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 Kreer et al.
Classical influence functions face significant challenges when applied to deep neural networks, primarily due to non-invertible Hessians and high-dimensional parameter spaces.
By Adam et al.
We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network.
By Wang et al.
Understanding how language models develop their internal computational structure is a central problem in the science of deep learning.
Watch our latest discussions on singular learning theory and AI safety.
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.
July 9, 2025
MATS 8.0 seminar by Jesse Hoogland. Singular learning theory (SLT) suggests that the geometry of the loss landscape is key to developing a better scientific understanding of deep neural networks, along with new practical tools for engineering safer systems.
July 5, 2025
Daniel Murfet from Timaeus tells us how to think about Turning machines as critical points of an analytic function, from a recent paper with Will Troiani.
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.
Learn more A collection of posts written by various people associated with Developmental Interpretability (since before the agenda was conceived).
View AllAugust 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.
Learn more 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.
Learn more August 30, 2024
_Thanks to Jesse Hoogland and George Wang for feedback on these exercises._ In learning singular learning theory (SLT), I found it was often much easier to understand by working through examples, rather than try to work through the (fairly technical) theorems in their full generality. These exercises are an attempt to collect the sorts of examples that I worked through to understand SLT. Before doing these exercises, you should have read the Distilling Singular Learning Theory (DSLT) sequence, watched the SLT summit YouTube videos, or studied something equivalent. DSLT is a good reference to keep open while solving these problems, perhaps alongside Watanabe's textbook, the Gray Book.
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