Topic: measurements

Operational definitions identify subsystems through the transformations an agent can perform. This talk classifies complementary, bicommutant-closed subsystems using unitary channels, whose disregard for global phase permits possibilities beyond conventional operator subalgebras. The classification involves graded subalgebras. Some resulting subsystems are nontrivial yet support no measurements, raising a foundational choice between excluding them and accepting agents that act without being able to observe.

Score-based generation need not reverse a forward diffusion process. This talk presents an alternative based on Langevin MCMC at a fixed noise level, with effective noise falling as measurements accumulate. Suitable noise choices keep the sampling problems log-concave, and extensions connect the construction to discrete-data generation.