Predictive Feedback Can Account for Biphasic Responses in the Lateral
                    Geniculate Nucleus
[['Cells in the LGN exhibit striking receptive field dynamics .', 'Besides their well-known', 'center-surround organization , LGN receptive fields are characterized by', 'bright-excitatory ( dark-excitatory ) regions that become dark-excitatory', '( bright-excitatory ) over time intervals that may be as short as 20 milliseconds', '[1]–[3] .', 'Biphasic responses', 'have been described not only in the LGN , but seem to be characteristic of neurons in', 'many visual areas .', 'For example , biphasic responses have been observed in primary', 'visual cortex [3] , [4] , and also in MT , where the optimal stimulation', 'changes from one direction of motion to a 180° reversal in motion preference', 'with time [5] , [6] .', 'What computational reason would neurons have to', 'change their preferred stimulus over such short periods of time ?', 'Here , we argue that', 'biphasic dynamics naturally follow from neural mechanisms of predictive coding .', 'A longstanding approach to understanding early-level processing has been to consider', 'it in terms of efficient coding of natural images [7]–[10] .', 'Natural images are typically highly correlated in both space and time , and a neural', 'code that ignores these correlations would be very inefficient .', 'It has therefore', 'been postulated that early-level visual processing removes correlations in the', 'input , resulting in a more sparse and statistically independent output .', 'Building along these lines , it has been suggested that early visual areas remove', 'correlations by removing the predictable , and hence redundant , components in their', 'input .', 'For example , the center-surround structure of LGN receptive fields can be', 'explained using predictive coding mechanisms [11] , [12] .', 'Because a center pixel', 'intensity value in natural images can often be predicted from its surrounding', 'values , its value can be replaced with the difference between the center value and a', 'prediction from a linear weighted sum of its surrounding values .', 'This decorrelates', 'the neuronal input and removes redundancy in the outputs [7] , [13] .', 'Predictive coding may have further value as a general principle that works through', 'interactions between all lower-order and higher-order visual areas [14]–[16] .', 'Low-order and', 'high-order visual areas are reciprocally connected [17] , and responses of', 'neurons in these areas are often correlated due to their overlapping receptive', 'fields .', 'To reduce redundancy and decorrelate the visual responses , low-level visual', 'input could therefore be replaced by the difference between the input and a', 'prediction from higher-level structures .', 'Put another way , higher-level receptive', 'fields could represent the predictions of the visual world , while lower-level areas', 'could signal the error between predictions and the actual visual input [14]–[16] , [18] , [19] .', 'An advantage of', 'feedback interactions over local , within-area computations is that higher-level', 'cortical receptive fields are larger and encode more complex stimuli , therefore', 'allowing for complex predictions about large portions of the visual field .', 'This', 'hypothesis has been shown to account for steady state extra-classical receptive', 'field effects such as end-stopping [14] .', 'Here , we show by simulation that biphasic responses may result from similar', 'interactions with higher-order areas , which remove redundancy by removing the', 'predictable components in their input .', 'We focus on the LGN and V1 , for which the', 'feedforward-feedback connectivity structure and bottom-up inputs are fairly', 'well-known .', 'Although responses of LGN cells tend to follow many of the', 'characteristics of their retinal input [20] , biphasic responses are', 'stronger in geniculate neurons than in the retinal neurons driving their response', '[21] .', 'We show that these stronger rebound effects in LGN may result from predictive', 'feedback interactions with area V1 .', 'Moreover , after training on natural images , the', "model exhibits the brain's LGN-V1 connectivity structure , and it displays a", 'phase-reversed pattern of influence of feedback on LGN cells .', 'This phase-reversed', 'pattern of influence was recently observed in neurophysiology [22] .'], ['The model consists of two layers ( Fig . 