956 research outputs found
Action and behavior: a free-energy formulation
We have previously tried to explain perceptual inference and learning under a free-energy principle that pursues Helmholtz’s agenda to understand the brain in terms of energy minimization. It is fairly easy to show that making inferences about the causes of sensory data can be cast as the minimization of a free-energy bound on the likelihood of sensory inputs, given an internal model of how they were caused. In this article, we consider what would happen if the data themselves were sampled to minimize this bound. It transpires that the ensuing active sampling or inference is mandated by ergodic arguments based on the very existence of adaptive agents. Furthermore, it accounts for many aspects of motor behavior; from retinal stabilization to goal-seeking. In particular, it suggests that motor control can be understood as fulfilling prior expectations about proprioceptive sensations. This formulation can explain why adaptive behavior emerges in biological agents and suggests a simple alternative to optimal control theory. We illustrate these points using simulations of oculomotor control and then apply to same principles to cued and goal-directed movements. In short, the free-energy formulation may provide an alternative perspective on the motor control that places it in an intimate relationship with perception
Online Discrimination of Nonlinear Dynamics with Switching Differential Equations
How to recognise whether an observed person walks or runs? We consider a
dynamic environment where observations (e.g. the posture of a person) are
caused by different dynamic processes (walking or running) which are active one
at a time and which may transition from one to another at any time. For this
setup, switching dynamic models have been suggested previously, mostly, for
linear and nonlinear dynamics in discrete time. Motivated by basic principles
of computations in the brain (dynamic, internal models) we suggest a model for
switching nonlinear differential equations. The switching process in the model
is implemented by a Hopfield network and we use parametric dynamic movement
primitives to represent arbitrary rhythmic motions. The model generates
observed dynamics by linearly interpolating the primitives weighted by the
switching variables and it is constructed such that standard filtering
algorithms can be applied. In two experiments with synthetic planar motion and
a human motion capture data set we show that inference with the unscented
Kalman filter can successfully discriminate several dynamic processes online
Stable representations of dynamic stimuli in perceptual decision making
Models of perceptual decision making, which are based on dynamic stimuli such as random dot motion, are predominantly concerned with how evidence for a stimulus is accumulated over time (e.g., Wang, 2008; Beck, 2008). However, it is unclear how the brain derives this evidence from the sensory dynamics. While it is conceivable that simple feature-detecting neurons can, for example, directly signal evidence for motion in a specific direction, it is less clear how evidence for complex motion, such as human movements, is computed from sensory input. We present a model of the perceptual lower level system which is based on probabilistic inference for dynamical systems (Friston, 2008) and can be used to provide input for higher level decision making systems. We illustrate this mechanism using a random dot motion paradigm, where we (i) consider simple uni-directional motion as typically used in neuroscience experiments and (ii) show that the same system can also infer, i.e. recognize, complex dot motion as generated by humans (cf. point light walkers) in an online fashion. The present model is implemented by a neuronal network and computes stable percepts rapidly, thereby enabling both fast decision (reaction) times and high accuracy. We suggest that the combination of the present model with recent models for evidence accumulation in perceptual decision making may be used to apply neurobiologically plausible decision making strategies to real-world stimuli like movements generated by humans
Free Energy and Dendritic Self-Organization
In this paper, we pursue recent observations that, through selective dendritic filtering, single neurons respond to specific sequences of presynaptic inputs. We try to provide a principled and mechanistic account of this selectivity by applying a recent free-energy principle to a dendrite that is immersed in its neuropil or environment. We assume that neurons self-organize to minimize a variational free-energy bound on the self-information or surprise of presynaptic inputs that are sampled. We model this as a selective pruning of dendritic spines that are expressed on a dendritic branch. This pruning occurs when postsynaptic gain falls below a threshold. Crucially, postsynaptic gain is itself optimized with respect to free energy. Pruning suppresses free energy as the dendrite selects presynaptic signals that conform to its expectations, specified by a generative model implicit in its intracellular kinetics. Not only does this provide a principled account of how neurons organize and selectively sample the myriad of potential presynaptic inputs they are exposed to, but it also connects the optimization of elemental neuronal (dendritic) processing to generic (surprise or evidence-based) schemes in statistics and machine learning, such as Bayesian model selection and automatic relevance determination
Bayesian sparsification for deep neural networks with Bayesian model reduction
Deep learning's immense capabilities are often constrained by the complexity
of its models, leading to an increasing demand for effective sparsification
techniques. Bayesian sparsification for deep learning emerges as a crucial
approach, facilitating the design of models that are both computationally
efficient and competitive in terms of performance across various deep learning
applications. The state-of-the-art -- in Bayesian sparsification of deep neural
networks -- combines structural shrinkage priors on model weights with an
approximate inference scheme based on stochastic variational inference.
