Beyond Statistical Learning: Exact Learning Is Essential for General Intelligence

This paper argues that artificial general intelligence (AGI), particularly in tasks requiring deductive reasoning, is hindered by the prevalent statistical learning paradigm. Current AI systems, relying on statistical methods like large language models (LLMs), often fail consistently on simple logical tasks despite impressive performance in other areas because they prioritize average accuracy over distributions rather than universal correctness. The authors propose a fundamental shift to exact learning, a more rigorous paradigm demanding flawless performance on all valid inputs. They demonstrate through examples and proofs that statistical shortcuts and inherent symmetries in learning algorithms prevent exact learning, suggesting that achieving true deductive capabilities requires new approaches to algorithm design, data utilization (teaching sets), and task formulation.