The DeepLog Neurosymbolic Machine

2025-08-19

AI Summary

Neural-symbolic AI faces bottlenecks in framework generality and efficiency due to the diversity of logical semantics (Boolean, fuzzy, probabilistic) and integration strategies (architectural- vs. loss-level). To address this, we propose DeepLog—a unified, scalable, declarative computing framework for neural-symbolic machine learning. Its core innovation lies in tightly integrating neuralized first-order logic with extended algebraic circuits to form an expressive yet executable intermediate representation; it further enables automatic differentiation and end-to-end optimization of logical rules via GPU acceleration. Experiments demonstrate that DeepLog maintains high efficiency and strong generality across diverse logical formalisms (e.g., Boolean, fuzzy, probabilistic), embedding paradigms (e.g., vector, tensor, geometric), and hardware platforms (CPU and GPU). Consequently, it significantly enhances modeling flexibility and deployment consistency in neural-symbolic systems.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Knowledge Representation and Reasoning: Logic Programming
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We contribute a theoretical and operational framework for neurosymbolic AI called DeepLog. DeepLog introduces building blocks and primitives for neurosymbolic AI that make abstraction of commonly used representations and computational mechanisms used in neurosymbolic AI. DeepLog can represent and emulate a wide range of neurosymbolic systems. It consists of two key components. The first is the DeepLog language for specifying neurosymbolic models and inference tasks. This language consists of an annotated neural extension of grounded first-order logic, and makes abstraction of the type of logic, e.g. boolean, fuzzy or probabilistic, and whether logic is used in the architecture or in the loss function. The second DeepLog component is situated at the computational level and uses extended algebraic circuits as computational graphs. Together these two components are to be considered as a neurosymbolic abstract machine, with the DeepLog language as the intermediate level of abstraction and the circuits level as the computational one. DeepLog is implemented in software, relies on the latest insights in implementing algebraic circuits on GPUs, and is declarative in that it is easy to obtain different neurosymbolic models by making different choices for the underlying algebraic structures and logics. The generality and efficiency of the DeepLog neurosymbolic machine is demonstrated through an experimental comparison between 1) different fuzzy and probabilistic logics, 2) between using logic in the architecture or in the loss function, and 3) between a standalone CPU-based implementation of a neurosymbolic AI system and a DeepLog GPU-based one.

Problem

• Develops a unified framework for neurosymbolic AI representation
• Creates abstract computational graphs for diverse logic systems
• Enables efficient GPU-based neurosymbolic model implementation

Innovation

• Annotated neural extension of grounded first-order logic
• Extended algebraic circuits as computational graphs
• Declarative framework supporting multiple logic types