Current AI frameworks for brain decoding and encoding, typically train and test models within the same datasets. This limits their utility for cognitive training (neurofeedback) for which it would be useful to pool experiences across individuals to better simulate stimuli not sampled during training. A key obstacle to model generalisation is the degree of variability of inter-subject cortical organisation, which makes it difficult to align or compare cortical signals across participants. In this paper we address this through use of surface vision transformers, which build a generalisable model of cortical functional dynamics, through encoding the topography of cortical networks and their interactions as a moving image across a surface. This is then combined with tri-modal self-supervised contrastive (CLIP) alignment of audio, video, and fMRI modalities to enable the retrieval of visual and auditory stimuli from patterns of cortical activity (and vice-versa). We validate our approach on 7T task-fMRI data from 174 healthy participants engaged in the movie-watching experiment from the Human Connectome Project (HCP). Results show that it is possible to detect which movie clips an individual is watching purely from their brain activity, even for individuals and movies *not seen during training*. Further analysis of attention maps reveals that our model captures individual patterns of brain activity that reflect semantic and visual systems. This opens the door to future personalised simulations of brain function. Code \& pre-trained models will be made available at https://github.com/metrics-lab/sim.

A crucial challenge in neuroscience involves characterising brain dynamics from high-dimensional brain recordings. Dynamic Functional Connectivity (dFC) is an analysis paradigm that aims to address this challenge. dFC consists of a time-varying matrix (dFC matrix) expressing how pairwise interactions across brain areas change over time. However, the main dFC approaches have been developed and applied mostly empirically, lacking a common theoretical framework and a clear view on the interpretation of the results derived from the dFC matrices. Moreover, the dFC community has not been using the most efficient algorithms to compute and process the matrices efficiently, which has prevented dFC from showing its full potential with high-dimensional datasets and/or real-time applications. In this paper, we introduce the Dynamic Symmetric Connectivity Matrix analysis framework (DySCo), with its associated repository. DySCo is a framework that presents the most commonly used dFC measures in a common language and implements them in a computationally efficient way. This allows the study of brain activity at different spatio-temporal scales, down to the voxel level. DySCo provides a single framework that allows to: (1) Use dFC as a tool to capture the spatio-temporal interaction patterns of data in a form that is easily translatable across different imaging modalities. (2) Provide a comprehensive set of measures to quantify the properties and evolution of dFC over time: the amount of connectivity, the similarity between matrices, and their informational complexity. By using and combining the DySCo measures it is possible to perform a full dFC analysis. (3) Leverage the Temporal Covariance EVD algorithm (TCEVD) to compute and store the eigenvectors and values of the dFC matrices, and then also compute the DySCo measures from the EVD. Developing the framework in the eigenvector space is orders of magnitude faster and more memory efficient than naïve algorithms in the matrix space, without loss of information. The methodology developed here is validated on both a synthetic dataset and a rest/N-back task experimental paradigm from the fMRI Human Connectome Project dataset. We show that all the proposed measures are sensitive to changes in brain configurations and consistent across time and subjects. To illustrate the computational efficiency of the DySCo toolbox, we performed the analysis at the voxel level, a task which is computationally demanding but easily afforded by the TCEVD.

The definition of a brain state remains elusive, with varying interpretations across different sub-fields of neuroscience-from the level of wakefulness in anaesthesia, to activity of individual neurons, voltage in EEG, and blood flow in fMRI. This lack of consensus presents a significant challenge to the development of accurate models of neural dynamics. However, at the foundation of dynamical systems theory lies a definition of what constitutes the 'state' of a system-i.e., a specification of the system's future. Here, we propose to adopt this definition to establish brain states in neuroimaging timeseries by applying Dynamic Causal Modelling (DCM) to low-dimensional embedding of resting and task condition fMRI data. We find that ~90% of subjects in resting conditions are better described by first-order models, whereas ~55% of subjects in task conditions are better described by second-order models. Our work calls into question the status quo of using first-order equations almost exclusively within computational neuroscience and provides a new way of establishing brain states, as well as their associated phase space representations, in neuroimaging datasets.

Two apparently unrelated fields — normalizing flows and causality — have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of autoregressive normalizing flows and identifiable causal models. We exploit the fact that autoregressive flow architectures define an ordering over variables, analogous to a causal ordering, to show that they are well-suited to performing a range of causal inference tasks, ranging from causal discovery to making interventional and counterfactual predictions. First, we show that causal models derived from both affine and additive autoregressive flows with fixed orderings over variables are identifiable, i.e. the true direction of causal influence can be recovered. This provides a generalization of the additive noise model well-known in causal discovery. Second, we derive a bivariate measure of causal direction based on likelihood ratios, leveraging the fact that flow models can estimate normalized log-densities of data. Third, we demonstrate that flows naturally allow for direct evaluation of both interventional and counterfactual queries, the latter case being possible due to the invertible nature of flows. Finally, throughout a series of experiments on synthetic and real data, the proposed method is shown to outperform current approaches for causal discovery as well as making accurate interventional and counterfactual predictions.

