Related papers: Unification and combination of iterative insertion…

Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…

Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…

An extension to classical unification, called {\em graded unification} is presented. It is capable of combining contradictory information. An interactive processing paradigm and parser based on this new operator are also presented.

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…

In this paper we present a combination framework for polynomial complexity analysis of term rewrite systems. The framework covers both derivational and runtime complexity analysis. We present generalisations of powerful complexity…

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…

We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…

We propose a method that learns a discriminative yet semantic space for object categorization, where we also embed auxiliary semantic entities such as supercategories and attributes. Contrary to prior work which only utilized them as side…

Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network…

This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…

Recently, the embedding-based recommendation models (e.g., matrix factorization and deep models) have been prevalent in both academia and industry due to their effectiveness and flexibility. However, they also have such intrinsic…

We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

Ensemble methods such as boosting combine multiple learners to obtain better prediction than could be obtained from any individual learner. Here we propose a principled framework for directly constructing ensemble learning methods from…

Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…

Model selection is a strategy aimed at creating accurate and robust models. A key challenge in designing these algorithms is identifying the optimal model for classifying any particular input sample. This paper addresses this challenge and…

Representing domain knowledge is crucial for any task. There has been a wide range of techniques developed to represent this knowledge, from older logic based approaches to the more recent deep learning based techniques (i.e. embeddings).…

Inference in current domains of application are often complex and require us to integrate the expertise of a variety of disparate panels of experts and models coherently. In this paper we develop a formal statistical methodology to guide…

We propose general principles for semantic networks allowing them to be implemented as dynamical neural networks. Major features of our scheme include: (a) the interpretation that each node in a network stands for a bound integration of the…

This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…