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Karl J Friston - One of the best experts on this subject based on the ideXlab platform.

  • Generalised Free Energy and active inference
    Biological Cybernetics, 2019
    Co-Authors: Thomas Parr, Karl J Friston
    Abstract:

    Active inference is an approach to understanding behaviour that rests upon the idea that the brain uses an internal generative model to predict incoming sensory data. The fit between this model and data may be improved in two ways. The brain could optimise probabilistic beliefs about the variables in the generative model (i.e. perceptual inference). Alternatively, by acting on the world, it could change the sensory data, such that they are more consistent with the model. This implies a common objective function (variational Free Energy) for action and perception that scores the fit between an internal model and the world. We compare two Free Energy functionals for active inference in the framework of Markov decision processes. One of these is a functional of beliefs (i.e. probability distributions) about states and policies, but a function of observations, while the second is a functional of beliefs about all three. In the former ( expected Free Energy), prior beliefs about outcomes are not part of the generative model (because they are absorbed into the prior over policies). Conversely, in the second ( generalised Free Energy), priors over outcomes become an explicit component of the generative model. When using the Free Energy function, which is blind to future observations, we equip the generative model with a prior over policies that ensure preferred (i.e. priors over) outcomes are realised. In other words, if we expect to encounter a particular kind of outcome, this lends plausibility to those policies for which this outcome is a consequence. In addition, this formulation ensures that selected policies minimise uncertainty about future outcomes by minimising the Free Energy expected in the future. When using the Free Energy functional—that effectively treats future observations as hidden states—we show that policies are inferred or selected that realise prior preferences by minimising the Free Energy of future expectations. Interestingly, the form of posterior beliefs about policies (and associated belief updating) turns out to be identical under both formulations, but the quantities used to compute them are not.

  • The Free-Energy principle: a unified brain theory?
    Nature Reviews Neuroscience, 2010
    Co-Authors: Karl J Friston
    Abstract:

    Adaptive agents must occupy a limited repertoire of states and therefore minimize the long-term average of surprise associated with sensory exchanges with the world. Minimizing surprise enables them to resist a natural tendency to disorder. Surprise rests on predictions about sensations, which depend on an internal generative model of the world. Although surprise cannot be measured directly, a Free-Energy bound on surprise can be, suggesting that agents minimize Free Energy by changing their predictions (perception) or by changing the predicted sensory inputs (action). Perception optimizes predictions by minimizing Free Energy with respect to synaptic activity (perceptual inference), efficacy (learning and memory) and gain (attention and salience). This furnishes Bayes-optimal (probabilistic) representations of what caused sensations (providing a link to the Bayesian brain hypothesis). Bayes-optimal perception is mathematically equivalent to predictive coding and maximizing the mutual information between sensations and the representations of their causes. This is a probabilistic generalization of the principle of efficient coding (the infomax principle) or the minimum-redundancy principle. Learning under the Free-Energy principle can be formulated in terms of optimizing the connection strengths in hierarchical models of the sensorium. This rests on associative plasticity to encode causal regularities and appeals to the same synaptic mechanisms as those underlying cell assembly formation. Action under the Free-Energy principle reduces to suppressing sensory prediction errors that depend on predicted (expected or desired) movement trajectories. This provides a simple account of motor control, in which action is enslaved by perceptual (proprioceptive) predictions. Perceptual predictions rest on prior expectations about the trajectory or movement through the agent's state space. These priors can be acquired (as empirical priors during hierarchical inference) or they can be innate (epigenetic) and therefore subject to selective pressure. Predicted motion or state transitions realized by action correspond to policies in optimal control theory and reinforcement learning. In this context, value is inversely proportional to surprise (and implicitly Free Energy), and rewards correspond to innate priors that constrain policies. A Free-Energy principle has been proposed recently that accounts for action, perception and learning. This Review looks at some key brain theories in the biological (for example, neural Darwinism) and physical (for example, information theory and optimal control theory) sciences from the Free-Energy perspective. Crucially, one key theme runs through each of these theories — optimization. Furthermore, if we look closely at what is optimized, the same quantity keeps emerging, namely value (expected reward, expected utility) or its complement, surprise (prediction error, expected cost). This is the quantity that is optimized under the Free-Energy principle, which suggests that several global brain theories might be unified within a Free-Energy framework. Karl Friston shows that different global brain theories all describe principles by which the brain optimizes value and surprise. He discusses how these brain theories fit into the Free-Energy framework, suggesting that this framework might provide a unified account of brain function.

  • The Free-Energy principle: A unified brain theory?
    Nature Reviews Neuroscience, 2010
    Co-Authors: Karl J Friston
    Abstract:

    A Free-Energy principle has been proposed recently that accounts for action, perception and learning. This Review looks at some key brain theories in the biological (for example, neural Darwinism) and physical (for example, information theory and optimal control theory) sciences from the Free-Energy perspective. Crucially, one key theme runs through each of these theories - optimization. Furthermore, if we look closely at what is optimized, the same quantity keeps emerging, namely value (expected reward, expected utility) or its complement, surprise (prediction error, expected cost). This is the quantity that is optimized under the Free-Energy principle, which suggests that several global brain theories might be unified within a Free-Energy framework.

  • Free-Energy and the brain
    Synthese, 2007
    Co-Authors: Karl J Friston, Klaas E Stephan
    Abstract:

    If one formulates Helmholtz's ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory inputs and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organisation and responses. In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a Free-Energy principle. The Free-Energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise Free-Energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of Free-Energy can explain its dynamics and structure.

Eric Vanden-eijnden - One of the best experts on this subject based on the ideXlab platform.

