Feynman Lectures on LLM Adaptation

A series of private 1-on-1 tutoring sessions in the style of Richard Feynman, covering how large language models adapt their behavior — from prompting to fine-tuning to cutting-edge parameter-efficient methods, composable AI review systems, cryptographic protocols, and the statistical foundations of machine learning.

Teaching Approach

• First-principles reasoning with vivid, mechanism-based analogies
• One concept at a time, with conceptual questions to verify understanding
• Socratic method: wrong answers are met with new analogies, not corrections
• Analogies adjusted to the student's learning style (mechanical/engineering-oriented)

Shared Vocabulary (Analogies Used Throughout)

Analogy	Concept
The Sculpture	Pre-trained model weights — carved during training, frozen afterward
The Stone	Parametric memory (weights) — permanent knowledge
The Water	Contextual memory (prompts) — temporary, flows through the sculpture
The Chisel	Training / gradient descent — reshapes the stone
The Ballroom Musician	The model's ability to read context and adapt output
The Piano	Pre-trained model; tuning = fine-tuning specific strings
The Bottleneck	LoRA's low-rank constraint — compressing adaptation through r dimensions
The Attachment	LoRA adapter — bolted onto the sculpture, removable
The TV Signal	Pre-trained weights as a complex broadcast; fine-tuning correction as a few knobs
The Dart Board	Bias-variance tradeoff — cluster center (bias) vs spread (variance) vs shaking wall (noise)
Eigenvectors / PCA	Orthogonal adapter training — decomposing useful adaptation into independent components
The Diagonal Bug	Interaction effects invisible to orthogonal specialists looking along single axes
The Ballroom Crowd vs Committee	Unstructured multi-reviewer output vs architected review pipeline
The Diamond vs Circle	L1 vs L2 constraint geometry — corners induce sparsity, smooth surfaces don't
The Orange Peel	Curse of dimensionality — in high dimensions, all volume is in the skin

Course Structure

Course 1: In-Context Learning vs Fine-Tuning

5 lessons — What are the two fundamental ways to change an LLM's behavior?

1. What Does an LLM Actually "Know"? — Parametric vs contextual memory; the sculpture analogy
2. In-Context Learning: The Art of the Reminder — Pattern activation, not learning; the ballroom musician
3. Fine-Tuning: Rewiring the Brain — Picking up the chisel; catastrophic forgetting; the tug-of-war
4. The Great Trade-Off — When to pour water vs carve stone; includes interlude on overfitting & dataset guidelines
5. The Frontier: Where the Line Gets Blurry — The spectrum between ICL and fine-tuning; includes interlude on transformer weight anatomy (MLP vs attention)

Course 2: LoRA Deep Dive

5 lessons — How do you efficiently adapt a frozen model?

1. The Core Intuition: Why Low-Rank? — Low-rank weight updates; A x B decomposition; includes bias-variance refresher
2. The Mechanics: How LoRA Actually Works — Parallel path, bottleneck, initialization, scaling factor alpha, merge vs swap
3. The Hyperparameters That Matter — Rank, alpha, layer targeting, learning rate; the practical starting recipe
4. LoRA in Practice — QLoRA, adapter merging, multi-adapter serving, production decision tree
5. The Frontier of Parameter-Efficient Methods — Prompt tuning, prefix tuning, adapter layers, DoRA, MoLoRA; why LoRA won

Course 3: Orthogonal Adapters & Composable Code Review Committees

5 lessons — How do you build diverse AI review systems with guaranteed unique perspectives?

1. The Blind Spot Problem — Why LLMs reviewing LLM code has inherent limits; the shared manifold problem; diversity hypothesis
2. Orthogonality: What It Means and Why It Guarantees Diversity — Projection constraints; the diagonal bug problem; includes interlude on training data & eigenvector analogy
3. Building the Committee — Three-tier architecture (specialists, composition, prioritization); bootstrapping via mutation testing
4. When Reviewers Disagree — Three categories of disagreement; confidence calibration; the disagreement matrix; composition model bias
5. Quis Custodiet Ipsos Custodes? — Third-order blind spots; defense in depth; the Kegan developmental parallel

Course 4: From Architecture to Enterprise

5 lessons — How do you build a defensible AI startup on the verification committee thesis?

