Original: Learning the Feedback Connections from V1 to LGN via Information Maximization
Revised: Learning the Feedback Connections from V1 to LGN via Information Maximization

Original: Abstract
Revised: Abstract

Original: The lateral geniculate nucleus (LGN) relay cells act as a gateway for transmittingvisual information from retina to the primary visual cortex (V1).
Revised: The lateral geniculate nucleus (LGN) relay cells act as a gateway for transmittingvisual information from retina to the primary visual cortex (V1).

Original: The activitiesof thalamic relay cells are modulated by feedback connections emanating fromlayer 6 of V1.
Revised: The activitiesof thalamic relay cells are modulated by feedback connections emanating fromlayer 6 of V1.

Original: While the receptive ﬁeld (RF) properties of these early parts ofthe visual system are relatively well understood, the function, computational role,and details of the feedback network from V1 to LGN are not.
Revised: While the receptive ﬁeld (RF) properties of these early parts ofthe visual system are relatively well understood, the function, computational role,and details of the feedback network from V1 to LGN are not.

Original: Computationalmodels of efﬁcient coding have been successful in deriving RF properties ofretinal ganglion and V1 simple cells by optimizing the Shannon information.
Revised: Computationalmodels of efﬁcient coding have been successful in deriving RF properties ofretinal ganglion and V1 simple cells by optimizing the Shannon information.

Original: Further, previous experimental results have suggested that the feedback increasesthe Shannon information.
Revised: Further, previous experimental results have suggested that the feedback increasesthe Shannon information.

Original: Motivated by this earlier work, we try to understandthe function of the feedback as optimizing the feedforward information to cortex.
Revised: Motivated by this earlier work, we try to understandthe function of the feedback as optimizing the feedforward information to cortex.

Original: We build a model that learns feedback weights by maximizing the feedforward
Revised: We build a model that learns feedback weights by maximizing the feedforward

Original: Shannon information on naturalistic stimuli.
Revised: Shannon information on naturalistic stimuli.

Original: Our model predicts the strengthand sign of feedback from a V1 cell to all ON- and OFF-center LGN relay cellsthat are within or surrounding the V1 cell RF.
Revised: Our model predicts the strengthand sign of feedback from a V1 cell to all ON- and OFF-center LGN relay cellsthat are within or surrounding the V1 cell RF.

Original: We ﬁnd a highly speciﬁc patternof inﬂuence on ON and OFF-center LGN overlapping the V1 RF depending onwhether they overlapped the ON or OFF zone of the V1 RF.
Revised: We ﬁnd a highly speciﬁc patternof inﬂuence on ON and OFF-center LGN overlapping the V1 RF depending onwhether they overlapped the ON or OFF zone of the V1 RF.

Original: In addition, we ﬁndgeneral inhibitory feedback in the further surround, which sharpens the RFs andincreases surround suppression in LGN relay cells.
Revised: In addition, we ﬁndgeneral inhibitory feedback in the further surround, which sharpens the RFs andincreases surround suppression in LGN relay cells.

Original: This is consistent with resultsof recent experiments exploring the impact of feedback on stimuli integration.
Revised: This is consistent with results of recent experiments exploring the impact of feedback on stimuli integration.

Original:  Introduction
Revised:  Introduction

Original: The lateral geniculate nucleus (LGN) acts as a relay of information from the retina to the primaryvisual cortex (V1).
Revised: The lateral geniculate nucleus (LGN) acts as a relay of information from the retina to the primaryvisual cortex (V1).

Original: This information ﬂow is modulated by top-down feedback from layer 6 of V1 to
Revised: This information ﬂow is modulated by top-down feedback from layer 6 of V1 to

Original: LGN.
Revised: LGN.

Original: While the input from the retina is the driver input for the LGN relay cells, the feedback is themodulating input for these cells [29].There is a large body of experimental work on the functionalityof the feedback pathway from V1 to LGN.
Revised: While the input from the retina is the driver input for the LGN relay cells, the feedback is themodulating input for these cells [29].There is a large body of experimental work on the functionalityof the feedback pathway from V1 to LGN.

