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Math Information Retrieval System Banner

Math Information Retrieval System

This repository contains both the Flutter frontend and the FastAPI backend for a Clustering-Based Mathematical Information Retrieval (MathIR) system.

It supports LaTeX/MathML search, cross-platform rendering, and fast retrieval of mathematical documents.

Developed by

  • @ak0586
  • @chirag0521
  • @er-vishalgour
  • @rajanks

📌 Features

Frontend (Flutter)

  • 🔍 Search LaTeX or math expressions
  • 📄 Render HTML with MathML on Android and Web
  • 💡 WebView for Android, iframe + MathJax for Web
  • ⏱ Show response time and result count
  • ✅ Clean UI with animation, loading indicators, and error handling

Backend (FastAPI)

  • ⚡ Cluster-based approximate nearest neighbor (ANN) search
  • 🔢 MiniBatchKMeans with Hamming distance for binary bit-vectors
  • 📂 Preprocessing of HTML to extract MathML & LaTeX
  • 🚀 Scalable and optimized for large datasets

🆕 Recent Updates & Key Improvements

We have recently optimized and refactored the system to improve performance, cross-platform compatibility, and deployment reliability:

1. 🔒 Secure Document Retrieval (CORS & Proxy Bypass)

  • B2 Private Streaming: To prevent exposing public URLs and avoid CDN/WAF blocks, the backend now fetches HTML documents privately from Backblaze B2 or local storage and base64-encodes them.
  • Multiplexed POST Route: Configured the client to retrieve documents via a POST request to /search using the __VIEW__:{session_id}:{file_id} query format. This bypasses Hugging Face Space proxy blocks on non-root paths and Backblaze B2's 400 POST not allowed CORS restrictions on redirect requests.

2. 📱 Android & Web Stability

  • Shadowing Compiler Error Fixed: Resolved a critical compilation error in mobile_html_viewer.dart where the local variable shadowed the state field. The frontend now compiles with 0 errors.
  • MathJax Integration: Enhanced web_html_viewer.dart and mobile_html_viewer.dart with MathJax embedding inside dynamic iframes/webviews to guarantee crisp mathematical rendering of equations.

3. 🌐 Environment-Aware API Routing

  • Auto-URL Switching: Modified getBaseUrl() to automatically detect local debugging (kDebugMode) and point to http://localhost:8000 (or http://10.0.2.2:8000 for Android Emulator) during testing, falling back automatically to the Hugging Face production Space in release builds.

4. ⚡ Core Backend Optimization (65x Speedup)

  • Combined Database Indexing: Removed all legacy pickle files (.pkl) and consolidated model centroids, hyperparameters, preprocess tracking, and cluster assignments into a single SQLite database (math_index.db).
  • Vectorized Hamming Distance: Vectorized loop calculations inside the K-Means Hamming distance logic using NumPy broadcasting, yielding a 65.5x performance gain.
  • Parallel Preprocessing: Implemented multi-process preprocessing with a fast regex scanner to skip HTML files lacking mathematical tags, speeding up initial indexing.

📁 Directory Structure

📦 math-ir-system
┣ 📂 frontend
┃ ┣ 📜 main.dart                  # Main search UI and routing logic
┃ ┣ 📜 mobile_html_viewer.dart    # WebView-based HTML renderer for Android
┃ ┣ 📜 web_html_viewer.dart       # iframe-based HTML renderer for Web
┃ ┗ 📜 pubspec.yaml               # Flutter dependencies
┃
┣ 📂 backend
┃ ┣ 📂 MIR_model
┃ ┃ ┣ 📜 cluster_index.py          # Handles cluster index loading and searching
┃ ┃ ┣ 📜 clustering_phase.py       # Performs clustering on bit-vector data
┃ ┃ ┣ 📜 driver_clustering.py      # Triggers clustering and index creation
┃ ┃ ┣ 📜 driver_preprocessing.py   # Preprocesses HTML documents
┃ ┃ ┣ 📜 hamming_mini_batch_kmeans.py  # MiniBatchKMeans adapted for Hamming distance
┃ ┃ ┣ 📜 preprocessing.py          # Extracts MathML & LaTeX, generates bit-vectors
┃ ┃ ┣ 📜 query_processing.py       # Identifies query type and processes
┃ ┃ ┣ 📜 query_to_bitvector.py     # Converts LaTeX → MathML → bit-vector
┃ ┃ ┣ 📜 search_query.py           # Main search execution logic
┃ ┣ 📜 main.py                     # FastAPI entry point
┃ ┣ 📜 requirements.txt            # contains all required library and modules to be install
┃ ┗ 📂 math_index_storage          # Stores models & clustering indices
┗ 📜 README.md

Query Set

If you want to directly copy the latex from the json file then please replace the '//' with '/' and '////' with '//' for perform searching on the UI. but queries given are already UI compatible no need make changes.