In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, a special case exists in which the action is scale invariant if it satisfies the following two constraints: 1) it must depend upon a scale-free Lagrangian, and 2) the Lagrangian must change under scale in the same way as the inverse time, [Formula: see text]. Our contribution lies in the derivation of a generalised Lagrangian, in the form of a power series expansion, that satisfies these constraints. This generalised Lagrangian furnishes a normal form for dynamic causal models-state space models based upon differential equations-that can be used to distinguish scale symmetry from scale freeness in empirical data. We establish face validity with an analysis of simulated data, in which we show how scale symmetry can be identified and how the associated conserved quantities can be estimated in neuronal time series.

The propagation of epileptic seizure activity in the brain is a widespread pathophysiology that, in principle, should yield to intervention techniques guided by mathematical models of neuronal ensemble dynamics. During a seizure, neural activity will deviate from its current dynamical regime to one in which there are significant signal fluctuations. In silico treatments of neural activity are an important tool for the understanding of how the healthy brain can maintain stability, as well as of how pathology can lead to seizures. The hope is that, contained within the mathematical foundations of such treatments, there lie potential strategies for mitigating instabilities, e.g. via external stimulation. Here, we demonstrate that the dynamic causal modelling neuronal state equation generalises to a Fokker-Planck formalism if one extends the framework to model the ways in which activity propagates along the structural connections of neural systems. Using the Jacobian of this generalised state equation, we show that an initially unstable system can be rendered stable via a reduction in diffusivity-i.e., by lowering the rate at which neuronal fluctuations disperse to neighbouring regions. We show, for neural systems prone to epileptic seizures, that such a reduction in diffusivity can be achieved via external stimulation. Specifically, we show that this stimulation should be applied in such a way as to temporarily mirror the activity profile of a pathological region in its functionally connected areas. This counter-intuitive method is intended to be used pre-emptively-i.e., in order to mitigate the effects of the seizure, or ideally even prevent it from occurring in the first place. We offer proof of principle using simulations based on functional neuroimaging data collected from patients with idiopathic generalised epilepsy, in which we successfully suppress pathological activity in a distinct sub-network prior to seizure onset. Our hope is that this technique can form the basis for future real-time monitoring and intervention devices that are capable of treating epilepsy in a non-invasive manner.

In recent years, there have been many computational simulations of spontaneous neural dynamics. Here, we describe a simple model of spontaneous neural dynamics that controls an agent moving in a simple virtual environment. These dynamics generate interesting brain-environment feedback interactions that rapidly destabilize neural and behavioral dynamics demonstrating the need for homeostatic mechanisms. We investigate roles for homeostatic plasticity both locally (local inhibition adjusting to balance excitatory input) as well as more globally (regional "task negative" activity that compensates for "task positive", sensory input in another region) balancing neural activity and leading to more stable behavior (trajectories through the environment). Our results suggest complementary functional roles for both local and macroscale mechanisms in maintaining neural and behavioral dynamics and a novel functional role for macroscopic "task-negative" patterns of activity (e.g., the default mode network).

Functional connections between brain regions are supported by structural connectivity. Both functional and structural connectivity are estimated from in vivo magnetic resonance imaging and offer complementary information on brain organization and function. However, imaging only provides noisy measures, and we lack a good neuroscientific understanding of the links between structure and function. Therefore, inter-subject joint modeling of structural and functional connectivity, the key to multimodal biomarkers, is an open challenge. We present a probabilistic framework to learn across subjects a mapping from structural to functional brain connectivity. Expanding on our previous work [1], our approach is based on a predictive framework with multiple sparse linear regression. We rely on the randomized LASSO to identify relevant anatomo-functional links with some confidence interval. In addition, we describe resting-state functional magnetic resonance imaging in the setting of Gaussian graphical models, on the one hand imposing conditional independences from structural connectivity and on the other hand parameterizing the problem in terms of multivariate autoregressive models. We introduce an intrinsic measure of prediction error for functional connectivity that is independent of the parameterization chosen and provides the means for robust model selection. We demonstrate our methodology with regions within the default mode and the salience network as well as, atlas-based cortical parcellation.

Much current research in functional magnetic resonance imaging (fMRI) employs multivariate machine learning approaches (e.g., support vector machines) to detect distributed spatial patterns from the temporal fluctuations of the neural signal. The aim of many studies is not classification, however, but investigation of multivariate spatial patterns, which pattern classifiers detect only indirectly. Here we propose a direct statistical measure for the existence of distributed spatial patterns (or spatial heterogeneity) applicable to fMRI datasets. We extend the univariate general linear model (GLM), typically used in fMRI analysis, to a multivariate case. We demonstrate that contrasting maximum likelihood estimations of different restrictions on this multivariate model can be used to estimate the extent of spatial heterogeneity in fMRI data. Under asymptotic assumptions inference can be made with reference to the χ(2) distribution. The test statistic is then assessed using simulated timecourses derived from real fMRI data followed by analyzing data from a real fMRI experiment. These analyses demonstrate the utility of the proposed measure of heterogeneity as well as considerations in its application. Measuring spatial heterogeneity in fMRI has important theoretical implications in its own right and may have potential uses for better characterising neurological conditions such as stroke and Alzheimer's disease.