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One approach to explaining the hierarchical levels of understanding within a machine learning model is the symbolic method of inductive logic programming (ILP), which is data efficient and capable of learning first-order logic rules that…

Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…

Recent years have witnessed the growing popularity of domain-specific accelerators (DSAs), such as Google's TPUs, for accelerating various applications such as deep learning, search, autonomous driving, etc. To facilitate DSA designs,…

Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in $\mathbb{R}^d$ are `bound' together to produce a new vector in the same space. VSAs support the commutativity and associativity of…

Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations or chain-of-thoughts (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for…

Sequences and time-series often arise in robot tasks, e.g., in activity recognition and imitation learning. In recent years, deep neural networks (DNNs) have emerged as an effective data-driven methodology for processing sequences given…

The neural network has become an integral part of modern software systems. However, they still suffer from various problems, in particular, vulnerability to adversarial attacks. In this work, we present a novel program reasoning framework…

The ability to encode and manipulate data structures with distributed neural representations could qualitatively enhance the capabilities of traditional neural networks by supporting rule-based symbolic reasoning, a central property of…

Pre-trained large language models (LMs) struggle to perform logical reasoning reliably despite advances in scale and compositionality. In this work, we tackle this challenge through the lens of symbolic programming. We propose DSR-LM, a…

This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging…

Symbolic computer vision represents diagrams through explicit logical rules and structured representations, enabling interpretable understanding in machine vision. This requires fundamentally different learning paradigms from pixel-based…

Large Language Models (LLMs) have emerged as a promising alternative to traditional static program analysis methods, such as symbolic execution, offering the ability to reason over code directly without relying on theorem provers or SMT…

Following the general theoretical framework of VSA (Vector Symbolic Architecture), a cognitive model with the use of sparse binary hypervectors is proposed. In addition, learning algorithms are introduced to bootstrap the model from…

We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments…

This paper presents a hybrid methodology that enhances the training process of deep learning (DL) models by embedding domain expert knowledge using ontologies and answer set programming (ASP). By integrating these symbolic AI methods, we…

Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…

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,…

Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture…

Grassroots Logic Programs (GLP) is a concurrent logic programming language in which logic variables are partitioned into paired readers and writers. An assignment is produced at most once via a writer and consumed at most once via its…

What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of…