A researcher/engineer exploring the theoretical, mathematical, and infrastructural foundations of modern AI and Machine Learning by building them from scratch (pure NumPy, PyTorch & JAX). No high-level libraries; just pure math, algorithmic depth, and high-performance computing.
Repositories are ordered as a learning path: Foundations → Machine Learning → Deep Learning & Frontier AI → Domains & Infrastructure.
🇹🇷 links point to the Turkish edition of the same course.
| Repository | Focus | 🇹🇷 |
|---|---|---|
| calculus_for_ai | ε–δ limits, complex-step differentiation, forward/reverse-mode autodiff, matrix calculus, calculus of variations — pure NumPy | TR |
| linear_algebra_for_ml | Geometric intuition, LU/QR decomposition, stable SVD, PCA from scratch | TR |
| probability | Probability theory with Python implementations and visualizations | TR |
| statistics | Statistical theory with Python implementations and visualizations | TR |
| discrete_mathematics | Propositional logic, set theory, combinatorics, graph & number theory, computational verification of theorems | TR |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| numerical_methods | Numerical analysis fundamentals with Python implementations | TR |
| numerical_methods_for_ml | Machine epsilon, Chebyshev interpolation, adaptive Gaussian quadrature, stiff ODE simulators | · |
| differential_equations | ODEs & PDEs from first principles to modern ML applications — 8-week course | TR |
| differential_equations_for_ai | Neural ODEs, PINNs, diffusion models, optimal control in NumPy + JAX | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| ai_optimization_algorithms | The deep learning optimizer family: SGD, Momentum, Nesterov, AdaGrad, RMSProp, Adam, AdamW, L-BFGS | TR |
| optimization_methods | KKT duality, proximal methods & ADMM, second-order and modern optimizers (K-FAC, Shampoo, Muon) | · |
| metaheuristic_optimization | SA, Tabu, GA, PSO, ACO, DE & CMA-ES; No Free Lunch, fitness landscapes, NSGA-II/MOEA-D, rigorous benchmarking | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| advanced_machine_learning | Statistical learning theory, kernel methods, regularization & sparsity, gradient boosting, conformal prediction | TR |
| data_mining | Classification (KNN → ensembles), imbalanced data, association analysis (Apriori, FP-Growth), clustering & anomaly detection | TR |
| prod_grade_tab_ml | Custom GBDT boosters; inner mechanics of XGBoost, LightGBM, and CatBoost | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| bayesian_machine_learning | Laplace approximation, from-scratch MCMC (HMC/NUTS), Variational Inference (ELBO, flows), Sparse GPs, Bayesian NNs | · |
| causal_inference_for_ai | d-separation oracles, propensity score IRLS, doubly-robust AIPW, Cross-Fitting DML, causal forests | · |
| time_series_analysis | Spectral analysis, ARCH/GARCH, multivariate VAR, state-space models with Kalman filters | TR |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| deep_learning | Deep learning foundations: backprop, loss functions, CNNs, Transformers, GANs, training dynamics | TR |
| advanced_deep_learning | Advanced topics: self-supervised learning, transfer learning, deep RL | TR |
| geometric_deep_learning | Manifolds, equivariance, symmetry groups, Riemannian geometry | · |
| graph_neural_networks | Spectral graph theory, graph Laplacian, over-smoothing, raw GCN/GAT/GIN implementations | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| generative_artificial_intelligence | From statistical theory to deep generative models: VAE, GAN, Diffusion, Mini-GPT with RoPE | TR |
| nlp_course | The full NLP stack: tokenization → PEFT/LoRA → DPO/RLHF alignment → production RAG | · |
| advanced_llm_architecture | Next-gen LLM components: quantization, TTT layers, differentiable logic, FlashAttention tiling, context extension | · |
| autonomous_ai_agents | Enterprise AI agents & advanced RAG: MCP architecture, hierarchical indexing, ReAct loops, multi-agent state | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| decision_theory | vNM utility & risk, Bayesian decision rules, value of information, MDPs/POMDPs & bandits, game theory & CFR, prospect theory, RLHF/DPO | · |
| reinforcement_learning | MDP foundations → TD(λ), Q-Learning, Policy Gradients (REINFORCE, Actor-Critic) | TR |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| mechanistic_interpretability | Reverse-engineering network internals: linear representations, superposition, SAEs, induction heads, causal scrubbing | · |
| data_vis_for_ai_research | High-dimensional embeddings (UMAP), model diagnostics, experiment tracking, XAI (SHAP, LIME, Grad-CAM) | · |
| tensorlens | Visualizing modern LLM mechanics, loss landscapes & HPC topologies | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| computer_vision | No OpenCV, no PyTorch: convolutions, Canny, Harris corners, Lucas–Kanade optical flow, CNN layers with full backward pass | TR |
| adv_pde_based_image_processing | PDE-based image processing: heat equation → Finsler/Randers/Miron metric flows, Numba/CUDA acceleration | · |
| A-Novel-Family-of-Edge-Preserving-Anisotropic-Filters | 📄 Research code — edge-preserving anisotropic filters via Finsler geometry & the Polyakov action | · |
| Riemannian-Curve-Evolution | 📄 Research code — Riemannian curve model analysis applied to image segmentation | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| distributed_systems_for_ml | Ring All-Reduce, parameter servers, 1F1B pipeline parallelism, ZeRO/FSDP sharding — from scratch | · |
| high_performance_computing | Systems engineering for training frontier-scale models | · |
| hpc_ai_infra_llmops | AI infrastructure & LLMOps: fine-tuning and serving frontier-scale LLMs | · |
| mlops_and_deployment | Experiment trackers, containerized model registries, dynamic-batching inference servers, LLM serving | · |
| Repository | Focus | 🇹🇷 |
|---|---|---|
| quantum_artificial_intelligence | Qubits & gates, entanglement & CHSH, Deutsch–Jozsa/Grover/QFT, VQE, quantum classifiers & kernels — NumPy → PennyLane | · |
- Languages: Python, C++, CUDA
- Math & Core ML: Pure NumPy, JAX, PyTorch, PennyLane, Numba
- Systems & Operations: Distributed Training, HPC Topologies, MLOps, Triton/LLM Serving Infra
- LinkedIn: https://linkedin.com/in/haydarkilicai
- Email: haydarkilicinfo@gmail.com