A Semantic Loss Function for Deep Learning with Symbolic Knowledge

By Jingyi Xu, Zilu Zhang, Tal Friedman, Yitao Liang, Guy Van den Broeck. 2017

549 citations recorded by the source corpus.

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 how close the neural network is to satisfying the constraints on its output. An experimental evaluation shows that it effectively guides the learner to achieve (near-)state-of-the-art results on semi-supervised multi-class classification. Moreover, it significantly increases the ability of the neural network to predict structured objects, such as rankings and paths. These discrete concepts are tremendously difficult to learn, and benefit from a tight integration of deep learning and symbolic reasoning methods.

Subfields: Artificial Intelligence

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Citations in the corpus

Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems (2019, background): “The integration of logic rules into the learning algorithm is often accomplished via additional, semantic loss terms [10], [11], [13], [21], [83], [84], [85].”
Right for the Right Concept: Revising Neuro-Symbolic Concepts by Interacting with their Explanations (2020, background): “Using a semantic loss [56] would allow one to stay at the conceptual level directly.”
Property-driven Training: All You (N)Ever Wanted to Know About (2021, methodology): “…one to ask whether a more general approach to property formulation may exist, and several attempts in the literature addressed this research question (Xu et al. 2018; Fischer et al. 2019), by proposing methods that can translate a ﬁrst-order logical formula C into a constraint loss function L C .”
Three Modern Roles for Logic in AI (2020, background): “robabilistic reasoning and machine learning include the utilization of tractable circuits for uniform sampling [75] and improving deep learning through the injection of symbolic knowledge; see, e.g., [91, 92]. 4 LOGIC FOR LEARNING FROM DATA AND KNOWLEDGE The second role we consider for logic is in l”
Exploring End-to-End Differentiable Natural Logic Modeling (2020, methodology): “One uses symbolic constraints as regularizers to equip neural models with the corresponding inductive bias (Demeester et al., 2016; Diligenti et al., 2017; Donadello et al., 2017; Xu et al., 2018; Li and Srikumar, 2019).”
A Logic-Driven Framework for Consistency of Neural Models (2019, background): “Xu et al. (2018) proposed a general framework for designing a semantically informed loss, without tnorms, for constraining a complex output space.”
Neuro-Symbolic = Neural + Logical + Probabilistic (2019, background): “For example, [Xu et al., 2018] show that neural networks trained with the additional regularization term cannot consistently make predictions coherent with the logic they were trained on.”
Learning from Rules Generalizing Labeled Exemplars (2020, background): “…interest in integrating logical rules with labeled examples for training networks, speciﬁcally for structured outputs (Manhaeve et al., 2018; Xu et al., 2018; Fischer et al., 2019; Sun et al., 2018; Ren et al., 2018a The primary difference of these methods from ours is that they assume that…”
Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations (2019, methodology): “To encourage the distribution over permutations to be peaked, one can add entropy regularization [15] or semantic loss [44].”
Neurosymbolic AI: the 3rd wave (2020, background): “…of weights of a network (d’Avila Garcez and Zaverucha 1999; d’Avila Garcez et al. 2002, 2009; Ham-mer and Hitzler 2007; Hu et al. 2016) and systems that translate and encode symbolic knowledge into the network’s loss function (Serafini and d’Avila Garcez 2016; Marra et al. 2019; Xu et al. 2018).”
Towards Verified Artificial Intelligence (2016, methodology): “edly, several methods have been proposed for safe reinforcement learning (see [34]). Another promising direction is to enforce properties on ML models through the use of semantic loss functions (e.g. [87,25]), though this problem is largely unsolved. Finally, the use of theorem proving for ensuring ”
Using Machine Learning Safely in Automotive Software: An Assessment and Adaption of Software Process Requirements in ISO 26262 (2018, background): “[45] show how to incorporate such knowledge as a constraint directly in the loss function used during learning, whereas Vedaldi et al.”
Explainable AI for Intelligence Augmentation in Multi-Domain Operations (2019, background): “…for interaction with humans (Ribeiro, Singh, and Guestrin 2016); (2) there are tasks for which a symbolic AI can support a subsymbolic AI agent (Xu et al. 2018); and (3) there are tasks for which humans can support symbolic and/or subsymbolic AI agents (Phan et al. 2016), hence AI agents need…”
Shades of Knowledge-Infused Learning for Enhancing Deep Learning (2019, background): “The two popular choices in capturing background information are first, training a shallow neural architecture or a statistical model on a large corpus and feeding the learned statistical signature as an input to a task-specific model(2) or second, making the task-specific model objective directly aw”