Title: Neuro-Symbolic VAEs for Temporal Point Processes: Logic-Guided Controllable Generation
Primary area: learning on time series and dynamical systems
Keywords: Neuro-Symbolic Reasoning, LLM, Temporal Point Process, Generative Model

Abstract: In safety-critical domains such as healthcare, sequential data (e.g., patient trajectories in electronic health records) are often sparse, incomplete, and privacy-sensitive, limiting their utility for downstream modeling. Synthetic sequence generation can mitigate these issues by imputing missing histories and synthesizing new trajectories. However, generation must respect domain constraints to ensure reliability. We propose the Neuro-Symbolic Variational Autoencoder with Temporal Point Processes (NS-VAE-TPP), a framework for logic-aware sequence generation in continuous time. NS-VAE-TPP combines a temporal point process backbone for modeling event times and types with a novel reasoning layer in the latent space. The encoder maps raw streams to high-level predicate variables, while forward-chaining inference enforces logical consistency and imputes missing structure, enabling reliable generation under data scarcity. Symbolic rules are specified as predicate embeddings and enforced as constraints, with flexibility enhanced by querying and refining rule embeddings using large language models (LLMs). Experiments on synthetic data, LogiCity, MIMIC-IV, EPIC-100, and IKEA ASM demonstrate that NS-VAE-TPP achieves more accurate, controllable, and reliable sequence generation under scarce data conditions, highlighting the potential of neuro-symbolic approaches for robust modeling in safety-critical domains.

TL;DR: We introduce a neuro-symbolic generative framework that incorporates LLM-refined logic rules into the generative process, enabling high-fidelity and interpretable event sequence generation in low-data and zero-shot regimes.