Original: It has been observed that this feedback can play animportant role in burst vs tonic ﬁring of relay cells [28], increase the timing precision [1, 16], andaffect the spatial speciﬁcity of LGN relay cells [12, 19].
Revised: It has been observed that this feedback can play an important role in burst vs tonic ﬁring of relay cells [28], increase the timing precision [1, 16], andaffect the spatial speciﬁcity of LGN relay cells [12, 19].

Original: Anatomical evidence indicates that the corticogeniculate feedback monosynaptically excites an LGNrelay cell and disynaptically inhibits it through the thalamic reticular nucleus or the local inhibitoryneuron in LGN [10].
Revised: Anatomical evidence indicates that the corticogeniculate feedback monosynaptically excites an LGNrelay cell and disynaptically inhibits it through the thalamic reticular nucleus or the local inhibitoryneuron in LGN [10].

Original: Thus, the feedback can have both signs, it can be excitatory or inhibitory.
Revised: Thus, the feedback can have both signs, it can be excitatory or inhibitory.

Original: Moreover, the experiments conducted on primates suggest that this feedback is pathway-speciﬁc, withparvocellular, magnocellular, and koniocellular LGN cells each receiving input from distinct classesof layer 6 cell [8].
Revised: Moreover, the experiments conducted on primates suggest that this feedback is pathway-speciﬁc, withparvocellular, magnocellular, and koniocellular LGN cells each receiving input from distinct classesof layer 6 cell [8].

Original: In dual recordings of V1 and LGN, Tsumoto et al.
Revised: In dual recordings of V1 and LGN, Tsumoto et al.

Original: observed mostly excitatoryfeedback if the V1 and LGN RFs were within 2 . 4 ◦ and inhibitory impact beyond that up to 3 .
Revised: observed mostly excitatoryfeedback if the V1 and LGN RFs were within 2 . 4 ◦ and inhibitory impact beyond that up to 3 .

Original: 1 ◦ [30].
Revised: 1 ◦ [30].

Original: These types of experimental ﬁndings have inspired the modeling of the feedback as an excitatorycenter inhibitory-surround network [14].
Revised: These types of experimental ﬁndings have inspired the modeling of the feedback as an excitatorycenter inhibitory-surround network [14].

Original: A model proposed by Mobarhan et al., in which the feedbackcenter and surround effects were ﬁtted to experimental data on spatial integration in the dorsal LGN[24] also showed an excitatory-center inhibitory-surround.
Revised: A model proposed by Mobarhan et al., in which the feedbackcenter and surround effects were ﬁtted to experimental data on spatial integration in the dorsal LGN[24] also showed an excitatory-center inhibitory-surround.

Original: Dual recording experiments conductedby Want et al.
Revised: Dual recording experiments conductedby Want et al.

Original: [32, 33] suggest an even more speciﬁc pattern of connections.
Revised: [32, 33] suggest an even more speciﬁc pattern of connections.

Original: Speciﬁcally, in [32],the authors observe that LGN cells were signiﬁcantly more likely to be impacted by feedback, eitherthrough facilitation or suppression, when their location was displaced in parallel or orthogonaldirections relative to the preferred orientation of the V1 cells.
Revised: Speciﬁcally, in [32],the authors observe that LGN cells were signiﬁcantly more likely to be impacted by feedback, eitherthrough facilitation or suppression, when their location was displaced in parallel or orthogonaldirections relative to the preferred orientation of the V1 cells.

Original: In [33], by measuring the burst-to-tonicratio in LGN, they established a phase-reversed pattern of connections for LGN cells that overlap the
Revised: In [33], by measuring the burst-to-tonicratio in LGN, they established a phase-reversed pattern of connections for LGN cells that overlap the

Original: V1 RF.
Revised: V1 RF.

Original: There is no shortage of existing hypotheses about the functional role of feedback from V1 to LGN,probably starting with [15], who suggested the feedback could modify LGN responses iteratively tohelp the interpretation of the input.
Revised: There is no shortage of existing hypotheses about the functional role of feedback from V1 to LGN,probably starting with [15], who suggested the feedback could modify LGN responses iteratively tohelp the interpretation of the input.

Original: Feedback models were designed and discussed in the contextof different visual tasks, such as line perception [27], visual grouping [13, 14], visual attention[6, 9, 22, 25], etc.
Revised: Feedback models were designed and discussed in the contextof different visual tasks, such as line perception [27], visual grouping [13, 14], visual attention[6, 9, 22, 25], etc.

