arXiv subjects

Tehseen Rug

Publications and source records attributed to Tehseen Rug.

5 recordsLinked to original sources

arXiv2025

From Logic to Language: A Trust Index for Problem Solving with LLMs

Classical computation, grounded in formal, logical systems, has been the engine of technological progress for decades, excelling at problems that can be described with unambiguous rules. This paradigm, however, leaves a vast ocean of human problems -- those characterized by ambiguity, dynamic environments, and subjective context -- largely untouched. The advent of Large Language Models (LLMs) represents a fundamental shift, enabling computational systems to engage with this previously inaccessible domain using natural language. This paper introduces a unified framework to understand and contrast these problem-solving paradigms. We define and delineate the problem spaces addressable by formal languages versus natural language. While solutions to the former problem class can be evaluated using binary quality measures, the latter requires a much more nuanced definition of approximate solution space taking into account the vagueness, subjectivity and ambiguity inherent to natural language. We therefore introduce a vector-valued trust index Q, which reflects solution quality and distinguishes the binary correctness of formal solutions from the continuous adequacy spectrum characteristic of natural language solutions. Within this framework, we propose two statistical quality dimensions. Normalized bi-semantic entropy measures robustness and conceptual diversity of LLM answers given semantic variation in problem formulations. Emotional valence maps subjective valuation of a solution to a quantifiable metric that can be maximized by invoking statistical measures. The concepts introduced in this work will provide a more rigorous understanding of the capabilities, limitations, and inherent nature of problem-solving in the age of LLMs.

cs.AI↗

arXiv2015

Towards a Quantum Theory of Solitons

We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

hep-th↗

arXiv2014

Probing the Constituent Structure of Black Holes

Based on recent ideas, we propose a framework for the description of black holes in terms of constituent graviton degrees of freedom. Within this formalism a large black hole can be understood as a bound state of N longitudinal gravitons. In this context black holes are similar to baryonic bound states in quantum chromodynamics which are described by fundamental quark degrees of freedom. As a quantitative tool we employ a quantum bound state description originally developed in QCD that allows to consider black holes in a relativistic Hartree like framework. As an application of our framework we calculate the cross section for scattering processes between graviton emitters outside of a Schwarzschild black hole and absorbers in its interior, that is gravitons. We show that these scatterings allow to directly extract structural observables such as the momentum distribution of black hole constituents.

hep-th↗

arXiv2014

A Quantum Bound-State Description of Black Holes

A relativistic framework for the description of bound states consisting of a large number of quantum constituents is presented, and applied to black-hole interiors. At the parton level, the constituent distribution, number and energy density inside black holes are calculated, and gauge corrections are discussed. A simple scaling relation between the black hole mass and constituent number is established.

hep-th↗

arXiv2012

Holography of Species in Cascading DGP

In this paper we generalize the idea of species holography to the case of Cascading DGP theories. Essence of the phenomenon is that a 4D field theory with N particle species coupled to a high-dimensional bulk gravity propagating solely a graviton becomes strongly coupled at the scale that would be the quantum gravity scale of the bulk theory if all the species were propagating in the bulk. We will see that both, crossover scales and Vainshtein scales, can be understood as holographic scales in the above sense. We confirm our results by an explicit effective field theoretic derivation of these scales in Cascading DGP.

hep-th↗