1. The Generalization: From Code Review to Universal Verification Committees — Domain suitability framework; scoring domains; why crypto is the best first vertical
2. The TAM: Mapping the Opportunity Space — Bottom-up TAM, continuous monitoring market creation, wedge strategy, data flywheel, pricing paradox
3. Formal Verification of Cryptographic Protocols with Lean 4 — The four levels of correctness; why LLMs fail at Level 4; orthogonal adapters for verification gaps; mutation of specs and proofs
4. The Moat Question: What Frontier Labs Can't Copy — Five layers of moat; horizontal tax; reputation ratchet; winner-take-most dynamics
5. Building the Company: Architecture as Strategy — Architecture-to-strategy mapping; go-to-market; team; fundraising; 18-month roadmap; the deepest risk

Course 5: The Self-Improving Harness

6 lessons — How do you build a system that bootstraps from cloud dependence to local autonomy?

1. The Harness: Orchestrating Cloud and Local — Cascade routing, cost-quality curve, sending failures to the teacher
2. Distillation from First Principles — Dark knowledge, soft targets, temperature; selective distillation into LoRA specialists; sequence-level distillation from cloud APIs
3. Distillation into LoRA: Merging Teacher Knowledge with Task Adaptation — Rank expansion for dual signals; four combination strategies; LR/epoch/sampling balance
4. Micro Fine-Tuning: Learning While Serving — Quality filter, replay buffer, micro learning rate, EWC anchoring, validation gate, three firewalls against model collapse
5. The Full Architecture — Seven data flows, graceful degradation, build sequence, composition model co-evolution
6. The Bootstrap Paradox and the Economic Inflection — Learning starvation, sawtooth improvement, proactive red-teaming, when student surpasses teacher, AGI as civilization

Course 6: Cryptography from First Principles

5 lessons — Math foundations through core crypto primitives (for understanding the BABE protocol)

1. The Lock and Key Universe — Security parameter, negligible functions, PPT adversaries, security games, why negligible must be exponential
2. Finite Fields and Modular Arithmetic — Clock arithmetic, why primes give division, generators, discrete log problem
3. Hash Functions and the Random Oracle — Hash properties, ROM, notation boot camp (sampling, probability, oracle access)
4. Digital Signatures and Security Games — EUF-CMA, Lamport one-time signatures, the Lamport=GC coincidence, dot notation for oracles
5. Polynomials and Arithmetic Circuits — Schwartz-Zippel, R1CS, the polynomial bridge to Groth16, CRS and trusted setup

Course 7: The Cryptographic Toolkit

5 lessons — The algebraic machinery BABE is built from

1. Elliptic Curves — Point addition, scalar multiplication, ECDLP, BN254, implicit notation [x]_s
2. Bilinear Pairings — The pairing map, bilinearity, Groth16 verification equation, one-shot limitation
3. SNARKs and Groth16 — Complete Groth16 flow (Gen/Prove/Verify), knowledge soundness, extractors, role in BABE
4. Garbled Circuits — Wire labels, gate garbling, evaluation, free-XOR, half-gates, adaptive privacy
5. Witness Encryption — Encrypt under NP statement, BABE's pairing-based WE, extractable security, the Lemma 10 fix, WE+GC=BABE

Course 8: BABE — The Protocol and Its Security

5 lessons — The complete protocol, its security proof, and the Lean mechanization

1. Bitcoin as a Cryptographic Platform — UTXO model, locking scripts, 6-transaction graph, unstoppable transactions
2. The BABE Construction — WE+GC split, randomized encodings, DRE, linearization by lifting, 1000x size reduction
3. The Security Proof — Robustness, knowledge soundness, hybrid arguments, reduction chain, why four proof assistants
4. The Mechanization — Four proof assistants, axiom boundaries, audit findings, trust surface, stopping criterion
5. The Full Circle — Recursive verification, the complete map, biological parallels, "billions of years of pre-training followed by a lifetime of LoRAs"

Course 9: Remedial — Strengthening the Weak Spots

5 lessons — Focused drilling on reductions, precise definitions, and component boundaries

