Multitask learning over shared subspaces.

This paper uses constructs from machine learning to define pairs of learning tasks that either shared or did not share a common subspace. Human subjects then learnt these tasks using a feedback-based approach and we hypothesised that learning would be boosted for shared subspaces. Our findings broadly supported this hypothesis with either better performance on the second task if it shared the same subspace as the first, or positive correlations over task performance for shared subspaces. These empirical findings were compared to the behaviour of a Neural Network model trained using sequential Bayesian learning and human performance was found to be consistent with a minimal capacity variant of this model. Networks with an increased representational capacity, and networks without Bayesian learning, did not show these transfer effects. We propose that the concept of shared subspaces provides a useful framework for the experimental study of human multitask and transfer learning.

Prefrontal Dynamics Associated with Efficient Detours and Shortcuts: A Combined Functional Magnetic Resonance Imaging and Magnetoencenphalography Study.

Central to the concept of the "cognitive map" is that it confers behavioral flexibility, allowing animals to take efficient detours, exploit shortcuts, and avoid alluring, but unhelpful, paths. The neural underpinnings of such naturalistic and flexible behavior remain unclear. In two neuroimaging experiments, we tested human participants on their ability to navigate to a set of goal locations in a virtual desert island riven by lava, which occasionally spread to block selected paths (necessitating detours) or receded to open new paths (affording real shortcuts or false shortcuts to be avoided). Detours activated a network of frontal regions compared with shortcuts. Activity in the right dorsolateral PFC specifically increased when participants encountered tempting false shortcuts that led along suboptimal paths that needed to be differentiated from real shortcuts. We also report modulation in event-related fields and theta power in these situations, providing insight to the temporal evolution of response to encountering detours and shortcuts. These results help inform current models as to how the brain supports navigation and planning in dynamic environments.

Backtracking during navigation is correlated with enhanced anterior cingulate activity and suppression of alpha oscillations and the 'default-mode' network.

Successful navigation can require realizing the current path choice was a mistake and the best strategy is to retreat along the recent path: 'back-track'. Despite the wealth of studies on the neural correlates of navigation little is known about backtracking. To explore the neural underpinnings of backtracking we tested humans during functional magnetic resonance imaging on their ability to navigate to a set of goal locations in a virtual desert island riven by lava which constrained the paths that could be taken. We found that on a subset of trials, participants spontaneously chose to backtrack and that the majority of these choices were optimal. During backtracking, activity increased in frontal regions and the dorsal anterior cingulate cortex, while activity was suppressed in regions associated with the core default-mode network. Using the same task, magnetoencephalography and a separate group of participants, we found that power in the alpha band was significantly decreased immediately prior to such backtracking events. These results highlight the importance for navigation of brain networks previously identified in processing internally-generated errors and that such error-detection responses may involve shifting the brain from default-mode states to aid successful spatial orientation.

Bayesian population receptive field modelling.

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain.

Multivariate dynamical modelling of structural change during development.

Here we introduce a multivariate framework for characterising longitudinal changes in structural MRI using dynamical systems. The general approach enables modelling changes of states in multiple imaging biomarkers typically observed during brain development, plasticity, ageing and degeneration, e.g. regional gray matter volume of multiple regions of interest (ROIs). Structural brain states follow intrinsic dynamics according to a linear system with additional inputs accounting for potential driving forces of brain development. In particular, the inputs to the system are specified to account for known or latent developmental growth/decline factors, e.g. due to effects of growth hormones, puberty, or sudden behavioural changes etc. Because effects of developmental factors might be region-specific, the sensitivity of each ROI to contributions of each factor is explicitly modelled. In addition to the external effects of developmental factors on regional change, the framework enables modelling and inference about directed (potentially reciprocal) interactions between brain regions, due to competition for space, or structural connectivity, and suchlike. This approach accounts for repeated measures in typical MRI studies of development and aging. Model inversion and posterior distributions are obtained using earlier established variational methods enabling Bayesian evidence-based comparisons between various models of structural change. Using this approach we demonstrate dynamic cortical changes during brain maturation between 6 and 22 years of age using a large openly available longitudinal paediatric dataset with 637 scans from 289 individuals. In particular, we model volumetric changes in 26 bilateral ROIs, which cover large portions of cortical and subcortical gray matter. We account for (1) puberty-related effects on gray matter regions; (2) effects of an early transient growth process with additional time-lag parameter; (3) sexual dimorphism by modelling parameter differences between boys and girls. There is evidence that the regional pattern of sensitivity to dynamic hidden growth factors in late childhood is similar across genders and shows a consistent anterior-posterior gradient with strongest impact to prefrontal cortex (PFC) brain changes. Finally, we demonstrate the potential of the framework to explore the coupling of structural changes across a priori defined subnetworks using an example of previously established resting state functional connectivity.