Original: Here we asked whether there could be an even simpler explanation of the feedback circuitry, theadaptation of the circuit for maximizing the LGN to V1 information ﬂow.
Revised: Here we asked whether there could be an even simpler explanation of the feedback circuitry, theadaptation of the circuit for maximizing the LGN to V1 information ﬂow.

Original: Originating in the work of[4, 2], this idea has gathered a lot of momentum.
Revised: Originating in the work of[4, 2], this idea has gathered a lot of momentum.

Original: Experiments conducted by Mcclurkin et al.
Revised: Experiments conducted by Mcclurkin et al.

Original: revealedthat cooling V1 in awake monkeys reduced the average stimulus-related information transmittedby LGN neurons [23].
Revised: revealedthat cooling V1 in awake monkeys reduced the average stimulus-related information transmittedby LGN neurons [23].

Original: Further, principles of information maximization and efﬁcient coding havebeen widely successful in understanding the structure of feedforward connections in the early visualsystem.
Revised: Further, principles of information maximization and efﬁcient coding havebeen widely successful in understanding the structure of feedforward connections in the early visualsystem.

Original: These principles lead to normative models that learn V1-like receptive ﬁelds from naturalimages [5, 31, 26].
Revised: These principles lead to normative models that learn V1-like receptive ﬁelds from naturalimages [5, 31, 26].

Original: Similarly, the same principles, when combined with realistic noise levels presentin the 
Revised: Similarly, the same principles, when combined with realistic noise levels presentin the retina, yield models that reproduce the center-surround receptive ﬁelds of retinal ganglion cells[20].

Original: We designed a novel type of normative model that employs the same information objective, in acircuitry with feedback.
Revised: We designed a novel type of normative model that employs the same information objective, in acircuitry with feedback.

Original: As forward connections, we use the known RF structure of LGN and cortex,the feedback connections are optimized by learning during naturalistic stimulation.
Revised: As forward connections, we use the known RF structure of LGN and cortex,the feedback connections are optimized by learning during naturalistic stimulation.

Original: The learnedfeedback weights show reciprocal excitation of LGN cells that are exciting the V1 cells, and inhibitionof the LGN cells that inhibit the V1 cell.
Revised: The learnedfeedback weights show reciprocal excitation of LGN cells that are exciting the V1 cells, and inhibitionof the LGN cells that inhibit the V1 cell.

Original: These weights also show a pattern of suppression for LGNcells that are retinotopically displaced relative to the V1 RF within 4 - 6 times the receptive ﬁeld size.
Revised: These weights also show a pattern of suppression for LGNcells that are retinotopically displaced relative to the V1 RF within 4 - 6 times the receptive ﬁeld size.

Original: Testing the impact of this learned feedback on spatial integration in LGN points to an accentuation ofsurround suppression as a result of feedback which is also consistent with experimental results in [7].
Revised: Testing the impact of this learned feedback on spatial integration in LGN points to an accentuation ofsurround suppression as a result of feedback which is also consistent with experimental results in [7].

Original:  Model
Revised:  Model

Original: We use rate code models of retina, LGN, and V1 to represent the feedforward pathway from retinato V1.
Revised: We use rate code models of retina, LGN, and V1 to represent the feedforward pathway from retinato V1.

Original: Given a two-dimensional gray-scale input image X , the retinal output is calculated as
Revised: Given a two-dimensional gray-scale input image X , the retinal output is calculated as

Original: Y p retina =
Revised: Y p retina =

Original: f p retina ( W p retina ∗ X ) for p ∈ { ON , OFF } , where W ONretina and W OFFretina are the ON and OFFcenter retinal ganglion cell linear ﬁlter weights and ∗ denotes the two-dimensional convolutionoperator.
Revised: f p retina ( W p retina ∗ X ) for p ∈ { ON , OFF } , where W ONretina and W OFFretina are the ON and OFFcenter retinal ganglion cell linear ﬁlter weights and ∗ denotes the two-dimensional convolutionoperator.