1 ) .', 'The first layer , which corresponds to part of the lateral', 'geniculate nucleus , consists of on-center and off-center type units , with', 'on-center type units coding for brighter stimulus regions and off-center type', 'units coding for darker regions .', "The model's next higher level , which", 'corresponds to an orientation column in primary visual cortex , receives input', 'from the model LGN through feedforward connections .', 'After receiving its LGN', 'input , the feedforward V1 receptive field that best matches the input ( i . e . the', 'one that makes the most likely prediction ) is selected with high probability ,', 'and the selected neuron feeds its prediction back to model LGN .', 'The layout of', 'feedback connections follows the structure of feedforward connections , as has', 'been found experimentally [22] , [23] .', 'LGN neurons then', 'compute the error between the higher-level prediction and the actual input .', 'This', 'error is sent forward to correct the higher-level prediction , and the entire', 'process is repeated in the next feedforward-feedback cycle .', 'Thus , a', 'feedforward-feedback cycle comprises lower-level error detectors correcting', 'higher-level predictions , and higher-level responses updating the lower-level', 'error signals , similar to some previous models [14] , [16] , [18] , [19] , [24] .', 'We', 'assume that a single feedforward-feedback cycle takes around 20 milliseconds ,', 'but our results do not critically depend on the value of this parameter ( see', 'Methods ) .', 'Connection weights of the model are adapted to the input by minimizing the', 'description length or entropy of the joint distribution of inputs and neural', 'responses ( Methods , see also [25] ) .', "This minimizes the model's prediction errors and improves the", 'sparseness of the neural code .', 'Thus , for any given input , the model converges to', 'a set of connection weights that is optimal for predicting that input .', 'The model', 'is trained on image patches extracted from natural scenes , as receptive field', 'properties might be largely determined by the statistics of their natural input', '[7] , [11] , [14] , [26] .', 'To characterize V1 model receptive fields , feedforward connection weights from', 'on-center type and off-center type LGN cells coding for the same spatial', "location are summed for each of the model's 128 V1 cells .", 'These summed', 'weights are shown in Figure', '2 .', 'This gives an indication of the V1 receptive fields , as V1 responses', 'in the model are linear across their on and off inputs ( Methods , equation 7 ) .', 'After training , the receptive fields', 'show orientation tuning as found for simple cells in V1 .', 'In Figure 3 , the relation', 'between the learned receptive fields in model V1 and the properties of LGN units', 'is further investigated .', 'The figure depicts the connection weights from', 'on-center type cells to a given V1 model neuron , as well as those from', 'off-center type cells to the same V1 neuron .', 'The on- and off-center units are', 'spatially aligned with the on- and off-zones of the model V1 receptive field , as', 'first proposed by Hubel and Wiesel [27] and later confirmed', 'experimentally [22] , [28]–[30] .', 'Similar results are found for the connection structure of other V1 model neurons', '( results not shown ) .', 'Note that this alignment is not predetermined in the model .', 'The connections are initially random and are adjusted as a consequence of the', "model's learning rule together with exposure to natural images .", 'To ascertain whether biphasic responses can be interpreted as the result of', 'predictive feedback , we first consider a model with non-biphasic inputs ( Fig . 4A and 4C ) .', 'The', 'spatio-temporal response of model on-center type geniculate cells is calculated', 'using a reverse correlation algorithm ( Methods , see also [1] , [2] , [31] ) .', 'The time course', 'of the model response is shown by a series of receptive field maps calculated', 'for different delays between stimulus and response in Figure 4A .', 'For comparison Figure 4B shows results', 'obtained from on-center type cells in cat LGN [1] .', 'As in cat LGN ,', 'model on-center type receptive fields are arranged in center and surround , and', 'the bright-excitatory phase is followed by a dark-excitatory phase .', 'Removing', 'feedback in the model causes the previously biphasic responses to disappear', '( Fig . 4C ) , supporting', 'the idea that predictive feedback may be important for rebound effects in neural', 'response profiles .', 'To determine whether predictive feedback can result in', 'geniculate biphasic responses stronger than those in the retina , the model is', 'modified to simulate biphasic retinal inputs ( Methods ) .', 'The temporal response profile of model on-center type', 'cells is obtained using reverse correlation and illustrated in Figure 4D .', 'Predictive feedback', 'interactions cause reversals of polarity in LGN to be more pronounced than the', 'retinal input , as has been observed in physiology [21] .', 'Why do biphasic responses appear in the mapped model LGN receptive fields ?', 'Recall', 'that reverse correlation uses a large number of white noise stimuli presented in', 'rapid succession , resulting in visual changes much faster than most natural', 'input the system would encode .', 'Consider when a stimulus consisting primarily of', 'bright regions is presented to the model ( Fig . 