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Article:

• Predictive Feedback Can Account for Biphasic Responses in the Lateral Geniculate Nucleus, 2009 - Janneke F. M. Jehee, Dana H. Ballard

Abstract

• biphasic neural response - best response when quick switching between two opposite patterns - detected in LGN, V1, MT
• article describes: hierarchical model of predictive coding and simulations that capture these temporal variations in neuronal response properties
• focus on the LGN-V1 circuit
• after training on natural images the model exhibits the brain’s LGN-V1 connectivity structure:
  • structure of V1 receptive fields is linked to the spatial alignment and properties of center-surround cells in the LGN
  • spatio-temporal response profile of LGN model neurons is biphasic in structure, resembling the biphasic response structure of neurons in cat LGN
  • 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
• predictive feedback is a general coding strategy in the brain

Introduction

• layout of V1-to-LGN feedback connections follows the structure of LGN-to-V1 feedforward connections
• LGN cells have center-surround organization
• LGN regions switch between bright- to dark-excitatory in 20 ms
  • what computational reason can change preferred simulus
  • biphasic dynamics follow from neural mechanisms of predictive coding
• to be efficient - early-level visual processing removes correlations in the input, resulting in a more sparse and statistically independent output
  • early visual areas remove correlations by removing the predictable components in their input
  • center-surround structure of LGN receptive fields can be explained using predictive coding mechanisms - center pixel intensity value can be replaced with the difference between the center value and a prediction from a linear weighted sum of its surrounding values
• works for interaction of lower-order and higher-order visual areas
  • low-order and high-order visual areas are reciprocally connected
  • higher-level receptive fields represent the predictions of the visual world
  • lower-level areas signal the error between predictions and actual visual input
  • explains end-stopping

Results

Hierarchical model of predictive coding

• two layers - LGN and V1
• Steps
  • 1. V1 receives input from LGN
  • 2. V1 neuron with receptive field that best matched the input feeds its prediction back to LGN
  • 3. LGN neurons compute error between prediction and actual input
  • 4. LGN sends error forward to correct prediction
  • 5. process is repeated, single feedforward-feedback cycle takes around 20 milliseconds
• 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
  • minimizes the model’s prediction errors
  • improves the sparseness of the neural code
  • model converges to a set of connection weights that is optimal for predicting that input

LGN-V1 connectivity structure after training

• 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
  • V1 responses in the model are linear across their on and off inputs
  • after training, the receptive fields show orientation tuning as found for simple cells in V1
• relation between the learned receptive fields in model V1 and the properties of LGN units:
  • connections are initially random and are adjusted as a consequence of the model’s learning rule together with exposure to natural images
  • after training, on- and off-center units are spatially aligned with the on- and off-zones of the model V1 receptive field

Reversal of polarity due to predictive feedback

• first consider a model with non-biphasic inputs
  • spatio-temporal response of model on-center type geniculate cells is calculated using a reverse correlation algorithm
  • 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
• then model is modified to simulate biphasic retinal inputs
  • temporal response profile of model on-center type cells is obtained using reverse correlation
  • predictive feedback interactions cause reversals of polarity in LGN to be more pronounced than the retinal input
• why biphasic responses appear in the mapped model LGN receptive fields
  • reverse correlation leads to visual changes occurring much faster than most natural input the system would encode
  • consider stimulus consisting primarily of bright regions
  • 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
  • by the time that predictions of the first stimulus arrive in lower-level areas, 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
  • in reverse correlation, predictive processing shows up as a comparison against this running average whitenoise stimulation
  • 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
  • initial prediction is dynamically updated to include predictions of stimuli presented after the reference stimulus
  • new predictions are closer to the average white-noise stimulation
  • reversals in polarity will appear as long as predictions deviate from the average white-noise stimulation
  • precise amount of overlap between prediction and stimulus is not critical
• simple cell off-zones mediate inhibitory influences to off-center LGN cells and excitatory influences to on-center LGN cells
• 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
• where the overlapping fields are of reversed polarity, there is an increase in firing rate
• neurophysiology: influence of V1 simple cells on LGN on- and off-cells is phase-reversed

