Deliberate-When-Needed: Flow-Reasoner for Neuro-Symbolic Continuous Thought

We present Flow-Reasoner, a Deliberate-When-Needed neuro-symbolic model that integrates continuous latent cognition with selective symbolic reasoning. The mental module is a latent state vector evolving smoothly under a first-order ordinary differential equation (ODE), capturing continuous thought that drifts and decays between interventions. The action module is a temporal point process whose intensities are modulated by symbolic rules. Crucially, reasoning is not constant: it is triggered only at irregular instants—when an observed action arrives or when a latent state crosses a threshold—at which point a bounded differentiable forward-chaining procedure updates beliefs and adjusts event likelihoods. Between these triggers, cognition evolves autonomously under the ODE without symbolic intervention. This design yields a model that (i) unifies continuous-time dynamics with selective logical reasoning, (ii) predicts both the type and timing of future actions, and (iii) produces concise rule traces that explain predictions. Empirical studies on synthetic benchmarks and real-world behavioral datasets demonstrate that Flow-Reasoner consistently outperforms strong temporal point process baselines, while providing interpretable, cognitively inspired explanations of decision dynamics. The code is publicly available at \url{https://github.com/shennnnwj/flow-reasoner.}