Original: Each linear ﬁlter has an associated rectifying nonlinearity f p retina which is applied entry-wiseto the two-dimensional convolution W p retina ∗ X .
Revised: Each linear ﬁlter has an associated rectifying nonlinearity f p retina which is applied entry-wiseto the two-dimensional convolution W p retina ∗ X .

Original: The rectifying nonlinearity is given as
Revised: The rectifying nonlinearity is given as

Original: [Equation]
Revised: [Equation]

Original: where R > 0 and v are nonlinearity parameters.
Revised: where R > 0 and v are nonlinearity parameters.

Original: Note that the scaling factor R is required sincethe linear ﬁlter weights are ﬁxed.
Revised: Note that the scaling factor R is required sincethe linear ﬁlter weights are ﬁxed.

Original: The ON and OFF-center ﬁlters are shown in Figure 1A. The twolinear ﬁlters are 27 by 27 pixel discrete approximations of a two-dimensional difference-of-Gaussians(DoG) ﬁlter given by ±
Revised: The ON and OFF-center ﬁlters are shown in Figure 1A. The twolinear ﬁlters are 27 by 27 pixel discrete approximations of a two-dimensional difference-of-Gaussians ON-center filter OFF-center filter 0.03 0.02 0.01 0.

Original: [Equation]
Revised: [Figure]

Revised: (DoG) ﬁlter given by ± 1 2 πσ 21 e − ( v 21 + v 22 ) /

Revised: (2 σ 21 )

Original: ∓ k 2 πσ 22 e − ( v 21 + v 22 ) / (2 σ 22 ) .
Revised: ∓ k 2 πσ 22 e − ( v 21 + v 22 ) / (2 σ 22 ) .

Original: We set σ 2 /σ 1 = 7 and k = 0 .
Revised: We set σ 2 /σ 1 = 7 and k = 0 .

Original: 9which are biologically plausible based on measurements in cat retina [11].
Revised: 9which are biologically plausible based on measurements in cat retina [11].

Original: The convolution operationhas a stride (spacing between neighboring cells) of 2 σ 1 .
Revised: The convolution operationhas a stride (spacing between neighboring cells) of 2 σ 1 .

Original: This spacing is chosen based on reportedmeasurements of the retina and computational work showing that information from natural imagespeaks at a receptive ﬁeld spacing of ∼ 2 σ 1 [3].
Revised: This spacing is chosen based on reportedmeasurements of the retina and computational work showing that information from natural imagespeaks at a receptive ﬁeld spacing of ∼ 2 σ 1 [3].

Original: In our model each LGN relay cell is driven by a single RGC and the LGN output is Y p LGN =
Revised: In our model each LGN relay cell is driven by a single RGC and the LGN output is Y p LGN =

Original: f p LGN ( Y p retina ) for p ∈ { ON , OFF } , where f p LGN are rectifying nonlinearities of type given in (1).
Revised: f p LGN ( Y p retina ) for p ∈ { ON , OFF } , where f p LGN are rectifying nonlinearities of type given in (1).

Original: The
Revised: The

Original: LGN output then serves as input to V1.
Revised: LGN output then serves as input to V1.

Original: To create the V1 output, we form Hubel and Wiesel V1 simplecells [17] by assigning equal positive weights to 8 ON LGN and 8 OFF-center LGN cells along [-
 ON-center filter OFF-center filter 0.03 0.02 0.01 0. [Figure]-]
Revised: To create the V1 output, we form Hubel and Wiesel V1 simplecells [17] by assigning equal positive weights to 8 ON LGN and 8 OFF-center LGN cells along [-
 ON-center filter OFF-center filter 0.03 0.02 0.01 0. [Figure]-]8different directions.

Original: different directions.

Original: These 8 ﬁlters alongside their phased-reversed version form the V1 ﬁlterbank ofsize 16 (see Figure 1B).
Revised: These 8 ﬁlters alongside their phased-reversed version form the V1 ﬁlterbank ofsize 16 (see Figure 1B).

Original: The V1 output is given by Y kV 1 = f k V 1 ( (cid:80) p ∈{ ON , OFF } W k,pV 1 ∗ Y p LGN ) for k ∈{ 0 , 1 , . . .
Revised: The V1 output is given by Y kV 1 = f k V 1 ( (cid:80) p ∈{ ON , OFF } W k,pV 1 ∗ Y p LGN ) for k ∈{ 0 , 1 , . . .

