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
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 .
Figure 2: An FFG representation of one time step of the state space model defined in ( 1 ), constrained by ut=u^t and yt=y^t .
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 ut:t+T conditioned on preferences p′(yt:t+T) .
Figure 4: NEF-based function transformation between two spiking neural populations. Input signal x is encoded into input currents IP for ensemble P . Synaptic weights W connect population P to population Q , implementing the transformation f(x) implicitly. The decoder DQ reconstructs the output signal z≈f(x) from the spiking activity RQ .
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.
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.
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.
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
In biological circuits, sequential neural activity evolves along dynamic, low-dimensional manifolds to enable flexible behavior. Spiking network models link aspects of this sequential activity to features of manifold geometry through specific circuit mechanisms, making dynamic neural manifolds parameterizable, and thereby offering an explainable framework for neural computation. Extending this framework to neuromorphic engineering, we present an implementation on the SpiNNaker 2 chip for real-time, closed-loop control. By allowing sensory inputs to modulate heterogeneous inhibition, gain, and transient currents, our architecture drives rapid subspace rotations to switch between behaviors, as well as fine-grained trajectory control within them. We validate this via a robotic simulation where an agent uses sensory feedback to dynamically reconfigure its manifold geometry to navigate through a maze. Our results establish dynamic manifolds as a feasible approach for explainable neuromorphic architectures and a substrate for investigating biological neural dynamics.
Oskar von Seeler, Christian Tetzlaff, Andrew Lehr
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
Biological neural systems achieve remarkable robustness and adaptability in uncertain environments through sparse, event-driven spike-based information processing and adaptive regulation. Inspired by this paradigm, this paper develops a neuromorhpic disturbance observer (NDO) and control framework that replaces conventional continuous-time signal representations with spike-timing encoding. Both disturbance estimates and control inputs are constructed via integrate-and-fire (IF) neuron dynamics from discrete spike events, yielding intrinsically event-driven updates. An adaptive-threshold triggering mechanism is inspired by spike-frequency adaptation (SFA), enabling history-dependent regulation of spike generation. Simulation results demonstrate that the proposed framework achieves neurally inspired robustness and adaptability, while the adaptive-threshold spiking scheme reduces spike events to 42.6% of the fixed-threshold case under noisy conditions.
Hongfu Xu, Xiaoyu Guo, Shengbo Wang +1
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