We show how any system with morphological degrees of freedom and locally limited free energy will, under the constraints of the free energy principle, evolve toward a neuromorphic morphology that supports hierarchical computations in which each level of the hierarchy enacts a coarse-graining of its inputs, and dually a fine-graining of its outputs. Such hierarchies occur throughout biology, from the architectures of intracellular signal transduction pathways to the large-scale organization of perception and action cycles in the mammalian brain. Formally, the close formal connections between cone-cocone diagrams (CCCD) as models of quantum reference frames on the one hand, and between CCCDs and topological quantum field theories on the other, allow the representation of such computations in the fully-general quantum-computational framework of topological quantum neural networks.
Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. In this Part I, we introduce the free-energy principle (FEP) and the idea of active inference as Bayesian prediction-error minimization, and show how the control problem arises in active inference systems. We then review classical and quantum formulations of the FEP, with the former being the classical limit of the latter. In the accompanying Part II, we show that when systems are described as executing active inference driven by the FEP, their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implemented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales.
Abstract Functional neuroimaging can be used to characterize two types of abnormality in patients with neurological deficits: abnormal functional segregation and abnormal functional integration. In this paper we consider the factors that influence the experimental design, analysis, and interpretation of such studies. With respect to experimental design, we emphasize that: 1) task selection is constrained to tasks the patient is able to perform correctly, and 2) the most sensitive designs entail presenting stimuli of the same type close together. In terms of data preprocessing, prior to statistical analysis, we note that structural pathology may call for constraints on nonlinear transformations, used by spatial normalization, to prevent distortion of intact tissue. This means that one may have to increase spatial smoothing to reduce the impact of inaccurate normalization. Important issues in statistical modeling concern the first level of analysis (estimation of activation within subject), which has to distinguish correct from incorrect responses. At the second level (between subjects), inference should be based on between‐subjects variance. Provided that these and other constraints are met, deficits in functional segregation are indicated when activation in one or a set of regions is higher or lower in patients relative to control subjects. In contrast, deficits in functional integration are implied when the influence of one brain region on another is stronger or weaker in patients relative to control subjects. J. Magn. Reson. Imaging 2006. © 2006 Wiley‐Liss, Inc.
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.
This paper reviews hierarchical observation models, used in functional neuroimaging, in a Bayesian light. It emphasizes the common ground shared by classical and Bayesian methods to show that conventional analyses of neuroimaging data can be usefully extended within an empirical Bayesian framework. In particular we formulate the procedures used in conventional data analysis in terms of hierarchical linear models and establish a connection between classical inference and parametric empirical Bayes (PEB) through covariance component estimation. This estimation is based on an expectation maximization or EM algorithm. The key point is that hierarchical models not only provide for appropriate inference at the highest level but that one can revisit lower levels suitably equipped to make Bayesian inferences. Bayesian inferences eschew many of the difficulties encountered with classical inference and characterize brain responses in a way that is more directly predicated on what one is interested in. The motivation for Bayesian approaches is reviewed and the theoretical background is presented in a way that relates to conventional methods, in particular restricted maximum likelihood (ReML). This paper is a technical and theoretical prelude to subsequent papers that deal with applications of the theory to a range of important issues in neuroimaging. These issues include; (i) Estimating nonsphericity or variance components in fMRI time-series that can arise from serial correlations within subject, or are induced by multisubject (i.e., hierarchical) studies. (ii) Spatiotemporal Bayesian models for imaging data, in which voxels-specific effects are constrained by responses in other voxels. (iii) Bayesian estimation of nonlinear models of hemodynamic responses and (iv) principled ways of mixing structural and functional priors in EEG source reconstruction. Although diverse, all these estimation problems are accommodated by the PEB framework described in this paper.
Abstract We combine theoretical biology and systems neuroscience to relate the mechanisms of post-traumatic stress disorder (PTSD) models to biopsychosocial complexity. Moving beyond fear conditioning, extinction and habits formed by associative learning, we consider conserved neuromodulatory mechanisms related to harm expectation, defensive mobilisation, and context (in)sensitivity. Our account of harm-mitigating, neurobehavioural responses furnishes a mechanistic understanding of maladaptive behaviour and impaired belief-updating, which are often underspecified in conceptual analyses. Grounded in neurobiological evidence, we specify PTSD-related impairment in terms of Bayesian belief-updating and establish an adaptive/maladaptive boundary using active inference and simulation studies. The ensuing model plausibly illustrates PTSD pathogenesis, which remains understudied relative to aetiology. We locate pathogenesis in maladaptive precision following traumatic learning, characterised by aberrant Bayesian credit assignment. Future scientific and clinical studies can test the validity of these insights, which could underwrite our understanding of the phenomenology, diagnostics and ultimately treatment intervention in post-traumatic disorders.
