Mathematics
The theoretical underpinning of machine learning and statistics.
Math is the underpinning of machine learning and statistics.
The accuracy of a model depends on the mathematical assumptions we instill. The quality of an algorithm is the distance between its prediction and the truth, as so defined by mathematics. We can even estimate the amount by which we'll be wrong.
This is more than just numbers and equations.
We ask: what is the geometry of an ideal and accurate model? What does it mean that a neural network linearly transforms dimensions to make its predictions? What does the world look like in the space where these algorithms do their thinking?
Sometimes the answers are surprising, and sometimes they are not. But they are always interesting.
Check out the papers we're reading.
- Deep Learning Interpretation via ManifoldsZhang et al.
Deep learning algorithms are notoriously difficult to interpret. Mathematicians give it a shot anyway.
optimizationgeometry - Manifolds: an Information-Theoretic ApproachChigirev et al.
Geometric methods for optimization with structure.
optimizationgeometry - Manifold Learning via Mixture ModelsAlberto et al.
Geometric methods for optimization with structure.
optimizationgeometry
Posts related to this pillar.
- Local MDL-Based Divergence for Structural Complexity Analysisresearch
In this work, we introduce a localized, MDL-based divergence measure that quantifies the structural complexity of induced subgraphs relative to a global reference model. The measure compares the compressibility of local neighborhoods under globally fitted and locally optimized comparator models while penalizing model flexibility, yielding a statistically grounded notion of local structural surprise. The results show that the measure converges under controlled ablations, is robust to sampling choices, and detects meaningful structural irregularities that are invariant to geometric embedding. This framework generalizes MDL-based network analysis to arbitrary information graphs and provides a principled bridge between global structure and agent-level experience.
2026-03-27 - The Problem of Optimizationblog
The mathematical route to the best possible cities.
2025-09-19 - Sigma-Algebras: a Principled Approach to Asking Good Questionsresearch
Continuing our Foundations series, we explore sigma-algebras—the mathematical scaffolding that makes probability rigorous and connects abstract theory to real-world randomness in our models.
2025-09-18