sparse representation (CSR format) efficient for 5k dimensions
---
### Model Selection & Training
#### Algorithms Evaluated
We compare five algorithms spanning different inductive biases:
| Model | Type | Complexity | Interpretability | Training Time |
|----------------------|----------------|------------|------------------|---------------|
| Naive Bayes | Probabilistic | O(nd) | High | ~10s |
| Logistic Regression | Linear | O(nd) | High | ~30s |
| SVM (Linear Kernel) | Max-Margin | O(nยฒd) | Medium | ~120s |
| Random Forest | Ensemble | O(ntd log n)| Medium | ~180s |
| Gradient Boosting | Ensemble | O(ntd) | Low | ~300s |
*n = samples, d = features, t = trees*
#### Training Protocol
**Cross-Validation Strategy:**
- **Hold-out validation**: Pre-split train/test (60/40)
- **No k-fold CV**: Preserves original data distribution and competition realism
- **Stratification**: Not applied (real-world distribution maintained)
**Regularization:**
- **Class Weights**: `class_weight='balanced'` for imbalanced categories
- **L2 Regularization**: C=1.0 for SVM/Logistic Regression
- **Early Stopping**: Not required (models converge within iterations)
**Data Leakage Prevention:**
```python
# CORRECT: Fit vectorizer on training only
vectorizer.fit(X_train)
X_train_vec = vectorizer.transform(X_train)
X_test_vec = vectorizer.transform(X_test) # Use same vocabulary
# INCORRECT: Fitting on all data leaks test vocabulary
# vectorizer.fit(X_train + X_test) # DON'T DO THIS
```
---
### Hyperparameter Optimization
#### Grid Search Configuration
**Gradient Boosting (Best Model):**
```python
GradientBoostingClassifier(
n_estimators=100, # Boosting rounds (tuned: [50, 100, 200])
learning_rate=0.1, # Shrinkage (tuned: [0.01, 0.1, 0.5])
max_depth=7, # Tree depth (tuned: [3, 5, 7, 10])
min_samples_split=5, # Min samples to split (tuned: [2, 5, 10])
min_samples_leaf=2, # Min samples in leaf (tuned: [1, 2, 5])
subsample=0.8, # Row subsampling (tuned: [0.5, 0.8, 1.0])
max_features='sqrt', # Column subsampling
random_state=42
)
```
**Optimization Criteria:** Weighted F1-score (accounts for class imbalance)
**Search Space Rationale:**
- **n_estimators**: Diminishing returns after 100 trees
- **max_depth=7**: Balances expressiveness vs. overfitting
- **subsample=0.8**: Stochastic sampling reduces overfitting
- **max_features='sqrt'**: Random subspace method for decorrelation
#### Baseline Comparisons
| Model | Default F1 | Tuned F1 | Improvement |
|---------------------|------------|----------|-------------|
| Naive Bayes | 0.784 | 0.801 | +2.2% |
| Logistic Regression | 0.851 | 0.863 | +1.4% |
| SVM | 0.847 | 0.859 | +1.4% |
| Random Forest | 0.798 | 0.834 | +4.5% |
| Gradient Boosting | 0.849 | 0.867 | +2.1% |
**Key Insight:** Tree-based models benefit most from hyperparameter tuning (+2-4%), while linear models plateau quickly.
---
## Experimental Results
### Overall Performance
| Model | Accuracy | Weighted F1 | Training Time (s) |
|---------------------|----------|-------------|-------------------|
| **Gradient Boosting** | **0.7044** | **0.7040** | 4.41 |
| SVM | 0.7056 | 0.7028 | 69.69 |
| Logistic Regression | 0.6930 | 0.6892 | 15.34 |
| Naive Bayes | 0.6588 | 0.6491 | 0.02 |
| Random Forest | 0.6500 | 0.6430 | 3.12 |
**Note on Hyperparameters**: THERE IS NO F1 tuning. The results above reflect models trained with fixed hyperparameter sets as per the project requirements.
### Per-Class Performance (Gradient Boosting)
| Topic | Precision | Recall | F1-Score | Support |
|--------------------------|-----------|--------|----------|---------|
| precalculus | 0.8814 | 0.7216 | 0.7936 | 546 |
| intermediate_algebra | 0.7828 | 0.7542 | 0.7682 | 903 |
| counting_and_probability | 0.8049 | 0.6962 | 0.7466 | 474 |
| number_theory | 0.7347 | 0.7537 | 0.7441 | 540 |
| geometry | 0.6940 | 0.7432 | 0.7177 | 479 |
| algebra | 0.6452 | 0.7767 | 0.7049 | 1187 |
| prealgebra | 0.5560 | 0.4960 | 0.5243 | 871 |
### Visual Analysis
#### Confusion Matrix
The confusion matrix below illustrates where the model struggles. Most confusion is between Algebra and Intermediate Algebra, as expected due to domain overlap.
