La soluzione di OpenAI alle equazioni di Navier–Stokes non corrisponde alla sua verifica Lean.

4 days ago by macfranc to c/matematica

Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be mechanically verified. The purpose of this article is to demonstrate why this process may offer no confidence in the original NL argument, owing to the various difficulties in performing the translation semantically faithfully. In particular, we highlight that the problem of resolving ambiguities in mathematical NL text, which is necessary in order to provide semantically faithful translation, is arbitrarily high up in the Solvability Complexity Index (SCI) hierarchy/arithmetical hierarchy (the SCI $= \infty$). Hence, informally, providing semantically faithful AI autoformalisation is harder than any computational problem including the Halting problem (which has SCI $= 1$). To demonstrate the effect of this result we provide several examples of AI mistranslations of NL statements and proofs into Lean in practice, resulting in mismatches between NL proofs and their Lean `verifications'. These include OpenAI's announced Navier-Stokes proof. In particular, we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations.
matematica
matematica

@feddit.it

login for more options
127
233
9

Benvenuti alla comunità dedicata alla regina delle scienze: la matematica!

Vi ricordiamo di dare un'occhiata alla Guida all’utilizzo di Feddit

Ovviamente vi raccomandiamo di proporre link a tema, in italiano ma anche in inglese. In quest'ultimo caso postate il link con il suo titolo originale non tradotto, mentre per il testo potete tranquillamente pubblicare una sintesi in italiano. Ovviamente non sono ammessi articoli che rimandano alla pseudoscienza o che non hanno attinenza con la matematica.

#matematica #algebra #analisi #italian #fedi22 #gruppi #forum

go to feed...