Publications

Possible principles for aligned structure learning agents

This paper offers a roadmap for the development of scalable aligned artificial intelligence (AI) from first principle descriptions of natural intelligence. In brief, a possible path toward scalable aligned AI rests upon enabling artificial agents to learn a good model of the world that includes a good model of our preferences. For this, the main objective is creating agents that learn to represent the world and other agents' world models; a problem that falls under structure learning (a.k.a. causal representation learning). We expose the structure learning and alignment problems with this goal in mind, as well as principles to guide us forward, synthesizing various ideas across mathematics, statistics, and cognitive science. 1) We discuss the essential role of core knowledge, information geometry and model reduction in structure learning, and suggest core structural modules to learn a wide range of naturalistic worlds. 2) We outline a way toward aligned agents through structure learning and theory of mind. As an illustrative example, we mathematically sketch Asimov's Laws of Robotics, which prescribe agents to act cautiously to minimize the ill-being of other agents. We supplement this example by proposing refined approaches to alignment. These observations may guide the development of artificial intelligence in helping to scale existing -- or design new -- aligned structure learning systems.

With an eye on uncertainty: Modelling pupillary responses to environmental volatility

Living creatures must accurately infer the nature of their environments. They do this despite being confronted by stochastic and context sensitive contingencies-and so must constantly update their beliefs regarding their uncertainty about what might come next. In this work, we examine how we deal with uncertainty that evolves over time. This prospective uncertainty (or imprecision) is referred to as volatility and has previously been linked to noradrenergic signals that originate in the locus coeruleus. Using pupillary dilatation as a measure of central noradrenergic signalling, we tested the hypothesis that changes in pupil diameter reflect inferences humans make about environmental volatility. To do so, we collected pupillometry data from participants presented with a stream of numbers. We generated these numbers from a process with varying degrees of volatility. By measuring pupillary dilatation in response to these stimuli-and simulating the inferences made by an ideal Bayesian observer of the same stimuli-we demonstrate that humans update their beliefs about environmental contingencies in a Bayes optimal way. We show this by comparing general linear (convolution) models that formalised competing hypotheses about the causes of pupillary changes. We found greater evidence for models that included Bayes optimal estimates of volatility than those without. We additionally explore the interaction between different causes of pupil dilation and suggest a quantitative approach to characterising a person's prior beliefs about volatility.

Effective degrees of freedom and the RFT resel count

In one of neuroimaging's key papers, Worsley et al. (1992) introduced the concept of a resolution element (resel) as an intuitive parametrisation of the roughness-adjusted search volume underlying random field theory's expression for corrected p-values. In another key development, Worsley and Friston (1995) showed that temporal correlation in a linear model reduced the effective degrees of freedom (eDF). Here, we illustrate a surprising connection between these quantities, which may have application to multiple comparison correction on data with elaborate statistical dependence that can make RFT over-conservative.

Topological Inference

Characterizing Dynamic Brain Responses with fMRI: A Multivariate Approach

In this paper we present a multivariate analysis of evoked hemodynamic responses and their spatiotemporal dynamics as measured with fast fMRI. This analysis uses standard multivariate statistics (MANCOVA) and the general linear model to make inferences about effects of interest and canonical variates analysis (CVA) to describe the important features of these effects. We have used these techniques to characterize the form of hemodynamic transients that are evoked during a cognitive or sensorimotor task. In particular we do not assume that the neural or hemodynamic response reaches some "steady state" but acknowledge that these physiological changes could show profound task-dependent adaptation and time-dependent changes during the task. To address this issue we have modeled hemodynamic responses using appropriate temporal basis functions and estimated their exact form within the general linear model using MANCOVA. We do not propose that this analysis is a particularly powerful way to make inferences about functional specialization (or more generally functional anatomy) because it only provides statistical inferences about the distributed (whole brain) responses evoked by different conditions. However, its application to characterizing the temporal aspects of evoked hemodynamic responses reveals some compelling and somewhat unexpected perspectives on transient but stereotyped responses to changes in cognitive or sensorimotor processing. The most remarkable observation is that these responses can be biphasic and show profound differences in their form depending on the extant task or condition. Furthermore these differences can be seen in the absence of changes in mean signal.

