Related papers: Consistency Strengths of Modified Maximality Princ…
In recent developments, a novel set of necessary optimality conditions for mixed constrained optimal control problems, termed the asymptotic weak maximum principle, has been formulated. These novel conditions deviate from the classical ones…
Generic absoluteness is the phenomenon that certain truths in the set-theoretic universe remain stable under forcing expansions. A classical result by Kripke asserts that every complete Boolean algebra completely embeds into a countably…
A novel perspective on the design of robust model predictive control (MPC) methods is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. Necessary and sufficient conditions…
The strong maximum principle ((SMP) in short) for subsolutions of the radiative transfer type equations is shown in this paper. We treat a general class of integro-differential equations, defined in the product space of the space variable…
Multiplicative Programming (MP) pertains to a spectrum of optimization problems that involve product term(s). As computational paradigms of communication systems continue to evolve, particularly concerning the offloading strategies of…
The minimum unsatisfiability version of a constraint satisfaction problem (MinCSP) asks for an assignment where the number of unsatisfied constraints is minimum possible, or equivalently, asks for a minimum-size set of constraints whose…
We discuss the notion of mass, mostly for fermions, and its relation to the breaking of CP invariance, the natural symmetry of gauge interactions. In a first model, we show how compactification on a Vortex in 2 extra dimensions leads to a…
It is shown that the resurrection axiom and the maximality principle may be consistently combined for various iterable forcing classes. The extent to which resurrection and maximality overlap is explored via the local maximality principle.
Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way,…
If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K…
In most practical applications of reinforcement learning, it is untenable to maintain direct estimates for individual states; in continuous-state systems, it is impossible. Instead, researchers often leverage state similarity (whether…
The quality of Large Language Model (LLM) pretraining depends on multiple factors, including the compute budget and the choice of optimization algorithm. Empirical scaling laws are widely used to predict loss as model size and training data…
Why do larger language models generalize better? To investigate this question, we develop generalization bounds on the pretraining objective of large language models (LLMs) in the compute-optimal regime, as described by the Chinchilla…
In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can be served as a mini review of PMC. We emphasize that the purpose of the PMC is to achieve precise…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
In the classification of complete first-order theories, many dividing lines have been defined in order to understand the complexity and the behavior of some classes of theories. In this paper, using the concept of patterns of consistency…
Large Language Models (LLMs) can generate code from natural language, but their performance is highly sensitive to prompt formulation. We propose a reinforcement-learning-based framework that models prompt refinement as a sequential…
The concept of (stable) weak containment for measure-preserving actions of a countable group $\Gamma$ is analogous to the classical notion of (stable) weak containment of unitary representations. If $\Gamma$ is amenable then the Rokhlin…
We lay the ground for an Isabelle/ZF formalization of Cohen's technique of forcing. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize the definition of forcing notions as…
In this paper we study the approximability of (Finite-)Valued Constraint Satisfaction Problems (VCSPs) with a fixed finite constraint language {\Gamma} consisting of finitary functions on a fixed finite domain. An instance of VCSP is given…