  • Some recent techniques for Free Energy calculations.
    Journal of Computational Chemistry, 2009
    Co-Authors: Eric Vanden-eijnden
    Abstract:

    A few recent techniques to calculate Free energies in the context of molecular dynamics simulations are discussed: temperature-accelerated molecular dynamics, which is a method to explore fast the important regions in the Free Energy landscape associated with a set of continuous collective variables without having to know where these regions are beforehand; the single sweep method, which is a variational method to interpolate the Free Energy globally given a set of mean forces (i.e., a set of gradients of the Free Energy) calculated at specific points, or centers, on the Free Energy landscape; and a Voronoi-based Free Energy method for the calculation of the Free Energy of the Voronoi tessellation associated with a set of centers. We also discuss how this last technique can be used in conjunction with the string method, and how kinetic information such as reaction rates can be calculated by milestoning using the edges of a Voronoi tessellation as milestones. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009

  • Some recent techniques for Free Energy calculations.
    Journal of computational chemistry, 2009
    Co-Authors: Eric Vanden-eijnden
    Abstract:

    A few recent techniques to calculate Free energies in the context of molecular dynamics simulations are discussed: temperature-accelerated molecular dynamics, which is a method to explore fast the important regions in the Free Energy landscape associated with a set of continuous collective variables without having to know where these regions are beforehand; the single sweep method, which is a variational method to interpolate the Free Energy globally given a set of mean forces (i.e., a set of gradients of the Free Energy) calculated at specific points, or centers, on the Free Energy landscape; and a Voronoi-based Free Energy method for the calculation of the Free Energy of the Voronoi tessellation associated with a set of centers. We also discuss how this last technique can be used in conjunction with the string method, and how kinetic information such as reaction rates can be calculated by milestoning using the edges of a Voronoi tessellation as milestones.

  • Single-Sweep Methods for Free Energy Calculations
    Journal of Chemical Physics, 2008
    Co-Authors: Luca Maragliano, Eric Vanden-eijnden
    Abstract:

    A simple, efficient, and accurate method is proposed to map multidimensional Free Energy landscapes. The method combines the temperature-accelerated molecular dynamics (TAMD) proposed in [L. Maragliano and E. Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006)] with a variational reconstruction method using radial-basis functions for the representation of the Free Energy. TAMD is used to rapidly sweep through the important regions of the Free Energy landscape and to compute the gradient of the Free Energy locally at points in these regions. The variational method is then used to reconstruct the Free Energy globally from the mean force at these points. The algorithmic aspects of the single-sweep method are explained in detail, and the method is tested on simple examples and used to compute the Free Energy of the solvated alanine dipeptide in two and four dihedral angles.

Yasukiyo Ueda - One of the best experts on this subject based on the ideXlab platform.

  • the lowest surface Free Energy based on cf3 alignment
    Langmuir, 1999
    Co-Authors: Takashi Nishino, Masashi Meguro, Katsuhiko Nakamae, Motonori Matsushita, Yasukiyo Ueda
    Abstract:

    Free Energy was measured for the surface of regular aligned closest hexagonal packed −CF3 groups. n-Perfluoroeicosane was vapor deposited onto glass, which gave epitaxially grown single-like crystallites with their molecular axes perpendicular to the glass surface. The dynamic contact angle of water on its surface was 119°, which corresponds to a surface Free Energy of 6.7 mJ/m2. This value is considered to be the lowest surface Free Energy of any solid, based on the hexagonal closed alignment of −CF3 groups on the surface.

Benoit Roux - One of the best experts on this subject based on the ideXlab platform.

  • Free Energy perturbation hamiltonian replica exchange molecular dynamics fep h remd for absolute ligand binding Free Energy calculations
    Journal of Chemical Theory and Computation, 2010
    Co-Authors: Wei Jiang, Benoit Roux
    Abstract:

    Free Energy Perturbation with Replica Exchange Molecular Dynamics (FEP/REMD) offers a powerful strategy to improve the convergence of Free Energy computations. In particular, it has been shown previously that a FEP/REMD scheme allowing random moves within an extended replica ensemble of thermodynamic coupling parameters “λ” can improve the statistical convergence in calculations of absolute binding Free Energy of ligands to proteins [J. Chem. Theory Comput. 2009, 5, 2583]. In the present study, FEP/REMD is extended and combined with an accelerated MD simulations method based on Hamiltonian replica-exchange MD (H-REMD) to overcome the additional problems arising from the existence of kinetically trapped conformations within the protein receptor. In the combined strategy, each system with a given thermodynamic coupling factor λ in the extended ensemble is further coupled with a set of replicas evolving on a biased Energy surface with boosting potentials used to accelerate the interconversion among different...

Gabor Csanyi - One of the best experts on this subject based on the ideXlab platform.

  • exploration sampling and reconstruction of Free Energy surfaces with gaussian process regression
    Journal of Chemical Theory and Computation, 2016
    Co-Authors: Letif Mones, Noam Bernstein, Gabor Csanyi
    Abstract:

    Practical Free Energy reconstruction algorithms involve three separate tasks: biasing, measuring some observable, and finally reconstructing the Free Energy surface from those measurements. In more than one dimension, adaptive schemes make it possible to explore only relatively low lying regions of the landscape by progressively building up the bias toward the negative of the Free Energy surface so that Free Energy barriers are eliminated. Most schemes use the final bias as their best estimate of the Free Energy surface. We show that large gains in computational efficiency, as measured by the reduction of time to solution, can be obtained by separating the bias used for dynamics from the final Free Energy reconstruction itself. We find that biasing with metadynamics, measuring a Free Energy gradient estimator, and reconstructing using Gaussian process regression can give an order of magnitude reduction in computational cost.