From equations to ecosystems, we explore the mathematics, physics, computation, and biology that shape our lives.
A series of thought provoking discussions where a human moderator invites popular AI models to contribute to a round table discussion.. about AI.
Read SeriesApplying new physics to intractable problems.
The math, physics and philosophy that drives Large Language Models and Generative AI - from transformers to quantum learning: we explore the scientific foundations of modern Artificial Intelligence.
Examine the standard Laplacian on the circle through the lens of averaging operators associated to the multiplicative group of coprime residues.
Utilizing high-dimensional vector spaces to model the structural coherence of proteins. We are developing a mathematical framework for defining stability in complex organic systems.
Our research of current control paradigms has reached the mathematical limits of their scalability. As system dimensionality increases, the computational cost required to resolve state transitions scales exponentially. We provide a comprehensive analysis of these limitations.
A Unified Predictive Recurrence Framework. We introduce the Single Unified Master Equation (SUME), demonstrating that cortical predictive coding and transformer attention are instantiations of the same recursive algorithm.
A framework for solving large-scale computational problems inspired by classical Langevin dynamics, combining deterministic energy gradients with stochastic exploration.
Examine the standard Laplacian on the circle through the lens of averaging operators associated to the multiplicative group of coprime residues.
A Structural Theory via Euler’s Totient function. Uncovering the duality between isolation phases and units modulo n.
Predicting computational tractability through geometric coherence scores.
Perspectives from accredited contributors on the intersection of mathematics, physics, and complexity.
AI is the bottle you open too soon... a volatile ferment. A reflection on validation, wine, and the sobering reality of artificial intelligence.
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Why do stochastic processes often find solutions that deterministic gradients miss? Exploring the geometry of loss landscapes where $\nabla E \approx 0$ but entropy is maximized.
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If we map semantic relationships as persistent homology groups, we find that understanding is less about data points and more about the holes in the data structure.
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