4E ) .', 'On-center type LGN cells will', 'respond to the onset of this stimulus .', 'On zones in the LGN are linked to on', 'zones of receptive fields in V1 , which soon start to increase activation and', 'make predictions .', 'However , by the time that predictions of the first stimulus', 'arrive in lower-level areas , the initial representation of the bright stimulus', 'has been replaced by a second white noise stimulus , and the prediction is', 'compared against a new and unexpected stimulus representation .', 'Any given second', 'white-noise stimulus region can be of either high or low luminance; however , the', 'running average luminance will lie in between .', 'In reverse correlation ,', 'predictive processing shows up as a comparison against this running average', 'white-noise stimulation .', 'The predicted bright region is of higher luminance than', 'the average second stimulus , causing off-center type cells to respond to the', 'offset of the bright reference stimulus .', 'Reversals in polarity of model LGN cells are most profound in a small time window', 'after presentation of the reference stimulus but disappear gradually later on .', 'This happens because the initial prediction is dynamically updated to include', 'predictions of stimuli presented after the reference stimulus , bringing new', 'predictions closer to the average white-noise stimulation .', 'Note that reversals', 'in polarity will appear as long as predictions deviate from the average', 'white-noise stimulation; the precise amount of overlap between prediction and', 'stimulus is not critical .', 'These findings suggest a specific pattern of influence of feedback on LGN cells ,', 'in which the simple cell off-zones mediate inhibitory influences to off-center', 'LGN cells and excitatory influences to on-center LGN cells .', 'This effect is', 'further investigated and quantified in Figure 5 .', 'For all model on- or off-center LGN', 'receptive fields that are aligned over a V1 receptive field region of the same', 'polarity , firing rates decrease due to feedback ( Fig . 5 , top ) .', 'Where the overlapping fields', 'are of reversed polarity , there is an increase in firing rate ( Fig . 5 , bottom ) .', 'This effect', 'is consistent with recent results from neurophysiology showing that the', 'influence of V1 simple cells on LGN on- and off-cells is phase-reversed [22] , and', 'further corroborates the hypothesis that predictive feedback is important in', 'mediating responses of LGN cells .'], ['We have shown that a model that encodes an image using predictive', "feedforward-feedback cycles can learn the brain's LGN-V1 connectivity", 'structure , in which the structure of V1 receptive fields is linked to the spatial', 'alignment and properties of center-surround cells in the LGN [27] , [28] , [30] .', 'In addition , the model', 'captures reversals in polarity of neuronal responses in LGN [1]–[3] and a', 'phase-reversed pattern of influence from V1 simple cells on LGN cells [22] .', 'These', 'results corroborate the idea that the visual system uses predictive', 'feedforward-feedback interactions to efficiently encode natural input .', 'The natural visual world is dominated by low temporal frequencies [32] , causing', 'the retinal image to be relatively stable over the periods of time considered in the', 'model .', 'However , under certain conditions visual inputs do change', 'rapidly—more rapidly than most natural inputs the system would encode .', 'One', 'such situation is brought about by reverse correlation mapping , in which a', 'white-noise stimulus is presented at a temporal frequency much higher than the', 'temporal dynamics of natural visual input .', 'In such a case , higher-level predictions', 'of the reference stimulus are compared against a new and unexpected white-noise', 'stimulus , which emerges in the responses of on-center type model cells as a', 'bright-excitatory phase followed by a dark-excitatory phase .', 'We hypothesize that', 'similar predictive coding mechanisms are at play in geniculate and cortical cells', 'whose spatiotemporal response profiles also display reversals in polarity over short', 'periods of time [3] , [5] , [6] , [33] .', 'Geniculate cells receive many more feedback connections ( around 30% ) than', 'feedforward connections ( around 10% ) [34] .', 'In addition , it is', 'known from both cat and monkey neurophysiology that feedback signals from primary', 'visual cortex affect the response properties of LGN cells ( [35] , [36] see for', 'review [34] , [37] , [38] ) .', 'For example , feedback from V1 seems to affect', 'the strength of center-surround interactions in LGN ( [34] , [37] , [38] but see [39] ) .', 'Geniculate cells respond strongly to bars that are roughly the same size as the', 'center of their receptive field , but responses are attenuated or eliminated when the', 'bar extends beyond the receptive field center [35] , [40] .', 'Neurons that respond in this way are also known as end-stopped neurons , and this', 'property has been found to depend on feedback signals from primary visual cortex', '[35] , [40] .', 'A previously published model has successfully captured end-stopping and some other', 'modulations due to surround inhibition in terms of predictive feedback [14] .', 'Like', 'here , the predictive feedback model was trained on natural images , in which lines', 'are usually longer rather than shorter , resulting in higher-level receptive fields', 'optimized for representing longer bars .', 'Thus , when presented with shorter bars , the', "model's higher-level units could not predict their lower-level input , and", 'error responses in the lower-level neurons could not be suppressed .', 'This resulted in', 'more vigorous responses for shorter bars than for longer bars , similar to', 'end-stopping in geniculate neurons [35] .', 'Here , we have', 'extended the predictive feedback framework to also include rebound effects in LGN .', 'Although responses of LGN cells tend to follow many of the characteristics of their', 'strongest retinal inputs [20] , biphasic responses are stronger in geniculate', 'neurons than in the retinal neurons driving their response [21] , suggesting that the', 'cells may receive further sources of input .', 'Our simulations indicate that these', 'stronger components in the biphasic geniculate response may result from predictive', 'feedback interactions , similar to end-stopping and some other inhibitory effects', '[34] , [37] , [38] .', 'Reversals in polarity have also been described', 'for several cortical areas that do not receive direct input from biphasic retinal', 'cells [3]–[6] and that are too complex', 'to result from retinal responses ( e . g . , for orientation or motion [4] , [6] ) .', 'We', 'hypothesize that these response profiles result from similar mechanisms of', 'predictive feedback .', 'Indeed , neurophysiological studies have ascribed some cortical', 'rebound effects to network interactions [4] , [6] , and computational work', 'similarly suggests the involvement of cortical projections [41] .', 'Our work extends these', 'studies by providing a computational explanation for these effects .', 'Previous authors have suggested mechanisms that could account for the stronger', 'biphasic responses in the LGN , such as higher LGN thresholds [42] , inhibitory feedback', 'from the perigeniculate nucleus , or feedforward inhibition [20] .', 'In addition , a variety', 'of models has been proposed to account for orientation selectivity in early visual', 'cortex [9] , [43]–[45] .', 'However , our model', 'differs from earlier work in that it offers a computational , not a mechanistic ,', 'explanation of these early visual response properties [8] .', 'Furthermore , the', 'framework provides a parsimonious explanation for a number of neurophysiological', 'effects .', 'For example , the model not only captures biphasic responses and orientation', 'selectivity , but also a phase-reversed influence of cortical feedback to LGN , as', 'well as end-stopping and some other modulations due to surround inhibition in V1 and', 'LGN [14] .', 'Reversals in polarity have also been described for many areas in cortex [3]–[6] .', 'Consistent with our', 'interpretation , neurophysiological studies have ascribed some of these biphasic', 'responses to network interactions [4] , [6] .', 'While a number of mechanisms can be proposed to', 'account for many of these effects individually , the computational explanation', 'proposed here offers a simple , unifying framework in which to understand all of', 'these effects .', 'While predictive coding could work through local computations between neighboring', 'neurons ( providing a possible explanation for biphasic responses in the retina [13] , [46] ) , we argue that it would be computationally', 'advantageous to ( also ) implement predictive operations through feedback projections .', 'Feedback mechanisms allow the system to remove redundancy and decorrelate visual', 'responses between areas .', 'Moreover , higher-level cortical receptive fields are larger', 'and encode more complex stimuli , allowing for predictions of higher complexity and', 'larger regions in the visual field .', 'A strong prediction of the model would therefore', 'be that biphasic responses are attenuated in the LGN , or absent in cortex , without', 'cortical feedback .', 'The model uses subtractive feedback to compare higher-level predictions with actual', 'lower-level input .', 'In physiology , this process could be mediated by , for example ,', 'local inhibitory neurons in the same-level area together with long-range excitatory', 'connections from the next higher-level area ( for a similar connectivity scheme , see', 'e . g . [34] ) .', 'Here we have shown that these comparisons can', 'result in reduced as well as enhanced lower-level responses .', 'Support for a', 'dependence of some inhibitory and excitatory effects on top-down feedback has been', 'found in neurophysiology [47]–[50] .', 'We have considered only two hierarchical levels but the model could easily be', 'extended to include more cortical areas .', 'In an extended model , each level would have', 'both coding units and difference detecting units ( for a concrete example , see Figure 2 in [15] ) .', 'Coding units would', 'not only predict their lower-level input but also convey the current estimate to the', 'error detectors of the same-level area .', 'Error detectors then signal the difference', 'between their input and its prediction to the