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

arXiv: https://arxiv.org/abs/2602.03486 · HTML: https://mlsanity.com/paper/2602.03486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 62 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 30 of 34)

- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [LTL2Action: Generalizing LTL Instructions for Multi-Task RL](https://mlsanity.com/paper/2102.06858/) (2021)
- [Foundations for Restraining Bolts: Reinforcement Learning with LTLf/LDLf restraining specifications](https://mlsanity.com/paper/1807.06333/) (2018)
- [Environment-Independent Task Specifications via GLTL](https://mlsanity.com/paper/1704.04341/) (2017)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Reinforcement Learning with Non-Markovian Rewards](https://mlsanity.com/paper/1912.02552/) (2019)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [Modular Deep Reinforcement Learning for Continuous Motion Planning with Temporal Logic](https://mlsanity.com/paper/2102.12855/) (2021)
- [Encoding formulas as deep networks: Reinforcement learning for zero-shot execution of LTL formulas](https://mlsanity.com/paper/2006.01110/) (2020)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)
- [Induction and Exploitation of Subgoal Automata for Reinforcement Learning](https://mlsanity.com/paper/2009.03855/) (2020)
- [Active Finite Reward Automaton Inference and Reinforcement Learning Using Queries and Counterexamples](https://mlsanity.com/paper/2006.15714/) (2020)
- [Reinforcement Learning Based Temporal Logic Control with Maximum Probabilistic Satisfaction](https://mlsanity.com/paper/2010.06797/) (2020)
- [Symbolic LTLf Synthesis](https://mlsanity.com/paper/1705.08426/) (2017)
- [Specification Patterns for Robotic Missions](https://mlsanity.com/paper/1901.02077/) (2019)
- [Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications](https://mlsanity.com/paper/1911.08145/) (2019)
- [Joint Learning of Reward Machines and Policies in Environments with Partially Known Semantics](https://mlsanity.com/paper/2204.11833/) (2022)
- [Reward Machines for Deep RL in Noisy and Uncertain Environments](https://mlsanity.com/paper/2406.00120/) (2024)
- [Markov Abstractions for PAC Reinforcement Learning in Non-Markov Decision Processes](https://mlsanity.com/paper/2205.01053/) (2022)
- [Noisy Symbolic Abstractions for Deep RL: A case study with Reward Machines](https://mlsanity.com/paper/2211.10902/) (2022)
- [NeSyA: Neurosymbolic Automata](https://mlsanity.com/paper/2412.07331/) (2024)
- [DeepDFA: Automata Learning through Neural Probabilistic Relaxations](https://mlsanity.com/paper/2408.08622/) (2024)
- [Neural Reward Machines](https://mlsanity.com/paper/2408.08677/) (2024)
- [Reinforcement Learning with Stochastic Reward Machines](https://mlsanity.com/paper/2510.14837/) (2025)

## Abstract (arXiv)

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.