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WIREs Cogn Sci
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Predictive coding

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Abstract Predictive coding is a unifying framework for understanding redundancy reduction and efficient coding in the nervous system. By transmitting only the unpredicted portions of an incoming sensory signal, predictive coding allows the nervous system to reduce redundancy and make full use of the limited dynamic range of neurons. Starting with the hypothesis of efficient coding as a design principle in the sensory system, predictive coding provides a functional explanation for a range of neural responses and many aspects of brain organization. The lateral and temporal antagonism in receptive fields in the retina and lateral geniculate nucleus occur naturally as a consequence of predictive coding of natural images. In the higher visual system, predictive coding provides an explanation for oriented receptive fields and contextual effects as well as the hierarchical reciprocally connected organization of the cortex. Predictive coding has also been found to be consistent with a variety of neurophysiological and psychophysical data obtained from different areas of the brain. WIREs Cogni Sci 2011 2 580–593 DOI: 10.1002/wcs.142 This article is categorized under: Computer Science > Neural Networks

Predictive coding in space. (a) An example natural image (Reprinted with permission from Ref 32. Copyright 1998 Royal Society Publishing), shown here in logarithmic scale for better visualization of pixel values. (b) Blue curve: pixel intensities measured along a horizontal line of the image in (a). Red curve: the residual error between the actual intensity and predicted intensity from neighboring pixels. (c) Blue curve: autocorrelation function of intensities shown in the blue curve in (b). Red curve: autocorrelation function of the residual error shown in the red curve in (b). (d) Optimal spatial weighting coefficients W calculated from Eq. 2 for this example.

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Learned feedforward receptive fields in a predictive coding model of the middle temporal–medial superior temporal area (MT–MST) circuit. Receptive fields show preferred responses to translation and expansion similar to MST neurons. (Reprinted with permission from Ref 24. Copyright 2006 Elsevier).

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Extraclassical receptive field effects in the hierarchical predictive coding model. (a) End‐stopping in a layer 2/3 complex cell in cat striate cortex. Tuning curves are shown for inactivation of layer 6 (dotted curve) and for the control case (solid curve). (b) Tuning curve of lower level model neuron after inactivation of feedback from higher level (dotted curve) and for the control case (solid curve). (c) Extraclassical receptive field effect (contextual modulation). Responses of an error‐detecting model neuron for oriented texture stimuli with center and surround are the same (dotted line) versus different (solid line) orientations. (Reprinted with permission from Ref 21. Copyright 1999 Nature Publishing Group).

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Receptive field properties of feedforward neurons in the hierarchical predictive coding model. (a) Natural images used for training the hierarchical model. Several thousand natural image patches were extracted from these five images. (b) Feedforward synaptic weights of level 1 neurons learned from the natural images in (a) using a Gaussian prior. These synaptic weights determine the receptive field properties of the feedforward neurons. (c) Feedforward synaptic weights of level 2 neurons. These weights resemble various combinations of the synaptic weights in level 1. (d) Localized feedforward synaptic weights (rows in basis matrix UT) learned by using a sigmoidal nonlinear generative model and a sparse kurtotic prior distribution. Values can be zero (always represented by the same gray level), negative (inhibitory, black regions) and positive (excitatory, bright regions). (Reprinted with permission from Ref 21. Copyright 1999 Nature Publishing Group).

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Hierarchical predictive coding model of the visual cortex. (a) General architecture of the hierarchical predictive coding model. Higher level units attempt to predict the responses of units in the next lower level via feedback connections. Lower level units sent back the error between the higher level predictions and the actual activity through feedforward connections. This residual error signal is then used by the predictive estimator (PE) at each level to correct the higher level estimations of input signal. (b) Components of a PE unit. Each unit consists of several kinds of neurons: feedforward neurons encoding the synaptic weights UT, predictor‐estimator neurons maintaining the current estimate r of the input signal, feedback neurons encoding U and carrying the prediction f(Ur) to lower level, and error‐detecting neurons computing the discrepancy (rrtd) between the current prediction r and its top‐down prediction rtd from a yet higher level. (c) An example of three‐level hierarchical network. Three image patches at level 0 are processed by three level 1 PE units. The estimates from these three level 1 units are input to a single level 2 unit. This convergence effectively increases the receptive field size of neurons as one ascends the hierarchy. (Reprinted with permission from Ref 21. Copyright 1999 Nature Publishing Group).

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Predictive coding in time. (a) Blue curve: time‐varying intensities measured at a fixed pixel of a natural video (Reprinted with permission from Ref 32. Copyright 1998 Royal Society Publishing). The sampling frequency is 50 frames/second. Red curve: the residual error between the actual intensity and predicted intensity from past time steps. (b) Blue curve: autocorrelation function of intensities shown in the blue curve in (a). Red curve: autocorrelation function of the residual error shown in the red curve in (a). (c) Optimal temporal weighting coefficients for this example.

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Temporal predictive coding in the lateral geniculate nucleus (LGN). (a) Comparison between theoretically predicted temporal tuning curve (solid curve) and experimental data (points) in the LGN.37 The predicted curve is generated from Eq.11 with ωc = 5.5 Hz. (b) Temporal receptive field derived from (a) (Reprinted with permission from Ref 12. Copyright 1995 Informa PLC). Note the similarity to the temporal predictive coding filter in Figure 2(c).

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Adaptation to spatial image statistics. (a) Stimulus with two checkerboard regions X and Y. (b) Time‐varying stimuli used to test adaptation in retinal ganglion cells. Environment A has perfect positive correlation between all image points, whereas environment B has perfect negative correlation between X and Y regions. An uncorrelated probe stimulus P lasting 1.5 seconds was used to test the cell's spatiotemporal receptive field after adapting to environment A or B for 13.5 seconds. (c) Spatial receptive field of a ganglion cell from salamander retina. (d) Sensitivity of the ganglion cell in response to P for stimulus regions X and Y after adaptation to environment A (left) or B (right) (Reprinted with permission from Ref 13. Copyright 2005 Nature Publishing Group).

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Spatial and temporal predictive coding in the retina. (a) Classic center–surround receptive field found in the retina. (Reprinted with permission from Ref 34. Copyright 1992 Sinauer Assoicates) Compare to the center–surround weighting profile in Figure 1(d). (b) Shape of the receptive field depends on the signal‐to‐noise ratio (SNR). (Upper) Higher SNR; (Lower) Lower SNR. (c) Comparison of theoretically optimal (dotted curves) with experimentally measured (solid curves) receptive fields of large monopolar cells in the compound eye of the fly. (Upper) SNR = 1.45 at luminance 10 cd m−2. (Lower) SNR = 0.58 at luminance 1.26 cd m2. Note that the receptive field is more diffuse for the lower SNR as predicted in (b), although the effect is not as pronounced. (d) Effect of SNR on the temporal weight profile. (Upper) Low SNR; (Lower) High SNR. (e) Temporal receptive fields of large monopolar cells in the fly's eye for increasing SNR (top left to bottom right) (Reprinted with permission from Ref 7). Note that the receptive field is inverted compared to (d). As predicted by the theoretical result in (d), the temporal receptive field sharpens as SNR increases.

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