However, model inversion of the full generative model is exceptionally
computationally demanding, especially when compared to standard deep learning
of point estimates. In this context, we advocate for the use of Bayesian model
reduction (BMR) as a more efficient alternative for pruning of model weights.
As a generalization of the Savage-Dickey ratio, BMR allows a post-hoc
elimination of redundant model weights based on the posterior estimates under a
straightforward (non-hierarchical) generative model. Our comparative study
highlights the advantages of the BMR method relative to established approaches
based on hierarchical horseshoe priors over model weights. We illustrate the
potential of BMR across various deep learning architectures, from classical
networks like LeNet to modern frameworks such as Vision Transformers and
MLP-Mixers
Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks
Recurrent neural networks (RNNs) are widely used in computational
neuroscience and machine learning applications. In an RNN, each neuron computes
its output as a nonlinear function of its integrated input. While the
importance of RNNs, especially as models of brain processing, is undisputed, it
is also widely acknowledged that the computations in standard RNN models may be
an over-simplification of what real neuronal networks compute. Here, we suggest
that the RNN approach may be made both neurobiologically more plausible and
computationally more powerful by its fusion with Bayesian inference techniques
for nonlinear dynamical systems. In this scheme, we use an RNN as a generative
model of dynamic input caused by the environment, e.g. of speech or kinematics.
Given this generative RNN model, we derive Bayesian update equations that can
decode its output. Critically, these updates define a 'recognizing RNN' (rRNN),
in which neurons compute and exchange prediction and prediction error messages.
The rRNN has several desirable features that a conventional RNN does not have,
for example, fast decoding of dynamic stimuli and robustness to initial
conditions and noise. Furthermore, it implements a predictive coding scheme for
dynamic inputs. We suggest that the Bayesian inversion of recurrent neural
networks may be useful both as a model of brain function and as a machine
learning tool. We illustrate the use of the rRNN by an application to the
online decoding (i.e. recognition) of human kinematics
Perception and Hierarchical Dynamics
In this paper, we suggest that perception could be modeled by assuming that sensory input is generated by a hierarchy of attractors in a dynamic system. We describe a mathematical model which exploits the temporal structure of rapid sensory dynamics to track the slower trajectories of their underlying causes. This model establishes a proof of concept that slowly changing neuronal states can encode the trajectories of faster sensory signals. We link this hierarchical account to recent developments in the perception of human action; in particular artificial speech recognition. We argue that these hierarchical models of dynamical systems are a plausible starting point to develop robust recognition schemes, because they capture critical temporal dependencies induced by deep hierarchical structure. We conclude by suggesting that a fruitful computational neuroscience approach may emerge from modeling perception as non-autonomous recognition dynamics enslaved by autonomous hierarchical dynamics in the sensorium
A Hierarchy of Time-Scales and the Brain
In this paper, we suggest that cortical anatomy recapitulates the temporal
hierarchy that is inherent in the dynamics of environmental states. Many aspects
of brain function can be understood in terms of a hierarchy of temporal scales
at which representations of the environment evolve. The lowest level of this
hierarchy corresponds to fast fluctuations associated with sensory processing,
whereas the highest levels encode slow contextual changes in the environment,
under which faster representations unfold. First, we describe a mathematical
model that exploits the temporal structure of fast sensory input to track the
slower trajectories of their underlying causes. This model of sensory encoding
or perceptual inference establishes a proof of concept that slowly changing
neuronal states can encode the paths or trajectories of faster sensory states.
We then review empirical evidence that suggests that a temporal hierarchy is
recapitulated in the macroscopic organization of the cortex. This
anatomic-temporal hierarchy provides a comprehensive framework for understanding
cortical function: the specific time-scale that engages a cortical area can be
inferred by its location along a rostro-caudal gradient, which reflects the
anatomical distance from primary sensory areas. This is most evident in the
prefrontal cortex, where complex functions can be explained as operations on
representations of the environment that change slowly. The framework provides
predictions about, and principled constraints on, cortical
structure–function relationships, which can be tested by manipulating
the time-scales of sensory input
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