Allen Institute for Artificial Intelligence

The Reflexive Path-Law Framework: Unpredictability, Identification, and Market Equilibrium

Return unpredictability is an observational property relative to a filtration, horizon, target, loss, and strategy class; it does not by itself establish correct valuation, no-arbitrage, net non-exploitability, causal exogeneity, or dynamic stability. This paper develops the Refl...

The Reflexive Path-Law Framework: Unpredictability, Identification, and Market Equilibrium

Return unpredictability is an observational property relative to a filtration, horizon, target, loss, and strategy class; it does not by itself establish correct valuation, no-arbitrage, net non-exploitability, causal exogeneity, or dynamic stability. This paper develops the Refl...

The Mathematics of Factors: Risk, Alpha, Detection, and Capacity

Quantitative finance uses "factor" for two distinct objects: a risk direction along which returns covary and an alpha direction along which returns are predictable. We assign each direction gauge-invariant common-covariance strength and predictive content, separating covariance r...

Density Modeling of Sequences: A Path-First Theory of Autoregression, Masked Diffusion, Adaptive Insertion, and the Price of Order

We develop a path-first theory of discrete sequence generation. A generator first defines a probability law on chronology-augmented construction paths; the terminal sequence law is the pushforward of that path law. The full geometric signature faithfully encodes every finite acti...

Density Modeling of Sequences: A Path-First Theory of Autoregression, Masked Diffusion, Adaptive Insertion, and the Price of Order

We develop a path-first theory of discrete sequence generation. A generator first defines a probability law on chronology-augmented construction paths; the terminal sequence law is the pushforward of that path law. The full geometric signature faithfully encodes every finite acti...

Structure Through Five Geometries: From Gauge Quotients to Transformer J-Space

This paper organizes structural questions in artificial intelligence and finance through five complementary geometries. Gauge geometry studies equivalent internal descriptions. Orbit and quotient geometry studies observational identification. Information geometry measures local s...