Recursively Enumerably Representable Classes and Computable Versions of the Fundamental Theorem of Statistical Learning
arXiv:2511.02644v2 Announce Type: replace Abstract: We study computable probably approximately correct (CPAC) learning, where learners are required to be computable functions. It had been previously observed that the Fundamental Theorem of Statistical Learning, which characterizes PAC learnability by finiteness of the Vapnik-Chervonenkis (VC-)dimension, no longer holds in this framework. Recent works recovered analogs of the Fundamental Theorem in the computable setting, for instance by introducing an effective VC-dimension. Guided by this, we investigate the connection between CPAC learning a
The paper builds upon previous observations that the Fundamental Theorem of Statistical Learning does not hold in the computable setting, highlighting ongoing research into the theoretical foundations of tractable AI. It is indicative of foundational research actively addressing limitations in current AI learning theory.
Understanding the computable limits of learning and developing effective versions of fundamental theorems is crucial for designing robust, predictable, and ultimately safer AI systems with guaranteed performance characteristics.
The research aims to establish new theoretical frameworks, such as an effective VC-dimension, that can provide a foundational understanding for computable AI, potentially altering how AI learnability is defined and engineered.
- · AI researchers (theory)
- · Developers of provably robust AI
- · Organizations requiring certifiable AI outcomes
- · AI development without clear theoretical bounds
- · Systems relying on non-computable learning assumptions
Refinement of theoretical understanding of AI learnability and its practical implications for algorithm design.
Development of new classes of AI algorithms with stronger theoretical guarantees regarding their learning limits and efficiency.
Potential for regulatory frameworks to incorporate 'computable learnability' as a criterion for AI system deployment.
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