ReviewAttractors and noise: Twin drivers of decisions and multistability
Introduction
Brain activity is nothing if not dynamic. At whatever scale of volume or time one cares to examine it, brain tissue ceaselessly produces waves, bursts, oscillations, sudden transitions, spindles, fluctuations, transients, and many other dynamic patterns of activity. So it seems mildly paradoxical that some aspects of brain function may depend on the existence of decidedly “undynamic” states, namely, on stable patterns of reverberating activity that sustain and support themselves, at least for some time, against the relentless onslaught from the rest of the brain. Starting from early seminal intuitions (De No, 1938, Hebb, 1949), reverberating patterns of activity, also called “attractor states,” have been considered as a possible mechanism for various cognitive processes and functions, among them working memory (Zipser et al., 1993, Amit and Brunel, 1997, Amit and Mongillo, 2003, Del Giudice et al., 2003), recall of long-term memory (Hopfield, 1982, Amit, 1995, Hasselmo and McClelland, 1999), attentional selection (Deco and Rolls, 2005a), rule-based choice behavior (Vasilaki et al., 2009, Fusi et al., 2007) and, most recently, the formation of perceptual states (Wong et al., 2007, Furman and Wang, 2008).
Of course, “attractor states” are a theoretical notion, not an empirical finding. When neuronal activity is described at an appropriate level of abstraction, simulations of populations of spiking neurons capture the collective dynamics that is generated by recurrent interactions between such populations. The existence of attractor states is revealed when a reduced version of the spiking network is analyzed with so-called mean-field techniques (Amit and Brunel, 1997, Brunel and Wang, 2001, Renart et al., 2003). These methods are borrowed from statistical physics and, when applied to networks of formal and spiking neuron models (Hopfield, 1982, Amit and Brunel, 1997), identify sets of average activity levels at which the various interactions between populations of neurons exactly balance each other and thus create a collective steady-state. The charm of this approach is that the properties of these models, and the conditions needed to support such dynamical regimes, can be tested at very different levels of experimental analysis: the biophysical parameters of neurons and synapses, the spiking activity of single neurons and of cell assemblies, the aggregate metabolic demand of neural tissue, the timeevolution of cognitive processes and, indeed, the animal's behavior (Deco et al., 2009).
What would attractor states “look like” in the brain? Their stability is guaranteed only for idealized networks with infinitely many neurons. In the brain, where neuron numbers are finite, spontaneous activity fluctuations would destabilize and, sooner or later, overthrow any self-sustaining pattern of activity. Accordingly, an attractor state should remain stable up to the time-scale of cognitive processes and should terminate due to spontaneous activity fluctuations. In addition, neuronal populations participating in an attractor state should exhibit stereotypical activity levels so that the trial-to-trial variability should be significantly smaller than in other populations. Further, an incomplete attractor state, in which only a subset of participating populations exhibits steady-state activity levels, should tend to complete itself and to impose steady-state activity levels also on the remaining populations (Amit, 1995).
Of course, this overly simplistic picture offers only a starting point for understanding complex dynamical representations (Destexhe and Contreras, 2006, Durstewitz and Deco, 2008). Instead of approaching and remaining in a steady-state, the population activity would follow a complex trajectory, jumping from one attractor state to another, or traversing entire sequences of attractor states (Sompolinsky and Kanter, 1986, Kleinfeld, 1986, Amit, 1988, Tsuda, 2001). The impetus for this movement would come from attractive and repulsive forces within the network and each transition of the population activity would in turn change these forces. As an analogy, let population activity be represented by a ball that rolls downhill in an energy landscape which is not static but which is overturned whenever the ball reaches a new valley (Hopfield, 1982). In addition to these deterministic effects, spontaneous activity fluctuations would drive stochastic transitions and ensure that this rich landscape of metastable states is widely explored (Hopfield, 1984, Buhmann and Schulten, 1987).
Here, we summarize recent evidence suggesting that the dynamics of perception may reflect transitions among attractor states. Indeed, this notion has intuitive appeal, as perceptual states do seem to share many characteristics of attractor states: they are self-completing in the sense that missing evidence is “filled in” while conflicting evidence is suppressed, they form in a probabilistic rather than in a deterministic manner, and they often terminate spontaneously even when the sensory input has remained unchanged.
In three sections, we consider both experimental and theoretical work bearing on the role of attractor states in perception. The first section concerns spontaneous activity fluctuations in sensory cortices and across the brain (Grinvald et al., 2003, Fox and Raichle, 2007, Ringach, 2009). A second section considers perceptual decision making, that is, situations in which a perceptual choice is made and expressed with a stereotypical motor response (Gold and Shadlen, 2007, Romo and Salinas, 2003). A third section discusses multistable perception, in other words, the spontaneous reversals of perceptual experience that are often induced by ambiguous sensory situations (Leopold and Logothetis, 1999, Blake and Logothetis, 2002).
