Related papers: Compiling with Arrays
The logic of information flows (LIF) has recently been proposed as a general framework in the field of knowledge representation. In this framework, tasks of procedural nature can still be modeled in a declarative, logic-based fashion. In…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in…
In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
Explainable AI (XAI) aims to address the human need for safe and reliable AI systems. However, numerous surveys emphasize the absence of a sound mathematical formalization of key XAI notions -- remarkably including the term "explanation"…
Consider a linear programming problem with n primal and m dual variables paired with n dual and m primal slack variables respectively, and aggregately denote these variables and slack variables as a vector z of length 2(n+m). Unlike…
We present a novel graphical framework for modeling non-negative sequential data with hierarchical structure. Our model corresponds to a network of coupled non-negative matrix factorization (NMF) modules, which we refer to as a positive…
Recent research on model interpretability in natural language processing extensively uses feature scoring methods for identifying which parts of the input are the most important for a model to make a prediction (i.e. explanation or…
Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
Accelerating programs is typically done by recognizing code idioms matching high-performance libraries or hardware interfaces. However, recognizing such idioms automatically is challenging. The idiom recognition machinery is difficult to…
Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a…
Despite their popularity, to date, the application of normalizing flows on categorical data stays limited. The current practice of using dequantization to map discrete data to a continuous space is inapplicable as categorical data has no…
In coding theory, constructing codes with good parameters is one of the most important and fundamental problems. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes equal to prime powers.…
MIRGE is a computational approach for scientific computing based on NumPy-like array computation, but using lazy evaluation to recast computation as data-flow graphs, where nodes represent immutable, multi-dimensional arrays. Evaluation of…
We describe a machine learning method for predicting the value of a real-valued function, given the values of multiple input variables. The method induces solutions from samples in the form of ordered disjunctive normal form (DNF) decision…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
Context: Tables are ubiquitous formats for data. Therefore, techniques for writing correct programs over tables, and debugging incorrect ones, are vital. Our specific focus in this paper is on rich types that articulate the properties of…