For example, a prediction market on whether GPT -4 will be able to consistently solve "easy" Sudoku puzzles from the LA Times has remained open for several months at the time of

In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models.

Neurosymbolic (NeSy) frameworks combine neural representations and learning with symbolic representations and reasoning. Combining the reasoning capacities, explainability, and interpretability of symbolic processing with the flexibility and power of neural computing allows us to solve complex problems with more reliability while being data-efficient. However, this recently growing topic poses a challenge to developers with its learning curve, lack of user-friendly tools, libraries, and unifying frameworks. In this paper, we characterize the technical facets of existing NeSy frameworks, such as the symbolic representation language, integration with neural models, and the underlying algorithms. A majority of the NeSy research focuses on algorithms instead of providing generic frameworks for declarative problem specification to leverage problem solving. To highlight the key aspects of Neurosymbolic modeling, we showcase three generic NeSy frameworks - \textit{DeepProbLog}, \textit{Scallop}, and \textit{DomiKnowS}. We identify the challenges within each facet that lay the foundation for identifying the expressivity of each framework in solving a variety of problems. Building on this foundation, we aim to spark transformative action and encourage the community to rethink this problem in novel ways.

This paper introduces a method for incorporating prior knowledge encoded as logical rules to improve the performance of deep learning models. In particular, it takes logical rules which are in decomposable and deterministic negation normal form (d-DNNF), and proposes using an augmented graph convolution network to embed them into a vector space. This embedding is then regularised according to the logical constraints, allowing the addition of a "logic loss" term to train models obeying these logical rules. Incorporating (symbolic) background knowledge to improve performance of deep learning methods is an interesting and valuable direction, and from the experiments using a d-DNNF rather than a CNF appears to be beneficial. However, for me the notion of using a d-DNNF as the source of background knowledge raises a few issues which I feel are not addressed in the paper.

Small Language Models (SLMs) are attracting attention due to the high computational demands and privacy concerns of Large Language Models (LLMs). Some studies fine-tune SLMs using Chains of Thought (CoT) data distilled from LLMs, aiming to enhance their reasoning ability. Furthermore, Some CoT distillation methods introduce external symbolic knowledge into the generation process to improve the limited knowledge memory, reasoning ability and out-of-domain (OOD) generalization of SLMs. However, the introduction of symbolic knowledge increases computational overhead and introduces potential noise. In this paper, we introduce $\textit{SKIntern}$, an innovative approach that empowers SLMs to internalize symbolic knowledge and few-shot examples gradually through a progressive fine-tuning process, guided by a predefined linear decay schedule under curriculum learning. By efficiently internalizing knowledge, $\textit{SKIntern}$ reduces computational overhead and speeds up the reasoning process by focusing solely on the question during inference. It outperforms state-of-the-art baselines by over 5\%, while reducing inference costs (measured in FLOPs) by up to $4\times$ across a wide range of SLMs in both in-domain (ID) and out-of-domain (OOD) tasks. Our code will be available at \url{https://github.com/Xnhyacinth/SKIntern}.

Inspired by Bayesian approaches to brain function in neuroscience, we give a simple theory of probabilistic inference for a unified account of reasoning and learning. We simply model how data cause symbolic knowledge in terms of its satisfiability in formal logic. The underlying idea is that reasoning is a process of deriving symbolic knowledge from data via abstraction, i.e., selective ignorance. The logical consequence relation is discussed for its proof-based theoretical correctness. The MNIST dataset is discussed for its experiment-based empirical correctness.

Artificial neural networks (ANNs) have shown to be amongst the most important artificial intelligence (AI) techniques in educational applications, providing adaptive educational services. However, their educational potential is limited in practice due to three major challenges: i) difficulty in incorporating symbolic educational knowledge (e.g., causal relationships, and practitioners' knowledge) in their development, ii) learning and reflecting biases, and iii) lack of interpretability. Given the high-risk nature of education, the integration of educational knowledge into ANNs becomes crucial for developing AI applications that adhere to essential educational restrictions, and provide interpretability over the predictions. This research argues that the neural-symbolic family of AI has the potential to address the named challenges. To this end, it adapts a neural-symbolic AI framework and accordingly develops an approach called NSAI, that injects and extracts educational knowledge into and from deep neural networks, for modelling learners computational thinking. Our findings reveal that the NSAI approach has better generalizability compared to deep neural networks trained merely on training data, as well as training data augmented by SMOTE and autoencoder methods. More importantly, unlike the other models, the NSAI approach prioritises robust representations that capture causal relationships between input features and output labels, ensuring safety in learning to avoid spurious correlations and control biases in training data. Furthermore, the NSAI approach enables the extraction of rules from the learned network, facilitating interpretation and reasoning about the path to predictions, as well as refining the initial educational knowledge. These findings imply that neural-symbolic AI can overcome the limitations of ANNs in education, enabling trustworthy and interpretable applications.

Neural-symbolic computing (NeSy), which pursues the integration of the symbolic and statistical paradigms of cognition, has been an active research area of Artificial Intelligence (AI) for many years. As NeSy shows promise of reconciling the advantages of reasoning and interpretability of symbolic representation and robust learning in neural networks, it may serve as a catalyst for the next generation of AI. In the present paper, we provide a systematic overview of the recent developments and important contributions of NeSy research. Firstly, we introduce study history of this area, covering early work and foundations. We further discuss background concepts and identify key driving factors behind the development of NeSy. Afterward, we categorize recent landmark approaches along several main characteristics that underline this research paradigm, including neural-symbolic integration, knowledge representation, knowledge embedding, and functionality. Next, we briefly discuss the successful application of modern NeSy approaches in several domains. Then, we benchmark several NeSy methods on three representative application tasks. Finally, we identify the open problems together with potential future research directions. This survey is expected to help new researchers enter this rapidly evolving field and accelerate the progress towards data-and knowledge-driven AI.

A key objective in field of artificial intelligence is to develop cognitive models that can exhibit human-like intellectual capabilities. One promising approach to achieving this is through neural-symbolic systems, which combine the strengths of deep learning and symbolic reasoning. However, current approaches in this area have been limited in their combining way, generalization and interpretability. To address these limitations, we propose a general bi-level probabilistic graphical reasoning framework called GBPGR. This framework leverages statistical relational learning to effectively integrate deep learning models and symbolic reasoning in a mutually beneficial manner. In GBPGR, the results of symbolic reasoning are utilized to refine and correct the predictions made by the deep learning models. At the same time, the deep learning models assist in enhancing the efficiency of the symbolic reasoning process. Through extensive experiments, we demonstrate that our approach achieves high performance and exhibits effective generalization in both transductive and inductive tasks.