# Neuro-Symbolic Predictive Process Monitoring

arXiv: https://arxiv.org/abs/2509.00834 · HTML: https://mlsanity.com/paper/2509.00834/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 60 references that are in the map.
- First posted on arXiv 31 Aug 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [NeuroLogic A*esque Decoding: Constrained Text Generation with Lookahead Heuristics](https://mlsanity.com/paper/2112.08726/) (2021)
- [NeuroLogic Decoding: (Un)supervised Neural Text Generation with Predicate Logic Constraints](https://mlsanity.com/paper/2010.12884/) (2020)
- [Predictive Business Process Monitoring with LSTM Neural Networks](https://mlsanity.com/paper/1612.02130/) (2016)
- [CGMH: Constrained Sentence Generation by Metropolis-Hastings Sampling](https://mlsanity.com/paper/1811.10996/) (2018)
- [Large Concept Models: Language Modeling in a Sentence Representation Space](https://mlsanity.com/paper/2412.08821/) (2024)
- [Predicting Process Behaviour using Deep Learning](https://mlsanity.com/paper/1612.04600/) (2016)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [Deep Learning for Predictive Business Process Monitoring: Review and Benchmark](https://mlsanity.com/paper/2009.13251/) (2020)
- [ROAD-R: The Autonomous Driving Dataset with Logical Requirements](https://mlsanity.com/paper/2210.01597/) (2022)
- [Adaptable Logical Control for Large Language Models](https://mlsanity.com/paper/2406.13892/) (2024)
- [Symbolic LTLf Synthesis](https://mlsanity.com/paper/1705.08426/) (2017)
- [A Deep Adversarial Model for Suffix and Remaining Time Prediction of Event Sequences](https://mlsanity.com/paper/2102.07298/) (2021)
- [Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications](https://mlsanity.com/paper/1911.08145/) (2019)
- [Embedding Symbolic Temporal Knowledge into Deep Sequential Models](https://mlsanity.com/paper/2101.11981/) (2021)
- [NeSyA: Neurosymbolic Automata](https://mlsanity.com/paper/2412.07331/) (2024)
- [DeepDFA: Automata Learning through Neural Probabilistic Relaxations](https://mlsanity.com/paper/2408.08622/) (2024)
- [What Averages Do Not Tell -- Predicting Real Life Processes with Sequential Deep Learning](https://mlsanity.com/paper/2110.10225/) (2021)
- [Neural Reward Machines](https://mlsanity.com/paper/2408.08677/) (2024)

## Built on by (most cited first, 7 of 7)

- [Autonomous Business System via Neuro-symbolic AI](https://mlsanity.com/paper/2601.15599/) (2026)
- [Neuro-Symbolic Learning for Predictive Process Monitoring via Two-Stage Logic Tensor Networks with Rule Pruning](https://mlsanity.com/paper/2603.26944/) (2026)
- [Compliance-Aware Predictive Process Monitoring: A Neuro-Symbolic Approach](https://mlsanity.com/paper/2603.26948/) (2026)
- [DIFF-ERO: A Conformance-Aware Loss for Deep Learning in Process Mining](https://mlsanity.com/paper/2606.14283/) (2026)
- [First-Order Temporal Logic Tensor Networks](https://mlsanity.com/paper/2606.29972/) (2026)
- [Neuro-Symbolic Injection of LTLf Constraints in Autoregressive Reinforcement Learning Policies](https://mlsanity.com/paper/2606.08312/) (2026)
- [Decision-Aware Suffix Prediction and Reasoning of Business Processes](https://mlsanity.com/paper/2609.06169/) (2026)

## Abstract (arXiv)

This paper addresses the problem of suffix prediction in Business Process Management (BPM) by proposing a Neuro-Symbolic Predictive Process Monitoring (PPM) approach that integrates data-driven learning with temporal logic-based prior knowledge. While recent approaches leverage deep learning models for suffix prediction, they often fail to satisfy even basic logical constraints due to the lack of explicit integration of domain knowledge during training. We propose a novel method to incorporate Linear Temporal Logic over finite traces (LTLf) into the training process of autoregressive sequence predictors. Our approach introduces a differentiable logical loss function, defined using a soft approximation of LTLf semantics and the Gumbel-Softmax trick, which can be combined with standard predictive losses. This ensures that the model learns to generate suffixes that are both accurate and logically consistent. Experimental evaluation on three real-world datasets shows that our method improves suffix prediction accuracy and compliance with temporal constraints. We also introduce two variants of the logic loss (local and global) and demonstrate their effectiveness under noisy and realistic settings. While developed in the context of BPM, our framework is applicable to any symbolic sequence generation task and contributes to advancing Neuro-Symbolic AI.