Auditory training changes temporal lobe connectivity in 'Wernicke's aphasia': a randomised trial.

INTRODUCTION: Aphasia is one of the most disabling sequelae after stroke, occurring in 25%-40% of stroke survivors. However, there remains a lack of good evidence for the efficacy or mechanisms of speech comprehension rehabilitation. TRIAL DESIGN: This within-subjects trial tested two concurrent interventions in 20 patients with chronic aphasia with speech comprehension impairment following left hemisphere stroke: (1) phonological training using 'Earobics' software and (2) a pharmacological intervention using donepezil, an acetylcholinesterase inhibitor. Donepezil was tested in a double-blind, placebo-controlled, cross-over design using block randomisation with bias minimisation. METHODS: The primary outcome measure was speech comprehension score on the comprehensive aphasia test. Magnetoencephalography (MEG) with an established index of auditory perception, the mismatch negativity response, tested whether the therapies altered effective connectivity at the lower (primary) or higher (secondary) level of the auditory network. RESULTS: Phonological training improved speech comprehension abilities and was particularly effective for patients with severe deficits. No major adverse effects of donepezil were observed, but it had an unpredicted negative effect on speech comprehension. The MEG analysis demonstrated that phonological training increased synaptic gain in the left superior temporal gyrus (STG). Patients with more severe speech comprehension impairments also showed strengthening of bidirectional connections between the left and right STG. CONCLUSIONS: Phonological training resulted in a small but significant improvement in speech comprehension, whereas donepezil had a negative effect. The connectivity results indicated that training reshaped higher order phonological representations in the left STG and (in more severe patients) induced stronger interhemispheric transfer of information between higher levels of auditory cortex.Clinical trial registrationThis trial was registered with EudraCT (2005-004215-30, https://eudract.ema.europa.eu/) and ISRCTN (68939136, http://www.isrctn.com/).

Annealed Importance Sampling for Neural Mass Models.

Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution.

Gradient-based MCMC samplers for dynamic causal modelling.

In this technical note, we derive two MCMC (Markov chain Monte Carlo) samplers for dynamic causal models (DCMs). Specifically, we use (a) Hamiltonian MCMC (HMC-E) where sampling is simulated using Hamilton's equation of motion and (b) Langevin Monte Carlo algorithm (LMC-R and LMC-E) that simulates the Langevin diffusion of samples using gradients either on a Euclidean (E) or on a Riemannian (R) manifold. While LMC-R requires minimal tuning, the implementation of HMC-E is heavily dependent on its tuning parameters. These parameters are therefore optimised by learning a Gaussian process model of the time-normalised sample correlation matrix. This allows one to formulate an objective function that balances tuning parameter exploration and exploitation, furnishing an intervention-free inference scheme. Using neural mass models (NMMs)-a class of biophysically motivated DCMs-we find that HMC-E is statistically more efficient than LMC-R (with a Riemannian metric); yet both gradient-based samplers are far superior to the random walk Metropolis algorithm, which proves inadequate to steer away from dynamical instability.

Causal evidence that intrinsic beta-frequency is relevant for enhanced signal propagation in the motor system as shown through rhythmic TMS.

