Related papers: Separating Principles Below WKL0

In this paper, we provide a simple framework to derive and analyse several classes of effective one-step methods. The framework consists in the discretization of a local Fourier expansion of the continuous problem. Different choices of the…

This paper proposed a new regression model called $l_1$-regularized outlier isolation and regression (LOIRE) and a fast algorithm based on block coordinate descent to solve this model. Besides, assuming outliers are gross errors following a…

We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…

Rules have a number of desirable properties. It is easy to understand, infer new knowledge, and communicate with other inference systems. One weakness of the previous rule induction systems is that they only find rules within a knowledge…

Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural…

Let $\mathsf{TT}^2_k$ denote the combinatorial principle stating that every $k$-coloring of pairs of compatible nodes in the full binary tree has a homogeneous solution, i.e. an isomorphic subtree in which all pairs of compatible nodes have…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

We construct an $\ll^2$-solution (also known as a weakly low solution) to ${\mathrm{D}^2}$ within ${\mathrm{B}\Sigma^0_{3}}$ and prove the $\ll^2$-basis theorem for $\mathrm{RT}^2$ over ${\mathrm{B}\Sigma^0_{3}}$. The $\ll^2$-basis theorem…

Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…

The idea of automatic synthesis of reactive programs starting from temporal logic (LTL) specifications is quite old, but was commonly thought to be infeasible due to the known double exponential complexity of the problem. However, new ideas…

Reinforcement learning (RL) commonly relies on scalar rewards with limited ability to express temporal, conditional, or safety-critical goals, and can lead to reward hacking. Temporal logic expressible via the more general class of…

This work studies offline Reinforcement Learning (RL) in a class of non-Markovian environments called Regular Decision Processes (RDPs). In RDPs, the unknown dependency of future observations and rewards from the past interactions can be…

We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated…

Word segmentation stands as a cornerstone of Natural Language Processing (NLP). Based on the concept of "comprehend first, segment later", we propose a new framework to explore the limit of unsupervised word segmentation with Large Language…

This paper presents an online learning with regularized kernel based one-class extreme learning machine (ELM) classifier and is referred as online RK-OC-ELM. The baseline kernel hyperplane model considers whole data in a single chunk with…

In this paper, we discuss a proof system $\mathsf{NGL}$ for the logic $\mathbf{GL}$ of provability, which is equipped with an $\omega$-rule. We show the three classes of transitive Kripke frames, the class which strongly validates the…

We show how deep learning methods can be applied in the context of crowdsourcing and unsupervised ensemble learning. First, we prove that the popular model of Dawid and Skene, which assumes that all classifiers are conditionally…

While test-time reasoning enables language models (LMs) to tackle complex tasks, searching or planning in natural language can be slow, costly, and error-prone. But even when LMs struggle to emulate the precise reasoning steps needed to…

Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems,…

Continuing the study of complexity theory of Koepke's Ordinal Turing Machines (OTMs) that was started by Rin, L\"owe and the author, we prove the following results: (1) An analogue of Ladner's theorem for OTMs holds: That is, there are…