相关论文: Separating Principles Below WKL0

Large language models (LLMs) have shown incredible performance in completing various real-world tasks. The current paradigm of knowledge learning for LLMs is mainly based on learning from examples, in which LLMs learn the internal rule…

Reasoning over knowledge graphs (KGs) with first-order logic (FOL) queries is challenging due to the inherent incompleteness of real-world KGs and the compositional complexity of logical query structures. Most existing methods rely on…

The idea of blocking in configuration space has played an important role in the development of the RG ideas. However, despite being half a century old and having had a huge intellectual impact, generic numerical methods to perform blocking…

$\Omega$-rule was introduced by W. Buchholz to give an ordinal-free cut-elimination proof for a subsystem of analysis with $\Pi^{1}_{1}$-comprehension. His proof provides cut-free derivations by familiar rules only for arithmetical…

Ontologies have supported knowledge representation and white-box reasoning for decades; thus, the automated ontology generation (AOG) plays a crucial role in scaling their use. Software engineering standards (SES) consist of long,…

DGLAP integro-differential equation can be solved by applying certain map in the complex plane of Mellin moments. It may be re-written as Schr\"odinger equation for $n$ particles. By applying another map in the complex plane of Mellin…

Recent advances in applying reinforcement learning (RL) to large language models (LLMs) have led to substantial progress. In particular, a series of remarkable yet often counterintuitive phenomena have been reported in LLMs, exhibiting…

Traditionally, kernel methods rely on the representer theorem which states that the solution to a learning problem is obtained as a linear combination of the data mapped into the reproducing kernel Hilbert space (RKHS). While elegant from…

Neural models for NLP typically use large numbers of parameters to reach state-of-the-art performance, which can lead to excessive memory usage and increased runtime. We present a structure learning method for learning sparse,…

A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…

In this paper we propose a general framework to integrate supervised and unsupervised examples with background knowledge expressed by a collection of first-order logic clauses into kernel machines. In particular, we consider a multi-task…

Web image datasets curated online inherently contain ambiguous in-distribution (ID) instances and out-of-distribution (OOD) instances, which we collectively call non-conforming (NC) instances. In many recent approaches for mitigating the…

Offline reinforcement learning (RL) aims to find a near-optimal policy using pre-collected datasets. In real-world scenarios, data collection could be costly and risky; therefore, offline RL becomes particularly challenging when the…

Large language models (LLMs) have demonstrated impressive abilities in generating unstructured natural language according to instructions. However, their performance can be inconsistent when tasked with producing text that adheres to…

A new mean-field type theory is proposed to study order-disorder transitions (ODT) in block copolymers. The theory applies to both the weak segregation (WS) and the strong segregation (SS) regimes. A new energy functional is proposed…

Recently in [1, 2], Ali-Akbar Bromideh introduced the Kullback-Leibler Divergence (KLD) test statistic in discrim- inating between two models. It was found that the Ratio Minimized Kulback-Leibler Divergence (RMKLD) works better than the…

This paper provides an alternate characterization of type-two polynomial-time computability, with the goal of making second-order complexity theory more approachable. We rely on the usual oracle machines to model programs with subroutine…

Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…

The prevailing approach to distilling reasoning from Large Language Models (LLMs)-behavioral cloning from textual rationales-is fundamentally limited. It teaches Small Language Models (SLMs) to mimic surface-level patterns rather than the…

We introduce Options LLM (OLLM), a simple, general method that replaces the single next-token prediction of standard LLMs with a \textit{set of learned options} for the next token, indexed by a discrete latent variable. Instead of relying…