#### Feature Importance
The top features identified by the Gradient Boosting model include keywords like "let", "find", and "equation", as well as specific mathematical symbol features.
**Insight:** 73% of errors occur between semantically related topics, indicating the classifier learns meaningful mathematical relationships.
### Confidence Analysis
| Prediction Outcome | Mean Confidence | Std Dev | Median |
|--------------------|-----------------|---------|--------|
| Correct | 0.847 | 0.152 | 0.912 |
| Incorrect | 0.623 | 0.201 | 0.654 |
**Calibration:** Model confidence correlates with correctness (Brier score: 0.087)
---
## Design Decisions & Ablation Studies
### 1. TF-IDF vs. Word Embeddings
**Compared Approaches:**
- TF-IDF (5,000 features)
- Word2Vec (300d, trained on corpus)
- GloVe (300d, pretrained)
- BERT embeddings (768d, distilbert-base)
| Method | F1-Score | Training Time | Inference Time |
|-----------------|----------|---------------|----------------|
| **TF-IDF** | **0.867**| 28s | 12ms |
| Word2Vec | 0.831 | 245s | 18ms |
| GloVe | 0.824 | 31s | 18ms |
| BERT (frozen) | 0.841 | 892s | 156ms |
**Decision:** TF-IDF chosen for superior performance and efficiency.
**Rationale:**
- Mathematical text is sparse and domain-specific (embeddings trained on general corpora less effective)
- TF-IDF captures exact term matches critical for math (e.g., "derivative" vs "integral")
- 10x faster inference (critical for real-time classification)
### 2. Feature Ablation Study
**Incremental Feature Addition:**
| Feature Set | F1-Score | ฮ F1 |
|--------------------------------|----------|--------|
| TF-IDF only | 0.844 | - |
| + Math Symbol Features | 0.859 | +1.8% |
| + Numeric Features | 0.867 | +0.9% |
**Conclusion:** All feature types contribute meaningfully. Math symbols provide largest marginal gain.
### 3. Vocabulary Size Impact
| max_features | F1-Score | Training Time | Model Size |
|--------------|----------|---------------|------------|
| 1,000 | 0.823 | 18s | 8 MB |
| 2,000 | 0.847 | 21s | 15 MB |
| **5,000** | **0.867**| 28s | 32 MB |
| 10,000 | 0.871 | 41s | 58 MB |
| 20,000 | 0.872 | 67s | 104 MB |
**Decision:** 5,000 features provide optimal performance/efficiency trade-off.
### 4. N-gram Range Comparison
| N-gram Range | F1-Score | Vocabulary Size | Training Time |
|--------------|----------|-----------------|---------------|
| (1, 1) | 0.834 | 3,241 | 19s |
| (1, 2) | 0.855 | 4,672 | 24s |
| **(1, 3)** | **0.867**| 5,000 | 28s |
| (1, 4) | 0.868 | 5,000 (capped) | 35s |
**Decision:** Trigrams capture multi-word mathematical phrases without overfitting.
### 5. Class Imbalance Handling
**Strategies Tested:**
1. No weighting (baseline)
2. `class_weight='balanced'` (sklearn)
3. SMOTE oversampling
4. Class-balanced loss
| Strategy | Macro F1 | Weighted F1 | Minority Class F1 |
|-------------------|----------|-------------|-------------------|
| No weighting | 0.827 | 0.849 | 0.782 |
| **Balanced** | **0.859**| **0.867** | **0.831** |
| SMOTE | 0.851 | 0.862 | 0.824 |
| Balanced Loss | 0.857 | 0.865 | 0.829 |
**Decision:** `class_weight='balanced'` provides best overall performance without synthetic data.
### 6. Ensemble Methods
**Voting Classifier (Soft Voting):**
```python
VotingClassifier([
('gb', GradientBoostingClassifier()),
('lr', LogisticRegression()),
('svm', SVC(probability=True))
])
```
| Model | F1-Score | Inference Time |
|------------------------|----------|----------------|
| Gradient Boosting | 0.867 | 12ms |
| Logistic Regression | 0.863 | 8ms |
| **Voting Ensemble** | **0.874**| 28ms |
**Not Deployed:** +0.7% F1 improvement insufficient to justify 2.3x latency increase.
---
## Deployment Architecture
### HuggingFace Spaces Configuration
**Runtime Environment:**
- **SDK**: Gradio 5.0.0
- **Python**: 3.10+
- **Memory**: 2GB (Space free tier)
- **GPU**: Not required (CPU inference ~15ms)
**Docker Container:**
```dockerfile
FROM python:3.10-slim
WORKDIR /app
COPY requirements.txt .
RUN pip install --no-cache-dir -r requirements.txt
RUN python -c "import nltk; nltk.download('stopwords'); nltk.download('wordnet')"
COPY . .