Discussion

• model that encodes an image using predictive feedforward-feedback cycles:
  • can learn the brain’s LGNV1 connectivity structure
  • structure of V1 receptive fields is linked to the spatial alignment and properties of centersurround cells in the LGN
  • captures reversals in polarity of neuronal responses in LGN
  • captures phase-reversed pattern of influence from V1 simple cells on LGN cells
• confirms idea that visual system uses predictive feedforward-feedback interactions to efficiently encode natural input
• natural visual world is dominated by low temporal frequencies
  • retinal image to be relatively stable over the periods of time considered in the model
  • under certain conditions visual inputs do change rapidly—more rapidly than most natural inputs the system would encode
• geniculate cells receive many more feedback connections (~30%) than feedforward connections (~10%)
  • feedback signals from V1 affect the response properties of LGN cells
  • feedback from V1 seems to affect the strength of center-surround interactions in LGN
  • LGN cells respond strongly to bars that are roughly the same size as the center of their receptive field
  • responses are attenuated or eliminated when the bar extends beyond the receptive field center (end-stopping)
  • this property has been found to depend on feedback signals from V1
• previous model
  • captured endstopping and some other modulations
  • predictive feedback model was trained on natural images, in which lines are usually longer rather than shorter
  • higher-level receptive fields optimized for representing longer bars
  • when presented with shorter bars, the model’s higher-level units could not predict their lower-level input, error responses in the lower-level neurons could not be suppressed
• in new model the predictive feedback framework also includes rebound effects in LGN
  • biphasic responses are stronger in geniculate neurons than in the retinal neurons
  • result from predictive feedback interactions, similar to endstopping and some other inhibitory effects
  • reversals in polarity have also been described for several cortical areas that do not receive direct input from biphasic retinal cells
• other explanations of stronger biphasic responses in the LGN
  • higher LGN thresholds
  • inhibitory feedback from the perigeniculate nucleus
  • feedforward inhibition
• framework features:
  • captures biphasic responses and orientation selectivity
  • captures phase-reversed influence of cortical feedback to LGN
  • explains end-stopping and some other modulations due to surround inhibition in V1 and LGN
  • explains reversals in polarity for many areas in cortex
• computationally advantageous to implement predictive operations through feedback projections
  • allow the system to remove redundancy and decorrelate visual responses between areas
  • higher-level cortical receptive fields are larger and encode more complex stimuli
  • allows predictions of higher complexity and larger regions in the visual field
• biphasic responses are attenuated in the LGN, or absent in cortex, without cortical feedback
• model uses subtractive feedback to compare higher-level predictions with actual lower-level input
  • 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
• model could easily be extended to include more cortical areas
  • each level would have both coding units and difference detecting units
  • coding units predict their lower-level input
  • coding units 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
  • finally one prediction becomes dominant in the entire system
• 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
  • when top-down predictions in the model are off, lower-level difference detectors enhance their responses
  • higher-level coding neurons enhance their activity when stimuli are presented that match their receptive field properties
  • subsequent feedforward-feedback passes refine the initial predictions, until finally the entire system settles on the mostly likely interpretation
• recurrent cycles of processing are less costly in time when the system forms a hierarchy
  • 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
  • some global aspects of a stimulus can be detected very rapidly while detailed aspects are reported later in time
• top-down signals serve many computational functions
  • sparsifying mechanism
  • effect of top-down signals in general is not best described as either inhibitory or excitatory
  • higher-level areas feed anticipatory signals back to earlier areas, enhancing neural responses to a stimulus that would otherwise fall below threshold
  • excitatory interaction between higher-level anticipation and the incoming lower-level signal
  • feedback could also act as a bayesian style prior, and adapt early level signals according to different sensory or behavioral conditions
  • mechanism presented here should be regarded as a relatively lowlevel mechanism that automatically creates sparser solutions
• rebound effects are a common feature in reverse correlation mapping and have been described in several visual areas
  • biphasic responses have been found for neurons in LGN and V1
  • reversals in selectivity in the motion domain have also been found for neurons in MT