1. Reductions: The Technique — Four worked examples, the three-step recipe, student constructs a case-split reduction
2. Reduction Drills (upcoming)
3. The Confusion Matrix — Six confused concept pairs with precise distinctions and tests
4. The BABE Component Map — Which operation belongs to which system, the math type test
5. Remedial Exam — 15 focused questions, 12/15 clean, all major gaps closed

Course 10: Statistical Learning Theory

5 lessons — The mathematical foundations of generalization, estimation, and high-dimensional learning

1. Bias, Variance, and Empirical Risk Minimization — Bias-variance decomposition derivation, dart board analogy, ERM pathologies (overfitting, distribution shift)
2. Regularization — Ridge Regression and Sparsity — Ridge derivation with eigenvalue analysis, Bayesian interpretation, L1 sparsity (geometric and subdifferential arguments)
3. VC Dimension and PAC Learning — Shattering, VC dimension examples, generalization bounds, PAC framework, sample complexity
4. MLE, MAP, and Consistency — MLE consistency conditions, failure cases (mixtures, Neyman-Scott), MAP as regularized MLE, prior-penalty duality
5. Dimensionality and KL Divergence — Curse of dimensionality (orange peel, distance concentration), KL asymmetry, forward vs reverse KL, JS divergence

Course 11: Optimization in ML

5 lessons — How do optimizers navigate loss landscapes, and why does the "wrong" method often win?

1. SGD, Generalization, and Saddle Points — SGD noise as implicit regularization, flat minima, SDE approximation, saddle points vs local minima in high dimensions
2. Adam vs SGD, and Convergence Guarantees — Adam update rules, sharp minima with adaptive methods, AMSGrad, convergence conditions (L-smoothness, strong convexity, PL condition)
3. Gradient Pathologies — Vanishing gradients (chain rule, sigmoid, ReLU, residuals, init), exploding gradients (clipping, batch norm, LSTM gating, transformers)
4. Second-Order Methods — Hessian and curvature, Newton's method, why O(n²) is infeasible, L-BFGS, Hessian-free, natural gradient, Fisher information, KFAC
5. Loss Landscape Geometry — Sharp vs flat minima, PAC-Bayes, Dinh et al. controversy, SAM, line search vs schedules, warmup mystery for transformers

Course 12: Probabilistic ML & Inference

5 lessons — EM, MCMC, variational inference, Bayesian foundations, and when the machinery breaks

1. The EM Algorithm — MLE with latent variables, Jensen's inequality, ELBO, E-step/M-step, monotonic improvement, GMM example, failure modes (local optima, singular covariances, intractable E-step)
2. MCMC Methods — Metropolis-Hastings (propose-accept/reject, detailed balance, proposal tuning), Gibbs sampling (full conditionals, MH with acceptance=1, correlated variables problem), VI overview (optimization vs sampling, ELBO, mean-field, speed vs accuracy tradeoffs)
3. The ELBO and VI Bias — Full ELBO derivation, log P(x) = ELBO + KL(Q||P), reverse KL is mode-seeking, mean-field misses correlations, normalizing flows as fix
4. Bayesian Foundations — Exchangeability, de Finetti's theorem, Bayesian justification for parametric models, Dirichlet Process (CRP, stick-breaking), Gaussian Process (kernel as function prior)
5. Priors and Posterior Collapse — Prior sensitivity, Bernstein-von Mises, Jeffreys prior, posterior collapse in VAEs (powerful decoder problem, KL annealing, free bits)

Course 13: Deep Learning Theory

5 lessons — Transformers, residual connections, overparameterization, scaling laws, and the phenomena that defy classical intuition (Q31–Q40)

1. Transformers vs RNNs — Sequential bottleneck, hidden state compression, parallel processing, attention O(n²d) complexity, sparse/linear/FlashAttention solutions
2. Positional Encoding and Normalization — Permutation equivariance without PE, sinusoidal/learned/RoPE/ALiBi, layer norm vs batch norm, pre-norm vs post-norm, RMSNorm
3. Residual Connections and Overparameterization — y=F(x)+x gradient math, 2^L paths, ensemble interpretation, ODE connection, interpolation threshold, NTK, implicit regularization
4. Lottery Tickets and Double Descent — Sparse subnetworks matching full performance, iterative magnitude pruning, supermasks, three regimes of double descent, epoch-wise double descent
5. Scaling Laws and Why ReLU Dominates — Kaplan/Chinchilla power laws, compute-optimal frontier, sigmoid→tanh→ReLU→GELU arc, dying ReLU, why GELU won in transformers

