Spike-based Belief Propagation in Nonlinear Dynamical Systems

Sepideh Adamiat; Hongye Wang; Wouter M. Kouw; Bert de Vries

cs.AIAug 20, 2026

Spike-based Belief Propagation in Nonlinear Dynamical Systems

Authors: Sepideh Adamiat, Hongye Wang, Wouter M. Kouw, Bert de Vries

Organizations: Electrical Engineering Department, Eindhoven University of Technology, Eindhoven, the Netherlands · Biomedical Signals and Systems, Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS), University of Twente, Enschede, The Netherlands

Abstract

This paper presents a Bayesian control framework that integrates spike-based dynamics with probabilistic inference for adaptive control. Bayesian inference is widely regarded as a core computational principle of brain function, providing a normative framework for perception, decision-making, and learning under uncertainty. By combining a biologically inspired spiking neural model with Bayesian inference principles, we propose a brain-like control algorithm capable of operating in uncertain environments. We use the mountain car parking problem as a benchmark with non-linear dynamics. Our results demonstrate that the proposed controller can successfully update states in real time and generate goal-directed action plans through spike-driven dynamics. The results highlight the proposed model's potential as a bridge between computational neuroscience and probabilistic control theory.

Figures & tables

Figure 1: (left) The Mountain Car environment; (right) trajectory of the car position when the agent naively applies the maximum forward engine force at every time step. The orange curve shows the resulting position over time, while the dashed green line indicates the goal position. This strategy fails to reach the goal state; see Section 2 .

Panel of Figure 2 — Figure 2: An FFG representation of one time step of the state space model defined in ( 1 ), constrained by $u_{t}=\hat{u}_{t}$ and $y_{t}=\hat{y}_{t}$ .

Panel of Figure 3 — Figure 3: FFG of the extended model in ( 5 ). This model extends the state update model over a horizon of $T$ future time steps from time step $t$ . The "control as inference" objective is to infer the posterior belief for $u_{t:t+T}$ conditioned on preferences $p^{\prime}(y_{t:t+T})$ .

Figure 4: NEF-based function transformation between two spiking neural populations. Input signal $x$ is encoded into input currents $I_{P}$ for ensemble $P$ . Synaptic weights $W$ connect population $P$ to population $Q$ , implementing the transformation $f(x)$ implicitly. The decoder $D_{Q}$ reconstructs the output signal $z\approx f(x)$ from the spiking activity $R_{Q}$ .

Figure 5: Illustration of the unscented transform. A Gaussian distribution is represented by a deterministic set of sigma points, which are propagated through a nonlinear function. The transformed points are then used to reconstruct a Gaussian approximation of the resulting distribution.

Panel of Figure 6 — Figure 6: Comparison of the reference active inference controller (left), versus the proposed controller (right) for the Mountain Car environment. The top panel shows the vehicle position over time, with the dashed horizontal line indicating the goal position. The bottom panel shows the corresponding engine force applied at each time step. Both methods exhibit the characteristic Mountain Car strategy of initially moving away from the goal to build momentum before ascending the hill. In both cases, the vehicle successfully reaches and overshoots the goal position, demonstrating successful task completion.

Explore similar work

Efficient and robust control with spikes that constrain free energy
Mar 10, 2026André Urbano, Pablo Lanillos, Sander KeeminkRobust Control Spiking Neural Networks
Cajal Neuroscience Center, Spanish National Research Council, Madrid, Spain · Department of Machine Learning and Neural Computing, Donders Institute for Brain Cognition and Behaviour, Radboud University, Nijmegen, The Netherlands
Dynamic neural manifolds for flexible closed-loop control on neuromorphic hardware
Jul 8, 2026Oskar von Seeler, Christian Tetzlaff, Andrew LehrRobotic Control Neural Representation Geometry
Group of Computational Synaptic Physiology, Department of Neuro- and Sensory Physiology, University Medical Center Göttingen, Germany · Campus Institute Data Science, University of Göttingen, Germany · Circulant Labs, Bensheim, Germany
Bio-plausible Neuromorphic Disturbance Observer Based on Emulation Theory: Extended Version
May 5, 2026Hongfu Xu, Xiaoyu Guo, Shengbo Wang +1Robust Control Spiking Neural Networks
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China · Department of Mechanical Engineering, City University of Hong Kong, Hong Kong · Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong +1

Mar 10, 2026J/K move · Enter open · S save

Efficient and robust control with spikes that constrain free energy

André Urbano, Pablo Lanillos, Sander Keemink

Cajal Neuroscience Center, Spanish National Research Council, Madrid, Spain · Department of Machine Learning and Neural Computing, Donders Institute for Brain Cognition and Behaviour, Radboud University, Nijmegen, The Netherlands

Robust Control Spiking Neural Networks Free Energy Principle

Open paper AskPDF arXiv

Animal brains exhibit remarkable efficiency in perception and action, while being robust to both external and internal perturbations. The means by which brains accomplish this remains, for now, poorly understood, hindering our understanding of animal and human cognition, as well as our own implementation of efficient algorithms for control of dynamical systems.A potential candidate for a robust mechanism of state estimation and action computation is the free energy principle, but existing implementations of this principle have largely relied on conventional, biologically implausible approaches without spikes. We propose a novel, efficient, and robust spiking control framework with realistic biological characteristics. The resulting networks function as free energy constrainers, in which neurons only fire if they reduce the free energy of their internal representation. The networks offer efficient operation through highly sparse activity while matching performance with other similar spiking frameworks, and have high resilience against both external (e.g. sensory noise or collisions) and internal perturbations (e.g. synaptic noise and delays or neuron silencing) that such a network would be faced with when deployed by either an organism or an engineer. Overall, our work provides a novel mathematical account for spiking control through constraining free energy, providing both better insight into how brain networks might leverage their spiking substrate and a new route for implementing efficient control algorithms in neuromorphic hardware.

Abstract

Explore similar work

Efficient and robust control with spikes that constrain free energy

Dynamic neural manifolds for flexible closed-loop control on neuromorphic hardware

Bio-plausible Neuromorphic Disturbance Observer Based on Emulation Theory: Extended Version