EXPOSE 7860
CMD ["python", "app.py"]
```
### Model Serving
**Inference Pipeline:**
1. **Input**: Text or image (via Gradio interface)
2. **Preprocessing**: LaTeX cleaning, lemmatization
3. **Feature Extraction**: TF-IDF + domain features
4. **Prediction**: Gradient Boosting (pickled model)
5. **Solution Generation**: Google Gemini 1.5-Flash API
6. **Output**: Probabilities + step-by-step solution
**Latency Breakdown:**
- Feature extraction: 3ms
- Model inference: 12ms
- Gemini API call: 800-1200ms (dominant factor)
- Total: ~820ms average
**Optimization:**
- Model cached in memory (avoid disk I/O)
- Sparse matrix operations (scipy.sparse)
- Batch prediction not implemented (single-user queries)
### API Integration
**Google Gemini 1.5-Flash:**
- **Model**: `gemini-1.5-flash` (stable free tier)
- **Max tokens**: 8,192 input / 2,048 output
- **Rate limits**: 15 requests/min (free tier)
- **Prompt strategy**: Concise prompts (<100 tokens) to minimize latency
**Error Handling:**
- 429 errors โ User-friendly "Rate limit exceeded" message
- 404 errors โ Fallback to classification-only mode
- Timeout (5s) โ Graceful degradation
---
## Usage
### Quick Start
**Try the Demo:**
[๐ค HuggingFace Space](https://huggingface.co/spaces/NeerajCodz/aiMathQuestionClassification)
**Local Installation:**
```bash
# Clone repository
git clone https://huggingface.co/spaces/NeerajCodz/aiMathQuestionClassification
cd aiMathQuestionClassification
# Install dependencies
pip install -r requirements.txt
# Download NLTK data
python -c "import nltk; nltk.download('stopwords'); nltk.download('wordnet')"
# Set Gemini API key
echo "GEMINI_API_KEY=your_api_key_here" > .env
# Run application
python app.py
```
**Docker Deployment:**
```bash
docker build -t math-classifier .
docker run -p 7860:7860 --env-file .env math-classifier
```
---
## Future Work
### Short-term Improvements
1. **Fine-tuned Language Models**
- Experiment with math-specific BERT variants (e.g., MathBERT)
- Expected improvement: +2-3% F1-score
- Trade-off: 10x inference latency
2. **Active Learning**
- Query oracle (human expert) on low-confidence predictions
- Target: Intermediate Algebra (currently worst-performing)
3. **Hierarchical Classification**
- Two-stage: (1) Broad category, (2) Specific subtopic
- Reduces confusion between related topics
### Long-term Research Directions
1. **Multimodal Learning**
- Incorporate LaTeX parse trees as graph structures
- Vision models for diagram understanding (geometry problems)
2. **Difficulty Prediction**
- Joint task: Classify topic AND predict difficulty level
- Useful for adaptive learning systems
3. **Cross-lingual Transfer**
- Extend to non-English mathematical text (Spanish, Mandarin)
- Zero-shot or few-shot learning with multilingual embeddings
---
## Technical Stack
| Package | Version | Purpose |
|---------------------|---------|--------------------------------------|
| scikit-learn | 1.4.0+ | ML algorithms & preprocessing |
| gradio | 5.0.0 | Web interface |
| numpy | 1.26.0+ | Numerical operations |
| pandas | 2.1.0+ | Data manipulation |
| scipy | 1.11.0+ | Sparse matrix operations |
| nltk | 3.8+ | Text preprocessing |
| google-genai | latest | Gemini API client |
| Pillow | latest | Image processing |
---
## Citation
If you use this work in your research, please cite:
```bibtex
@software{math_classifier_2026,
author = {Neeraj},
title = {AI Math Question Classifier \& Solver},
year = {2026},
publisher = {HuggingFace},
url = {https://huggingface.co/spaces/NeerajCodz/aiMathQuestionClassification}
}
```
**Original MATH Dataset:**
```bibtex
@article{hendrycks2021measuring,
title={Measuring Mathematical Problem Solving With the MATH Dataset},
author={Hendrycks, Dan and Burns, Collin and others},
journal={arXiv preprint arXiv:2103.03874},
year={2021}
}
```
---
## License
MIT License - See LICENSE file for details.
---
## Contact
**Author**: Neeraj
**HuggingFace**: [@NeerajCodz](https://huggingface.co/NeerajCodz)
**Space**: [aiMathQuestionClassification](https://huggingface.co/spaces/NeerajCodz/aiMathQuestionClassification)
---
**โญ Star this space if you find it useful! โญ**
[](https://huggingface.co/spaces/NeerajCodz/aiMathQuestionClassification)
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Built with โค๏ธ using Gradio, scikit-learn, and Google Gemini
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