DEPENDENCY-ORDERED AI ENGINEERING GENOME (First-Principles Architecture for Training Top 1% AI Engineers)
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STAGE 0 — COGNITIVE INFRASTRUCTURE (NON-NEGOTIABLE)
0.1 Mathematical Thinking
- Logic fundamentals
- Proof techniques
- induction
- contradiction
- construction
- Functions as mappings
- Sets and relations
Unlocks: linear algebra rigor, probability clarity, learning theory.
0.2 Algorithmic Reasoning
- Time complexity
- Space complexity
- Recursion
- Divide and conquer
- Randomized thinking
Unlocks: optimization intuition, scalable ML thinking.
0.3 Data Structures for Computational Modeling
- Arrays vs linked memory
- Hash tables
- Trees
- Heaps
- Graphs
- Directed acyclic graphs (DAGs)
Unlocks: computational graphs, autodiff, neural network frameworks.
0.4 Numerical Literacy
- Floating point representation
- Precision loss
- Overflow / underflow
- Conditioning
- Numerical stability
Unlocks: safe optimization and large-scale training understanding.
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STAGE 1 — GEOMETRIC INTELLIGENCE (LINEAR ALGEBRA FIRST)
1.1 Vectors as Objects in Space
- Norms
- Distance
- Angles
- Dot product
Unlocks: similarity, embeddings, attention.
1.2 Vector Spaces
- Span
- Basis
- Linear independence
- Dimension
Unlocks: feature spaces, kernel intuition.
1.3 Linear Transformations
- Matrices as operators
- Kernel
- Image
- Rank
Unlocks: projections, least squares.
1.4 Orthogonality and Projection
- Orthogonal bases
- Gram–Schmidt process
- Projection matrices
Unlocks: regression geometry, PCA.
1.5 Spectral Thinking
- Eigenvalues
- Eigenvectors
- Diagonalization
Unlocks: covariance structure, latent spaces.
1.6 Singular Value Decomposition (SVD)
- Low-rank approximation
- Compression
- Noise filtering
Unlocks: recommender systems, embeddings.
1.7 Positive Definite Matrices
- Quadratic forms
- Mahalanobis distance
Unlocks: Gaussian geometry.
1.8 Numerical Linear Algebra
- QR decomposition
- Power iteration
- Stability analysis
Unlocks: large-model training intuition.
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STAGE 2 — MOTION AND SENSITIVITY (CALCULUS)
2.1 Derivatives as Sensitivity
- Rates of change
- Local linearity
2.2 Multivariable Calculus
- Gradients
- Jacobian
- Hessian
Unlocks: backpropagation.
2.3 Chain Rule Mastery Required before neural networks.
2.4 Taylor Expansion Unlocks: why gradient descent works.
2.5 Constrained Optimization
- Lagrange multipliers
- KKT conditions (intuition)
Unlocks: Support Vector Machines.
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STAGE 3 — MODELING UNCERTAINTY (PROBABILITY)
3.1 Probability Foundations
- Axioms
- Conditional probability
- Independence
3.2 Random Variables
- Discrete vs continuous
- PMF / PDF / CDF
3.3 Expectation Framework
- Expectation
- Variance
- Covariance
- Correlation
Unlocks: noise modeling.
3.4 Major Distributions
- Gaussian
- Bernoulli
- Binomial
- Poisson
- Exponential
- Beta
- Dirichlet
Unlocks: generative modeling.
3.5 Law of Large Numbers
3.6 Central Limit Theorem
Unlocks: statistical learning validity.
3.7 Bayesian Thinking
- Prior
- Likelihood
- Posterior
Unlocks: MAP, EM, VAEs.
CRITICAL NODE — Multivariate Gaussian Requires covariance + eigenvectors. Unlocks a large portion of modern ML.
