The paper titled "Pessimistic Meta-Induction and Its Limits: Lessons from Frequentist Statistics and Machine Learning Theory" critiques the pessimistic meta-inductive argument against scientific realism by attacking its inductive step rather than its historical premise. It introduces a new challenge, drawing on frequentist statistics, machine learning, and formal epistemology to assess induction through convergence to truth. The authors argue that ordinary enumerative induction can achieve convergence everywhere, whereas meta-induction fails to achieve even almost everywhere convergence, and in contexts where meta-induction applies, no inference method can achieve almost everywhere convergence.
By Hanti Lin
arXiv:2608.30246v1 Announce Type: cross
Abstract: The fundamental theorem of statistical learning states that, under suitable measurability assumptions, finite Vapnik--Chervonenkis (VC) dimension gua...
By Mateus Jesus de Arruda Campos, Gabriel Fernandes, Vinicius de Oliveira Rodrigues
We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results).
The paper argues that empirical results in Machine Learning are often difficult to reproduce due to limited availability of code and supporting materials, which hampers research progress. It analyzes and quantifies these challenges and proposes concrete measures to enhance the verifiability of results, even if full reproducibility cannot be guaranteed. The authors provide their code and supporting resources on GitHub for reference.
By Samet Hicsonmez, Nermin Samet, Renaud Marlet
arXiv:2608. 11181v1 Announce Type: cross Abstract: When a probabilistic predictor answers many conditional-probability queries, are its answers self-consistent, and can this be verified in polynomial time?
By Orr Paradise, Oliver Richardson, Yoshua Bengio, Shafi Goldwasser
The paper presents an interactive probabilistically checkable proof (PCP) protocol that allows a polynomial‑time verifier to check the approximate consistency of a probabilistic predictor defined by two circuits, P and Q. By evaluating these circuits at a few points and querying a proof oracle that encodes a witnessing probability distribution, the verifier can confirm that the predictor’s many conditional‑probability claims are self‑consistent. The authors also establish that the problem of verifying l₂‑approximate consistency for explicit probabilistic claims lies in NP, with certificates of size O(mn + log B), and show how to eliminate dependence on the input bit‑precision B through a small additive gap.
By Orr Paradise, Oliver Richardson, Yoshua Bengio, Shafi Goldwasser
arXiv:2606. 29346v1 Announce Type: new Abstract: Post-hoc explanation methods are routinely used to interpret scientific machine learning models, with the deliverable understood to be insight into the phenomenon the model has been trained on.
By Nick Oh, Helen Jin
arXiv:2608. 04049v1 Announce Type: cross Abstract: The principle of Occam's razor, which instructs us to prefer simplicity in inductive inference, has attracted much scrutiny both in the philosophy of science and in machine learning.
By Tom F. Sterkenburg
arXiv:2606. 28572v1 Announce Type: cross Abstract: The axiom of choice has divided the foundations of mathematics for over a century, but the distinction between classical and constructive proofs has remained a philosophical and methodological one.
By Rodrigo Mendoza-Smith
arXiv:2606. 10777v1 Announce Type: new Abstract: Uncertainty estimation is critical for deploying machine learning models in high-stakes settings.
By Arthur Hoarau
arXiv:2608. 01320v1 Announce Type: cross Abstract: Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples.
By Ziyi Cai, Shuangping Li, Yiheng Shen, Kangning Wang, Peng Zhang
arXiv:2608. 05702v1 Announce Type: new Abstract: Scientific machine learning commonly validates models at the level of a subdomain, a benchmark split, or an explanation for one prediction.
By Gnankan Landry Regis N'guessan, Bum Jun Kim