Machine Learning

Reverse-Process Synthetic Data Generation for Math Reasoning

Training LLMs on mathematical reasoning by inverting easy-to-solve problems: generate derivatives, reverse them into integration exercises with full step-by-step solutions.

Value Functions Over Reasoning Traces

What if reasoning traces could learn their own usefulness? A simple RL framing for trace memory, and why one reward signal is enough.

From A* to GPT: Rational Agents and the Representation Problem

The classical AI curriculum teaches rational agents as utility maximizers. The progression from search to RL to LLMs is really about one thing: finding representations that make decision-making tractable.

The Incomputability of Simple Learning

Why the simplest forms of learning are incomputable, and what that means for the intelligence we can build.

Bayesian Reasoning and Machine Learning

Machine Learning: A Probabilistic Perspective

Pattern Recognition and Machine Learning

Patterns, Predictions, and Actions: A Story About Machine Learning

Notes

Modern graduate ML text with causal inference, decision making, and ML foundations. Accessible free textbook with strong conceptual framing.

The Elements of Statistical Learning

The Master Algorithm

Infinigram: Corpus-Based Language Modeling via Suffix Arrays with LLM Probability Mixing

MCTS-Reasoning: A Canonical Specification of Monte Carlo Tree Search for LLM Reasoning

The Policy: Q-Learning vs Policy Learning

SIGMA uses Q-learning rather than direct policy learning. This architectural choice makes it both transparent and terrifying. You can read its value function, but what you read is chilling.

DreamLog: Logic Programming That Dreams to Improve Itself

A logic programming system that alternates between wake and sleep phases, using LLMs for knowledge generation during wake and compression-based learning during sleep.

An Algebraic Framework for Language Model Composition: Unifying Projections, Mixtures, and Constraints

Automatic Fuzzy Rule Discovery Through Differentiable Soft Circuits

DreamLog: Neural-Symbolic Integration through Compression-Based Learning and Wake-Sleep Cycles

Learning Fuzzy Logic: Automatic Rule Discovery Through Differentiable Circuits

Learning fuzzy membership functions and inference rules automatically through gradient descent on soft circuits, instead of hand-crafting them.

Differentiation: Three Ways

Three approaches to computing derivatives, forward-mode AD, reverse-mode AD, and finite differences, each with different trade-offs for numerical computing and machine learning.

Science as Verifiable Search

Science is search through hypothesis space. Intelligence prunes; testing provides signal. Synthetic worlds could accelerate the loop.

MCTS-Reasoning: Tree Search for LLM Reasoning

Applying Monte Carlo Tree Search to large language model reasoning, with a formal specification of the algorithm.

Cluster-Aware Retrieval for RAG Systems

Using GMM clustering to improve retrieval in topically diverse knowledge bases

Latent Reasoning Traces: Memory as Learned Prior

What if LLMs could remember their own successful reasoning? A simple experiment in trace retrieval, and why 'latent' is the right word.

All Induction Is the Same Induction

Solomonoff induction, MDL, speed priors, and neural networks are all special cases of one Bayesian framework with four knobs.

Fisher Flow: Optimization on the Statistical Manifold

Gradient descent in Euclidean space ignores the geometry of probability distributions. Natural gradient descent uses the Fisher information metric instead. Fisher Flow makes this continuous.

FemtoGrad: A Minimal Automatic Differentiation Library

A tiny autodiff library for understanding how backpropagation actually works.

Everything is Utility Maximization

The AI course this semester keeps hammering one idea: intelligence is utility maximization under uncertainty. A* search, reinforcement learning, Bayesian networks, MDPs. One principle connects all of it.

Uses and limits of abstractions

Abstractions let us reason about complex systems despite our cognitive limits. But some systems resist compression entirely.

Working Memory as an Inductive Bias

How the limited capacity of human working memory acts as regularization, shaping our reasoning and possibly preventing cognitive overfitting.

Reverse-Mode Automatic Differentiation

Reverse-mode automatic differentiation is just the chain rule applied systematically. I built one in C++20 to understand what PyTorch and JAX are actually doing.

Discovering ChatGPT: The Theory Was Already There

I finally tried ChatGPT after weeks of ignoring it. My reaction was not surprise. It was recognition. The Solomonoff connection, language models as compression, prediction as intelligence. The pieces were all there.

Forward-Mode Automatic Differentiation

Dual numbers extend the reals with an infinitesimal epsilon where epsilon^2 = 0. Evaluate f(x + epsilon) and you get f(x) + f'(x)*epsilon. The derivative falls out of the algebra.

Femtograd: Like Micrograd, But Worse

Introduction to Sequential Prediction

The problem of predicting what comes next, from compression to language models