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Neuro-Symbolic (NeSy) predictive models hold the promise of improved compliance with given constraints, systematic generalization, and interpretability, as they allow to infer labels that are consistent with some prior knowledge by…

Machine Learning · Computer Science 2023-12-19 Emanuele Marconato , Stefano Teso , Antonio Vergari , Andrea Passerini

Neuro-Symbolic (NeSy) predictors that conform to symbolic knowledge - encoding, e.g., safety constraints - can be affected by Reasoning Shortcuts (RSs): They learn concepts consistent with the symbolic knowledge by exploiting unintended…

Machine Learning · Computer Science 2024-02-20 Emanuele Marconato , Samuele Bortolotti , Emile van Krieken , Antonio Vergari , Andrea Passerini , Stefano Teso

Numerous neuro-symbolic approaches have recently been proposed typically with the goal of adding symbolic knowledge to the output layer of a neural network. Ideally, such losses maximize the probability that the neural network's predictions…

Machine Learning · Computer Science 2023-03-01 Kareem Ahmed , Kai-Wei Chang , Guy Van den Broeck

We introduce Neuro-Symbolic Continual Learning, where a model has to solve a sequence of neuro-symbolic tasks, that is, it has to map sub-symbolic inputs to high-level concepts and compute predictions by reasoning consistently with prior…

Machine Learning · Computer Science 2023-12-20 Emanuele Marconato , Gianpaolo Bontempo , Elisa Ficarra , Simone Calderara , Andrea Passerini , Stefano Teso

Neural reasoning accuracy improves when generating intermediate reasoning steps. However, the source of this improvement is yet unclear. Here, we investigate and factorize the benefit of generating intermediate steps for symbolic reasoning.…

Artificial Intelligence · Computer Science 2023-02-17 Yoichi Aoki , Keito Kudo , Tatsuki Kuribayashi , Ana Brassard , Masashi Yoshikawa , Keisuke Sakaguchi , Kentaro Inui

Concept-based Models are neural networks that learn a concept extractor to map inputs to high-level concepts and an inference layer to translate these into predictions. Ensuring these modules produce interpretable concepts and behave…

Machine Learning · Computer Science 2026-01-15 Samuele Bortolotti , Emanuele Marconato , Paolo Morettin , Andrea Passerini , Stefano Teso

Structured output prediction problems are ubiquitous in machine learning. The prominent approach leverages neural networks as powerful feature extractors, otherwise assuming the independence of the outputs. These outputs, however, jointly…

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures…

Artificial Intelligence · Computer Science 2018-06-11 Jingyi Xu , Zilu Zhang , Tal Friedman , Yitao Liang , Guy Van den Broeck

In recent years, neuro-symbolic methods have become a popular and powerful approach that augments artificial intelligence systems with the capability to perform abstract, logical, and quantitative deductions with enhanced precision and…

Artificial Intelligence · Computer Science 2025-02-04 Yuxuan Wu , Hideki Nakayama

In structured prediction, the goal is to jointly predict many output variables that together encode a structured object -- a path in a graph, an entity-relation triple, or an ordering of objects. Such a large output space makes learning…

Machine Learning · Computer Science 2022-01-28 Kareem Ahmed , Eric Wang , Kai-Wei Chang , Guy Van den Broeck

The ubiquitous independence assumption among symbolic concepts in neurosymbolic (NeSy) predictors is a convenient simplification: NeSy predictors use it to speed up probabilistic reasoning. Recent works like van Krieken et al. (2024) and…

Machine Learning · Computer Science 2025-07-16 Emile van Krieken , Pasquale Minervini , Edoardo Ponti , Antonio Vergari

Neurosymbolic AI is growing in popularity thanks to its ability to combine neural perception and symbolic reasoning in end-to-end trainable models. However, recent findings reveal these are prone to shortcut reasoning, i.e., to learning…

Machine Learning · Computer Science 2026-02-02 Luca Andolfi , Eleonora Giunchiglia

In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs, a task that Large…

Artificial Intelligence · Computer Science 2025-12-19 Marianne Defresne , Romain Gambardella , Sophie Barbe , Thomas Schiex

Neuro-symbolic AI bridges the gap between purely symbolic and neural approaches to learning. This often requires maximizing the likelihood of a symbolic constraint w.r.t the neural network's output distribution. Such output distributions…

Machine Learning · Computer Science 2024-01-30 Kareem Ahmed , Kai-Wei Chang , Guy Van den Broeck

Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural…

Artificial Intelligence · Computer Science 2024-10-29 Zenan Li , Yunpeng Huang , Zhaoyu Li , Yuan Yao , Jingwei Xu , Taolue Chen , Xiaoxing Ma , Jian Lu

Arguments in favor of injecting symbolic knowledge into neural architectures abound. When done right, constraining a sub-symbolic model can substantially improve its performance and sample complexity and prevent it from predicting invalid…

Machine Learning · Computer Science 2019-12-24 Stefano Teso

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty…

Artificial Intelligence · Computer Science 2025-11-19 Jiahao Wu , Shengwen Yu

In recent years, neural systems have demonstrated highly effective learning ability and superior perception intelligence. However, they have been found to lack effective reasoning and cognitive ability. On the other hand, symbolic systems…

Machine Learning · Computer Science 2023-06-27 Dongran Yu , Bo Yang , Dayou Liu , Hui Wang , Shirui Pan

Enabling neural networks to learn complex logical constraints and fulfill symbolic reasoning is a critical challenge. Bridging this gap often requires guiding the neural network's output distribution to move closer to the symbolic…

Artificial Intelligence · Computer Science 2025-08-25 Xuan Zhang , Zhijian Zhou , Weidi Xu , Yanting Miao , Chao Qu , Yuan Qi

The remarkable success in neural networks provokes the selective rationalization. It explains the prediction results by identifying a small subset of the inputs sufficient to support them. Since existing methods still suffer from adopting…

Machine Learning · Computer Science 2024-07-22 Linan Yue , Qi Liu , Yichao Du , Li Wang , Weibo Gao , Yanqing An
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