Original: , 15 } , where f k V 1 is applied entry-wise to the output of the convolution.
Revised: , 15 } , where f k V 1 is applied entry-wise to the output of the convolution.

Original: 2.1 Feedback model
Revised: 2.1 Feedback model

Original: The majority of the deriving axons from LGN relay cells target cells in layer 4C of the cortex, whilethe feedback to the LGN emanates from layer 6.
Revised: The majority of the deriving axons from LGN relay cells target cells in layer 4C of the cortex, whilethe feedback to the LGN emanates from layer 6.

Original: Hence a complete model of the feedback shouldinclude the mechanisms that give rise to layer 6 cells’ receptive ﬁelds requiring access to manyunknown parameters related to the micro-circuitry in a V1 column.
Revised: Hence a complete model of the feedback shouldinclude the mechanisms that give rise to layer 6 cells’ receptive ﬁelds requiring access to manyunknown parameters related to the micro-circuitry in a V1 column.

Original: To avoid these complications, wemodel the feedback as direct feedback from the same V1 cells that are being driven by LGN.
Revised: To avoid these complications, wemodel the feedback as direct feedback from the same V1 cells that are being driven by LGN.

Original: We allow a V1 cell to feedback on LGN relay cells directly overlapping the V1 cell RF or within aretinotopic neighborhood of the V1 cell RF.
Revised: We allow a V1 cell to feedback on LGN relay cells directly overlapping the V1 cell RF or within aretinotopic neighborhood of the V1 cell RF.

Original: Associated with each one of the 16 V1 ﬁlter types, thereare two sets of two-dimensional feedback weights which determine the feedback impact on ON and
Revised: Associated with each one of the 16 V1 ﬁlter types, thereare two sets of two-dimensional feedback weights which determine the feedback impact on ON and

Original: OFF-center LGN cells.
Revised: OFF-center LGN cells.

Original: These weights are denoted by W k, ON fb and W k, OFF fb for k ∈ { 0 , 1 , 2 , ..., 15 } .
Revised: These weights are denoted by W k, ON fb and W k, OFF fb for k ∈ { 0 , 1 , 2 , ..., 15 } .

Original: The V1 activation after applying the feedback will be the solution to the following equation:
Revised: The V1 activation after applying the feedback will be the solution to the following equation:

Original: Y k V1 = f k V  (cid:88) p ∈{ ON ,OFF } W k,p V 1 ∗ f pLGN (cid:32) Y p retina + 15 (cid:88) l =
Revised: [Equation]

Original: W l,p fb ∗ Y l V

Original: (cid:33)  for k ∈ { 0 , 1 , ..., 15 } .

Original: Figure 3A depicts a block diagram of the model.
Revised: Figure 3A depicts a block diagram of the model.

Original: To numerically estimate Y V1 , we unroll this feedbackloop in 3 steps, a standard technique used for recurrent neural networks.
Revised: To numerically estimate Y V1 , we unroll this feedbackloop in 3 steps, a standard technique used for recurrent neural networks.

Original:  Learning the feedback weights
Revised:  Learning the feedback weights

Original: To learn the feedback kernel and nonlinearity parameters in the feedforward model, we use aninformation objective.
Revised: To learn the feedback kernel and nonlinearity parameters in the feedforward model, we use aninformation objective.

Original: Since we are considering a noiseless channel from retina to V1, the mutualinformation between the input image patches and the V1 output is given by the differential entropyof the V1 output.
Revised: Since we are considering a noiseless channel from retina to V1, the mutualinformation between the input image patches and the V1 output is given by the differential entropyof the V1 output.

Original: Differential entropy increases when the ﬁring rates are scaled up.
Revised: Differential entropy increases when the ﬁring rates are scaled up.

Original: Therefore, ouroptimization objective, similar to the objective used in [20], has a penalty term that penalizes theaverage ﬁring rate.
Revised: Therefore, ouroptimization objective, similar to the objective used in [20], has a penalty term that penalizes theaverage ﬁring rate.