Dynamic diaschisis: Anatomically remote and context-sensitive human brain lesions

Functional neuroimaging was used to investigate how lesions to the Broca's area impair neuronal responses in remote undamaged cortical regions. Four patients with speech output problems, but relatively preserved comprehension, were scanned while viewing words relative to consonant letter strings. In normal subjects, this results in left lateralized activation in the posterior inferior frontal, middle temporal, and posterior inferior temporal cortices. Each patient activated normally in the middle temporal region but abnormally in the damaged posterior inferior frontal cortex and the undamaged posterior inferior temporal cortex. In the damaged frontal region, activity was insensitive to the presence of words but in the undamaged posterior inferior temporal region, activity decreased in the presence of words rather than increasing as it did in the normal individuals. The reversal of responses in the left posterior inferior temporal region illustrate the context-sensitive nature of the abnormality and that failure to activate the left posterior temporal region could not simply be accounted for by insufficient demands on the underlying function. We propose that, in normal individuals, visual word presentation changes the effective connectivity among reading areas and, in patients, posterior temporal responses are abnormal when they depend upon inputs from the damaged inferior frontal cortex. Our results serve to introduce the concept of dynamic diaschisis; the anatomically remote and context-sensitive effects of focal brain lesions. Dynamic diaschisis reveals abnormalities of functional integration that may have profound implications for neuropsychological inference, functional anatomy and, vicariously, cognitive rehabilitation.

Dynamic causal modelling of phase-amplitude interactions

Models of coupled oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that interactions can be described purely in terms of phase differences. Whilst mathematically convenient, the restrictive nature of phase-only models can limit their explanatory power. We therefore propose a generalisation of dynamic causal modelling that incorporates both phase and amplitude. This allows for the separate quantifications of phase and amplitude contributions to the connectivity between neural regions. We establish, using model-generated data and simulations of coupled pendula, that phase-only models perform well only under weak coupling conditions. We also show that, despite their higher complexity, phase-amplitude models can describe strongly coupled systems more effectively than their phase-only counterparts. We relate our findings to four metrics commonly used in neuroimaging: the Kuramoto order parameter, cross-correlation, phase-lag index, and spectral entropy. We find that, with the exception of spectral entropy, the phase-amplitude model is able to capture all metrics more effectively than the phase-only model. We then demonstrate, using local field potential recordings in rodents and functional magnetic resonance imaging in macaque monkeys, that amplitudes in oscillator models play an important role in describing neural dynamics in anaesthetised brain states.

A cortical field theory – dynamics and symmetries

The labile brain. II. Transients, complexity and selection

The successive expression of neuronal transients is related to dynamic correlations and, as shown in this paper, to dynamic instability. Dynamic instability is a form of complexity, typical of neuronal systems, which may be crucial for adaptive brain function from two perspectives. The first is from the point of view of neuronal selection and self–organizing systems: if selective mechanisms underpin the emergence of adaptive neuronal responses then dynamic instability is, itself, necessarily adaptive. This is because dynamic instability is the source of diversity on which selection acts and is therefore subject to selective pressure. In short, the emergence of order, through selection, depends almost paradoxically on the instabilities that characterize the diversity of brain dynamics. The second perspective is provided by information theory.

Comparing event-related and epoch analysis in blocked design fMRI

The neuroanatomy of autism

AUTISM is a biological disorder which affects social cognition, and understanding brain abnormalities of the former will elucidate the brain basis of the latter. We report structural MRI data on 15 high-functioning individuals with autistic disorder. A voxel-based whole brain analysis identified grey matter differences in an amygdala centered system relative to 15 age- and IQ-matched controls. Decreases of grey matter were found in anterior parts of this system (right paracingulate sulcus, left inferior frontal gyrus). Increases were found in posterior parts (amygdala/peri-amygdaloid cortex, middle temporal gyrus, inferior temporal gyrus), and in regions of the cerebellum. These structures are implicated in social cognition by animal, imaging and histopathological studies. This study therefore provides converging evidence of the physiological basis of social cognition.

