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Machine Learning Beyond Statistical Consistency for Hybrid AI — arXiv:2611.01914

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01914
License (as archived): CC0-1.0
Archived: 2026-11-03T10:57:32.762Z
SHA-256 of the archived text: 2479881ff3623efad3a9d8d02e22c576377ff7d9d68c77d490dba0b65cc6c7b8
Stable URL of this page: https://metraipolis.com/documento/dc_a42edf9fd01d

How to cite

Machine Learning Beyond Statistical Consistency for Hybrid AI — arXiv:2611.01914 — arXiv (en), https://arxiv.org/abs/2611.01914 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a42edf9fd01d (Metraipolis archive dc_a42edf9fd01d, sha256 2479881ff3623efad3a9d8d02e22c576377ff7d9d68c77d490dba0b65cc6c7b8)

BibTeX

@misc{dca42edf9fd01d,
  title = {Machine Learning Beyond Statistical Consistency for Hybrid AI — arXiv:2611.01914},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01914},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a42edf9fd01d; sha256 2479881ff3623efad3a9d8d02e22c576377ff7d9d68c77d490dba0b65cc6c7b8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01914. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose a new definition of machine learning, according to which a machine learns a function when it computes the function successfully, that is, when the value it returns for each input has a proper derivation in a formal system. We extend Gödel's Representability Theorem, which equates computation with derivation, to empirical targets in two ways: the theorem is extended to the computable reals, and the data are admitted into the system as empirical definitions that record what has been observed. We prove that a machine learns a true probability if and only if two conditions are met. The Truth Condition is that its estimate converges to the true probability, which is statistical consistency. The Assurance Condition is that the machine properly derives its own convergence inside the system. Learning thus lies beyond statistical consistency, for it requires a derivation of the convergence from the record. A global assumption about the data, such as the i.i.d. assumption, does not supply such a derivation, because it leads only to a circular one, as we show for PAC learning. On the other hand, the two conditions are met for the probability of a sentence over a finite ideal corpus. A real machine can approximate a true probability only if an ideal machine can learn it precisely, that is, only in a domain that meets the two conditions. Modern AI works in such a domain, and we offer this as a clue to its success. Modern AI is hybrid as well, in two senses: First, it performs two kinds of tasks, namely probabilistic ones such as predicting the next word and deductive ones such as proving and coding. Second, it combines two parts of different kinds, a statistical proposer and a deductive verifier, for proving and coding. Our framework explains both senses of hybridity in one formal system.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2611.01914 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T10:49:38.601Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).