next higher level , until finally one', 'prediction becomes dominant in the entire system .', 'The model suggests that more', 'accurate higher-level predictions , or equivalently greater overlap between the', 'visual input and higher-level receptive fields , results in reduced activity of', 'lower-level difference detectors .', 'In contrast , when top-down predictions in the', 'model are off , lower-level difference detectors enhance their responses .', 'Consistent', 'with this , recent fMRI studies have shown that increased activity in higher-level', 'areas accompanies decreased responses in lower-level areas , presumably due to', 'feedback processing [51]–[53] .', 'Other imaging', 'studies have found supporting evidence for predictive feedback as well [54] , [55] .', 'The predictive feedback framework suggests that higher-level coding neurons enhance', 'their activity when stimuli are presented that match their receptive field', 'properties ( rather than decrease [56] ) , in accordance with neurophysiology [27] , [57]–[59] .', 'Subsequent', 'feedforward-feedback passes refine the initial predictions , until finally the entire', 'system settles on the mostly likely interpretation .', 'Coding an image using recurrent', 'cycles of processing incurs a cost in time , but has the advantage of resolving error', 'signals in even the earliest sensory areas .', 'Moreover , recurrent cycles of processing', 'are less costly in time when the system forms a hierarchy .', 'The most likely', 'predictions are computed first and sent on to higher-level processing areas , which', 'do not have to wait to begin their own computations , enabling initial rapid', 'gist-of-the-scene processing and subsequent feedforward-feedback cycles to fill in', 'the missing details .', 'In accordance with this , psychophysical studies have shown that', 'some global aspects of a stimulus can be detected very rapidly while detailed', 'aspects are reported later in time [60]–[62] , and neurophysiological', 'studies have found dynamic changes in tuning properties of both lower-level and', 'higher-level neurons consistent with these ideas ( [33] , [63] , [64] see also [65] , [66] ) .', 'It is likely that top-down signals serve many computational functions , of which the', 'sparsifying mechanism suggested here is but one .', 'Also , the effect of top-down', 'signals in general is not best described as either inhibitory or excitatory .', 'The', 'effect can be of many different kinds , depending on the specific computational goals', 'the top-down interaction fulfills .', 'For example , it has been proposed that', 'higher-level areas feed anticipatory signals back to earlier areas , enhancing neural', 'responses to a stimulus that would otherwise fall below threshold [67] .', 'This is', 'probably best implemented as an excitatory interaction between higher-level', 'anticipation and the incoming lower-level signal .', 'Feedback could also act as a', 'bayesian style prior [68]–[70] , and adapt early level', 'signals according to different sensory or behavioral conditions [71] .', 'In', 'view of these previously suggested roles of feedback , the mechanism presented here', 'should be regarded as a relatively low-level mechanism that automatically creates', 'sparser solutions , rather than the more flexible , higher-level mechanism that sets', 'specific behavioral demands .', 'In conclusion , rebound effects are a common feature in reverse correlation mapping', 'and have been described in several visual areas .', 'For example , biphasic responses', 'have been found for neurons in LGN [1]–[3] , as well as in', 'primary visual cortex [3] , [4] , and reversals in selectivity in the motion domain', 'have also been found for neurons in MT [5] , [6] .', 'Here , we have explained', 'these biphasic sensory responses in terms of predictive feedback .', 'Moreover , we have', 'shown that a model that processes its inputs using predictive feedback can learn the', "brain's LGN-V1 connectivity structure [27] , [28] , [30] and captures a", 'phase-reversed pattern of influence of feedback [22] .', 'These results', 'corroborate the idea that predictive feedback is a general principle used by the', 'visual system to efficiently encode its natural inputs .'], ['Here we briefly discuss model equations and parameters .', 'The interested reader is', 'referred to [25] .', 'The input is obtained from 768 by 768 pixel', 'black-and-white images of natural surroundings ( Fig . 2A ) , filtered with a zero-phase', 'whitening/lowpass filter [7] , [9]: ( 1 ) where the tilde represents the fourier transform in 2D , and =\u200a300 cycles/image .', 'The', 'initial activation values of on-center type cells are obtained from the filtered', 'images by subtracting the mean and taking positive values: ( 2 ) The initial activation values of off-center type cells are obtained from negative', "pixel values that are rectified: ( 3 ) We limit the LGN input into the model's second layer to 8 by 8 ( 64 )", 'on-center type cells and 8 by 8 ( 64 ) off-center type cells .', 'This LGN', '‘patch’ is randomly selected from the filtered image and', 'represented as a single vector ( 128 values ) , unless described otherwise .', 'At any', 'given time step in the model , either the on-center cell or its off-center', 'counterpart coding for the same spatial location is active .', 'The second layer , which would correspond to an orientation column in cortical', 'area V1 , is represented by 128 units .', 'In the language of the model , the synaptic', 'weights between LGN and V1 units form basis vectors that represent the preferred', 'stimulus of the model V1 neurons ( Fig . 