Correlative evidence provides support for the idea that brain oscillations underpin neural computations. Recent work using rhythmic stimulation techniques in humans provide causal evidence but the interactions of these external signals with intrinsic rhythmicity remain unclear. Here, we show that sensorimotor cortex follows externally applied rhythmic TMS (rTMS) stimulation in the beta-band but that the elicited responses are strongest at the intrinsic individual beta peak frequency. While these entrainment effects are of short duration, even subthreshold rTMS pulses propagate through the network and elicit significant cortico-spinal coupling, particularly when stimulated at the individual beta-frequency. Our results show that externally enforced rhythmicity interacts with intrinsic brain rhythms such that the individual peak frequency determines the effect of rTMS. The observed downstream spinal effect at the resonance frequency provides evidence for the causal role of brain rhythms for signal propagation.

Behavioral modeling of human choices reveals dissociable effects of physical effort and temporal delay on reward devaluation.

There has been considerable interest from the fields of biology, economics, psychology, and ecology about how decision costs decrease the value of rewarding outcomes. For example, formal descriptions of how reward value changes with increasing temporal delays allow for quantifying individual decision preferences, as in animal species populating different habitats, or normal and clinical human populations. Strikingly, it remains largely unclear how humans evaluate rewards when these are tied to energetic costs, despite the surge of interest in the neural basis of effort-guided decision-making and the prevalence of disorders showing a diminished willingness to exert effort (e.g., depression). One common assumption is that effort discounts reward in a similar way to delay. Here we challenge this assumption by formally comparing competing hypotheses about effort and delay discounting. We used a design specifically optimized to compare discounting behavior for both effort and delay over a wide range of decision costs (Experiment 1). We then additionally characterized the profile of effort discounting free of model assumptions (Experiment 2). Contrary to previous reports, in both experiments effort costs devalued reward in a manner opposite to delay, with small devaluations for lower efforts, and progressively larger devaluations for higher effort-levels (concave shape). Bayesian model comparison confirmed that delay-choices were best predicted by a hyperbolic model, with the largest reward devaluations occurring at shorter delays. In contrast, an altogether different relationship was observed for effort-choices, which were best described by a model of inverse sigmoidal shape that is initially concave. Our results provide a novel characterization of human effort discounting behavior and its first dissociation from delay discounting. This enables accurate modelling of cost-benefit decisions, a prerequisite for the investigation of the neural underpinnings of effort-guided choice and for understanding the deficits in clinical disorders characterized by behavioral inactivity.

Replay of very early encoding representations during recollection.

Long-term memories are linked to cortical representations of perceived events, but it is unclear which types of representations can later be recollected. Using magnetoencephalography-based decoding, we examined which brain activity patterns elicited during encoding are later replayed during recollection in the human brain. The results show that the recollection of images depicting faces and scenes is associated with a replay of neural representations that are formed at very early (180 ms) stages of encoding. This replay occurs quite rapidly, ~500 ms after the onset of a cue that prompts recollection and correlates with source memory accuracy. Therefore, long-term memories are rapidly replayed during recollection and involve representations that were formed at very early stages of encoding. These findings indicate that very early representational information can be preserved in the memory engram and can be faithfully and rapidly reinstated during recollection. These novel insights into the nature of the memory engram provide constraints for mechanistic models of long-term memory function.

Gradient-free MCMC methods for dynamic causal modelling.

In this technical note we compare the performance of four gradient-free MCMC samplers (random walk Metropolis sampling, slice-sampling, adaptive MCMC sampling and population-based MCMC sampling with tempering) in terms of the number of independent samples they can produce per unit computational time. For the Bayesian inversion of a single-node neural mass model, both adaptive and population-based samplers are more efficient compared with random walk Metropolis sampler or slice-sampling; yet adaptive MCMC sampling is more promising in terms of compute time. Slice-sampling yields the highest number of independent samples from the target density - albeit at almost 1000% increase in computational time, in comparison to the most efficient algorithm (i.e., the adaptive MCMC sampler).

Transcranial electrical brain stimulation modulates neuronal tuning curves in perception of numerosity and duration.

Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation method with many putative applications and reported to effectively modulate behaviour. However, its effects have yet to be considered at a computational level. To address this we modelled the tuning curves underlying the behavioural effects of stimulation in a perceptual task. Participants judged which of the two serially presented images contained more items (numerosity judgement task) or was presented longer (duration judgement task). During presentation of the second image their posterior parietal cortices (PPCs) were stimulated bilaterally with opposite polarities for 1.6s. We also examined the impact of three stimulation conditions on behaviour: anodal right-PPC and cathodal left-PPC (rA-lC), reverse order (lA-rC) and no-stimulation condition. Behavioural results showed that participants were more accurate in numerosity and duration judgement tasks when they were stimulated with lA-rC and rA-lC stimulation conditions respectively. Simultaneously, a decrease in performance on numerosity and duration judgement tasks was observed when the stimulation condition favoured the other task. Thus, our results revealed a double-dissociation of laterality and task. Importantly, we were able to model the effects of stimulation on behaviour. Our computational modelling showed that participants' superior performance was attributable to a narrower tuning curve--smaller standard deviation of detection noise. We believe that this approach may prove useful in understanding the impact of brain stimulation on other cognitive domains.

Forward and backward inference in spatial cognition.

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of 'lower-level' computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus.

Changes in auditory feedback connections determine the severity of speech processing deficits after stroke.

We compared brain structure and function in two subgroups of 21 stroke patients with either moderate or severe chronic speech comprehension impairment. Both groups had damage to the supratemporal plane; however, the severe group suffered greater damage to two unimodal auditory areas: primary auditory cortex and the planum temporale. The effects of this damage were investigated using fMRI while patients listened to speech and speech-like sounds. Pronounced changes in connectivity were found in both groups in undamaged parts of the auditory hierarchy. Compared to controls, moderate patients had significantly stronger feedback connections from planum temporale to primary auditory cortex bilaterally, while in severe patients this connection was significantly weaker in the undamaged right hemisphere. This suggests that predictive feedback mechanisms compensate in moderately affected patients but not in severely affected patients. The key pathomechanism in humans with persistent speech comprehension impairments may be impaired feedback connectivity to unimodal auditory areas.

The problem of low variance voxels in statistical parametric mapping; a new hat avoids a 'haircut'.

Statistical parametric mapping (SPM) locates significant clusters based on a ratio of signal to noise (a 'contrast' of the parameters divided by its standard error) meaning that very low noise regions, for example outside the brain, can attain artefactually high statistical values. Similarly, the commonly applied preprocessing step of Gaussian spatial smoothing can shift the peak statistical significance away from the peak of the contrast and towards regions of lower variance. These problems have previously been identified in positron emission tomography (PET) (Reimold et al., 2006) and voxel-based morphometry (VBM) (Acosta-Cabronero et al., 2008), but can also appear in functional magnetic resonance imaging (fMRI) studies. Additionally, for source-reconstructed magneto- and electro-encephalography (M/EEG), the problems are particularly severe because sparsity-favouring priors constrain meaningfully large signal and variance to a small set of compactly supported regions within the brain. (Acosta-Cabronero et al., 2008) suggested adding noise to background voxels (the 'haircut'), effectively increasing their noise variance, but at the cost of contaminating neighbouring regions with the added noise once smoothed. Following theory and simulations, we propose to modify--directly and solely--the noise variance estimate, and investigate this solution on real imaging data from a range of modalities.

Age-related changes in causal interactions between cortical motor regions during hand grip.

Brain activity during motor performance becomes more widespread and less lateralized with advancing age in response to ongoing degenerative processes. In this study, we were interested in the mechanism by which this change in the pattern of activity supports motor performance with advancing age. We used both transcranial magnetic stimulation (TMS) and functional magnetic resonance imaging (fMRI) to assess age related changes in motor system connectivity during isometric hand grip. Paired pulse TMS was used to measure the change in interhemispheric inhibition (IHI) from contralateral M1 (cM1) to ipsilateral M1 (iM1) during right hand grip. Dynamic Causal Modelling (DCM) of fMRI data was used to investigate the effect of age on causal interactions throughout the cortical motor network during right hand grip. Bayesian model selection was used to identify the causal model that best explained the data for all subjects. Firstly, we confirmed that the TMS and DCM measures both demonstrated a less inhibitory/more facilitatory influence of cM1 on iM1 during hand grip with advancing age. These values correlated with one another providing face validity for our DCM measures of connectivity. We found increasing reciprocal facilitatory influences with advancing age (i) between all ipsilateral cortical motor areas and (ii) between cortical motor areas of both hemispheres and iM1. There were no differences in the performance of our task with ageing suggesting that the ipsilateral cortical motor areas, in particular iM1, play a central role in maintaining performance levels with ageing through increasingly facilitatory cortico-cortical influences.

