A free energy principle for the brain.

By formulating 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, the problems of inferring the causes of sensory input and learning the causal structure of their generation 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 input is caused. 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 cortical organisation and responses. In this paper, we show these perceptual processes are just one aspect of emergent behaviours of systems that conform to a free energy principle. The free energy considered here measures the difference between the probability distribution of environmental quantities that act on the system and an arbitrary distribution encoded by its configuration. The system can minimise free energy by changing its configuration to affect the way it samples the environment or change the distribution it encodes. 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 assumes that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at the models entailed by the brain and how minimisation of its free energy can explain its dynamics and structure.     

Variability of perceptual multistability: from brain state to individual trait

Few phenomena are as suitable as perceptual multistability to demonstrate that the brain constructively interprets sensory input. Several studies have outlined the neural circuitry involved in generating perceptual inference but only more recently has the individual variability of this inferential process been appreciated. Studies of the interaction of evoked and ongoing neural activity show that inference itself is not merely a stimulus-triggered process but is related to the context of the current brain state into which the processing of external stimulation is embedded. As brain states fluctuate, so does perception of a given sensory input. In multistability, perceptual fluctuation rates are consistent for a given individual but vary considerably between individuals. There has been some evidence for a genetic basis for these individual differences and recent morphometric studies of parietal lobe regions have identified neuroanatomical substrates for individual variability in spontaneous switching behaviour. Moreover, disrupting the function of these latter regions by transcranial magnetic stimulation yields systematic interference effects on switching behaviour, further arguing for a causal role of these regions in perceptual inference. Together, these studies have advanced our understanding of the biological mechanisms by which the brain constructs the contents of consciousness from sensory input.     

Sensory experience restructures thalamocortical axons during adulthood

The brain's capacity to rewire is thought to diminish with age. It is widely believed that development stabilizes the synapses from thalamus to cortex and that adult experience alters only synaptic connections between cortical neurons. Here we show that thalamocortical (TC) inputs themselves undergo massive plasticity in adults. We combined whole-cell recording from individual thalamocortical neurons in adult rats with a recently developed automatic tracing technique to reconstruct individual axonal trees. Whisker trimming substantially reduced thalamocortical axon length in barrel cortex but not the density of TC synapses along a fiber. Thus, sensory experience alters the total number of TC synapses. After trimming, sensory stimulation evoked more tightly time-locked responses among thalamorecipient layer 4 cortical neurons. These findings indicate that thalamocortical input itself remains plastic in adulthood, raising the possibility that the axons of other subcortical structures might also remain in flux throughout life.     

Predictive Coding or Evidence Accumulation? False Inference and Neuronal Fluctuations

Perceptual decisions can be made when sensory input affords an inference about what generated that input. Here, we report findings from two independent perceptual experiments conducted during functional magnetic resonance imaging (fMRI) with a sparse event-related design. The first experiment, in the visual modality, involved forced-choice discrimination of coherence in random dot kinematograms that contained either subliminal or periliminal motion coherence. The second experiment, in the auditory domain, involved free response detection of (non-semantic) near-threshold acoustic stimuli. We analysed fluctuations in ongoing neural activity, as indexed by fMRI, and found that neuronal activity in sensory areas (extrastriate visual and early auditory cortex) biases perceptual decisions towards correct inference and not towards a specific percept. Hits (detection of near-threshold stimuli) were preceded by significantly higher activity than both misses of identical stimuli or false alarms, in which percepts arise in the absence of appropriate sensory input. In accord with predictive coding models and the free-energy principle, this observation suggests that cortical activity in sensory brain areas reflects the precision of prediction errors and not just the sensory evidence or prediction errors per se.     

Integrated mismatch negativity (MMNi): a noise-free representation of evoked responses allowing single-point distribution-free statistical tests

If the repeated presentation of a single (standard) auditory stimulus is randomly interspersed with a second acoustically different (deviant) stimulus, the cortical activity evoked by the deviant stimulus can contain a negative component known as the mismatch negativity (MMN). The MMN is derived by subtracting the averaged response evoked by the standard stimulus from that evoked by the deviant stimulus. When the magnitude of the response is small or the signal-to-noise ratio is poor, it is difficult to judge the presence or absence of the MMN simply by visual inspection, and statistical detection techniques become necessary. A method of analysis is proposed to quantify the magnitude and statistically evaluate the presence of the MMN based on time-integrated evoked responses. This paper demonstrates the use of this integrated mismatch negativity (MMN_i) analysis to detect the MMN evoked by stimulus contrasts near the perceptual threshold of two subjects. The MMN_i, by virtue of being equivalent to a low-pass filtered response, presents an almost noise-free estimate of MMN magnitude. A single measure of the integrated evoked response at a fixed time point is used in a distribution-free statistic that compares the magnitude of the averaged response evoked by the deviant stimulus with a magnitude distribution derived from 200 subaveraged responses to the standard stimulus (with the number of sweeps per average equal to that of the deviant stimulus). This allows a calculation of the exact probability for the null hypothesis that the negative magnitude of the response evoked by the deviant stimulus is drawn from the magnitude distribution of responses evoked by the standard stimulus. Rejection of this hypothesis provides objective evidence of the presence of the MMN.     

