Geometric Algebra for Causal Discovery: Sector Rotation May Be a Market Bet in Disguise
The growth-to-defensive lead-lag survives every check but one. Condition on the market factor and the direct signal is gone.
Agus’s Substack
My personal Substack
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The Geometry of a Causal Arrow
Correlation gives you an angle. The arrow lives in a different grade of the same object.
Rotors, Reflections and Rigid Motions
This is the seventh post in Knowledge Graphs as Geometry, a weekly series that develops a single idea one chapter at a time: every relation in a knowledge graph is an operation in space, and the named models are that operation in different guises.
What Makes a Kernel Learnable
Chapter 7 of The Learned Kernel. The previous chapters argued that the geometry, the kernel, should be learned rather than chosen. Learning the geometry introduces a failure mode that a fixed kernel does not have: the model can overfit the geometry itself and then report a score it cannot reproduce on new data. This chapter is about detecting that failure, and the remedy is a single held-out fold.
Knowledge Graphs, Geometric Memory and Auditable Decisions
A design that lets a bank put a language model behind decisions without giving up the evidence and the reasoning underneath them.
Geometric Algebra from Linear Algebra
This is Chapter 6 in Knowledge Graphs as Geometry, a weekly series developing a single thesis: every knowledge graph relation is an operation in space, and the dozens of named embedding models are one operation in different notation.
Every Prediction Carries Its Own Evidence
Chapter 6 of Learning as a Geometry Discovery. An earlier chapter showed that a gradient-boosted tree ensemble is a kernel machine with a similarity learned from the labels https://agussudjianto.substack.com/p/trees-are-kernels-and-the-kernel. This chapter examines a single prediction from such a model and asks what it is made of: which historical cases supported it, how many of them effectively,…
Three Choices: Carrier, Operator, Comparator
This is the fifth post in Knowledge Graphs as Geometry, a weekly series that builds one idea, chapter by chapter: a knowledge graph stores facts as relations, every relation is an operation in space and predicting a missing fact is geometry.
What Your AI Cannot Prove
Governing AI in Regulated Industries
The Model That Scores Its Own Geometry
Chapter 5 of The Learned Kernel. Last time we saw that a gradient-boosted ensemble is secretly a kernel machine (https://agussudjianto.substack.com/p/trees-are-kernels-and-the-kernel), with a similarity it learned from the labels.
A Relation Is a Rotation On a Knowledge Graph
This is an example follow-up to the fourth post in Knowledge Graphs as Geometry. Last time a relation became a rotation and score by distance, symmetry stops being a trap. That earlier demonstration used six people in a family graph, and this week the same rotation runs a bank’s compliance memory, the geometry an AI agent has to obey when a customer complaint lands on its desk. The tool is
Trees Knew Where the Model Was Weak. Now a Mixture of Experts Repairs It.
Post 5 of The Learned Kernel. Last time we showed that a gradient-boosted ensemble carries its own map of where it fails — read the leaf kernel, cluster by it, and the weak regions surface on their own. I promised we’d act on that map. This is the repair — and we do it in credit, where the fix is only allowed if it keeps the model monotone and readable.
A Relation Is a Rotation
This is the fourth post in Knowledge Graphs as Geometry, a weekly series that turns the model zoo into one idea.
Trees Are Kernels — and the Kernel Knows Where the Model Is Weak
Chapter 4 of The Learned Kernel. Last time we said the geometry should be learned, not chosen, and named boosting as the first engine that does it. This time we take the kernel a boosted ensemble grows for free and use it for something the black box never offered: a map of exactly where the model fails.
A Relation in Knowledge Graph Is a Matching Matrix
This is the third post in Knowledge Graphs as Geometry, a weekly series that builds one idea, chapter by chapter: a knowledge graph stores facts as relations, every relation is an operation in space, and predicting a missing fact is geometry.
From Chosen to Learned Kernels
Chapter 3 of The Learned Kernel. Last time, five methods collapsed into one machine whose only real input is the kernel. This time we stop choosing that kernel by hand — and confront the two things that go wrong the moment you try to learn it instead.
TransE: Translation as a Decoder
This is the second post in Knowledge Graphs as Geometry, a weekly series that builds one idea, chapter by chapter: a knowledge graph stores facts as relations, every relation is an operation in space, and predicting a missing fact is geometry.
Row and Column Attention Are Kernel Smoothing
The language around tabular transformers makes row attention and column attention sound like new modeling primitives.
The Kernel as the Normal Form
Post #2 of The Learned Kernel.
A Relation Is an Operation
This is the first post in Knowledge Graphs as Geometry, a weekly series that builds one idea, chapter by chapter: a knowledge graph stores facts as relations, every relation is an operation in space, and predicting a missing fact is geometry.
The Geometry Hidden in Every Model
This is the first post in The Learned Kernel, a weekly series that builds one idea, chapter by chapter: learning is the discovery of geometry, the kernel is what carries it, and the kernel should be learned, not chosen.