Related papers: fc: A Package for Generalized Function Composition…
We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…
This work introduces a novel R package for concise, informative summaries of machine learning models. We take inspiration from the summary function for (generalized) linear models in R, but extend it in several directions: First, our…
How to usefully encode compositional task structure has long been a core challenge in AI. Recent work in chain of thought prompting has shown that for very large neural language models (LMs), explicitly demonstrating the inferential steps…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
Core spanners are a class of document spanners that capture the core functionality of IBM's AQL. FC is a logic on strings built around word equations that when extended with constraints for regular languages can be seen as a logic for core…
Function merging is a pivotal technique for reducing code size by combining identical or similar functions into a single function. While prior research has extensively explored this technique, it has not been assessed in conjunction with…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We present a conceptual framework that unifies a variety of evaluation metrics for different structured prediction tasks (e.g. event and relation extraction, syntactic and semantic parsing). Our framework requires representing the outputs…
Building on top of a regression model, Conformal Prediction methods produce distribution free prediction sets, requiring only i.i.d. data. While R packages implementing such methods for the univariate response framework have been developed,…
Industry Foundation Classes (IFC) files are commonly used for data exchange of Building Information Models (BIMs). Due to the equivalent transformations in the graph structure of IFC data, it is a challenge to perform version comparison and…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
Order statistics provide an intuition for combining multiple lists of scores over a common index set. This intuition is particularly valuable when the lists to be combined cannot be directly compared in a sensible way. We describe here the…
$f,g\colon\mathbb{R}\longrightarrow\mathbb{R}$, it is natural to define $f+g$ as the function that maps $x\in\mathbb{R}$ to $f(x) + g(x)$. However, in base R, objects of class function do not have arithmetic methods defined, so idiom such…
This paper introduces a new method for redefining the Roman factorial using universally applicable functions that are not expressed in closed form. We present a set of foundational functions, similar to Boolean operations, to simplify the…
The FC-Gram algorithm approximates non-periodic functions to high order by constructing a periodic extension with controlled boundary behavior and applying trigonometric interpolation. In this paper we introduce a generalized FC-Gram…
Compositional generalization is a basic and essential intellective capability of human beings, which allows us to recombine known parts readily. However, existing neural network based models have been proven to be extremely deficient in…
When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, we…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
In this paper, we introduce Functional Generalized Canonical Correlation Analysis (FGCCA), a new framework for exploring associations between multiple random processes observed jointly. The framework is based on the multiblock Regularized…