Where’s the Noise? Key Features of Spontaneous Activity and Neural Variability Arise through Learning in a Deterministic Network

Even in the absence of sensory stimulation the brain is spontaneously active. This background “noise” seems to be the dominant cause of the notoriously high trial-to-trial variability of neural recordings. Recent experimental observations have extended our knowledge of trial-to-trial variability and spontaneous activity in several directions: 1. Trial-to-trial variability systematically decreases following the onset of a sensory stimulus or the start of a motor act. 2. Spontaneous activity states in sensory cortex outline the region of evoked sensory responses. 3. Across development, spontaneous activity aligns itself with typical evoked activity patterns. 4. The spontaneous brain activity prior to the presentation of an ambiguous stimulus predicts how the stimulus will be interpreted. At present it is unclear how these observations relate to each other and how they arise in cortical circuits. Here we demonstrate that all of these phenomena can be accounted for by a deterministic self-organizing recurrent neural network model (SORN), which learns a predictive model of its sensory environment. The SORN comprises recurrently coupled populations of excitatory and inhibitory threshold units and learns via a combination of spike-timing dependent plasticity (STDP) and homeostatic plasticity mechanisms. Similar to balanced network architectures, units in the network show irregular activity and variable responses to inputs. Additionally, however, the SORN exhibits sequence learning abilities matching recent findings from visual cortex and the network’s spontaneous activity reproduces the experimental findings mentioned above. Intriguingly, the network’s behaviour is reminiscent of sampling-based probabilistic inference, suggesting that correlates of sampling-based inference can develop from the interaction of STDP and homeostasis in deterministic networks. We conclude that key observations on spontaneous brain activity and the variability of neural responses can be accounted for by a simple deterministic recurrent neural network which learns a predictive model of its sensory environment via a combination of generic neural plasticity mechanisms.     

A Neurocomputational Model of the Mismatch Negativity

The mismatch negativity (MMN) is an event related potential evoked by violations of regularity. Here, we present a model of the underlying neuronal dynamics based upon the idea that auditory cortex continuously updates a generative model to predict its sensory inputs. The MMN is then modelled as the superposition of the electric fields evoked by neuronal activity reporting prediction errors. The process by which auditory cortex generates predictions and resolves prediction errors was simulated using generalised (Bayesian) filtering – a biologically plausible scheme for probabilistic inference on the hidden states of hierarchical dynamical models. The resulting scheme generates realistic MMN waveforms, explains the qualitative effects of deviant probability and magnitude on the MMN – in terms of latency and amplitude – and makes quantitative predictions about the interactions between deviant probability and magnitude. This work advances a formal understanding of the MMN and – more generally – illustrates the potential for developing computationally informed dynamic causal models of empirical electromagnetic responses.     

Adult visual cortical plasticity

The visual cortex has the capacity for experience-dependent change, or cortical plasticity, that is retained throughout life. Plasticity is invoked for encoding information during perceptual learning, by internally representing the regularities of the visual environment, which is useful for facilitating intermediate-level vision-contour integration and surface segmentation. The same mechanisms have adaptive value for functional recovery after CNS damage, such as that associated with stroke or neurodegenerative disease. A common feature to plasticity in primary visual cortex (V1) is an association field that links contour elements across the visual field. The circuitry underlying the association field includes a plexus of long-range horizontal connections formed by cortical pyramidal cells. These connections undergo rapid and exuberant sprouting and pruning in response to removal of sensory input, which can account for the topographic reorganization following retinal lesions. Similar alterations in cortical circuitry may be involved in perceptual learning, and the changes observed in V1 may be representative of how learned information is encoded throughout the cerebral cortex.     

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.     

Reduced variability of ongoing and evoked cortical activity leads to improved behavioral performance

Sensory responses of the brain are known to be highly variable, but the origin and functional relevance of this variability have long remained enigmatic. Using the variable foreperiod of a visual discrimination task to assess variability in the primate cerebral cortex, we report that visual evoked response variability is not only tied to variability in ongoing cortical activity, but also predicts mean response time. We used cortical local field potentials, simultaneously recorded from widespread cortical areas, to gauge both ongoing and visually evoked activity. Trial-to-trial variability of sensory evoked responses was strongly modulated by foreperiod duration and correlated both with the cortical variability before stimulus onset as well as with response times. In a separate set of experiments we probed the relation between small saccadic eye movements, foreperiod duration and manual response times. The rate of eye movements was modulated by foreperiod duration and eye position variability was positively correlated with response times. Our results indicate that when the time of a sensory stimulus is predictable, reduction in cortical variability before the stimulus can improve normal behavioral function that depends on the stimulus.     

