Related papers: A Universal Logic Operator for Interpretable Deep …

A. Tarski proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and…

Recent research (arXiv:2310.11453, arXiv:2402.17764) has proposed binary and ternary transformer networks as a way to significantly reduce memory and improve inference speed in Large Language Models (LLMs) while maintaining accuracy. In…

Application domains that require considering relationships among objects which have real-valued attributes are becoming even more important. In this paper we propose NeuralLog, a first-order logic language that is compiled to a neural…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

Deep learning models with convolutional and recurrent networks are now ubiquitous and analyze massive amounts of audio, image, video, text and graph data, with applications in automatic translation, speech-to-text, scene understanding,…

Modern deep learning algorithms tend to optimize an objective metric, such as minimize a cross entropy loss on a training dataset, to be able to learn. The problem is that the single metric is an incomplete description of the real world…

We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…

Perception and reasoning are basic human abilities that are seamlessly connected as part of human intelligence. However, in current machine learning systems, the perception and reasoning modules are incompatible. Tasks requiring joint…

Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…

As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem…

This paper presents an unsupervised method to learn a neural network, namely an explainer, to interpret a pre-trained convolutional neural network (CNN), i.e., explaining knowledge representations hidden in middle conv-layers of the CNN.…

We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…

Human reasoning can distill principles from observed patterns and generalize them to explain and solve novel problems. The most powerful artificial intelligence systems lack explainability and symbolic reasoning ability, and have therefore…

Logic gates can be written in terms of complex differential operators, where the inputs and outputs are holomorphic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection…

There have been many advances in the artificial intelligence field due to the emergence of deep learning. In almost all sub-fields, artificial neural networks have reached or exceeded human-level performance. However, most of the models are…

Because of the pervasive usage of Neural Networks in human sensitive applications, their interpretability is becoming an increasingly important topic in machine learning. In this work we introduce a simple way to interpret the output…

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric…

Neural networks have achieved remarkable success across various fields. However, the lack of interpretability limits their practical use, particularly in critical decision-making scenarios. Post-hoc interpretability, which provides…