DeepDFA: Injecting Temporal Logic in Deep Learning for Sequential Subsymbolic Applications

Abstract: Integrating logical knowledge into deep neural network training is still a hard challenge, especially for sequential or temporally extended domains involving subsymbolic observations. To address this problem, we propose DeepDFA, a neurosymbolic framework that integrates high-level temporal logic - expressed as Deterministic Finite Automata (DFA) or Moore Machines - into neural architectures. DeepDFA models temporal rules as continuous, differentiable layers, enabling symbolic knowledge injection into subsymbolic domains. We demonstrate how DeepDFA can be used in two key settings: (i) static image sequence classification, and (ii) policy learning in interactive non-Markovian environments. Across extensive experiments, DeepDFA outperforms traditional deep learning models (e.g., LSTMs, GRUs, Transformers) and novel neuro-symbolic systems, achieving state-of-the-art results in temporal knowledge integration. These results highlight the potential of DeepDFA to bridge subsymbolic learning and symbolic reasoning in sequential tasks.