Linear Algebra for High-Dimensional Spaces
Vector spaces, linear mappings, dot products as geometric similarity, eigenvalues, and Singular Value Decomposition (SVD) underlying modern embeddings.
Artificial Intelligence Academy & Research Hub
XBI, AI Education and Applied Engineering Guides
A multi-page curriculum from first-principles linear algebra, multivariable optimization, and backpropagation to frontier transformer architectures, autonomous agent loops, and enterprise workflow playbooks.
23 Modules
Crawlable Guides
Levels 100–600
Academic Tiers
Applied Track
Work, Business & Code
Zero Fabrication
Tested Derivations
Multivariable Calculus & Gradient Optimization
Deriving partial derivatives, gradients, the Jacobian, and Hessian matrices. Visualizing high-dimensional loss landscapes and building gradient descent solvers.
Probability, Distributions & Information Theory
Conditional probability, Bayes' theorem, maximum likelihood estimation (MLE), Shannon entropy, cross-entropy, and Kullback-Leibler (KL) divergence.
Supervised Regression, Classification & Regularization
Ordinary Least Squares (OLS), L1 Lasso and L2 Ridge penalties, logistic odds ratios, and Newton-Raphson numerical solvers.
Generalization Theory & Statistical Validation
The mathematical bias-variance decomposition, cross-validation architectures, hyperparameter tuning, and ROC-AUC curves.
Tree Ensembles & Non-Parametric Models
Information gain, Gini impurity, CART decision trees, Random Forest bagging mechanics, Gradient Boosted Decision Trees (XGBoost), and Kernel SVMs.
The Multilayer Perceptron & Backpropagation
Matrix calculus derivations of backward gradient flow and writing a fully functional neural network in 100 lines of raw Python without PyTorch.
Activation Dynamics & Modern Optimizers
Vanishing/exploding gradients, ReLU vs. GELU vs. SwiGLU gating, momentum, RMSprop, Adam, and AdamW decoupled weight decay mechanics.
Convolutional Networks & Spatial Inductive Biases
Discrete 2D convolutions, receptive fields, pooling layers, residual connections (ResNet), and translation equivariance in computer vision.
The Self-Attention Mechanism Derived
Scaled dot-product attention formulated as content-based associative retrieval in embedding space, temperature scaling, and causal masking.
The Complete Modern Transformer Architecture
Multi-Head Attention (MHA), Grouped-Query Attention (GQA), Rotary Position Embeddings (RoPE), RMSNorm, and pre-layer normalization.
Tokenization & Pretraining Dynamics
Byte-Pair Encoding (BPE), vocabulary compression, token boundary effects, loss curves, compute budgets, and Chinchilla scaling laws.
Supervised Fine-Tuning & Parameter-Efficient LoRA
Full parameter adaptation vs. Low-Rank Adaptation (LoRA), 4-bit NormalFloat quantization (QLoRA), and rank selection algebra.
Preference Alignment: RLHF & Direct Preference Optimization
PPO reinforcement learning from human feedback, Bradley-Terry preference models, Direct Preference Optimization (DPO) derivations.
Test-Time Compute Scaling & Reasoning Models
Inference-time compute frontiers, Tree-of-Thought search, Monte Carlo planning, Process Reward Models (PRMs), and self-correction verification.
Autonomous Agents & Model Context Protocol (MCP)
ReAct execution loops, Model Context Protocol (MCP) standardized transport, tool sandboxing, and deterministic state verification.
Distributed Training Clusters & Hardware Topologies
Distributed Data Parallel (DDP), Fully Sharded Data Parallel (FSDP), Megatron-LM tensor and pipeline parallelism, and InfiniBand interconnects.
The Daily Knowledge-Worker AI Stack
The battle-tested daily operating system for triaging inboxes, drafting high-stakes memos, synthesizing 100-page regulatory PDFs, and accelerating desk output.
Prompting as Structured Thinking
Transition from open-ended chat prompts to deterministic system instructions: Context, Role, Constraints, Few-Shot Demonstrations, and Strict JSON Output Schemas.
Enterprise Support Automation without Hallucinations
Deploying retrieval-augmented generation (RAG) customer support systems with strict fail-closed verification rules so assistants answer strictly from verified documentation.
Personal Document Intelligence with NotebookLM
Grounding personal AI assistants on tax forms, healthcare records, lease agreements, and family schedules to answer complex life questions with verifiable citations.
The Socratic AI Study Partner for Accelerated Learning
Configuring language models as rigorous Socratic tutors that force active recall, pinpoint conceptual misconceptions, and drill complex STEM derivations.
From Plain English to Deployed Web Application
The complete software engineering workflow for solo founders and engineers using Cursor, Claude, and modern deployment pipelines to ship full applications in hours.