Related papers: Parametrised Functional Interpretations
Numerous approaches have been recently proposed for learning fair representations that mitigate unfair outcomes in prediction tasks. A key motivation for these methods is that the representations can be used by third parties with unknown…
There is a need of ensuring machine learning models that are interpretable. Higher interpretability of the model means easier comprehension and explanation of future predictions for end-users. Further, interpretable machine learning models…
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…
Human parsing is for pixel-wise human semantic understanding. As human bodies are underlying hierarchically structured, how to model human structures is the central theme in this task. Focusing on this, we seek to simultaneously exploit the…
Natural language processing covers a wide variety of tasks predicting syntax, semantics, and information content, and usually each type of output is generated with specially designed architectures. In this paper, we provide the simple…
This paper outlines a theoretical framework using which different automatic metrics can be designed for evaluation of Machine Translation systems. It introduces the concept of {\em cognitive ease} which depends on {\em adequacy} and {\em…
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…
The concept of functionality oriented programming is proposed, and some of its aspects are discussed, such as: (1) implementation independent basic types and generic collection types; (2) syntax requirements and recommendations for…
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
Multilingual language models achieve strong aggregate performance yet often behave unpredictably across languages, scripts, and cultures. We argue that mechanistic explanations for such models should satisfy a \emph{causal} standard: claims…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…
The remarkable performance of convolutional neural networks (CNNs) is entangled with their huge number of uninterpretable parameters, which has become the bottleneck limiting the exploitation of their full potential. Towards network…
The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.
Charts are very popular for analyzing data, visualizing key insights and answering complex reasoning questions about data. To facilitate chart-based data analysis using natural language, several downstream tasks have been introduced…
This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).
In this paper, we present an algebraic approach to idempotent functional analysis, which is an abstract version of idempotent analysis. The basic concepts and results are expressed in purely algebraic terms. We consider idempotent versions…
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.