arXiv:2606.21585v2 Announce Type: replace Abstract: A finite machine's digital twin of a system observes the territory through finite, noisy sensors; we model its coherent output as a belief, a probability density over states, the Bayes posterior, never a point. Certainty, the perfect twin, is denied twice, by observation and by physics, both read off the Fisher information. To make this finiteness geometric, we model what it costs to change a belief: a belief-cost geometry, optimal transport in Wasserstein space reweighted conformally by Fisher information. The framework rests on two posed co
This research emerges as the limitations of current AI systems in handling uncertainty and resource constraints become more apparent, necessitating foundational theoretical advancements.
It introduces a geometric framework for understanding belief updates under finite resources and noisy observations, potentially leading to more robust and resource-efficient AI models.
The theoretical understanding of AI systems' interaction with uncertainty and resource limitations is deepened, offering a new lens for designing intelligent agents.
- · AI researchers
- · Robotics engineers
- · Autonomous systems developers
- · Theoretical computer science
- · AI models lacking robust uncertainty quantification
- · Systems heavily reliant on unbounded computational resources
- · Engineering approaches ignoring information costs
This framework could lead to the development of AI algorithms more explicitly designed to manage computational and informational costs.
More resource-aware AI systems could significantly improve the efficiency and applicability of AI in constrained environments, such as edge computing or space exploration.
A deeper understanding of 'belief-cost geometry' might influence the philosophical understanding of intelligence, linking it inextricably to resource management and information friction.
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