Mathematical Queries that are provided by NTCIR-12: http://ntcir-math.nii.ac.jp/

  1. Raw LaTeX — shows the exact LaTeX code.
  2. Rendered — shows how it will appear on GitHub.

1

Raw LaTeX:
-0.026838601\ldots

Rendered:

$$-0.026838601\ldots$$

2

Raw LaTeX:
\mathfrak{P}

Rendered:

$$\mathfrak{P}$$

3

Raw LaTeX:
N = \left\lfloor 0.5 - \log_{2} \left(\frac{\text{Frequency of this item}}{\text{Frequency of most common item}}\right) \right\rfloor

Rendered:

$$N = \left\lfloor 0.5 - \log_{2} \left(\frac{\text{Frequency of this item}}{\text{Frequency of most common item}}\right) \right\rfloor$$

4

Raw LaTeX:
\nabla \times \mathbf{B} = \mu_{0} \mathbf{J} +\underbrace{\mu_{0}\epsilon_{0} \frac{\partial}{\partial t}\mathbf{E}}_{\text{Maxwell's term}}

Rendered:

$$\nabla \times \mathbf{B} = \mu_{0} \mathbf{J} +\underbrace{\mu_{0}\epsilon_{0} \frac{\partial}{\partial t}\mathbf{E}}_{\text{Maxwell's term}}$$

5

Raw LaTeX:
1 + \cfrac{1}{2 + \cfrac{1}{5 + \cfrac{1}{5 + \cfrac{1}{4 + \ddots}}}}

Rendered:

$$1 + \cfrac{1}{2 + \cfrac{1}{5 + \cfrac{1}{5 + \cfrac{1}{4 + \ddots}}}}$$

6

Raw LaTeX:
^{238}{92}\mathrm{U} + ^{64}{28}\mathrm{Ni} ;\rightarrow;^{302}_{120}\mathrm{Ubn}^{*} ;\rightarrow; \textit{fission only}

Rendered:

$$^{238}_{92}\mathrm{U} + ^{64}_{28}\mathrm{Ni} \;\rightarrow\;^{302}_{120}\mathrm{Ubn}^{*} \;\rightarrow\; \textit{fission only}$$

7

Raw LaTeX:
0 \rightarrow G^\wedge \xrightarrow{\pi^\wedge} X^\wedge \xrightarrow{i^\wedge} H^\wedge \rightarrow 0

Rendered:

$$0 \rightarrow G^\wedge \xrightarrow{\pi^\wedge} X^\wedge \xrightarrow{i^\wedge} H^\wedge \rightarrow 0$$

8

Raw LaTeX:
w = \begin{cases} w^* & \text{if } w^* > \frac{1}{2}, \ \frac{1}{2} & \text{if } w^* \le \frac{1}{2}. \end{cases}

Rendered:

$$w = \begin{cases} w^* & \text{if } w^* > \frac{1}{2}, \\ \frac{1}{2} & \text{if } w^* \le \frac{1}{2}. \end{cases}$$

9

Raw LaTeX:
\begin{bmatrix} V_1 \ I_2 \end{bmatrix} = \begin{bmatrix} h_{11} & h_{12} \ h_{21} & h_{22} \end{bmatrix} \begin{bmatrix} I_1 \ V_2 \end{bmatrix}

Rendered:

$$\begin{bmatrix} V_1 \\ I_2 \end{bmatrix} = \begin{bmatrix} h_{11} & h_{12} \\ h_{21} & h_{22} \end{bmatrix} \begin{bmatrix} I_1 \\ V_2 \end{bmatrix}$$

10

Raw LaTeX:
L(\lambda, \alpha, s) = \sum_{n=0}^{\infty} \frac{\exp(2\pi i\lambda n)}{(n+\alpha)^s}.

Rendered:

$$L(\lambda, \alpha, s) = \sum_{n=0}^{\infty} \frac{\exp(2\pi i\lambda n)}{(n+\alpha)^s}.$$

11

Raw LaTeX:
ax^{2} + bx + c = 0

Rendered:

$$ax^{2} + bx + c = 0$$

12

Raw LaTeX:
O(mn \log m)

Rendered:

$$O(mn \log m)$$

13

Raw LaTeX:
A \oplus B = (A^c \ominus B^s)^c

Rendered:

$$A \oplus B = (A^c \ominus B^s)^c$$

14

Raw LaTeX:
\cos \alpha = -\cos \beta \cos \gamma + \sin \beta \sin \gamma \cosh \frac{a}{k},

Rendered:

$$\cos \alpha = -\cos \beta \cos \gamma + \sin \beta \sin \gamma \cosh \frac{a}{k}$$

15

Raw LaTeX:
\forall x, y \in A \ [x \neq y \rightarrow \neg \exists z \in X \ [z \leq x \wedge z \leq y]]

Rendered:

$$\forall x, y \in A \ [x \neq y \rightarrow \neg \exists z \in X \ [z \leq x \wedge z \leq y]]$$

16

Raw LaTeX:
\tau_{\text{rms}} = \sqrt{\frac{\int_{0}^{\infty} (\tau - \bar{\tau})^{2} A_c(\tau), d\tau}{\int_{0}^{\infty} A_c(\tau), d\tau}}