Course 14: Computer Vision & NLP

5 lessons — From convolution priors to tokenization failures and hallucination (Q41–Q50)

1. Why Convolution Works — Locality and stationarity priors, weight sharing (FC N⁴ vs conv k²), inductive bias, translation equivariance vs invariance, proof sketch
2. Pooling and Dilated Convolutions — Receptive field growth, max vs avg pooling, strided conv, global average pooling, dilated convolutions, WaveNet, gridding artifact
3. Feature Hierarchies and Word2Vec — Edges→textures→parts→objects, GradCAM, transfer learning, Skip-gram/CBOW, softmax bottleneck, king−man+woman≈queen
4. Negative Sampling and Pretraining — Binary classification reframing, noise distribution P(w)∝freq^(3/4), NCE connection, BERT vs GPT (bidirectional vs causal), convergence toward autoregressive scale
5. Tokenization and Hallucination — Character/word/subword (BPE), arithmetic and multilingual impact, byte-level BPE, five causes of hallucination, mitigation strategies (RAG, CoT, calibration)

Course 15: Reinforcement Learning

5 lessons — Bellman equations to deep RL instability, exploration, and sample efficiency (Q51–Q60)

1. Bellman Equations and Dynamic Programming — Value function derivation, Bellman recursion, optimality equation, Q-function, policy iteration vs value iteration, contraction mapping convergence
2. Q-Learning Instability and Exploration — Tabular convergence, three sources of DQN instability (correlated samples, non-stationary targets, maximization bias), the deadly triad, ε-greedy vs UCB vs Thompson Sampling
3. Actor-Critic and Credit Assignment — REINFORCE variance, advantage function, TD error as advantage estimate, A2C/PPO/SAC, temporal credit assignment, eligibility traces, λ-return, HER
4. On-Policy vs Off-Policy and Function Approximation Issues — Behavioral vs target policy, importance sampling variance, PPO clipping, SAC entropy, convergence hierarchy (tabular → linear → neural), Baird's counterexample
5. Reward Shaping and Sample Efficiency — Potential-based shaping (Ng et al. theorem), telescoping argument, reward hacking, five root causes of sample inefficiency, model-based RL, offline RL

Course 16: Generalization Theory & Graph Neural Networks

5 lessons — Why deep nets generalize, compression and stability views, information bottleneck, and the expressivity limits of GNNs (Q61–Q70)

1. Why Deep Nets Generalize — Zhang et al. random labels puzzle, SGD's simplicity bias, function space perspective, implicit regularization (min-norm, min nuclear norm, LR as regularizer, early stopping)
2. Compression and Stability — MDL principle, compression bounds, noise stability, PAC-Bayes, algorithmic stability, Hardt et al. SGD stability proof, connection to differential privacy
3. Information Bottleneck and GNN Oversmoothing — Tishby's IB framework, two-phase training, Saxe et al. criticism, oversmoothing as low-pass filtering, eigenvalue convergence, DropEdge/PairNorm fixes
4. Message Passing and Spectral vs Spatial GNNs — MPNN framework, 1-WL expressivity ceiling, graph Laplacian Fourier domain, ChebNet, GCN as 1st-order Chebyshev, spectral vs spatial comparison
5. Graph Isomorphism and GNN Expressivity — GI complexity status, Babai's algorithm, GIN (injective aggregation = 1-WL), beyond-1-WL strategies (higher-order, random features, positional encodings)

Course 17: Causality & Practical ML

5 lessons — Causal inference, Simpson's paradox, class imbalance, data leakage, and the engineering of reliable ML systems (Q71–Q80)

1. Causation Formalized — Pearl's SCMs, structural equations, DAGs, do-operator, adjustment formula, backdoor criterion, frontdoor criterion
2. Instrumental Variables and Counterfactuals — Unmeasured confounders, IV conditions, 2SLS, weak instruments, potential outcomes Y(1)/Y(0), fundamental problem of causal inference, Pearl's three-level ladder
3. Simpson's Paradox and Class Imbalance — Berkeley admissions, aggregate vs stratify (causal structure decides), SMOTE, focal loss, AUPRC vs accuracy, threshold tuning
4. Data Leakage and Feature Engineering — Target/temporal/train-test leakage, detection and prevention, feature engineering techniques, feature selection methods
5. Cross-Validation and Hyperparameter Tuning — K-fold, stratified, time series split, nested CV, grid vs random (Bergstra & Bengio), Bayesian optimization, learning rate as most important hyperparameter

