Alphabeta Math

Machine Learning Algorithms

76 pages in 8 parts

Machine learning algorithms construct representations, model data distributions, and learn decisions from feedback. These pages develop self-supervised and contrastive objectives, reconstruction and latent-variable models, energy and adversarial learning, transport duality, normalizing flows, flow matching, and diffusion. Multimodal alignment and foundation-model transfer connect representation methods to broader modeling tasks. The sequential-decision branch covers online regret, adaptive confidence, stochastic and adversarial bandits, finite MDPs, tabular control, policy gradients, function approximation, planning, and offline evaluation. Further topics include partial observability, imitation, constrained policies, preference optimization, and verifiable generation.

Probability, Measure Theory, and Mathematical Statistics provide sampling, concentration, and inference tools; Statistical Learning and Classical Models supplies risk, prediction, and generalization methods. Neural Networks and Learning Dynamics contributes architectures and differentiation, while Linear Algebra and Functional Analysis support approximation. Numerical Optimization, Inverse Problems and Uncertainty Quantification informs training and policy optimization; Numerical Differential Equations and Stochastic Dynamics supports continuous flows and diffusion. The reading pathway connects these foundations to representation, generation, and sequential decisions, with example companions alongside the theory pages. Guarantees retain each algorithm’s feedback protocol, comparator, regularity, approximation, and solver assumptions, and empirical scaling evidence remains distinct from mathematical conclusions.

Pathway

The parts run in order. Everything a page needs from this group has been read by the time you reach it, and the level on each row is how many dependency steps into the group that page sits.

  1. Part 1 · Representation objectives and transfer

    5 pages

    Begin with contrastive representations, reconstruction, and latent-variable objectives, then explore multimodal alignment and foundation-model transfer. Read the neural and statistical prerequisites in their own collections. Distinguish mathematical guarantees about objectives from empirical scaling evidence.

  2. Part 2 · Generative objectives and transport

    5 pages

    Study energy and adversarial models alongside their divergence and score formulations. Finite-metric transport duality precedes compact-metric Kantorovich–Rubinstein duality and the Wasserstein-GAN applications. Ideal objective identities retain their stated optimization assumptions.

  3. Part 3 · Flows, diffusion, and reverse generation

    7 pages

    Follow exact-density and continuous flows into flow matching, using the transport prerequisites from the preceding part. Discrete diffusion and masked generation form a separate route; the continuous branch proceeds from reverse-time diffusion to score-SDE generation. Keep density, regularity, sampling, and solver assumptions explicit.

  4. Part 4 · Online protocols, regret, and confidence

    4 pages

    Begin the sequential-decision branch with its protocol and comparator class. Hedge and online gradient descent precede adaptive mirror descent. Confidence sequences supply tools for adaptive sampling and stopping under their stated assumptions.

  5. Part 5 · Bandit feedback and contextual decisions

    4 pages · after Part 4

    Move from stochastic finite-armed bandits to adversarial and contextual feedback. Contextual expert methods follow importance weighting; linear contextual bandits use their linear-prediction prerequisites. Each guarantee depends on the feedback the learner actually observes.

  6. Part 6 · MDPs, Bellman operators, and tabular learning

    4 pages

    Read finite MDPs and Bellman operators before tabular prediction and control. PAC exploration and average-reward regret add their own horizon, confidence, and communication conditions. Known-model planning and learning through interaction retain distinct assumptions.

  7. Part 7 · Policies, planning, offline learning, and safety

    7 pages · after Parts 4 and 6

    Continue to policy gradients, function approximation, model-based planning, and offline evaluation. Partial observability and imitation change the information or training protocol; constrained MDPs follow the policy-gradient prerequisites. Approximation and off-policy results preserve their stated limitations.

  8. Part 8 · Preferences and verifiable generation

    2 pages · after Part 7

    Preference learning and direct preference optimization use classical calibration, classification, and neural differentiation. Verifiable generation follows the policy-gradient and offline-evaluation interfaces. Objective and sampling results retain their stated verification and feedback assumptions.