The Brain Ages Optimally to Model Its Environment: Evidence from Sensory Learning over the Adult Lifespan

The aging brain shows a progressive loss of neuropil, which is accompanied by subtle changes in neuronal plasticity, sensory learning and memory. Neurophysiologically, aging attenuates evoked responses—including the mismatch negativity (MMN). This is accompanied by a shift in cortical responsivity from sensory (posterior) regions to executive (anterior) regions, which has been interpreted as a compensatory response for cognitive decline. Theoretical neurobiology offers a simpler explanation for all of these effects—from a Bayesian perspective, as the brain is progressively optimized to model its world, its complexity will decrease. A corollary of this complexity reduction is an attenuation of Bayesian updating or sensory learning. Here we confirmed this hypothesis using magnetoencephalographic recordings of the mismatch negativity elicited in a large cohort of human subjects, in their third to ninth decade. Employing dynamic causal modeling to assay the synaptic mechanisms underlying these non-invasive recordings, we found a selective age-related attenuation of synaptic connectivity changes that underpin rapid sensory learning. In contrast, baseline synaptic connectivity strengths were consistently strong over the decades. Our findings suggest that the lifetime accrual of sensory experience optimizes functional brain architectures to enable efficient and generalizable predictions of the world.     

Cortical feedback and gating in odor discrimination and generalization

A central question in neuroscience is how context changes perception. In the olfactory system, for example, experiments show that task demands can drive divergence and convergence of cortical odor responses, likely underpinning olfactory discrimination and generalization. Here, we propose a simple statistical mechanism for this effect based on unstructured feedback from the central brain to the olfactory bulb, which represents the context associated with an odor, and sufficiently selective cortical gating of sensory inputs. Strikingly, the model predicts that both convergence and divergence of cortical odor patterns should increase when odors are initially more similar, an effect reported in recent experiments. The theory in turn predicts reversals of these trends following experimental manipulations and in neurological conditions that increase cortical excitability.     

Learning to hear: plasticity of auditory cortical processing

Sensory experience and auditory cortex plasticity are intimately related. This relationship is most striking during infancy when changes in sensory input can have profound effects on the functional organization of the developing cortex. But a considerable degree of plasticity is retained throughout life, as demonstrated by the cortical reorganization that follows damage to the sensory periphery or by the more controversial changes in response properties that are thought to accompany perceptual learning. Recent studies in the auditory system have revealed the remarkably adaptive nature of sensory processing and provided important insights into the way in which cortical circuits are shaped by experience and learning.     

Brain states: top-down influences in sensory processing

All cortical and thalamic levels of sensory processing are subject to powerful top-down influences, the shaping of lower-level processes by more complex information. New findings on the diversity of top-down interactions show that cortical areas function as adaptive processors, being subject to attention, expectation, and perceptual task. Brain states are determined by the interactions between multiple cortical areas and the modulation of intrinsic circuits by feedback connections. In perceptual learning, both the encoding and recall of learned information involves a selection of the appropriate inputs that convey information about the stimulus being discriminated. Disruption of this interaction may lead to behavioral disorders, including schizophrenia.     

Surprised at all the entropy: hippocampal, caudate and midbrain contributions to learning from prediction errors

Influential concepts in neuroscientific research cast the brain a predictive machine that revises its predictions when they are violated by sensory input. This relates to the predictive coding account of perception, but also to learning. Learning from prediction errors has been suggested for take place in the hippocampal memory system as well as in the basal ganglia. The present fMRI study used an action-observation paradigm to investigate the contributions of the hippocampus, caudate nucleus and midbrain dopaminergic system to different types of learning: learning in the absence of prediction errors, learning from prediction errors, and responding to the accumulation of prediction errors in unpredictable stimulus configurations. We conducted analyses of the regions of interests' BOLD response towards these different types of learning, implementing a bootstrapping procedure to correct for false positives. We found both, caudate nucleus and the hippocampus to be activated by perceptual prediction errors. The hippocampal responses seemed to relate to the associative mismatch between a stored representation and current sensory input. Moreover, its response was significantly influenced by the average information, or Shannon entropy of the stimulus material. In accordance with earlier results, the habenula was activated by perceptual prediction errors. Lastly, we found that the substantia nigra was activated by the novelty of sensory input. In sum, we established that the midbrain dopaminergic system, the hippocampus, and the caudate nucleus were to different degrees significantly involved in the three different types of learning: acquisition of new information, learning from prediction errors and responding to unpredictable stimulus developments. We relate learning from perceptual prediction errors to the concept of predictive coding and related information theoretic accounts.     

