From Signal Processing to AGI: A Mathematical Foundation: Volume III: Safety, Synthesis, and Open Frontiers
English | April 2, 2026 | ASIN: B0GF85XSPH | 324 pages | Epub | 1.26 MB
Volume III brings the trilogy to its most ambitious stage by moving from representation and learning to agency, causality, planning, robustness, and the long-range mathematical future of intelligent systems. Here artificial intelligence is no longer treated merely as a collection of predictive models, but as an organized adaptive structure capable of building internal world models, reasoning across modalities, selecting actions, managing uncertainty, and operating under constraints of safety and verification. The volume develops the mathematics of predictive state representations, internal simulation, hierarchical planning, tool use, modular coordination, intervention, and control, while also addressing the emerging demands of advanced AI systems: stability, interpretability, certification, corrigibility, and governance. In this sense, Volume III asks what happens when signal-processing architectures become decision-making systems embedded in complex environments.At the deepest level, the volume argues that any serious path toward more general intelligence must unify inference, memory, abstraction, action, and oversight within a single mathematical framework. It therefore explores frontier topics such as causal intelligence, hybrid symbolic-neural architectures, distributed and collective intelligence, scientific AI, and the open theoretical limits of adaptive systems. Rather than presenting AGI as a vague aspiration, the book treats it as a rigorous research program grounded in control theory, probability, operator theory, optimization, and information geometry. The result is a forward-looking synthesis in which the tools developed across the earlier volumes culminate in a theory of intelligent systems that can not only represent and generate, but also reason, intervene, cooperate, and remain accountable under real-world constraints.
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