Learning in Volatile Environments With the Bayes Factor Surprise

Fast adaptation to rule switching using neuronal surprise

In humans and animals, surprise is a physiological reaction to an unexpected event, but how surprise can be linked to plausible models of neuronal activity is an open problem. We propose a self-supervised spiking neural network model where a surprise signal is extracted from an increase in neural activity after an imbalance of excitation and inhibition. The surprise signal modulates synaptic plasticity via a three-factor learning rule which increases plasticity at moments of surprise. The surprise signal remains small when transitions between sensory events follow a previously learned rule but increases immediately after rule switching. In a spiking network with several modules, previously learned rules are protected against overwriting, as long as the number of modules is larger than the total number of rules-making a step towards solving the stability-plasticity dilemma in neuroscience. Our model relates the subjective notion of surprise to specific predictions on the circuit level.

Surprise and novelty in the brain

Notions of surprise and novelty have been used in various experimental and theoretical studies across multiple brain areas and species. However, 'surprise' and 'novelty' refer to different quantities in different studies, which raises concerns about whether these studies indeed relate to the same functionalities and mechanisms in the brain. Here, we address these concerns through a systematic investigation of how different aspects of surprise and novelty relate to different brain functions and physiological signals. We review recent classifications of definitions proposed for surprise and novelty along with links to experimental observations. We show that computational modeling and quantifiable definitions enable novel interpretations of previous findings and form a foundation for future theoretical and experimental studies.

P3-like signatures of temporal predictions: a computational EEG study

Many cognitive processes, ranging from perception to action, depend on the ability to predict the timing of forthcoming events. Yet, how the brain uses predictive models in the temporal domain is still an unsolved question. In previous work, we began to explore the neural correlates of temporal predictions by using a computational approach in which an ideal Bayesian observer learned the temporal probabilities of target onsets in a simple reaction time task. Because the task was specifically designed to disambiguate updating of predictive models and surprise, changes in temporal probabilities were explicitly cued. However, in the real world, we are usually incidentally exposed to changes in the statistics of the environment. Here, we thus aimed to further investigate the electroencephalographic (EEG) correlates of Bayesian belief updating and surprise associated with incidental learning of temporal probabilities. In line with our previous EEG study, results showed distinct P3-like modulations for updating and surprise. While surprise was indexed by an early fronto-central P3-like modulation, updating was associated with a later and more posterior P3 modulation. Moreover, updating was associated with a P2-like potential at centro-parietal electrodes, likely capturing integration processes between prior beliefs and likelihood of the observed event. These findings support previous evidence of trial-by-trial variability of P3 amplitudes as an index of dissociable inferential processes. Coupled with our previous findings, the present study strongly bolsters the view of the P3 as a key brain signature of temporal Bayesian inference. Data and scripts are shared on OSF: osf.io/sdy8j/.

A characterization of the neural representation of confidence during probabilistic learning

Learning in a stochastic and changing environment is a difficult task. Models of learning typically postulate that observations that deviate from the learned predictions are surprising and used to update those predictions. Bayesian accounts further posit the existence of a confidence-weighting mechanism: learning should be modulated by the confidence level that accompanies those predictions. However, the neural bases of this confidence are much less known than the ones of surprise. Here, we used a dynamic probability learning task and high-field MRI to identify putative cortical regions involved in the representation of confidence about predictions during human learning. We devised a stringent test based on the conjunction of four criteria. We localized several regions in parietal and frontal cortices whose activity is sensitive to the confidence of an ideal observer, specifically so with respect to potential confounds (surprise and predictability), and in a way that is invariant to which item is predicted. We also tested for functionality in two ways. First, we localized regions whose activity patterns at the subject level showed an effect of both confidence and surprise in qualitative agreement with the confidence-weighting principle. Second, we found neural representations of ideal confidence that also accounted for subjective confidence. Taken together, those results identify a set of cortical regions potentially implicated in the confidence-weighting of learning.

Active inference and the two-step task

Sequential decision problems distill important challenges frequently faced by humans. Through repeated interactions with an uncertain world, unknown statistics need to be learned while balancing exploration and exploitation. Reinforcement learning is a prominent method for modeling such behaviour, with a prevalent application being the two-step task. However, recent studies indicate that the standard reinforcement learning model sometimes describes features of human task behaviour inaccurately and incompletely. We investigated whether active inference, a framework proposing a trade-off to the exploration-exploitation dilemma, could better describe human behaviour. Therefore, we re-analysed four publicly available datasets of the two-step task, performed Bayesian model selection, and compared behavioural model predictions. Two datasets, which revealed more model-based inference and behaviour indicative of directed exploration, were better described by active inference, while the models scored similarly for the remaining datasets. Learning using probability distributions appears to contribute to the improved model fits. Further, approximately half of all participants showed sensitivity to information gain as formulated under active inference, although behavioural exploration effects were not fully captured. These results contribute to the empirical validation of active inference as a model of human behaviour and the study of alternative models for the influential two-step task.

