arXiv subjects

Peter Thestrup Waade

Publications and source records attributed to Peter Thestrup Waade.

3 recordsLinked to original sources

arXiv2026

Robust volatility updates for Hierarchical Gaussian Filtering

Hierarchical Gaussian Filtering (HGF) networks allow for efficient updating of posterior distributions (beliefs) about hidden states of an agent's environment. HGF parent nodes can target the mean or variance of their children. New information entering at input nodes leads to a cascade of belief updates across the network according to one-step update equations for each node's mean and precision (inverse variance). However, the original form of the update equations for variance-targeting parents(volatility coupling) can in some regions of parameter space lead to negative posterior precision, a logical impossibility which causes the updating algorithm to terminate with an error. In this report, we introduce a modified quadratic approximation to the variational energy of volatility-coupled nodes that avoids negative posterior precision. The key idea is to interpolate between two quadratic expansions of the variational energy: one at the prior prediction and one at a second mode whose location is obtained in closed form via the Lambert W function. The resulting update equations are robust across the entire parameter space and faithfully track the variational posterior even for large prediction errors.

cs.LG↗

arXiv2025

The generalized Hierarchical Gaussian Filter

Hierarchical Bayesian models of perception and learning feature prominently in contemporary cognitive neuroscience where, for example, they inform computational concepts of mental disorders. This includes predictive coding and hierarchical Gaussian filtering (HGF), which differ in the nature of hierarchical representations. In this work, we present a new class of artificial neural networks that unifies computational principles of PC and HGFs. We extend the space of generative models underlying HGF to include a form of nonlinear hierarchical coupling between state values akin to predictive coding and artificial neural networks in general. We derive the update equations corresponding to this generalization of HGF and conceptualize them as connecting a network of (belief) nodes where parent nodes either predict the state of child nodes or their rate of change. This enables us to (1) create modular architectures with generic computational steps in each node of the network, and (2) disclose the hierarchical message passing implied by generalized HGF models and to compare this to comparable schemes under predictive coding. The practical advances of this work are twofold: on the one hand, our extension allows for a modular construction of ANNs of arbitrarily complex hierarchical structure under the general principles of HGF. On the other hand, by providing a highly flexible implementation of hierarchical Bayesian models available as open source software, it enables new types of empirical data analysis in computational psychiatry.

cs.NE↗

arXiv2025

pyhgf: A neural network library for predictive coding

Bayesian models of cognition have gained considerable traction in computational neuroscience and psychiatry. Their scopes are now expected to expand rapidly to artificial intelligence, providing general inference frameworks to support embodied, adaptable, and energy-efficient autonomous agents. A central theory in this domain is predictive coding, which posits that learning and behaviour are driven by hierarchical probabilistic inferences about the causes of sensory inputs. Biological realism constrains these networks to rely on simple local computations in the form of precision-weighted predictions and prediction errors. This can make this framework highly efficient, but its implementation comes with unique challenges on the software development side. Embedding such models in standard neural network libraries often becomes limiting, as these libraries' compilation and differentiation backends can force a conceptual separation between optimization algorithms and the systems being optimized. This critically departs from other biological principles such as self-monitoring, self-organisation, cellular growth and functional plasticity. In this paper, we introduce \texttt{pyhgf}: a Python package backed by JAX and Rust for creating, manipulating and sampling dynamic networks for predictive coding. We improve over other frameworks by enclosing the network components as transparent, modular and malleable variables in the message-passing steps. The resulting graphs can implement arbitrary computational complexities as beliefs propagation. But the transparency of core variables can also translate into inference processes that leverage self-organisation principles, and express structure learning, meta-learning or causal discovery as the consequence of network structural adaptation to surprising inputs. The code, tutorials and documentation are hosted at: https://github.com/ilabcode/pyhgf.

cs.NE↗