Active inference, stressors, and psychological trauma: A neuroethological model of (mal)adaptive explore-exploit dynamics in ecological context

This paper offers a formal account of emotional inference and stress-related behaviour, using the notion of active inference. We formulate responses to stressful scenarios in terms of Bayesian belief-updating and subsequent policy selection; namely, planning as (active) inference. Using a minimal model of how creatures or subjects account for their sensations (and subsequent action), we deconstruct the sequences of belief updating and behaviour that underwrite stress-related responses - and simulate the aberrant responses of the sort seen in post-traumatic stress disorder (PTSD). Crucially, the model used for belief-updating generates predictions in multiple (exteroceptive, proprioceptive and interoceptive) modalities, to provide an integrated account of evidence accumulation and multimodal integration that has consequences for both motor and autonomic responses. The ensuing phenomenology speaks to many constructs in the ecological and clinical literature on stress, which we unpack with reference to simulated inference processes and accompanying neuronal responses. A key insight afforded by this formal approach rests on the trade-off between the epistemic affordance of certain cues (that resolve uncertainty about states of affairs in the environment) and the consequences of epistemic foraging (that may be in conflict with the instrumental or pragmatic value of 'fleeing' or 'freezing'). Starting from first principles, we show how this trade-off is nuanced by prior (subpersonal) beliefs about the outcomes of behaviour - beliefs that, when held with unduly high precision, can lead to (Bayes optimal) responses that closely resemble PTSD.

Degeneracy and cognitive anatomy

Cognitive models indicate that there are multiple ways of completing the same task. This implicit degeneracy cannot be revealed by functional imaging studies of normal subjects if more than one of the sufficient neural systems is activated. Nor can it be detected by neuropsychological studies of patients because their performance might not be impaired when only one degenerate system is damaged. We propose that degenerate sets of sufficient neural systems can only be identified by an iterative approach that integrates the lesion-deficit model and functional imaging studies of normal and neurologically damaged subjects.

Decoding episodic memory in ageing: A Bayesian analysis of activity patterns predicting memory

Normal ageing is associated with a decline in episodic memory, and neuroimaging studies in older adults have shown reduced activity in prefrontal cortex and other regions critical for memory function in the young. However, older adults also activate additional regions, suggesting a degree of functional reorganisation that has been attributed variously to detrimental and adaptive changes. Evaluation of these competing hypotheses depends critically upon inferences about the relative location and distribution of activity that are not well supported by current univariate or multivariate analyses. Here, we employed a recently developed model-based multivariate 'decoding' approach (Friston et al., 2008) to re-analyse a rich episodic encoding dataset and examine directly how the patterns of activity change in ageing. We assessed which spatial activity patterns, within lateral prefrontal cortex, best predict successful memory formation. Bayesian model comparison showed that the older adults had more distributed and bilateral (fragmented) predictive patterns of activity in anterior inferior frontal gyrus and middle frontal gyrus. With this direct multivariate test for changes in patterns of activity, we replicate and extend earlier findings of reduced prefrontal lateralisation in ageing. These findings extend conclusions based on conventional analyses, and support the notion that ageing alters the spatial deployment of neuronal activity, to render it less spatially coherent and regionally specific. This greater distribution of activity in older adults was also linked to poorer individual memory performance, suggesting that it reflects neural ageing, rather than adaptive compensatory responses.

Acquisition methods, methods and modeling

The Paradox of the Self-Studying Brain

Stochastic Dynamic Causal Modelling

Computational modeling of perceptual inference: A hierarchical Bayesian approach that allows for individual and contextual differences in weighting of input