Related papers: Recursive querying of neural networks via weighted…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…

Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…

After the tremendous development of neural networks trained by backpropagation, it is a good time to develop other algorithms for training neural networks to gain more insights into networks. In this paper, we propose a new algorithm for…

A fundamental problem in studying and modeling economic and financial systems is represented by privacy issues, which put severe limitations on the amount of accessible information. Here we introduce a novel, highly nontrivial method to…

Despite their impressive performance, contemporary neural networks often lack structural safeguards that promote stable learning and interpretable behavior. In this work, we introduce a reformulation of layer-level transformations that…

We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…

The approximation power of general feedforward neural networks with piecewise linear activation functions is investigated. First, lower bounds on the size of a network are established in terms of the approximation error and network depth…

Unitary neural networks are promising alternatives for solving the exploding and vanishing activation/gradient problem without the need for explicit normalization that reduces the inference speed. However, they often require longer training…

Performing the inference step of deep learning in resource constrained environments, such as embedded devices, is challenging. Success requires optimization at both software and hardware levels. Low precision arithmetic and specifically low…

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…

We explore end-to-end trained differentiable models that integrate natural logic with neural networks, aiming to keep the backbone of natural language reasoning based on the natural logic formalism while introducing subsymbolic vector…

We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and…

Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and…

Relu Fully Connected Networks are ubiquitous but uninterpretable because they fit piecewise linear functions emerging from multi-layered structures and complex interactions of model weights. This paper takes a novel approach to piecewise…

We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds…

Deep reinforcement learning techniques have demonstrated superior performance in a wide variety of environments. As improvements in training algorithms continue at a brisk pace, theoretical or empirical studies on understanding what these…

Lifted Relational Neural Networks (LRNNs) describe relational domains using weighted first-order rules which act as templates for constructing feed-forward neural networks. While previous work has shown that using LRNNs can lead to…