6A ) .', 'Model V1 predicts its LGN input as a linear combination of active basis vectors , where the weighting coefficient of each', 'basis vector is given by the response of its corresponding V1 neuron: ( 4 ) in which is a stochastic noise process .', 'The 64 on-type and 64 off-type', 'connections are combined to form a single basis vector of 128 values , unless', 'described otherwise .', 'To choose the V1 neurons that best predict a given input ( i . e . , neurons that', 'are active ) , we use a modified version of the matching pursuit algorithm [72] .', 'Matching-pursuit uses the least number of basis vectors or equivalently the', 'least number of active V1 neurons to accurately predict its input [72] .', 'In', 'a deterministic version of the algorithm , the first vector is chosen as the', 'vector that minimizes ( 5 ) At the next time step , an additional vector is chosen that minimizes ( 6 ) and so on , where the response of the vectors is given by ( 7 ) and the vectors are subdivided into 64 on-values and 64', 'off-values .', 'This deterministic version was modified for the learning algorithm', 'to be optimal in terms of sparseness [25] .', 'Thus , after', 'learning not only do the V1 units make more accurate predictions , but also few', 'of them participate in any given prediction .', 'The modification is as follows: at', 'each time step , a V1 unit is selected randomly from the distribution ( 8 ) where is the index of the unit in the iteration , is given by equation ( 7 ) , is the Heaviside function , is a temperature parameter and is a normalizing term given by: ( 9 ) Thus , the probability with which a unit is selected increases when its receptive', 'field structure better predicts the lower level input and its response is', 'higher .', 'To guarantee optimality , the response of a selected unit should be drawn from a normal distribution with small variance [25] , but the effect of', 'this process is negligible so that in practice the response of a neuron in the', 'modified model is given by equation ( 7 ) .', 'The selected basis vector weighted by', 'its neuronal response is then subtracted from the input .', 'This subtraction', 'represents the predictive feedback process assumed to take place between V1 and', 'LGN , and is essential to the predictive coding theory: it reduces output', 'redundancy by allowing LGN difference detectors to represent only the error', 'signal , and no longer the predicted components now represented in V1 .', 'Furthermore , it optimizes the higher-level predictions ( or equivalently ,', 'minimizes the prediction error ) .', 'For a further discussion of the effectiveness', 'of this approach , see [25] .', 'The LGN on-center type cell and LGN', 'off-center type cell code for two opposite sides of the same dimension .', 'Thus ,', 'wherever the subtraction process results in negative LGN values , or equivalently', 'when the value crosses the dividing edge between the two dimensional sides , the', "value is rectified and added to the activation value of the unit's", 'counterpart ( i . e . negative value of on-center unit is rectified and added to', 'activation value of off-center unit coding for the same location , and vice', 'versa ) .', 'The feedforward-feedback cycle is then repeated on the residual input so', 'that after iterations the residual LGN input is given by ( 10 ) In words , the number of active V1 neurons increases at each time step in the', 'model , and their combined prediction is subtracted from the actual LGN input .', 'To', 'see how combining active V1 units results in better predictions of the input ,', 'consider when a bar of a certain orientation is presented to the model , together', 'with a small dot next to the bar .', 'A likely first prediction could capture the', 'bar , but not necessarily also the dot .', 'However , this initial prediction will be', 'updated in later feedforward-feedback cycles when other V1 neurons become', 'active , so that the neurons will together represent both the bar and the dot .', 'This is what combining V1 neurons represents , a prediction that is updated in', 'each cycle to better capture the V1 input ( see also Fig . 