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AI Core Research (Zero to Hero in AI Mathematics,Coding & Framework Building)

This module builds deep foundational and advanced expertise in AI through rigorous study of mathematics, coding, and research-driven framework development. It takes learners from theoretical underpinnings to hands-on implementation, reproducible experimentation, and final research paper dissemination—equipping them to become independent AI researchers.

Day 1-15: Foundational Mathematics & AI Fundamentals​

Topics Covered​

  • Mathematical Foundations:
    • Linear algebra (matrix operations, eigenvalues/eigenvectors), calculus (differentiation, integration), probability, and statistics.
  • Coding Exercises:
    • Implementing basic linear algebra routines and probability simulations using NumPy and pandas.

Hands‐on Tasks​

  • Solve mathematical problems and document solutions in Jupyter Notebooks.
  • Write Python scripts to demonstrate matrix operations and gradient calculations.

Deliverables​

  • A summary report on foundational mathematics for AI.
  • Annotated coding notebooks and a public GitHub repository with initial exercises.

Day 16-30: Advanced Mathematics for AI​

Topics Covered​

  • Optimization Techniques:
    • Gradient descent variants (SGD, Adam, RMSProp), convex optimization, and duality theory.
  • Theoretical Derivations:
    • Detailed proofs of update rules and convergence analyses.

Hands‐on Tasks​

  • Implement optimization algorithms from scratch and compare with library implementations.
  • Derive and document convergence proofs in a LaTeX document.

Deliverables​

  • A detailed research document with mathematical proofs and Python notebooks.
  • A public blog post tutorial with code demonstrations.

Day 31–45: Theoretical Frameworks in Machine Learning​

Topics Covered​

  • Statistical Learning Theory:
    • Bias‐variance trade‐off, VC-dimension, and overfitting/underfitting.
  • Kernel Methods & SVMs:
    • Detailed exploration of support vector machines and decision boundaries.

Hands‐on Tasks​

  • Implement SVMs and kernel methods using scikit‐learn and custom code.
  • Analyze bias‐variance trade‐offs with experiments.

Deliverables​

  • A draft research paper with detailed mathematical derivations.
  • Code demonstrations and a public GitHub repository containing experiments.

Day 46–60: Deep Learning Theory​

Topics Covered​

  • Neural Networks:
    • Architecture design, backpropagation, activation functions, and convergence analysis.
  • Challenges:
    • Addressing vanishing/exploding gradients and analyzing CNNs, RNNs, and transformers.

Hands‐on Tasks​

  • Develop sample neural networks in TensorFlow and PyTorch.
  • Visualize gradient flows and convergence curves.

Deliverables​

  • A comprehensive whitepaper and research report with mathematical derivations.
  • Sample code implementations and visualizations hosted in a public repository.

Day 61–75: Advanced Topics in AI Research​

Topics Covered​

  • Generative Models:
    • In-depth study of Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs).
  • Challenges:
    • Loss functions, regularization, and mode collapse in GANs.

Hands‐on Tasks​

  • Implement a simple VAE and GAN, analyze training stability, and experiment with loss adjustments.

Deliverables​

  • A detailed research report and public blog tutorial with complete code examples.
  • Presentation slides summarizing theoretical insights and experimental findings.

Day 76–90: Framework Building & Modular Code Architecture​

Topics Covered​

  • Custom AI Frameworks:
    • Designing modular, reusable code architectures for research experiments.
  • Best Practices:
    • Dependency injection, design patterns, and extensibility.

Hands‐on Tasks​

  • Architect and implement a custom AI research framework with clearly defined modules.
  • Document the code structure and contribution guidelines.

Deliverables​

  • An initial code structure for the custom AI framework on GitHub.
  • A detailed design document (with Draw.io diagrams) and public documentation.

Day 91–105: Experimentation & Reproducibility​

Topics Covered​

  • Reproducible Research:
    • Best practices for experiment tracking, version control, and environment management.
  • Tools:
    • Docker and DVC for data versioning and experiment reproducibility.

Hands‐on Tasks​

  • Create reproducible experiment scripts and integrate them with version control.
  • Document the experiment process and challenges in a blog post.

Deliverables​

  • A public GitHub repository with reproducible experiment code.
  • A research report on best practices for reproducibility and a detailed blog tutorial.

Day 106–120: Performance Evaluation & Benchmarking​

Topics Covered​

  • Evaluation Metrics:
    • Standard metrics (accuracy, F1 score, precision, recall) and task‐specific measures.
  • Benchmarking Pipelines:
    • Automating evaluations and comparing models using standard datasets.

Hands‐on Tasks​

  • Develop evaluation pipelines and benchmark several AI models.
  • Analyze and visualize performance data.

Deliverables​

  • A comprehensive benchmarking report with integrated code and charts.
  • A public blog tutorial on setting up evaluation pipelines, with code examples.

Day 121–135: Scalability in AI Research​

Topics Covered​

  • High‐Performance Computing:
    • Parallel processing, GPU/TPU utilization, and distributed training frameworks (e.g., Horovod, PyTorch DDP).
  • Challenges:
    • Scaling experiments and managing resource allocation.

Hands‐on Tasks​

  • Set up distributed training experiments and document performance improvements.
  • Create architecture diagrams to illustrate distributed setups.

Deliverables​

  • A research report on scalability strategies with supporting code examples.
  • Detailed architecture diagrams (Draw.io) and a public GitHub repository.

Day 136–150: Peer Review & Collaborative Research​

Topics Covered​

  • Academic Writing:
    • Structuring research papers, best practices in drafting and revising.
  • Peer Review Processes:
    • Conducting internal peer reviews and simulating conference reviews.

Hands‐on Tasks​

  • Draft a research paper and organize peer review sessions.
  • Incorporate feedback into iterative improvements.

Deliverables​

  • A draft research paper with accompanying presentation slides.
  • Internal peer review reports and a public blog post describing the process.

Day 151–165: Exploration of Novel AI Algorithms​

Topics Covered​

  • Innovation in AI:
    • Identifying gaps in current literature and proposing new approaches.
  • Proof‐of‐Concept:
    • Designing experiments to test emerging algorithms or architectures.

Hands‐on Tasks​

  • Develop a detailed research proposal including methodology, experiments, and expected outcomes.
  • Prototype a novel algorithm or architecture and document initial results.

Deliverables​

  • A detailed research proposal document with methodology and preliminary experimental results.
  • A public GitHub repository with prototype code and detailed documentation.

Day 166–180: Finalization & Dissemination​

Topics Covered​

  • Final Revisions:
    • Polishing the research paper, finalizing experiments, and preparing for dissemination.
  • Outreach:
    • Organizing internal symposiums or webinars and preparing conference submissions.

Hands‐on Tasks​

  • Finalize the research paper and presentation materials.
  • Develop a dissemination plan including future work.

Deliverables​

  • A final research paper ready for submission, along with conference presentation slides.
  • A public blog post summarizing the research journey, comprehensive documentation, and a roadmap for future work.

Tech Stack​

  • Languages & Tools:
    • Python, Julia, MATLAB
  • Mathematical Libraries:
    • NumPy, SciPy, Sympy
  • Deep Learning Frameworks:
    • TensorFlow, PyTorch
  • Development & Documentation:
    • Jupyter Notebooks, LaTeX, Git, Overleaf
  • Visualization:
    • Matplotlib, Seaborn
  • Reproducibility & Containerization:
    • Docker, CI/CD tools (GitHub Actions)