Revealing human sensitivity to a latent temporal structure of changes

Precisely timed behavior and accurate time perception plays a critical role in our everyday lives, as our wellbeing and even survival can depend on well-timed decisions. Although the temporal structure of the world around us is essential for human decision making, we know surprisingly little about how representation of temporal structure of our everyday environment impacts decision making. How does the representation of temporal structure affect our ability to generate well-timed decisions? Here we address this question by using a well-established dynamic probabilistic learning task. Using computational modeling, we found that human subjects' beliefs about temporal structure are reflected in their choices to either exploit their current knowledge or to explore novel options. The model-based analysis illustrates a large within-group and within-subject heterogeneity. To explain these results, we propose a normative model for how temporal structure is used in decision making, based on the semi-Markov formalism in the active inference framework. We discuss potential key applications of the presented approach to the fields of cognitive phenotyping and computational psychiatry.

Neuromorphic computing hardware and neural architectures for robotics

Neuromorphic hardware enables fast and power-efficient neural network-based artificial intelligence that is well suited to solving robotic tasks. Neuromorphic algorithms can be further developed following neural computing principles and neural network architectures inspired by biological neural systems. In this Viewpoint, we provide an overview of recent insights from neuroscience that could enhance signal processing in artificial neural networks on chip and unlock innovative applications in robotics and autonomous intelligent systems. These insights uncover computing principles, primitives, and algorithms on different levels of abstraction and call for more research into the basis of neural computation and neuronally inspired computing hardware.

A Bayesian Surprise Approach in Designing Cognitive Radar for Autonomous Driving

This article proposes the Bayesian surprise as the main methodology that drives the cognitive radar to estimate a target’s future state (i.e., velocity, distance) from noisy measurements and execute a decision to minimize the estimation error over time. The research aims to demonstrate whether the cognitive radar as an autonomous system can modify its internal model (i.e., waveform parameters) to gain consecutive informative measurements based on the Bayesian surprise. By assuming that the radar measurements are constructed from linear Gaussian state-space models, the paper applies Kalman filtering to perform state estimation for a simple vehicle-following scenario. According to the filter’s estimate, the sensor measures the contribution of prospective waveforms—which are available from the sensor profile library—to state estimation and selects the one that maximizes the expectation of Bayesian surprise. Numerous experiments examine the estimation performance of the proposed cognitive radar for single-target tracking in practical highway and urban driving environments. The robustness of the proposed method is compared to the state-of-the-art for various error measures. Results indicate that the Bayesian surprise outperforms its competitors with respect to the mean square relative error when one-step and multiple-step planning is considered.

An empirical evaluation of active inference in multi-armed bandits

A key feature of sequential decision making under uncertainty is a need to balance between exploiting-choosing the best action according to the current knowledge, and exploring-obtaining information about values of other actions. The multi-armed bandit problem, a classical task that captures this trade-off, served as a vehicle in machine learning for developing bandit algorithms that proved to be useful in numerous industrial applications. The active inference framework, an approach to sequential decision making recently developed in neuroscience for understanding human and animal behaviour, is distinguished by its sophisticated strategy for resolving the exploration-exploitation trade-off. This makes active inference an exciting alternative to already established bandit algorithms. Here we derive an efficient and scalable approximate active inference algorithm and compare it to two state-of-the-art bandit algorithms: Bayesian upper confidence bound and optimistic Thompson sampling. This comparison is done on two types of bandit problems: a stationary and a dynamic switching bandit. Our empirical evaluation shows that the active inference algorithm does not produce efficient long-term behaviour in stationary bandits. However, in the more challenging switching bandit problem active inference performs substantially better than the two state-of-the-art bandit algorithms. The results open exciting venues for further research in theoretical and applied machine learning, as well as lend additional credibility to active inference as a general framework for studying human and animal behaviour.

Novelty is not surprise: Human exploratory and adaptive behavior in sequential decision-making

Classic reinforcement learning (RL) theories cannot explain human behavior in the absence of external reward or when the environment changes. Here, we employ a deep sequential decision-making paradigm with sparse reward and abrupt environmental changes. To explain the behavior of human participants in these environments, we show that RL theories need to include surprise and novelty, each with a distinct role. While novelty drives exploration before the first encounter of a reward, surprise increases the rate of learning of a world-model as well as of model-free action-values. Even though the world-model is available for model-based RL, we find that human decisions are dominated by model-free action choices. The world-model is only marginally used for planning, but it is important to detect surprising events. Our theory predicts human action choices with high probability and allows us to dissociate surprise, novelty, and reward in EEG signals.