A dedicated, non-diluted curriculum connecting core mathematical foundations to production deep learning, modern LLMs, retrieval pipelines, autonomous multi-agent systems, and enterprise LLMOps.
The non-negotiable mathematical bedrock of modern AI. Learn to think in high-dimensional vector spaces, compute multivariate gradients by hand, model uncertainty with Bayesian inference, and build a pure Python scalar autograd engine.
Dot products, projections, matrix transformations, eigenvalues/eigenvectors, and Singular Value Decomposition (SVD).
Partial derivatives, gradient vectors, Jacobians, Hessians, and Gradient Descent optimization variants.
Bayes' theorem, MLE, MAP, Gaussian distributions, Shannon Entropy, Cross-Entropy, and KL Divergence.
Writing pure NumPy matrix pipelines and a complete scratch scalar autograd engine inspired by micrograd.
Bridge pure math into live software. Master Scikit-Learn data pipelines without data leakage, Gradient Boosted Decision Trees (XGBoost), PyTorch from scratch, backpropagation, AdamW, Deep Residual Networks (ResNets), and the mathematics of Self-Attention.
Bias-variance tradeoff, leakage prevention, PR-AUC evaluation, and 2nd-order Taylor boosting in XGBoost & LightGBM.
Multi-Layer Perceptrons, activation functions (GELU, ReLU, Softmax), exact vector calculus backprop, and Kaiming initialization.
2D convolutions, receptive fields, stride/padding formulas, and solving degradation with ResNet identity skip connections.
Word2Vec, Byte-Pair Encoding (BPE), LSTM gates, and Vaswani et al.'s Scaled Dot-Product Attention: softmax(QK^T / √d_k)V.
Deconstruct how modern billion-parameter LLMs (GPT, Llama, Gemini) are architected, pre-trained on internet-scale tokens, and aligned. Master Multi-Head Attention, RoPE positional encodings, LoRA parameter-efficient fine-tuning, and RLHF/DPO.
Causal masking, Rotary Position Embeddings (RoPE), SwiGLU activations, RMSNorm, and KV Cache mechanics.
Next-token prediction, cross-entropy scaling laws, data deduplication, synthetic data filtering, and perplexity.
Supervised instruction tuning, low-rank adapter decomposition ($W = W_0 + B A$), 4-bit NormalFloat quantization.
Reward modeling, PPO policy optimization, and Direct Preference Optimization (DPO) eliminating reward models.
Eliminate LLM hallucinations by connecting models to private enterprise knowledge bases. Master advanced chunking, dense semantic embeddings, hybrid vector search (BM25 + HNSW), cross-encoder reranking, and automated Ragas evaluation.
Layout-aware PDF parsing (OCR, tables), recursive chunking, semantic splitters, and metadata tagging.
Dense bi-encoders (text-embedding-3, nomic), Matryoshka embeddings (MRL), HNSW graphs, and IVFFlat inverted files.
Reciprocal Rank Fusion (RRF) combining dense cosine similarity with sparse BM25; 2nd-stage cross-encoder scoring.
Hypothetical Document Embeddings (HyDE), Multi-Query decomposition, Self-RAG, and automated Faithfulness metrics.
Shift from passive text generators to active reasoning engines. Master ReAct loops, deterministic schema function calling, Model Context Protocol (MCP) tool integration, stateful graph workflows (LangGraph), and multi-agent coordination.
Pydantic strict JSON schema enforcement, function calling protocols, parameter coercion, and error recovery.
Thought → Action → Observation cycles, Plan-and-Solve decomposition, Self-Refine loops, and Tree-of-Thoughts.
Building Anthropic MCP servers, exposing secure tools, resources, and prompts over standard JSON-RPC transport.
Deterministic state transitions in LangGraph, episodic memory, human-in-the-loop approvals, and multi-agent debate.
Operating models in high-scale production. Master high-throughput inference engines (vLLM, TensorRT-LLM), continuous batching, PagedAttention, quantization (AWQ, FP8), LLM observability (LangSmith, Phoenix), cost governance, and prompt injection security.
Continuous batching, chunked prefill, virtual memory PagedAttention, speculative decoding, and tensor parallelism.
Post-Training Quantization (PTQ), AWQ, GPTQ, FP8 inference, and hardware-accelerated kernels.
Direct & indirect prompt injection defenses, NeMo Guardrails, Llama Guard, PII redaction, and output schema filters.
Distributed OpenTelemetry tracing, latency profiling (TTFT, ITL), semantic caching, cost routing, and automated CI evals.
How each stage builds mathematically and practically on the previous tier.
| Stage | Focus Domain | Pacing | Core Stack & Tools | Primary Deliverable | Status |
|---|---|---|---|---|---|
| Stage 01 | AI Foundations & Applied Math | Weeks 1–4 | Python, NumPy, Calculus, Linear Algebra | Autograd Engine & Gradient Descent | Live Course → |
| Stage 02 | Machine Learning & Deep Learning | Weeks 5–8 | Scikit-Learn, PyTorch, XGBoost, Torchvision | Deep ResNet Classifier & Attention Layer | Live Course → |
| Stage 03 | GenAI, LLMs & Transformers | Weeks 9–12 | Transformers, HuggingFace, PEFT, TRL, LoRA | Domain QLoRA Fine-Tuned 8B Model | Next Course |
| Stage 04 | Production RAG & Vector Databases | Weeks 13–16 | Qdrant, Chroma, LlamaIndex, BM25, Ragas | Enterprise Financial Hybrid RAG Engine | Planned |
| Stage 05 | Autonomous Agents & MCP | Weeks 17–20 | Model Context Protocol (MCP), LangGraph, Pydantic | Autonomous Tool-Using Coding Agent | Planned |
| Stage 06 | Enterprise LLMOps & Serving | Weeks 21–24 | vLLM, Triton, Docker, OpenTelemetry, AWQ | Production High-Throughput Serving Cluster | Planned |