Bayesian comparison of neurovascular coupling models using EEG-fMRI.

Functional magnetic resonance imaging (fMRI), with blood oxygenation level-dependent (BOLD) contrast, is a widely used technique for studying the human brain. However, it is an indirect measure of underlying neuronal activity and the processes that link this activity to BOLD signals are still a topic of much debate. In order to relate findings from fMRI research to other measures of neuronal activity it is vital to understand the underlying neurovascular coupling mechanism. Currently, there is no consensus on the relative roles of synaptic and spiking activity in the generation of the BOLD response. Here we designed a modelling framework to investigate different neurovascular coupling mechanisms. We use Electroencephalographic (EEG) and fMRI data from a visual stimulation task together with biophysically informed mathematical models describing how neuronal activity generates the BOLD signals. These models allow us to non-invasively infer the degree of local synaptic and spiking activity in the healthy human brain. In addition, we use Bayesian model comparison to decide between neurovascular coupling mechanisms. We show that the BOLD signal is dependent upon both the synaptic and spiking activity but that the relative contributions of these two inputs are dependent upon the underlying neuronal firing rate. When the underlying neuronal firing is low then the BOLD response is best explained by synaptic activity. However, when the neuronal firing rate is high then both synaptic and spiking activity are required to explain the BOLD signal.

An introduction to thermodynamic integration and application to dynamic causal models.

In generative modeling of neuroimaging data, such as dynamic causal modeling (DCM), one typically considers several alternative models, either to determine the most plausible explanation for observed data (Bayesian model selection) or to account for model uncertainty (Bayesian model averaging). Both procedures rest on estimates of the model evidence, a principled trade-off between model accuracy and complexity. In the context of DCM, the log evidence is usually approximated using variational Bayes. Although this approach is highly efficient, it makes distributional assumptions and is vulnerable to local extrema. This paper introduces the use of thermodynamic integration (TI) for Bayesian model selection and averaging in the context of DCM. TI is based on Markov chain Monte Carlo sampling which is asymptotically exact but orders of magnitude slower than variational Bayes. In this paper, we explain the theoretical foundations of TI, covering key concepts such as the free energy and its origins in statistical physics. Our aim is to convey an in-depth understanding of the method starting from its historical origin in statistical physics. In addition, we demonstrate the practical application of TI via a series of examples which serve to guide the user in applying this method. Furthermore, these examples demonstrate that, given an efficient implementation and hardware capable of parallel processing, the challenge of high computational demand can be overcome successfully. The TI implementation presented in this paper is freely available as part of the open source software TAPAS. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11571-021-09696-9.

Post hoc Bayesian model selection.

This note describes a Bayesian model selection or optimization procedure for post hoc inferences about reduced versions of a full model. The scheme provides the evidence (marginal likelihood) for any reduced model as a function of the posterior density over the parameters of the full model. It rests upon specifying models through priors on their parameters, under the assumption that the likelihood remains the same for all models considered. This provides a quick and efficient scheme for scoring arbitrarily large numbers of models, after inverting a single (full) model. In turn, this enables the selection among discrete models that are distinguished by the presence or absence of free parameters, where free parameters are effectively removed from the model using very precise shrinkage priors. An alternative application of this post hoc model selection considers continuous model spaces, defined in terms of hyperparameters (sufficient statistics) of the prior density over model parameters. In this instance, the prior (model) can be optimized with respect to its evidence. The expressions for model evidence become remarkably simple under the Laplace (Gaussian) approximation to the posterior density. Special cases of this scheme include Savage-Dickey density ratio tests for reduced models and automatic relevance determination in model optimization. We illustrate the approach using general linear models and a more complicated nonlinear state-space model.