Making a decision about whether something is there or not (detection) is qualitatively different from making a decision about what is there (discrimination). A key aspect of detection is the asymmetry in the availability of evidence for 'yes' and for 'no' responses. While discrimination requires a comparison between the relative evidence for different options, in a detection setting, evidence is only available for the presence of a stimulus and not for its absence. This means that confidence in the absence of a stimulus cannot rely on the magnitude of "evidence for absence" and must instead be based on other information. In line with this conceptual difference, previous studies identified behavioural dissimilarities between 'yes' and 'no' responses: confidence in 'no' responses is generally lower, and is less predictive of objective accuracy (Kanai, Walsh, & Tseng, 2010; Meuwese, van Loon, Lamme, & Fahrenfort, 2014) not only in visual detection but also in detection-like tasks (such as recognition memory; Higham, Perfect, & Bruno, 2009). Here, we set out to further characterise the distinct cognitive processes involved in reporting stimulus absence compared to reporting stimulus presence or identity. We present the results from two psychophysical experiments in which participants were asked to perform detection and discrimination tasks on the same class of stimuli, in different blocks. Although there was no difference in overall accuracy between the two tasks, we find markedly different behavioural signatures for discrimination and detection responses. Specifically, we replicate findings of a weaker relationship between accuracy and confidence for 'No' responses (lower area under the type 2 ROC) and show that 'No' responses exhibit a weaker negative association between reaction-time and confidence compared to both 'Yes' and discrimination responses. We discuss our observations in the context of possible cognitive models, such as unequal-variance SDT and temporal evidence accumulation models.
The active inference framework, and in particular its recent formulation as a partially observable Markov decision process (POMDP), has gained increasing popularity in recent years as a useful approach for modeling neurocognitive processes. This framework is highly general and flexible in its ability to be customized to model any cognitive process, as well as simulate predicted neuronal responses based on its accompanying neural process theory. It also affords both simulation experiments for proof of principle and behavioral modeling for empirical studies. However, there are limited resources that explain how to build and run these models in practice, which limits their widespread use. Most introductions assume a technical background in programming, mathematics, and machine learning. In this paper we offer a step-by-step tutorial on how to build POMDPs, run simulations using standard MATLAB routines, and fit these models to empirical data. We assume a minimal background in programming and mathematics, thoroughly explain all equations, and provide exemplar scripts that can be customized for both theoretical and empirical studies. Our goal is to provide the reader with the requisite background knowledge and practical tools to apply active inference to their own research. We also provide optional technical sections and multiple appendices, which offer the interested reader additional technical details. This tutorial should provide the reader with all the tools necessary to use these models and to follow emerging advances in active inference research.
This article is about how the brain data mines its sensory inputs. There are several architectural principles of functional brain anatomy that have emerged from careful anatomic and physiologic studies over the past century. These principles are considered in the light of representational learning to see if they could have been predicted a priori on the basis of purely theoretical considerations. We first review the organisation of hierarchical sensory cortices, paying special attention to the distinction between forward and backward connections. We then review various approaches to representational learning as special cases of generative models, starting with supervised learning and ending with learning based upon empirical Bayes. The latter predicts many features, such as a hierarchical cortical system, prevalent top-down backward influences and functional asymmetries between forward and backward connections that are seen in the real brain. The key points made in this article are: (i) hierarchical generative models enable the learning of empirical priors and eschew prior assumptions about the causes of sensory input that are inherent in non-hierarchical models. These assumptions are necessary for learning schemes based on information theory and efficient or sparse coding, but are not necessary in a hierarchical context. Critically, the anatomical infrastructure that may implement generative models in the brain is hierarchical. Furthermore, learning based on empirical Bayes can proceed in a biologically plausible way. (ii) The second point is that backward connections are essential if the processes generating inputs cannot be inverted, or the inversion cannot be parameterised. Because these processes involve many-to-one mappings, are non-linear and dynamic in nature, they are generally non-invertible. This enforces an explicit parameterisation of generative models (i.e. backward connections) to afford recognition and suggests that forward architectures, on their own, are not sufficient for perception. (iii) Finally, non-linearities in generative models, mediated by backward connections, require these connections to be modulatory, so that representations in higher cortical levels can interact to predict responses in lower levels. This is important in relation to functional asymmetries in forward and backward connections that have been demonstrated empirically.
