Related papers: Rule Algebras for Adhesive Categories
Quasitoposes encompass a wide range of structures, including various categories of graphs. They have proven to be a natural setting for reasoning about the metatheory of algebraic graph rewriting. In this paper we propose and motivate the…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
A superposition rule is a particular type of map that enables one to express the general solution of certain systems of first-order ordinary differential equations, the so-called Lie systems, out of generic families of particular solutions…
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner…
Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for…
Many algorithms for aligning LLMs with human preferences assume that human preferences are binary and deterministic. However, human preferences can vary across individuals, and therefore should be represented distributionally. In this work,…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
Direct Preference Optimization (DPO) guides large language models (LLMs) to generate recommendations aligned with user historical behavior distributions by minimizing preference alignment loss. However, our systematic empirical research and…
Modern self-supervised predictive architectures excel at capturing complex statistical correlations from high-dimensional data but lack mechanisms to internalize verifiable human logic, leaving them susceptible to spurious correlations and…
In this paper, we introduce the notion of differential graded Poisson algebra and study its universal enveloping algebra. From any differential graded Poisson algebra $A$, we construct two isomorphic differential graded algebras: $A^e$ and…
This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cram{\'e}r-Lundberg…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
In this paper, we propose a new paradigm for program optimization which is based on aggressive aggregation, i.e., on a partial evaluation-based decomposition of acyclic program fragments into a pair of computationally optimal structures: an…
We introduce a family of mathematical objects called $\mathcal{P}$-schemes, where $\mathcal{P}$ is a poset of subgroups of a finite group $G$. A $\mathcal{P}$-scheme is a collection of partitions of the right coset spaces $H\backslash G$,…
With the growing size of data sets, feature selection becomes increasingly important. Taking interactions of original features into consideration will lead to extremely high dimension, especially when the features are categorical and…
Direct Preference Optimisation (DPO) is effective at significantly improving the performance of large language models (LLMs) on downstream tasks such as reasoning, summarisation, and alignment. Using pairs of preferred and dispreferred…
We unite two themes in dyadic analysis and number theory by studying an analogue of the failure of the Hasse principle in harmonic analysis. Explicitly, we construct an explicit family of measures on the real line that are $p$-adic and…
Solutions to decentralized discrete-event systems problems are characterized by the way local decisions are fused to yield a global decision. A fusion rule is colloquially called an architecture. Current approaches do not provide a direct…