Related papers: A Symbolic Neural Network Representation and its A…

The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…

Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…

Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…

The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…

Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated features. A…

Binary representation is desirable for its memory efficiency, computation speed and robustness. In this paper, we propose adjustable bounded rectifiers to learn binary representations for deep neural networks. While hard constraining…

Deep neural networks (DNNs) have been shown lack of robustness for the vulnerability of their classification to small perturbations on the inputs. This has led to safety concerns of applying DNNs to safety-critical domains. Several…

Analogical Reasoning problems challenge both connectionist and symbolic AI systems as these entail a combination of background knowledge, reasoning and pattern recognition. While symbolic systems ingest explicit domain knowledge and perform…

In this paper, a family of neural network-based survival models is presented. The models are specified based on piecewise definitions of the hazard function and the density function on a partitioning of the time; both constant and linear…

The numerical sign problem poses a seemingly insurmountable barrier to the simulation of many fascinating systems. We apply neural networks to deform the region of integration, mitigating the sign problem of systems with strongly correlated…

Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given input set. However, often it is important to know whether a given property holds globally for…

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data.…

Neural network interpretability is a vital component for applications across a wide variety of domains. In such cases it is often useful to analyze a network which has already been trained for its specific purpose. In this work, we develop…

The remarkable advancements in artificial intelligence (AI), primarily driven by deep neural networks, are facing challenges surrounding unsustainable computational trajectories, limited robustness, and a lack of explainability. To develop…

In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems…

Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can…

Many machine learning strategies designed to automate mathematical tasks leverage neural networks to search large combinatorial spaces of mathematical symbols. In contrast to traditional evolutionary approaches, using a neural network at…

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty…

Neurosymbolic AI deals with models that combine symbolic processing, like classic AI, and neural networks, as it's a very established area. These models are emerging as an effort toward Artificial General Intelligence (AGI) by both…

We describe how hierarchical concepts can be represented in three types of layered neural networks. The aim is to support recognition of the concepts when partial information about the concepts is presented, and also when some of the…