Course 18: Systems, Robustness & the Frontier

6 lessons — Distributed training, memory/precision, adversarial robustness, fairness, privacy, generative models, RLHF, alignment, and open questions (Q81–Q100)

1. Distributed Training — AllReduce communication overhead, sync vs async SGD, linear scaling rule, LARS/LAMB, data/tensor/pipeline parallelism, ZeRO, 3D parallelism
2. Memory, Precision & Latency — Memory budget (params, gradients, optimizer, activations), gradient checkpointing, FP16/BF16 mixed precision, GPTQ/AWQ quantization, continuous batching, speculative decoding, paged attention, GQA
3. Adversarial Robustness — Goodfellow linearity hypothesis, FGSM/PGD attacks, features-vs-bugs debate, adversarial training min-max, accuracy-robustness tradeoff, certified defenses, randomized smoothing
4. Fairness and Bias — Demographic parity, equalized odds, calibration, Chouldechova impossibility theorem, bias taxonomy, disaggregated metrics, counterfactual fairness, proxy variables
5. Privacy and Generative Models — (ε,δ)-differential privacy, DP-SGD, composition theorem, federated learning, GANs vs diffusion (stability, mode coverage, conditioning), why diffusion training is stable
6. RLHF, Alignment & the Frontier — RLHF pipeline (SFT→reward model→PPO), DPO, Goodhart's law, mesa-optimization, Constitutional AI, CLIP, test-time compute, mechanistic interpretability, scaling laws, open questions

Key Takeaways Across All Courses

1. An LLM's knowledge lives in its weights (stone) — permanent patterns carved during training
2. In-context learning activates existing capabilities via the prompt (water) — nothing changes, nothing persists
3. Fine-tuning modifies weights (picks up the chisel) — powerful but expensive and risky
4. "Activating, not carving" — the student's own summary of ICL vs fine-tuning
5. LoRA represents weight changes as low-rank matrices — because fine-tuning updates are empirically low-rank
6. Orthogonal adapter training guarantees diverse perspectives — the constraint is in weight space, not data space
7. Orthogonality is like PCA/eigenvectors — each adapter captures the next most important independent direction of useful adaptation
8. A review committee needs both specialists (orthogonal) AND generalists (composition layer) to catch diagonal bugs
9. The distinction between "activation" and "learning" is a matter of where you draw the line — it's learning all the way down
10. The holy grail is continual learning — if LoRA adapters can be continually learned, merged, and composed, the line between training and adaptation dissolves
11. Every prediction error decomposes into bias² + variance + noise — the pattern of failure tells you what to fix
12. Regularization is prior knowledge in disguise — L2 = Gaussian prior, L1 = Laplace prior, MAP = MLE + regularization
13. Generalization depends on the ratio of model capacity to data, not capacity alone — VC theory and PAC learning formalize this
14. KL divergence is asymmetric by design — forward KL covers modes (blurry), reverse KL seeks modes (sharp) — this explains the VAE vs GAN divide
15. EM is the gateway to variational methods — bound what you can't compute, optimize the bound — but it only works when the E-step is tractable
16. Exchangeability justifies Bayesian modeling — de Finetti proves a parameter and prior must exist if data order is irrelevant
17. Posterior collapse in VAEs is a degenerate equilibrium, not a bug — the ELBO is doing what it's told, but a powerful decoder makes z unnecessary
18. Mean-field VI underestimates uncertainty — factorization + reverse KL = mode-seeking with no correlations — calibrated uncertainty requires richer families or MCMC

Student Profile

• Experience level: understands neural networks and transformer architecture
• Thinks mechanically — reasons about tokens, weights, and machinery rather than anthropomorphizing
• Prefers practical, engineering-grounded explanations over abstract theory
• Strong at synthesis — naturally connects ideas across lessons and extrapolates to frontier implications
• Pushes back on imprecise claims, leading to productive deeper discussions