Related papers: Deep Learning for Symbolic Mathematics

Recent artificial neural networks that process natural language achieve unprecedented performance in tasks requiring sentence-level understanding. As such, they could be interesting models of the integration of linguistic information in the…

We present a method for visualising the response of a deep neural network to a specific input. For image data for instance our method will highlight areas that provide evidence in favor of, and against choosing a certain class. The method…

Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…

Deep neural networks (DNN) have achieved unprecedented performance in computer-vision tasks almost ubiquitously in business, technology, and science. While substantial efforts are made to engineer highly accurate architectures and provide…

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…

Neural-symbolic integration aims to combine the connectionist subsymbolic with the logical symbolic approach to artificial intelligence. In this paper, we first define the answer set semantics of (boolean) neural nets and then introduce…

Symbolic execution is a powerful systematic software analysis technique, but suffers from the high cost of constraint solving, which is the key supporting technology that affects the effectiveness of symbolic execution. Techniques like…

Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…

Neural networks have to capture mathematical relationships in order to learn various tasks. They approximate these relations implicitly and therefore often do not generalize well. The recently proposed Neural Arithmetic Logic Unit (NALU) is…

Recently, strong results have been demonstrated by Deep Recurrent Neural Networks on natural language transduction problems. In this paper we explore the representational power of these models using synthetic grammars designed to exhibit…

We propose two new criteria to understand the advantage of deepening neural networks. It is important to know the expressivity of functions computable by deep neural networks in order to understand the advantage of deepening neural…

How can neural networks perform so well on compositional tasks even though they lack explicit compositional representations? We use a novel analysis technique called ROLE to show that recurrent neural networks perform well on such tasks by…

We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods. For nonparametric regression problems, it is well known that many standard methods attain the minimax…

Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks…

We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these…

Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to…

Machine learning is rapidly making its pathway across all of the natural sciences, including physical sciences. The rate at which ML is impacting non-scientific disciplines is incomparable to that in the physical sciences. This is partly…

Deep neural networks have become increasingly successful at solving classic perception problems such as object recognition, semantic segmentation, and scene understanding, often reaching or surpassing human-level accuracy. This success is…

Deep learning networks have been trained to recognize speech, caption photographs and translate text between languages at high levels of performance. Although applications of deep learning networks to real world problems have become…

Deep Neural Networks (DNNs) are rapidly gaining popularity in a variety of important domains. Formally, DNNs are complicated vector-valued functions which come in a variety of sizes and applications. Unfortunately, modern DNNs have been…