Related papers: Lions' representation theorem and applications
The success of deep reinforcement learning (DRL) lies in its ability to learn a representation that is well-suited for the exploration and exploitation task. To understand how the choice of representation can improve the efficiency of…
In this paper we study the representation theory of the algebras generated by the single bond transfer matrices in dilute lattice models. This representation theory is related to a tensor product of monoidal categories. This construction is…
Linear matrix Inequalities (LMIs) have had a major impact on control but formulating a problem as an LMI is an art. Recently there is the beginnings of a theory of which problems are in fact expressible as LMIs. For optimization purposes it…
Despite its centrality in the philosophy of cognitive science, there has been little prior philosophical work engaging with the notion of representation in contemporary NLP practice. This paper attempts to fill that lacuna: drawing on ideas…
An attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness and asymptotic analysis for fully nonlinear evolutionary game theoretic models. The model should be rich enough to…
Lurie's theorem states that there exists a sheaf of ring spectra on the site of formally \'etale Deligne--Mumford stacks over the moduli stack of $p$-divisible groups of height $n$, which agrees with the classical Landweber exact functor…
This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples.…
We studied framed deformations of two dimensional Galois representation of which the residue representation restrict to decomposition groups are scalars, and established a modular lifting theorem for certain cases. We then proved a family…
In this paper, we introduce the representation theory of $\delta$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and…
The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…
We provide a full self-contained proof of a famous Lemma of Ilmanen. This proof is based on a regularisation procedure similar to Lasry-Lions regularisation.
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…
In this work we state and prove versions of some classical results, in the framework of functionals defined in the space of functions of bounded variation in $\mathbb{R}^N$. More precisely, we present versions of the Radial Lemma of…
We discuss the theory of Lie algebras in Lean's Mathlib library. Using nilpotency as the theme, we outline a computer formalisation of Engel's theorem and an application to root space theory. We emphasise that all arguments work with…
Reinforcement Learning (RL) has shown remarkable abilities in learning policies for decision-making tasks. However, RL is often hindered by issues such as low sample efficiency, lack of interpretability, and sparse supervision signals. To…
The Lee, Oehme and Yang (LOY) theory of time evolution in two state subspace of states of the complete system is discussed. Some inconsistencies in assumptions and approximations used in the standard derivation of the LOY effective…
Reward Model (RM) has demonstrated impressive potential for enhancing Large Language Models (LLM), as RM can serve as a proxy for human preferences, providing signals to guide LLMs' behavior in various tasks. In this paper, we provide a…
In Reinforcement Learning (RL), the goal of agents is to discover an optimal policy that maximizes the expected cumulative rewards. This objective may also be viewed as finding a policy that optimizes a linear function of its state-action…
This work is based on the idea that extension of physical and mathematical theories to include the amount of space, time, momentum, and energy resources required to determine properties of systems may influence what is true in physics and…
In respect of b-linear functional, Riesz representation theorem in n-Hilbert space have been proved. We define b-sesquilinear functional in n-Hilbert space and establish the polarization identities. A generalized form of the Schwarz…