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Alex Towell

Research engineer and computer scientist working at the intersection of machine learning, statistical computing, and cryptography. Currently pursuing my PhD in Computer Science at Southern Illinois Un

Noisy Turing Machines: Noisy Logic Gates

Noisy Turing Machines: Noisy Logic Gates

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4 min read

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Kraft's Inequality

Kraft's Inequality

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9 min read
Lattices: Fixed Points and Iteration

Lattices: Fixed Points and Iteration

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3 min read
algebraic.mle: MLEs as Algebraic Objects

algebraic.mle: MLEs as Algebraic Objects

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3 min read
Choosing the Algebra

Choosing the Algebra

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4 min read
One Algorithm, Infinite Powers

One Algorithm, Infinite Powers

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4 min read
The Media Page

The Media Page

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3 min read
Succinct Bit Vectors and Rank/Select

Succinct Bit Vectors and Rank/Select

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6 min read
Arithmetic Coding

Arithmetic Coding

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7 min read
The Reality of Moral Properties: Do Values Exist?

The Reality of Moral Properties: Do Values Exist?

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5 min read
Bootstrap Methods: When Theory Meets Computation

Bootstrap Methods: When Theory Meets Computation

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2 min read
TD Learning for Exemplar Retrieval: Why It Doesn't Really Work

TD Learning for Exemplar Retrieval: Why It Doesn't Really Work

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2 min read
Building Languages to Solve Problems

Building Languages to Solve Problems

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4 min read
JSL: A Functional Language Where Code Is JSON

JSL: A Functional Language Where Code Is JSON

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8 min read
libdis: Disjoint Interval Sets as a Complete Boolean Algebra

libdis: Disjoint Interval Sets as a Complete Boolean Algebra

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3 min read
Perfect Hashing: Space Bounds, Entropy, and Cryptographic Security

Perfect Hashing: Space Bounds, Entropy, and Cryptographic Security

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2 min read
The Infinite Table

The Infinite Table

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5 min read
Bandwidth as Fundamental Constant: The 7 2 Limit in Call of Asheron

Bandwidth as Fundamental Constant: The 7 2 Limit in Call of Asheron

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6 min read
A Boolean Algebra Over Trapdoors

A Boolean Algebra Over Trapdoors

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19 min read
Free Will and Determinism: Can We Be Responsible in a Clockwork Universe?

Free Will and Determinism: Can We Be Responsible in a Clockwork Universe?

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7 min read
Narrating a Hugo Blog with Sentence Highlighting

Narrating a Hugo Blog with Sentence Highlighting

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3 min read
Why Open Source Matters for Reproducible Science

Why Open Source Matters for Reproducible Science

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1 min read
The Policy: Coherent Extrapolated Volition, the Paradox of Perfect Alignment

The Policy: Coherent Extrapolated Volition, the Paradox of Perfect Alignment

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8 min read
Reverse-Process Synthetic Data Generation for Math Reasoning

Reverse-Process Synthetic Data Generation for Math Reasoning

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3 min read
Universal Codes as Priors

Universal Codes as Priors

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8 min read
Beginning the PhD: Computer Science, AI, and Finite Time

Beginning the PhD: Computer Science, AI, and Finite Time

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4 min read
Numerical Integration with Generic Concepts

Numerical Integration with Generic Concepts

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4 min read
Entropy Maps

Entropy Maps

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7 min read
XTK: A Symbolic Expression Toolkit for Term Rewriting

XTK: A Symbolic Expression Toolkit for Term Rewriting

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3 min read
I Tried to Voice-Clone Myself in 90 MB

I Tried to Voice-Clone Myself in 90 MB

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5 min read
JAF: Streaming Boolean Algebra Over Nested JSON

JAF: Streaming Boolean Algebra Over Nested JSON

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6 min read
chop: When Every Command Returns the Same Kind of Thing

chop: When Every Command Returns the Same Kind of Thing

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5 min read
Uses and limits of abstractions

Uses and limits of abstractions

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4 min read
Language Calculus: An Algebraic Framework for LLM Composition

Language Calculus: An Algebraic Framework for LLM Composition

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2 min read
Persons and Moral Agency: What Makes Someone Special?

Persons and Moral Agency: What Makes Someone Special?

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4 min read
Modular Arithmetic as Rings

Modular Arithmetic as Rings

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3 min read
Reverse-Mode Automatic Differentiation

Reverse-Mode Automatic Differentiation

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4 min read
API Design as Value Imprinting

API Design as Value Imprinting

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2 min read
Review: A Symbolic Representation of Time Series, with Implications for Streaming Algorithms

Review: A Symbolic Representation of Time Series, with Implications for Streaming Algorithms

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7 min read
A Map of My Open Source Ecosystem

A Map of My Open Source Ecosystem

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17 min read
Homomorphisms: The Maps Between Structures

Homomorphisms: The Maps Between Structures

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5 min read
Long Echo: The Ghost That Speaks

Long Echo: The Ghost That Speaks

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6 min read
Diagnosed with Stage 3 Cancer

Diagnosed with Stage 3 Cancer

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2 min read
Graduate Statistics Problem Sets

Graduate Statistics Problem Sets

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2 min read
Model Selection for Weibull Series Systems: When Simpler Models Suffice

Model Selection for Weibull Series Systems: When Simpler Models Suffice

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3 min read
The Mocking Void: On the Computational Incompleteness of Meaning

The Mocking Void: On the Computational Incompleteness of Meaning

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4 min read
Random Oracles in Python

Random Oracles in Python

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2 min read
Watch an LLM Think

Watch an LLM Think

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165 min read
Preventing Ransomware Damages with Off-Site Backup

Preventing Ransomware Damages with Off-Site Backup

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2 min read
Algebraic Hashing: Composable Hash Functions Through XOR

Algebraic Hashing: Composable Hash Functions Through XOR

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2 min read
A Home Lab from Spare Parts

A Home Lab from Spare Parts

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2 min read
Unary and Elias Gamma

Unary and Elias Gamma

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7 min read
The AI Course: Everything is Utility Maximization

The AI Course: Everything is Utility Maximization

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3 min read
Suffering, Computation, and the Enigma of Reality

Suffering, Computation, and the Enigma of Reality

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2 min read
Chronicles of The Mechanism: The Order's Secret History

Chronicles of The Mechanism: The Order's Secret History

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6 min read
Alga: Algebraic Text Processing with Fuzzy Matching

Alga: Algebraic Text Processing with Fuzzy Matching

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3 min read
Accumux: Compositional Online Statistical Reductions in C++

Accumux: Compositional Online Statistical Reductions in C++

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3 min read
jsonl-algebra: Relational Algebra for Nested JSON

jsonl-algebra: Relational Algebra for Nested JSON

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6 min read
Introduction to Sequential Prediction

Introduction to Sequential Prediction

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4 min read
Forward-Mode Automatic Differentiation

Forward-Mode Automatic Differentiation

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3 min read
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