Learnability of state spaces of physical systems is undecidable

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11230%2F24%3A10485953" target="_blank" >RIV/00216208:11230/24:10485953 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6ha4DS1VHr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=6ha4DS1VHr</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jocs.2024.102452" target="_blank" >10.1016/j.jocs.2024.102452</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Learnability of state spaces of physical systems is undecidable

Popis výsledku v původním jazyce

Despite an increasing role of machine learning in science, there is a lack of results on limits of empirical exploration aided by machine learning. In this paper, we construct one such limit by proving undecidability of learnability of state spaces of physical systems. We characterize state spaces as binary hypothesis classes of the computable Probably Approximately Correct learning framework. This leads to identifying the first limit for learnability of state spaces in the agnostic setting. Further, using the fact that finiteness of the combinatorial dimension of hypothesis classes is undecidable, we derive undecidability for learnability of state spaces as well. Throughout the paper, we try to connect our formal results with modern neural networks. This allows us to bring the limits close to the current practice and make a first step in connecting scientific exploration aided by machine learning with results from learning theory.

Název v anglickém jazyce

Learnability of state spaces of physical systems is undecidable

Popis výsledku anglicky

Despite an increasing role of machine learning in science, there is a lack of results on limits of empirical exploration aided by machine learning. In this paper, we construct one such limit by proving undecidability of learnability of state spaces of physical systems. We characterize state spaces as binary hypothesis classes of the computable Probably Approximately Correct learning framework. This leads to identifying the first limit for learnability of state spaces in the agnostic setting. Further, using the fact that finiteness of the combinatorial dimension of hypothesis classes is undecidable, we derive undecidability for learnability of state spaces as well. Throughout the paper, we try to connect our formal results with modern neural networks. This allows us to bring the limits close to the current practice and make a first step in connecting scientific exploration aided by machine learning with results from learning theory.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50601 - Political science

Projekt

<a href="/cs/project/EH22_008%2F0004595" target="_blank" >EH22_008/0004595: Za hranice bezpečnosti: role konfliktu v posilování odolnosti</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Computational Science

ISSN

1877-7503

e-ISSN

1877-7511

Svazek periodika

83

Číslo periodika v rámci svazku

December 2024

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

7

Strana od-do

1-7

Kód UT WoS článku

001333517500001

EID výsledku v databázi Scopus

2-s2.0-85205572580