Explore the mathematical foundations of predictive processing theory in perception and consciousness in this 22-minute conference talk. Delve into the concept of the brain's generative model, which continuously predicts sensory input, and examine how Bayesian inference processes shape our experiences. Compare and contrast two key approaches: the Helmholtz machine and the free energy principle. Investigate the mathematical details of both methods, focusing on their use of free energy functional optimization. Discover how the Helmholtz machine performs gradual optimization over multiple data points, while the free energy principle finds parameter values for individual data. Gain insights into the ongoing debate surrounding the relationship between sensory input and conscious experience through this in-depth exploration of computational models in cognitive science.