Hierarchical Models in the Brain

By Karl J. Friston. PLoS Comput. Biol., 2008

957 citations recorded by the source corpus.

This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Signal Processing

View Paper: https://www.semanticscholar.org/paper/1a014a076cac3c7f5d81a084e296c095f9230437

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Citations in the corpus

The Computational Anatomy of Psychosis (2013, background): “3: its solutions grandfather nearly every known statistical estimation scheme, under parametric assumptions about additive or multiplicative noise (Friston, 2008).”
Effective connectivity: Influence, causality and biophysical modeling (2011, neutral): “In their most comprehensive form, these models can be formulated as Hierarchical Dynamical Models (HDM) (Friston, 2008a,b).”
Graph of Thoughts: Solving Elaborate Problems with Large Language Models (2023, background): “Similarly, brains form complex networks, with graph-like patterns such as recurrence [28].”
Neural Implementation of Hierarchical Bayesian Inference by Importance Sampling (2009, background): “However, few studies have proposed neural models that are capable of performing hierarchical Bayesian inference (although see [24]).”
Neural Elements for Predictive Coding (2016, background): “…minimization of prediction error through action, with consequent recession of the input layer for the ascending pathway, granular layer 4 (Adams et al., 2013a; Shipp et al., 2013) and modification of intrinsic microcircuitry (Godlove et al., 2014; Beul and Hilgetag, 2015; Ninomiya et al., 2015).”
Towards a Mathematical Theory of Cortical Micro-circuits (2009, methodology): “Friston recently expanded on this to suggest an inversion method for hierarchical Bayesian dynamic models and to point out that the brain, in principle, has the infrastructure needed to invert hierarchical dynamic models [6].”
Canonical microcircuits for predictive coding. (2012, neutral): “Forward (driving) and backward (driving and modulatory) connections mediate the (linear) influence of prediction errors and the (linear and nonlinear) construction of predictions (Friston, 2008, 2010).”
To belief or not belief: Children’s theory of mind (2014, background): “Timmermans, Schilbach, Pasquali, & Cleeremans, 2012 argue that metacognition of the kind demonstrated by Pasquali et al., is but one example of the brain’s widespread and automatic tendency to monitor its success (see also Friston, 2008).”
Reinforcement Learning or Active Inference? (2009, methodology): “Although generalised coordinates may appear to complicate matters, they actually simplify inference greatly; see [13] and [39] for details.”
Attention, Uncertainty, and Free-Energy (2010, methodology): “It is these parameters we associate with the slower dynamics of classical neuromodulation (e.g., cholinergic neurotransmission; Friston, 2008).”
Predictive Coding or Evidence Accumulation? False Inference and Neuronal Fluctuations (2010, background): “Put simply, under evidence accumulation models, activity increases with the evidence for a stimulus, whereas under predictive coding it reflects the precision of the prediction error [14].”
Perceptions as Hypotheses: Saccades as Experiments (2012, methodology): “The tilde notation ˜ x = x , x (cid:4) , x (cid:4)(cid:4) , . . . denotes variables in generalized coordinates of motion (Friston, ), where each prime denotes a temporal derivative (using Lagrange’s notation).”
Action and behavior: a free-energy formulation (2010, background): “Generalized states cover position, velocity, acceleration, jerk, and so on (Friston 2008).”
Free Energy, Value, and Attractors (2011, background): “Equation (4) assumes the fluctuations are temporally uncorrelated (Wiener) processes; however, because the fluctuations ω̃x(t) are in generalised coordinates of motion, the fluctuations on states per se can be smooth and analytic [34].”
Interactive Activation and Mutual Constraint Satisfaction in Perception and Cognition (2014, background): “One very general open question is whether top-down and between-modality influences should be viewed as an additional sources of constraint on interpretation, as in the interactive activation framework, or whether, instead, top-down signals should be viewed as predictions that are compared with botto”
The graphical brain: Belief propagation and active inference (2017, background): “Crucially, this equation is a generalized gradient descent on variational free energy (Friston et al., 2010; Friston, 2008): In this instance, belief propagation and variational message passing (i.e., variational ﬁlter-ing) are formally identical, because the messages in belief propagation are the…”