Related papers: Rule Algebras for Adhesive Categories
Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known…
Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…
``Fusion rules'' are laws of multiplication among eigenspaces of an idempotent. We establish fusion rules for flexible power-associative algebras, following Albert. We define the notion of an axis in the noncommutative setting (compare with…
We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…
This presentation is the sequel of a paper published in GETCO'00 proceedings where a research program to construct an appropriate algebraic setting for the study of deformations of higher dimensional automata was sketched. This paper…
Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are often subject to constraints, ruling out many candidates for composed rules. Focusing on the case of…
We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
Diffusion models have achieved state-of-the-art performance across multiple domains, with recent advancements extending their applicability to discrete data. However, aligning discrete diffusion models with task-specific preferences remains…
The inverse folding problem, aiming to design amino acid sequences that fold into desired three-dimensional structures, is pivotal for various biotechnological applications. Here, we introduce a novel approach leveraging Direct Preference…
Reinforcement learning (RL) in continuous state-action spaces remains challenging in scientific computing due to poor sample efficiency and lack of pathwise physical consistency. We introduce Differential Reinforcement Learning…
The theory of associative $n$-categories has recently been proposed as a strictly associative and unital approach to higher category theory. As a foundation for a proof assistant, this is potentially attractive, since it has the potential…
We study the confluence property of abstract rewriting systems internal to cubical categories. We introduce cubical contractions, a higher-dimensional generalisation of reductions to normal forms, and employ them to construct cubical…
We define novel fully combinatorial models of higher categories. Our definitions are based on a connection of higher categories to "directed spaces". Directed spaces are locally modelled on manifold diagrams, which are stratifications of…
These are extended notes for a series of lectures on Hall algebras given at the CRM Barcelona in February 2015. The basic idea of the theory of Hall algebras is that the collection of flags in an exact category encodes an associative…
Group Relative Policy Optimization (GRPO) has shown promise in discrete action spaces by eliminating value function dependencies through group-based advantage estimation. However, its application to continuous control remains unexplored,…
This study addresses the challenge of noise in training datasets for Direct Preference Optimization (DPO), a method for aligning Large Language Models (LLMs) with human preferences. We categorize noise into pointwise noise, which includes…