Related papers: Logic Tensor Networks: Deep Learning and Logical R…

Neural networks, as currently designed, fall short of achieving true logical intelligence. Modern AI models rely on standard neural computation-inner-product-based transformations and nonlinear activations-to approximate patterns from data.…

Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…

In this paper, a deep neural network approach and a neuro-symbolic one are proposed for classification and regression. The neuro-symbolic predictive models based on Logic Tensor Networks are capable of discriminating and in the same time of…

Representing knowledge as high-dimensional vectors in a continuous semantic vector space can help overcome the brittleness and incompleteness of traditional knowledge bases. We present a method for performing deductive reasoning directly in…

Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge…

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…

This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing…

We introduce a new logic programming language T-PRISM based on tensor embeddings. Our embedding scheme is a modification of the distribution semantics in PRISM, one of the state-of-the-art probabilistic logic programming languages, by…

Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the…

Knowledge graph embedding models have gained significant attention in AI research. Recent works have shown that the inclusion of background knowledge, such as logical rules, can improve the performance of embeddings in downstream machine…

We propose a new linear algebraic approach to the computation of Tarskian semantics in logic. We embed a finite model M in first-order logic with N entities in N-dimensional Euclidean space R^N by mapping entities of M to N dimensional…

While neural networks are good at learning unspecified functions from training samples, they cannot be directly implemented in hardware and are often not interpretable or formally verifiable. On the other hand, logic circuits are…

We propose a formal model of reasoning limitations in large neural net models for language, grounded in the depth of their neural architecture. By treating neural networks as linear operators over logic predicate space we show that each…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

Recent years have witnessed an increasing interest in training machines with reasoning ability, which deeply relies on accurately and clearly presented clue forms. The clues are usually modeled as entity-aware knowledge in existing studies.…

While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…

The AI community is increasingly focused on merging logic with deep learning to create Neuro-Symbolic (NeSy) paradigms and assist neural approaches with symbolic knowledge. A significant trend in the literature involves integrating axioms…

Human vision is able to compensate imperfections in sensory inputs from the real world by reasoning based on prior knowledge about the world. Machine learning has had a significant impact on computer vision due to its inherent ability in…

Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at…

In this work, we present a novel approach to ontology reasoning that is based on deep learning rather than logic-based formal reasoning. To this end, we introduce a new model for statistical relational learning that is built upon deep…