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STAGE 4 — STATISTICAL INFERENCE
4.1 Estimators
- Bias
- Variance
- Consistency
4.2 Maximum Likelihood Estimation
4.3 Maximum A Posteriori Estimation
4.4 Overfitting vs Underfitting Unlocks regularization.
4.5 Cross Validation
4.6 Bootstrap
4.7 Information Theory
- Entropy
- KL divergence
- Cross entropy
- Mutual information
Unlocks: loss functions, VAEs, diffusion.
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STAGE 5 — OPTIMIZATION FOR LEARNING
5.1 Convex Sets and Functions
5.2 Gradient Descent
5.3 Stochastic Gradient Descent
5.4 Momentum
5.5 Adaptive Methods (Adam, RMSProp)
Derive at least once.
5.6 Training Pathologies
- Exploding gradients
- Vanishing gradients
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STAGE 6 — LEARNING THEORY
6.1 Empirical Risk vs True Risk
6.2 Bias–Variance Decomposition
6.3 Model Capacity
6.4 Regularization
Optional but recommended:
- VC dimension (intuition)
Unlocks: model judgment.
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STAGE 7 — CLASSICAL MACHINE LEARNING
(Cover in this exact order.)
7.1 Linear Regression
Requires projections + Gaussian assumptions.
7.2 Logistic Regression
Requires probability + MLE.
7.3 Generative vs Discriminative Models
7.4 k-Nearest Neighbors
7.5 Decision Trees
7.6 Ensemble Methods
- Bagging
- Random Forests
- Boosting
7.7 Support Vector Machines
Requires convex optimization + geometry.
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STAGE 8 — UNSUPERVISED LEARNING
Distance metrics
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k-means
↓
Gaussian Mixture Models
↓
Expectation Maximization
PCA (Revisited Deeply) Covariance + eigenvectors integration.
Independent Component Analysis
Manifold intuition
Unlocks representation learning.
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STAGE 9 — NEURAL NETWORK FOUNDATIONS
9.1 Perceptron
9.2 Universal Approximation
9.3 Backpropagation
Requires chain rule + computational graphs.
9.4 Initialization
Requires variance intuition.
9.5 Regularization
- Dropout
- Weight decay
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STAGE 10 — REPRESENTATION LEARNING
- Autoencoders
- Latent spaces
- Manifold hypothesis
Unlocks generative models.
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STAGE 11 — SPATIAL INTELLIGENCE (CNN)
- Convolution as linear operator
- Receptive fields
- Feature hierarchies
Provides spatial grounding before transformers.
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STAGE 12 — SEQUENTIAL MODELING
- Recurrent Neural Networks
- LSTM
- GRU
Cover architectural evolution.
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STAGE 13 — ATTENTION
Requires:
- Dot products
- Similarity
- Scaling
- Softmax
Critical cognitive leap.
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STAGE 14 — TRANSFORMERS
- Self-attention
- Multi-head attention
- Positional encoding
- Encoder-decoder architecture
Signal of mastery: ability to critique architectures.
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STAGE 15 — MODERN GENERATIVE MODELING
Cover historically:
Autoregressive Models
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Variational Autoencoders
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GANs
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Diffusion Models
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Large Language Models
Builds research cognition.
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STAGE 16 — REINFORCEMENT LEARNING
Requires probability + expectation + optimization.
Markov Decision Processes
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Value Functions
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Bellman Equations
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Q-Learning
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Policy Gradients
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Actor–Critic Methods
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STAGE 17 — ML SYSTEMS (TOP 1% DIFFERENTIATOR)
Cover after you experience slow training.
- GPU architecture
- Batching
- Mixed precision
- Distributed training
- Inference optimization
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FINAL STAGE — RESEARCH COGNITION
- Reading research papers
- Reproducing results
- Designing experiments
- Scientific writing
Identity transformation: Engineer → Scientist.
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CRITICAL NODES TO PROTECT (NEVER RUSH)
- Linear Algebra
- Probability
- Optimization
- Backpropagation
- Attention
These are cognitive mutation points.
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END OF GENOME
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