Rendered:

$$\tau_{\text{rms}} = \sqrt{\frac{\int_{0}^{\infty} (\tau - \bar{\tau})^{2} A_c(\tau)\, d\tau}{\int_{0}^{\infty} A_c(\tau)\, d\tau}}$$

17

Raw LaTeX:
x - 1 - \frac{1}{2} - \frac{1}{4} - \frac{1}{5} - \frac{1}{6} - \frac{1}{9} - \cdots = 1

Rendered:

$$x - 1 - \frac{1}{2} - \frac{1}{4} - \frac{1}{5} - \frac{1}{6} - \frac{1}{9} - \cdots = 1$$

18

Raw LaTeX:
P(x_{i}) = \frac{N!}{n_{x}!(N-n_{x})!} p^{n_{x}}{x} (1-p{x})^{N-n_{x}}

Rendered:

$$P(x_{i}) = \frac{N!}{n_{x}!(N-n_{x})!} p^{n_{x}}_{x} (1-p_{x})^{N-n_{x}}$$

19

Raw LaTeX:
H_{ij} = \begin{bmatrix} \frac{\partial^{2}V_{ij}}{\partial x_{i}\partial x_{j}} & \frac{\partial^{2}V_{ij}}{\partial x_{i}\partial y_{j}} & \frac{\partial^{2}V_{ij}}{\partial x_{i}\partial z_{j}} \ \frac{\partial^{2}V_{ij}}{\partial y_{i}\partial x_{j}} & \frac{\partial^{2}V_{ij}}{\partial y_{i}\partial y_{j}} & \frac{\partial^{2}V_{ij}}{\partial y_{i}\partial z_{j}} \ \frac{\partial^{2}V_{ij}}{\partial z_{i}\partial x_{j}} & \frac{\partial^{2}V_{ij}}{\partial z_{i}\partial y_{j}} & \frac{\partial^{2}V_{ij}}{\partial z_{i}\partial z_{j}} \end{bmatrix}

Rendered:

$$H_{ij} = \begin{bmatrix} \frac{\partial^{2}V_{ij}}{\partial x_{i}\partial x_{j}} & \frac{\partial^{2}V_{ij}}{\partial x_{i}\partial y_{j}} & \frac{\partial^{2}V_{ij}}{\partial x_{i}\partial z_{j}} \\ \frac{\partial^{2}V_{ij}}{\partial y_{i}\partial x_{j}} & \frac{\partial^{2}V_{ij}}{\partial y_{i}\partial y_{j}} & \frac{\partial^{2}V_{ij}}{\partial y_{i}\partial z_{j}} \\ \frac{\partial^{2}V_{ij}}{\partial z_{i}\partial x_{j}} & \frac{\partial^{2}V_{ij}}{\partial z_{i}\partial y_{j}} & \frac{\partial^{2}V_{ij}}{\partial z_{i}\partial z_{j}} \end{bmatrix}$$

20

Raw LaTeX:
r_{xy} = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{(n-1) s_x s_y} = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i - \bar{x})^2 \sum_{i=1}^{n} (y_i - \bar{y})^2}},

Rendered:

$$r_{xy} = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{(n-1) s_x s_y} = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i - \bar{x})^2 \sum_{i=1}^{n} (y_i - \bar{y})^2}}$$

🚀 How It Works

Clustering & Indexing

  1. Extract MathML/LaTeX from HTML documents.
  2. Convert to binary bit-vector representation.
  3. Apply MiniBatchKMeans clustering with Hamming distance.
  4. Store cluster indices for fast lookup.

Searching

  1. User submits query (LaTeX or plain text).
  2. Query is processed into a bit-vector.
  3. Nearest clusters are found.
  4. Retrieve and rank top results.

🛠 Setup

Frontend

cd frontend
flutter run -d chrome   # For Web
dart pub get            # Install dependencies
flutter run -d emulator-5554  # For Android

Backend

cd backend
pip install -r requirements.txt
uvicorn main:app --reload

Runs at http://127.0.0.1:8000

📡 API Endpoints

POST /search

{
  "query": "\\frac{a}{b} + c^2"
}

Response:

{ "session_id" : "6bcf8ceb-0a51-416b-b52c-78eac5c955c9",
  "time_taken_in_second": 0.25,
  "results": [
    { "id": "1", "filename": "doc1.html" },
    { "id": "2", "filename": "doc2.html" }
  ]
}

GET /view/6bcf8ceb-0a51-416b-b52c-78eac5c955c9/2'

Returns HTML content with MathML.

📜 License & Usage

Author: Ankit Kumar, Chirag Sarda, Vishal Gaur, Rajan Kumar Singh Email: ankit.kumar@aus.ac.in, chiragsarda12@gmail.com, er.vishalgour@gmail.com.

This repository is for demonstration purposes only.

You may:

  • ✅ View the code
  • ✅ Access the demo

You may not:

  • ❌ Copy, clone, or reuse the code
  • ❌ Modify or distribute any part of this project

Violations will be prosecuted under copyright law.

🎯 Designed for cross-platform simplicity and full MathML compatibility.