Related papers: Structure and Power: an emerging landscape

Multi-valued functions are common in computable analysis (built upon the Type 2 Theory of Effectivity), and have made an appearance in complexity theory under the moniker search problems leading to complexity classes such as PPAD and PLS…

Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…

This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…

We explore whether the topology of energy landscapes in chemical systems obeys any rules and what these rules are. To answer this and related questions we use several tools: (i)Reduced energy surface and its density of states, (ii)…

Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…

Theory of Kingman's partition structures has two culminating points: the general paintbox representation, relating finite partitions to hypothetical infinite populations via a natural sampling procedure, known as Kingman's paintbox; a…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context…

Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…

This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…

Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…

We introduce loop spaces (in the sense of derived algebraic geometry) into the representation theory of reductive groups. In particular, we apply the theory developed in our previous paper arXiv:1002.3636 to flag varieties, and obtain new…

Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…

We propose a new line of attack to create a finite quantum theory which includes general relativity and (perhaps) the standard model in its low energy limit. The theory would emerge from the categorical approach. A structure is observed on…

We use reinforcement learning to learn tree-structured neural networks for computing representations of natural language sentences. In contrast with prior work on tree-structured models in which the trees are either provided as input or…

We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…

This paper describes a new technique, called "knowledge patterns", for helping construct axiom-rich, formal ontologies, based on identifying and explicitly representing recurring patterns of knowledge (theory schemata) in the ontology, and…

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…