Pre-attentive segmentation in the primary visual cortex

The activities of neurons in primary visual cortex have been shown to be significantly influenced by stimuli outside their classical receptive fields. We propose that these contextual influences serve pre-attentive visual segmentation by causing relatively higher neural responses to important or conspicuous image locations, making them more salient for perceptual pop-out. These locations include boundaries between regions, smooth contours, and pop-out targets against backgrounds. The mark of these locations is the breakdown of spatial homogeneity in the input. for instance, at the border between two texture regions of equal mean luminance. This breakdown causes changes in contextual influences, often resulting in higher responses at the border than at surrounding locations. This proposal is implemented in a biologically based model of VI in which contextual influences are mediated by intra-cortical horizontal connections. The behavior of the model is demonstrated using examples of texture segmentation, figure-ground segregation, target-distractor asymmetry, and contour enhancement, and is compared with psychophysical and physiological data. The model predicts (1) how neural responses should be tuned to the orientation of nearby texture borders, (2) a set of qualitative constraints on the structure of the intracortical connections, and (3) stimulus-dependent biases in estimating the locations of the region borders by pre-attentive vision.     

Unified neurophysical model of EEG spectra and evoked potentials

 Evoked potentials – the brain's transient electrical responses to discrete stimuli – are modeled as impulse responses using a continuum model of brain electrical activity. Previous models of ongoing brain activity are refined by adding an improved model of thalamic connectivity and modulation, and by allowing for two populations of excitatory cortical neurons distinguished by their axonal ranges. Evoked potentials are shown to be modelable as an impulse response that is a sum of component responses. The component occurring about 100 ms poststimulus is attributed to sensory activation, and this, together with positive and negative feedback pathways between the cortex and thalamus, results in subsequent peaks and troughs that semiquantitatively reproduce those of observed evoked potentials. Modulation of the strengths of positive and negative feedback, in ways consistent with psychological theories of attentional focus, results in d istinct responses resembling those seen in experiments involving attentional changes. The modeled impulse responses reproduce key features of typical experimental evoked response potentials: timing, relative amplitude, and number of peaks. The same model, with further modulation of feedback, also reproduces experimental spectra. Together, these results mean that a broad range of ongoing and transient electrocortical activity can be understood within a common framework, which is parameterized by values that are directly related to physiological and anatomical quantities. Received: 22 May 2001 / Accepted in revised form: 8 January 2002     

A major role for intracortical circuits in the strength and tuning of odor-evoked excitation in olfactory cortex

In primary sensory cortices, there are two main sources of excitation: afferent sensory input relayed from the periphery and recurrent intracortical input. Untangling the functional roles of these two excitatory pathways is fundamental for understanding how cortical neurons process sensory stimuli. Odor representations in the primary olfactory (piriform) cortex depend on excitatory sensory afferents from the olfactory bulb. However, piriform cortex pyramidal cells also receive dense intracortical excitatory connections, and the relative contribution of these two pathways to odor responses is unclear. Using a combination of in vivo whole-cell voltage-clamp recording and selective synaptic silencing, we show that the recruitment of intracortical input, rather than olfactory bulb input, largely determines the strength of odor-evoked excitatory synaptic transmission in rat piriform cortical neurons. Furthermore, we find that intracortical synapses dominate odor-evoked excitatory transmission in broadly tuned neurons, whereas bulbar synapses dominate excitatory synaptic responses in more narrowly tuned neurons.     

Attention controls multisensory perception via two distinct mechanisms at different levels of the cortical hierarchy

To form a percept of the multisensory world, the brain needs to integrate signals from common sources weighted by their reliabilities and segregate those from independent sources. Previously, we have shown that anterior parietal cortices combine sensory signals into representations that take into account the signals’ causal structure (i.e., common versus independent sources) and their sensory reliabilities as predicted by Bayesian causal inference. The current study asks to what extent and how attentional mechanisms can actively control how sensory signals are combined for perceptual inference. In a pre- and postcueing paradigm, we presented observers with audiovisual signals at variable spatial disparities. Observers were precued to attend to auditory or visual modalities prior to stimulus presentation and postcued to report their perceived auditory or visual location. Combining psychophysics, functional magnetic resonance imaging (fMRI), and Bayesian modelling, we demonstrate that the brain moulds multisensory inference via two distinct mechanisms. Prestimulus attention to vision enhances the reliability and influence of visual inputs on spatial representations in visual and posterior parietal cortices. Poststimulus report determines how parietal cortices flexibly combine sensory estimates into spatial representations consistent with Bayesian causal inference. Our results show that distinct neural mechanisms control how signals are combined for perceptual inference at different levels of the cortical hierarchy.

A combination of psychophysics, computational modelling and fMRI reveals novel insights into how the brain controls the binding of information across the senses, such as the voice and lip movements of a speaker.