First-order logic learning in artificial neural networks

Artificial Neural Networks have previously been applied in neuro-symbolic learning to learn ground logic program rules. However, there are few results of learning relations using neuro-symbolic learning. This paper presents the system PAN, which can learn relations. The inputs to PAN are one or more atoms, representing the conditions of a logic rule, and the output is the conclusion of the rule. The symbolic inputs may include functional terms of arbitrary depth and arity, and the output may include terms constructed from the input functors. Symbolic inputs are encoded as an integer using an invertible encoding function, which is used in reverse to extract the output terms. The main advance of this system is a convention to allow construction of Artificial Neural Networks able to learn rules with the same power of expression as first order definite clauses. The system is tested on three examples and the results are discussed

Embed2Sym - scalable neuro-symbolic reasoning via clustered embeddings

Neuro-symbolic reasoning approaches proposed in recent years combine a neural perception component with a symbolic reasoning component to solve a downstream task. By doing so, these approaches can provide neural networks with symbolic reasoning capabilities, improve their interpretability and enable generalization beyond the training task. However, this often comes at the cost of poor training time, with potential scalability issues. In this paper, we propose a scalable neuro-symbolic approach, called Embed2Sym. We complement a two-stage (perception and reasoning) neural network architecture designed to solve a downstream task end-to-end with a symbolic optimisation method for extracting learned latent concepts. Specifically, the trained perception network generates clusters in embedding space that are identified and labelled using symbolic knowledge and a symbolic solver. With the latent concepts identified, a neuro-symbolic model is constructed by combining the perception network with the symbolic knowledge of the downstream task, resulting in a model that is interpretable and transferable. Our evaluation shows that Embed2Sym outperforms state-of-the-art neuro-symbolic systems on benchmark tasks in terms of training time by several orders of magnitude while providing similar if not better accuracy

The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision

We propose the Neuro-Symbolic Concept Learner (NS-CL), a model that learns visual concepts, words, and semantic parsing of sentences without explicit supervision on any of them; instead, our model learns by simply looking at images and reading paired questions and answers. Our model builds an object-based scene representation and translates sentences into executable, symbolic programs. To bridge the learning of two modules, we use a neuro-symbolic reasoning module that executes these programs on the latent scene representation. Analogical to human concept learning, the perception module learns visual concepts based on the language description of the object being referred to. Meanwhile, the learned visual concepts facilitate learning new words and parsing new sentences. We use curriculum learning to guide the searching over the large compositional space of images and language. Extensive experiments demonstrate the accuracy and efficiency of our model on learning visual concepts, word representations, and semantic parsing of sentences. Further, our method allows easy generalization to new object attributes, compositions, language concepts, scenes and questions, and even new program domains. It also empowers applications including visual question answering and bidirectional image-text retrieval.Comment: ICLR 2019 (Oral). Project page: http://nscl.csail.mit.edu

Context-aware Collaborative Neuro-Symbolic Inference in Internet of Battlefield Things

IoBTs must feature collaborative, context-aware, multi-modal fusion for real-time, robust decision-making in adversarial environments. The integration of machine learning (ML) models into IoBTs has been successful at solving these problems at a small scale (e.g., AiTR), but state-of-the-art ML models grow exponentially with increasing temporal and spatial scale of modeled phenomena, and can thus become brittle, untrustworthy, and vulnerable when interpreting large-scale tactical edge data. To address this challenge, we need to develop principles and methodologies for uncertainty-quantified neuro-symbolic ML, where learning and inference exploit symbolic knowledge and reasoning, in addition to, multi-modal and multi-vantage sensor data. The approach features integrated neuro-symbolic inference, where symbolic context is used by deep learning, and deep learning models provide atomic concepts for symbolic reasoning. The incorporation of high-level symbolic reasoning improves data efficiency during training and makes inference more robust, interpretable, and resource-efficient. In this paper, we identify the key challenges in developing context-aware collaborative neuro-symbolic inference in IoBTs and review some recent progress in addressing these gaps