Lance Da Costa ~ Active Inference Insights 010 ~ Mathematics, Time, Selfhood
Apr 30, 2024
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Mathematician Lance Da Costa delves into world and self models in active inference, stochastic differential equations, solenoidal flows in living systems, recognition density, meditation attention, prior beliefs, and cutting-edge vision technology in this insightful podcast.
Solongial and gradient flows in the Langevin equation are linked to time-irreversibility and entropy production, showcasing the complexity of dynamic systems.
Detailed balance and the impact of solongial flows emphasize the dissipative nature of systems with life-like characteristics, shedding light on entropy production.
The Fisher information metric tensor in models aids in tracking beliefs and minimizing free energy over time, offering insights into adaptive behavior and minimizing surprise.
Deep dives
Solongial and gradient flows decomposition
Solongial and gradient flows are mathematical concepts that decompose the flow in the Langevin equation. Solongial flow entails motion around the contours of a probability distribution, without approaching or moving away from its peak. On the other hand, gradient flow involves motion towards or away from the peak of the distribution. Solongial flow is time-irreversible and linked to entropy production, while gradient flow relates to motion towards preferred or expected states.
Detailed balance and solongial flows
Detailed balance refers to the situation where the rate of transitions between states is equal in both directions, indicating a lack of net entropy production. Solongial flows break detailed balance, leading to time-irreversibility and entropy production in the system. This distinction between solongial and detailed balance underscores the role of dissipative aspects in systems that exhibit life-like characteristics.
Fisher information metric tensor
The Fisher information metric tensor quantifies changes in the Kullback-Leibler (KL) divergence - a measure of the difference between a recognition density and a true posterior distribution. It assesses how beliefs or information about the world need to change over time to minimize free energy. By integrating this metric into models, it allows for a more accurate representation of how beliefs evolve and adapt, providing insights into how systems adapt and minimize surprise over time.
Exploring Active Inference and Prediction Error Dynamics
Active inference theory explores the concept of prediction error dynamics, suggesting that we track our performance in minimizing free energy over time. This higher order prior guides our ability to optimize our interactions with the environment. The theory aligns this process with the psychological manifestations of positive or negative affect, indicating how our success in minimizing free energy relates to emotions like positive or negative affect. Additionally, the discussion delves into the intriguing explanation for why individuals do not naturally seek out dark rooms.
Investigating Core Knowledge Systems and Cognitive Processes
The conversation shifts towards core knowledge systems that underpin cognitive processes, particularly focusing on how these innate priors facilitate intelligent behavior and perception. The debate touches on the existence of innate priors and their role in shaping cognitive development. Vision is highlighted as a domain where core knowledge systems play a crucial role, with advancements such as utilizing world models for vision reconstruction showcasing the potential power of these systems in understanding complex visual information.
In this episode of Active Inference Insights, we welcome our first mathematician onto the show: Lance Da Costa. If you’re into Langevins, Fokker-Plancks, solenoidals and Fisher information metric tensors, this one is for you. However, if all that terrifies you to high heaven, don’t fret; Lance and Darius also explore eco-niche modelling, temporality, metacognition and far more in this deep dive into cutting-edge Active Inference theory.
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