Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes.

Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes. In the area of artificial intelligence (AI), the two abilities are usually realised by machine learning and logic programming, respectively. However, the two categories of techniques were developed separately throughout most of the history of AI. In this paper, we present the abductive learning targeted at unifying the two AI paradigms in a mutually beneficial way, where the machine learning model learns to perceive primitive logic facts from data, while logical reasoning can exploit symbolic domain knowledge and correct the wrongly perceived facts for improving the machine learning models. Furthermore, we propose a novel approach to optimise the machine learning model and the logical reasoning model jointly. We demonstrate that by using abductive learning, machines can learn to recognise numbers and resolve unknown mathematical operations simultaneously from images of simple hand-written equations. Moreover, the learned models can be generalised to longer equations and adapted to different tasks, which is beyond the capability of state-of-the-art deep learning models.

Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes.

Advances in artificial intelligence (AI), particularly large language models (LLMs) [1], have achieved remarkable success. This progress stems from "scaling laws" -- performance improves with greater computation, data, and model size [2]. They now excel at mathematics, medical, legal, and coding exams and competitions. Y et, this paradigm has a crucial vulnerability: scaling laws are effective only when data is abundant. Human reasoning, which relies on logical operations and abstractions rather than brute-force pattern matching on vast data, proves critical in tackling complex frontier domains, where usable data is often inherently scarce.

Abductive learning (ABL) that integrates strengths of machine learning and logical reasoning to improve the learning generalization, has been recently shown effective. However, its efficiency is affected by the transition between numerical induction and symbolical deduction, leading to high computational costs in the worst-case scenario. Efforts on this issue remain to be limited. In this paper, we identified three reasons why previous optimization algorithms for ABL were not effective: insufficient utilization of prediction, symbol relationships, and accumulated experience in successful abductive processes, resulting in redundant calculations to the knowledge base. To address these challenges, we introduce an optimization algorithm named as Probabilistic Symbol Perception (PSP), which makes a smooth transition between induction and deduction and keeps the correctness of ABL unchanged. We leverage probability as a bridge and present an efficient data structure, achieving the transfer from a continuous probability sequence to discrete Boolean sequences with low computational complexity. Experiments demonstrate the promising results.

Still, if you can do some version of the Mayan hieroglyphics, or work that example into the introduction, it would improve the paper even more. They restrict themselves to classification problems, i.e., a mapping from perceptual input to {0,1}; the discrete symbols output by the perception model act as latent variables sitting in between the input and the binary decision. Their approach is to alternate between (1) inferring a logic program consistent with the training examples, conditioned on the output of the perception model, and (2) training the perception model to predict the latent discrete symbols. Because the perception model may be unreliable, particularly early on in training, the logic program is allowed to revise or abduce the outputs of perception. The problem they pose -- integrating learned perception with learned symbolic reasoning -- is eminently important.

The reviewer consensus was that, despite requiring some improvements in terms of presentation, with some areas flagged by reviewers as necessitating more detail, and the toy-ish nature of the experiments, that this paper addresses an important problem with the NeurIPS community in attempting to reconcile deep networks with symbolic-like reasoning. The paper is thus deemed of an acceptable standard, but the authors should note that while they are not expected to change their experimental setting for the camera-ready, should the paper be included in the proceedings, they should pay careful attention to the reviewer comments and recommendations when revising their paper in order to insure that the points of clarification requested are expanded upon, possibly in an appendix.

Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes. In the area of artificial intelligence (AI), the two abilities are usually realised by machine learning and logic programming, respectively. However, the two categories of techniques were developed separately throughout most of the history of AI. In this paper, we present the abductive learning targeted at unifying the two AI paradigms in a mutually beneficial way, where the machine learning model learns to perceive primitive logic facts from data, while logical reasoning can exploit symbolic domain knowledge and correct the wrongly perceived facts for improving the machine learning models. Furthermore, we propose a novel approach to optimise the machine learning model and the logical reasoning model jointly. We demonstrate that by using abductive learning, machines can learn to recognise numbers and resolve unknown mathematical operations simultaneously from images of simple hand-written equations.

Perception and reasoning are two representative abilities of intelligence that are integrated seamlessly during human problem-solving processes. In the area of artificial intelligence (AI), the two abilities are usually realised by machine learning and logic programming, respectively. However, the two categories of techniques were developed separately throughout most of the history of AI. In this paper, we present the abductive learning targeted at unifying the two AI paradigms in a mutually beneficial way, where the machine learning model learns to perceive primitive logic facts from data, while logical reasoning can exploit symbolic domain knowledge and correct the wrongly perceived facts for improving the machine learning models. Furthermore, we propose a novel approach to optimise the machine learning model and the logical reasoning model jointly.