Show Reference: "A theory of cortical responses"

A theory of cortical responses Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, Vol. 360, No. 1456. (29 April 2005), pp. 815-836, doi:10.1098/rstb.2005.1622 by Karl Friston
    abstract = {This article concerns the nature of evoked brain responses and the principles underlying their generation. We start with the premise that the sensory brain has evolved to represent or infer the causes of changes in its sensory inputs. The problem of inference is well formulated in statistical terms. The statistical fundaments of inference may therefore afford important constraints on neuronal implementation. By formulating the original ideas of Helmholtz on perception, in terms of modern-day statistical theories, one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological {facts.It} turns out that the problems of inferring the causes of sensory input (perceptual inference) and learning the relationship between input and cause (perceptual learning) can be resolved using exactly the same principle. Specifically, both inference and learning rest on minimizing the brain's free energy, as defined in statistical physics. Furthermore, inference and learning can proceed in a biologically plausible fashion. Cortical responses can be seen as the brain's attempt to minimize the free energy induced by a stimulus and thereby encode the most likely cause of that stimulus. Similarly, learning emerges from changes in synaptic efficacy that minimize the free energy, averaged over all stimuli encountered. The underlying 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 organization and responses. The aim of this article is to encompass many apparently unrelated anatomical, physiological and psychophysical attributes of the brain within a single theoretical perspective. In terms of cortical architectures, the theoretical treatment predicts that sensory cortex should be arranged hierarchically, that connections should be reciprocal and that forward and backward connections should show a functional asymmetry (forward connections are driving, whereas backward connections are both driving and modulatory). In terms of synaptic physiology, it predicts associative plasticity and, for dynamic models, spike-timing-dependent plasticity. In terms of electrophysiology, it accounts for classical and extra classical receptive field effects and long-latency or endogenous components of evoked cortical responses. It predicts the attenuation of responses encoding prediction error with perceptual learning and explains many phenomena such as repetition suppression, mismatch negativity ({MMN}) and the P300 in electroencephalography. In psychophysical terms, it accounts for the behavioural correlates of these physiological phenomena, for example, priming and global precedence. The final focus of this article is on perceptual learning as measured with the {MMN} and the implications for empirical studies of coupling among cortical areas using evoked sensory responses.},
    address = {The Wellcome Department of Imaging Neuroscience, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK.},
    author = {Friston, Karl},
    day = {29},
    doi = {10.1098/rstb.2005.1622},
    issn = {0962-8436},
    journal = {Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences},
    keywords = {neural-coding},
    month = apr,
    number = {1456},
    pages = {815--836},
    pmcid = {PMC1569488},
    pmid = {15937014},
    posted-at = {2013-02-26 09:17:13},
    priority = {2},
    title = {A theory of cortical responses},
    url = {},
    volume = {360},
    year = {2005}

See the CiteULike entry for more info, PDF links, BibTex etc.

Sensation refers to the change of state of the nervous system induced purely by a stimulus. Perception integrates sensation with experience and training.

According to Friston, percepts are `the products of recognizing the causes of sensory input and sensation'.

Predictive coding can implement the EM algorithm.

Empirical Bayes methods estimate the prior from the data.

More formally, they choose some parametric form for the prior, and estimate an optimal set of parameters $\theta_{opt}$ by optimizaton: $$\theta_{opt} = \mathrm{arg\;max}_\theta\prod_n\int P_\theta(x)P(m_n\mid x)\;dx,$$ for measurements $m_n$ and possible latent variable values $x$.

In predictive coding, a model iterates the following steps:

  • assume values for latent variables,
  • predict sensory input (through a generative model),
  • observe prediction error,
  • adapt assumptions to minimize the error.

The EM algorithm is an iterative algorithm that solves a simplified version of Empirical Bayes.

Friston's predictive coding model predicts a hierarchical cortical system.

Functional segregation and integration are complementary principles of organization of the brain.

Backward connections in the visual cortex show less topographical organization (`show abundant axonal bifurcation'), are more abundant than forward connections.

The visual cortex is hierarchically organized.

Feedforward connections in the visual cortex seem to be driving while feedback connections seem to be modulatory.

In order to recognize ie. to identify the causes underlying a sensation (according to Friston), one has to mentally undo the transformation from causes to sensations.

These transformations may not be invertible—for example if different causes interact in non-linear ways.

Given a generative model, it can be possible to find the most likely cause (or causes) of a sensation even if the causes interact in complex ways.

Some authors see the lower stages of visual processing as implementing an inverse model of optics—a model deriving causes from sensations and higher stages as implementing a forward model—a model generating expected sensations from assumed causes.

In Friston's architecture, competitive learning serves to de-correlate error units.

Friston states that `models that do not show conditional independence (e.g. those used by connectionist and infomax schemes) depend on prior constraints for unique inference and do not invoke a hierarchical cortical organization;'

What does `models that do not show conditional independence' mean? Does it include SOMs?

If what Friston means by `models that do not show conditional independence' includes SOM, then that would explain why I can't find an error signal. Maybe the prior constraint invoked by SOMs is similarity between stimuli?

Possibly, this is a point for future work: model cortico-collicular connections as prediction. But, in Friston's framework, there would have to be ascending connections, too.

Grossberg's ART and Friston's theory of cortical responses appeal to the anatomical interpretation of 'top-down' and 'bottom-up' processing and stress feedback as well as feedforward connections.