Paul Kinghorn

Paul F Kinghorn, Beren Millidge, Christopher L Buckley

Predictive Coding Networks (PCNs) aim to learn a generative model of the world. Given observations, this generative model can then be inverted to infer the causes of those observations. However, when training PCNs, a noticeable pathology is often observed where inference accuracy peaks and then declines with further training. This cannot be explained by overfitting since both training and test accuracy decrease simultaneously. Here we provide a thorough investigation of this phenomenon and show that it is caused by an imbalance between the speeds at which the various layers of the PCN converge. We demonstrate that this can be prevented by regularising the weight matrices at each layer: by restricting the relative size of matrix singular values, we allow the weight matrix to change but restrict the overall impact which a layer can have on its neighbours. We also demonstrate that a similar effect can be achieved through a more biologically plausible and simple scheme of just capping the weights.

Francesco Innocenti, Paul Kinghorn, Will Yun-Farmbrough et al.

We introduce JPC, a JAX library for training neural networks with Predictive Coding. JPC provides a simple, fast and flexible interface to train a variety of PC networks (PCNs) including discriminative, generative and hybrid models. Unlike existing libraries, JPC leverages ordinary differential equation solvers to integrate the gradient flow inference dynamics of PCNs. We find that a second-order solver achieves significantly faster runtimes compared to standard Euler integration, with comparable performance on a range of tasks and network depths. JPC also provides some theoretical tools that can be used to study PCNs. We hope that JPC will facilitate future research of PC. The code is available at https://github.com/thebuckleylab/jpc.

Poppy Collis, Ryan Singh, Paul F Kinghorn et al.

An open problem in artificial intelligence is how systems can flexibly learn discrete abstractions that are useful for solving inherently continuous problems. Previous work in computational neuroscience has considered this functional integration of discrete and continuous variables during decision-making under the formalism of active inference (Parr, Friston & de Vries, 2017; Parr & Friston, 2018). However, their focus is on the expressive physical implementation of categorical decisions and the hierarchical mixed generative model is assumed to be known. As a consequence, it is unclear how this framework might be extended to learning. We therefore present a novel hierarchical hybrid active inference agent in which a high-level discrete active inference planner sits above a low-level continuous active inference controller. We make use of recent work in recurrent switching linear dynamical systems (rSLDS) which implement end-to-end learning of meaningful discrete representations via the piecewise linear decomposition of complex continuous dynamics (Linderman et al., 2016). The representations learned by the rSLDS inform the structure of the hybrid decision-making agent and allow us to (1) specify temporally-abstracted sub-goals in a method reminiscent of the options framework, (2) lift the exploration into discrete space allowing us to exploit information-theoretic exploration bonuses and (3) `cache' the approximate solutions to low-level problems in the discrete planner. We apply our model to the sparse Continuous Mountain Car task, demonstrating fast system identification via enhanced exploration and successful planning through the delineation of abstract sub-goals.

Poppy Collis, Paul F Kinghorn, Christopher L Buckley

The ability to invent new tools has been identified as an important facet of our ability as a species to problem solve in dynamic and novel environments. While the use of tools by artificial agents presents a challenging task and has been widely identified as a key goal in the field of autonomous robotics, far less research has tackled the invention of new tools by agents. In this paper, (1) we articulate the distinction between tool discovery and tool innovation by providing a minimal description of the two concepts under the formalism of active inference. We then (2) apply this description to construct a toy model of tool innovation by introducing the notion of tool affordances into the hidden states of the agent's probabilistic generative model. This particular state factorisation facilitates the ability to not just discover tools but invent them through the offline induction of an appropriate tool property. We discuss the implications of these preliminary results and outline future directions of research.

Poppy Collis, Ryan Singh, Paul F Kinghorn et al.

An open problem in artificial intelligence is how systems can flexibly learn discrete abstractions that are useful for solving inherently continuous problems. Previous work has demonstrated that a class of hybrid state-space model known as recurrent switching linear dynamical systems (rSLDS) discover meaningful behavioural units via the piecewise linear decomposition of complex continuous dynamics (Linderman et al., 2016). Furthermore, they model how the underlying continuous states drive these discrete mode switches. We propose that the rich representations formed by an rSLDS can provide useful abstractions for planning and control. We present a novel hierarchical model-based algorithm inspired by Active Inference in which a discrete MDP sits above a low-level linear-quadratic controller. The recurrent transition dynamics learned by the rSLDS allow us to (1) specify temporally-abstracted sub-goals in a method reminiscent of the options framework, (2) lift the exploration into discrete space allowing us to exploit information-theoretic exploration bonuses and (3) `cache' the approximate solutions to low-level problems in the discrete planner. We successfully apply our model to the sparse Continuous Mountain Car task, demonstrating fast system identification via enhanced exploration and non-trivial planning through the delineation of abstract sub-goals.

Ajith Anil Meera, Poppy Collis, Polina Arbuzova et al.

Robots today often miss a key ingredient of truly intelligent behavior: the ability to reflect on their own cognitive processes and decisions. In humans, this self-monitoring or metacognition is crucial for learning, decision making and problem solving. For instance, they can evaluate how confident they are in performing a task, thus regulating their own behavior and allocating proper resources. Taking inspiration from neuroscience, we propose a robot metacognition architecture centered on confidence (a second-order judgment on decisions) and we demonstrate it on the use case of autonomous tool invention. We propose the use of confidence as a metacognitive measure within the robot decision making scheme. Confidence-informed robots can evaluate the reliability of their decisions, improving their robustness during real-world physical deployment. This form of robotic metacognition emphasizes embodied action monitoring as a means to achieve better informed decisions. We also highlight potential applications and research directions for robot metacognition.

Mahault Albarracin, Ines Hipolito, Maria Raffa et al.

Active inference helps us simulate adaptive behavior and decision-making in biological and artificial agents. Building on our previous work exploring the relationship between active inference, well-being, resilience, and sustainability, we present a computational model of an agent learning sustainable resource management strategies in both static and dynamic environments. The agent's behavior emerges from optimizing its own well-being, represented by prior preferences, subject to beliefs about environmental dynamics. In a static environment, the agent learns to consistently consume resources to satisfy its needs. In a dynamic environment where resources deplete and replenish based on the agent's actions, the agent adapts its behavior to balance immediate needs with long-term resource availability. This demonstrates how active inference can give rise to sustainable and resilient behaviors in the face of changing environmental conditions. We discuss the implications of our model, its limitations, and suggest future directions for integrating more complex agent-environment interactions. Our work highlights active inference's potential for understanding and shaping sustainable behaviors.

Paul F. Kinghorn, Beren Millidge, Christopher L. Buckley

In cognitive science, behaviour is often separated into two types. Reflexive control is habitual and immediate, whereas reflective is deliberative and time consuming. We examine the argument that Hierarchical Predictive Coding (HPC) can explain both types of behaviour as a continuum operating across a multi-layered network, removing the need for separate circuits in the brain. On this view, "fast" actions may be triggered using only the lower layers of the HPC schema, whereas more deliberative actions need higher layers. We demonstrate that HPC can distribute learning throughout its hierarchy, with higher layers called into use only as required.