Section snippets
Spontaneous activity
Our perceptions and actions vary slightly even under identical conditions. This reflects the fact that brain activity fluctuates independently of external factors. At the level of individual neurons, the precise timing of spikes varies because of channel noise and variability in the mechanisms of synaptic transmissions (Shadlen and Newsome, 1998, Faisal et al., 2008). In addition, in neuronal populations of finite size, the variability of individual spike times will result in substantial
Perceptual decisions
It has long been apparent that perceptual performance is probabilistic. When observers try to distinguish between sensory events, they do not succeed or fail consistently. Instead, they succeed with a probability that increases with the physical difference between the events. This probabilistic performance is thought to reflect the presence of “internal noise,” which forms a basic ingredient of quantitative models of perceptual decisions (Green and Swets, 1966). A systematic analysis of
Multistable perception
With many displays, prolonged viewing does not produce a stable visual experience but provokes from time to time a discrete change in appearance. This phenomenon is called bistable or multistable perception, depending on whether two or more alternative appearances are observed. Well-known examples are the Necker cube, the perception of depth-from-motion, or binocular rivalry (Attneave, 1971, Leopold and Logothetis, 1999). Multistable phenomena are not restricted to the visual domain and occur
Conclusions
The neural mechanisms underlying perceptual decisions can be studied profitably with at least two paradigms. With perceptual choice tasks, the flow of sensory information and the formation of a perceptual decision can be traced in exquisite detail (i.e., in the activity of single neurons) through several cortical stages, which combine sensory representations, working-memory and decision representations, and representations of intended motor actions to varying proportions. The great strength of
Acknowledgments
The authors thank Paolo Del Giudice, Stefano Fusi, and Guido Gigante for many stimulating discussions. J.B. is supported by the BMBF Bernstein Network of Computational Neuroscience.
References (214)
- et al.
A simple growth model constructs critical avalanche networks
Prog. Brain Res.
(2007) - et al.
Visual motion retards alternations between conflicting perceptual interpretations
Neuron
(2003) Optimal decision-making theories: linking neurobiology with behaviour
Trends Cogn. Sci. (Regul. Ed.)
(2007)- et al.
A test of level's second proposition for binocular rivalry
Vision Res.
(1993) - et al.
Basic mechanisms for graded persistent activity: discrete attractors, continuous attractors, and dynamic representations
Curr. Opin. Neurobiol.
(2003) - et al.
Tactile rivalry demonstrated with an ambiguous apparent-motion quartet
Curr. Biol.
(2008) - et al.
Attention, short-term memory, and action selection: a unifying theory
Prog. Neurobiol.
(2005) - et al.
Stochastic dynamics as a principle of brain function
Prog. Neurobiol.
(2009) - et al.
Modelling the formation of working memory with networks of integrate-and-fire neurons connected by plastic synapses
J. Physiol. Paris
(2003) - et al.
Similarity effect and optimal control of multiple-choice decision making
Neuron
(2008)
A neural circuit model of flexible sensorimotor mapping: learning and forgetting on multiple timescales
Neuron
Toward a neurobiology of temporal cognition: advances and challenges
Curr. Opin. Neurobiol.
Neurophysiology of the bold fMRI signal in awake monkeys
Curr. Biol.
Neural models of memory
Curr. Opin. Neurobiol.
Temporal evolution of a decision-making process in medial premotor cortex
Neuron
The oblique plaid effect
Vision Res.
Neural model of temporal and stochastic properties of binocular rivalry
Neurocomputing
Perceptual manifestations of fast neural plasticity: motion priming, rapid motion aftereffect and perceptual sensitization
Vision Res.
Stochastic resonance in binocular rivalry
Vision Res.
An information theoretical approach to prefrontal executive function
Trends Cogn. Sci.
Correlations and brain states: from electrophysiology to functional imaging
Curr. Opin. Neurobiol.
Individual and interindividual differences in binocular retinal rivalry in man
Psychophysiology
Synaptic depression and cortical gain control
Science
The encoding of alternatives in multiple-choice decision making
Proc. Natl. Acad. Sci. U.S.A.
A biologically plausible model of time-scale invariant interval timing
J. Comput. Neurosci.
The Hebbian paradigm reintegrated: local reverberations as internal representations
Behav. Brain Sci.
Neural networks counting chimes
Proc. Natl. Acad. Sci. U.S.A.
Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex
Cereb. Cortex
Selective delay activity in the cortex: phenomena and interpretation
Cereb. Cortex
The bold response in the rat hippocampus depends rather on local processing of signals than on the input or output activity. a combined functional MRI and electrophysiological study
J. Neurosci.
Dynamics of ongoing activity: explanation of the large variability in evoked cortical responses
Science
Multistability in perception
Sci. Am.
Is the rostro-caudal axis of the frontal lobe hierarchical?
Nat. Rev. Neurosci.
Neuronal avalanches in neocortical circuits
J. Neurosci.
Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures
J. Neurosci.
Regulated criticality in the brain
Adv. Complex Systems
Functional connectivity in the motor cortex of resting human brain using echo-planar MRI
Magn. Reson. Med.
A neural theory of binocular rivalry
Psychol. Rev.
Visual competition
Nat. Rev. Neurosci.
Motion-induced blindness in normal observers
Nature
Reversal time distribution in the perception of visual ambiguous stimuli
Kybernetik
Multi-timescale perceptual history resolves visual ambiguity
PLoS ONE
The time course of binocular rivalry reveals a fundamental role of noise
J. Vis.
Distributions of alternation rates in various forms of bistable perception
J. Vis.
The analysis of visual motion: a comparison of neuronal and psychophysical performance
J. Neurosci.
Right parietal brain activity precedes perceptual alternation of bistable stimuli
Cereb. Cortex
Visual cortex allows prediction of perceptual states during ambiguous structure-from-motion
J. Neurosci.
Fast global oscillations in networks of integrate-and-fire neurons with low firing rates
Neural Comput.
Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition
J. Comput. Neurosci.
The brain's default network: anatomy, function, and relevance to disease
Ann. N. Y. Acad. Sci.
Cited by (107)
Motion-induced blindness as a noisy excitable system
2024, Vision ResearchStochastic bifurcations induced by Lévy noise in a fractional trirhythmic van der Pol system
2023, Chaos, Solitons and FractalsStructure and function in artificial, zebrafish and human neural networks
2023, Physics of Life ReviewsOscillatory Waveform Shape and Temporal Spike Correlations Differ across Bat Frontal and Auditory Cortex
2024, Journal of Neuroscience