Patterning: The Dual of Interpretability
By Wang and Murfet
Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures.
We use singular learning theory to understand how training data shapes AI behavior.
Our approach combines deep mathematical insights from algebraic geometry and statistical physics with empirical research to develop interpretability tools to understand how capabilities and values emerge during neural network training. This foundational work enables us to build interventions that ensure models are aligned with human values.
Our most recent publications on singular learning theory and AI safety.
By Wang and Murfet
Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures.
By Gordon et al.
Spectroscopy infers the internal structure of physical systems by measuring their response to perturbations.
By Elliott et al.
Singular learning theory characterizes Bayesian learning as an evolving tradeoff between accuracy and complexity, with transitions between qualitatively different solutions as sample size increases.
Watch our latest discussions on singular learning theory and AI safety.
December 18, 2025
In this seminar, Jesse Hoogland explores how singular learning theory provides a framework for connecting interpretability to the theory of generalization and the geometry of the loss landscape. He presents recent work at Timaeus applying SLT to different areas of interpretability, including an SLT-based generalization of influence functions for data attribution and an SLT-native approach to ablations for circuit discovery, and describes initial work on using these interpretability techniques to actively shape the learning process by controlling training data, with implications for developing better alignment techniques. Jesse Hoogland is the executive director of Timaeus, an AI safety non-profit working on interpretability and alignment, and a cofounder of the developmental interpretability research agenda and the broader program of applying singular learning theory to AI safety, which he is now pursuing with his team at Timaeus.

November 10, 2025
Jesse Hoogland presented "Singular Learning Theory and AI Safety" on September 17, 2025 at FAR.AI Labs Seminar.

July 28, 2025
In the SLT seminar, Jesse Hoogland from Timaeus talks to us about his research agenda applying singular learning theory to AI safety.

We are building tools and resources to spread our research to the broader community.
Partners: Monash University , Sydney Mathematical Research Institute
Some aspects of intelligence are becoming a commodity. They are bought and sold by the token and piped from large datacenters hosting artificial neural networks to our phones, laptops, cars and perhaps soon domestic robots. However our understanding of what neural networks do, and how they “learn” is limited. This makes it difficult to assess the downside risks of rapid adoption of AI across the economy and in our personal lives. The goal of this focus period will be to come to grips with these questions from a mathematical perspective. Many mathematicians want to contribute, but lack a clear entry point into the subject. A primary aim will be to articulate guiding questions, in consultation with experts at the forefront of AI development. We also aim to bring together some of the most interesting thinkers in this nascent field.
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ODYSSEY is a 5-day, multi-track conference bringing together researchers in theoretical AI alignment.
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A collection of posts written by various people associated with Developmental Interpretability (since before the agenda was conceived).
View AllJanuary 7, 2026
TLDR: We're hiring for research engineer and research scientist roles to work on applications of singular learning theory to alignment. About Us Timaeus' mission is to empower humanity by making breakthrough scientific progress on alignment. Our research focuses on applications of singular learning theory to foundational problems within alignment. Position Details Positions: Research Engineer, Research Scientist. Location: Remote.
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August 12, 2025
Research Engineer @ Timaeus TLDR: We're hiring for a research engineer role. The successful hire will work on applications of singular learning theory to alignment, including developmental interpretability. About Us Timaeus' mission is to empower humanity by making breakthrough scientific progress on alignment. Our research focuses on applications of singular learning theory to foundational problems within alignment.
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May 22, 2025
Updated 29 May 2025 About Us Timaeus is an AI safety research organization working on applications of singular learning theory (SLT) to AI safety. Our mission is to empower humanity by making breakthrough scientific progress on AI alignment and interpretability. We are a growing team of dedicated researchers applying cutting-edge mathematics to prevent AI risks that could affect billions of people, supported by advisors from leading AI research organizations worldwide.
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January 17, 2025
TLDR: We're hiring for research & engineering roles across different levels of seniority. Hires will work on applications of singular learning theory to alignment, including developmental interpretability. About Us Timaeus' mission is to empower humanity by making breakthrough scientific progress on alignment. Our research focuses on applications of singular learning theory to foundational problems within alignment. Position Details Positions: Research Lead, Research Scientist, Research Engineer.
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