6B and 6C ) .', 'We assume model V1 responses', 'to be stable and non-decaying over the time scales considered .', 'Note that', 'feedback connections in the model follow the alignment of feedforward', 'connections , which has been observed experimentally [22] , [23] .', 'We assume delays', 'of 20 milliseconds for predictive feedback effects to set in , which complies', 'with the usual response lag of about 10 milliseconds in the next higher-order', 'visual area [73] , [74] together with', 'similar conduction times for feedforward and feedback connections [75] .', 'Although this estimate is likely at the longer end of the range [76] ,', 'the model does not critically depend on the value of this parameter and similar', 'results would have been obtained using shorter time delays .', 'As the model does', 'not incorporate neural structures earlier than the LGN , we added 30 milliseconds', 'to the data points in the figures to account for the delays before the LGN [73] .', 'To enhance the sparseness of the neural code and better capture the input', 'statistics , basis vectors are updated in each feedforward-feedback cycle .', 'This', 'is done by minimizing the description length ( MDL ) or entropy of the joint', 'distribution of inputs and neural responses [25] .', 'MDL chooses as the', 'best model the one that enables the shortest code length for both prediction', 'error and model parameters in bits ( in base ) [77] , [78] .', 'As a', 'consequence , it favors accurate , yet sparse , neural representations .', 'However ,', 'the same learning rule can also be obtained from the gradient of the error', 'function for the feedforward-feedback cycle [25]: ( 11 ) where is the learning rate , in which is initially equal to 1 and increases by 1 every 1000 image', 'patches .', 'V1 basis vectors are normalized , and initialized using 64 random values', 'with zero mean: positive values are taken as the initial values of the entries', 'coding for on-type inputs , negative values are rectified and taken as the', 'initial values of the off-type entries of the basis vector , the remaining 64', 'entries are initialized with value zero .', 'Initializing all 128 entries of the', 'basis vector with random values gives similar results .', 'Because neuronal', 'receptive field properties might be largely determined by the statistics of', 'their natural input [7] , [11] , [14] , [16] , the basis vectors', 'are trained on 10 , 000 image patches extracted from 16 natural scenes .', 'The model', 'r
['Introduction', 'Results', 'Discussion', 'Methods']
['Biphasic neural response properties , where the optimal stimulus for driving a', 'neural response changes from one stimulus pattern to the opposite stimulus', 'pattern over short periods of time , have been described in several visual areas ,', 'including lateral geniculate nucleus ( LGN ) , primary visual cortex ( V1 ) , and', 'middle temporal area ( MT ) .', 'We describe a hierarchical model of predictive coding', 'and simulations that capture these temporal variations in neuronal response', 'properties .', 'We focus on the LGN-V1 circuit and find that after training on', "natural images the model exhibits the brain's LGN-V1 connectivity", 'structure , in which the structure of V1 receptive fields is linked to the', 'spatial alignment and properties of center-surround cells in the LGN .', 'In', 'addition , the spatio-temporal response profile of LGN model neurons is biphasic', 'in structure , resembling the biphasic response structure of neurons in cat LGN .', 'Moreover , the model displays a specific pattern of influence of feedback , where', 'LGN receptive fields that are aligned over a simple cell receptive field zone of', 'the same polarity decrease their responses while neurons of opposite polarity', 'increase their responses with feedback .', 'This phase-reversed pattern of influence', 'was recently observed in neurophysiology .', 'These results corroborate the idea', 'that predictive feedback is a general coding strategy in the brain .']
['For many neurons in the early visual brain the optimal stimulation for driving a', 'response changes from one stimulus pattern to the opposite stimulus pattern over', 'short periods of time .', 'For example , many neurons in the lateral geniculate', 'nucleus ( LGN ) respond to a bright stimulus initially but prefer a dark stimulus', 'only 20 milliseconds later in time , and similar changes in response preference', 'have been found for neurons in other areas .', 'What would be the computational', 'reason for these biphasic response dynamics ?', 'We describe a hierarchical model of', 'predictive coding that explains these response properties .', 'In the model ,', 'higher-level neurons attempt to predict their lower-level input , while', 'lower-level neurons signal the difference between actual input and the', 'higher-level predictions .', 'In our simulations we focus on the LGN and area V1 and', 'find that after training on natural images the layout of model connections', "resembles the brain's LGN-V1 connectivity structure .", 'In addition , the', 'responses of model LGN neurons are biphasic in time , resembling biphasic', 'responses as found in neurophysiology .', 'Moreover , the model displays a specific', 'pattern of influence of feedback from higher-level areas that was recently', 'observed in neurophysiology .', 'These results corroborate the idea that predictive', 'feedback is a general coding strategy in the brain .']
['neuroscience/theoretical neuroscience']