Original: We calculate an upper bound on the differential entropy of a 2 × 2 patch of V1cells, where each location is covered by 16 types of V1 cells.
Revised: We calculate an upper bound on the differential entropy of a 2 × 2 patch of V1cells, where each location is covered by 16 types of V1 cells.

Original: Let Y patch be the vectorized responsevector of these 64 cells.
Revised: Let Y patch be the vectorized responsevector of these 64 cells.

Original: We denote the differential entropy of Y patch by H ( Y patch ) and note that
Revised: We denote the differential entropy of Y patch by H ( Y patch ) and note that

Original: H ( Y patch ) ≤ 12 log det (cid:0) Σ Y patch (cid:1) + const., where Σ Y patch is the empirical covariance of Y patch .
Revised: H ( Y patch ) ≤ 12 log det (cid:0) Σ Y patch (cid:1) + const., where Σ Y patch is the empirical covariance of Y patch .

Original: Wemaximize a penalized version of this upper bound on the information:
Revised: Wemaximize a penalized version of this upper bound on the information:

Original: [Equation]
Revised: [Equation]

Original: (2) where λ ∈ (0 , 1) is the ﬁring rate penalty parameter and ¯ Y patch is the empirical mean of Y patch . We perform gradient ascent on the upper bound given in (2) to ﬁnd the feedback kernels and thenonlinearity parameters. The gradients are calculated using automatic differentiation available in the
Revised: [Figure]

Original: PyTorch library. We use step size of 10 − 4 and run the optimization for 2500 full batch iterations 1 . The parameter λ is varied in [0 . 775 , 1) . For each value of λ , we solved two optimization problems:
Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: [Table][Figure] [Table]
Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: [Table]
Revised: [Table]

Original: a t i
Revised: a t i

Original: [Table]
Revised: [Table]

Original: n / a v g .
Revised: n / a v g .

Original: ﬁ r
Revised: ﬁ r

Original: i
Revised: i

Original: [Table]
Revised: [Table]

Original: r a t
Revised: r a t

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: (cid:31)(cid:25)(cid:26)(cid:24) (cid:31)(cid:25)(cid:30)(cid:31) (cid:31)(cid:25)(cid:30)(cid:24) (cid:31)(cid:25)(cid:23)(cid:31) (cid:31)(cid:25)(cid:23)(cid:24) (cid:31)(cid:25)(cid:29)(cid:31) (cid:2) (cid:1) (cid:7) (cid:4) (cid:5) (cid:17) (cid:2) (cid:127) (cid:10) (cid:1) (cid:21) (cid:129) (cid:127) (cid:141)(cid:31) (cid:25) (cid:31)(cid:29) (cid:14) (cid:143) (cid:14) (cid:13) (cid:21) (cid:20) (cid:11) (cid:19) (cid:5) (cid:144) (cid:21) (cid:13)
Revised: (cid:31)(cid:25)(cid:26)(cid:24) (cid:31)(cid:25)(cid:30)(cid:31) (cid:31)(cid:25)(cid:30)(cid:24) (cid:31)(cid:25)(cid:23)(cid:31) (cid:31)(cid:25)(cid:23)(cid:24) (cid:31)(cid:25)(cid:29)(cid:31) (cid:2) (cid:1) (cid:7) (cid:4) (cid:5) (cid:17) (cid:2) (cid:127) (cid:10) (cid:1) (cid:21) (cid:129) (cid:127) (cid:141)(cid:31) (cid:25) (cid:31)(cid:29) (cid:14) (cid:143) (cid:14) (cid:13) (cid:21) (cid:20) (cid:11) (cid:19) (cid:5) (cid:144) (cid:21) (cid:13)

Original: [Figure]
Revised: [Figure]

Revised: where λ ∈ (0 , 1) is the ﬁring rate penalty parameter and ¯ Y patch is the empirical mean of Y patch

Revised: We perform gradient ascent on the upper bound given in (2) to ﬁnd the feedback kernels and thenonlinearity parameters.

Revised: The gradients are calculated using automatic differentiation available in the

Revised: PyTorch library.

Revised: We use step size of 10 − 4 and run the optimization for 2500 full batch iterations 2 .

Revised: The parameter λ is varied in [0 . 775 , 1) .

Revised: For each value of λ , we solved two optimization problems:one only over feedforward model nonlinearity parameters without any feedback, and one over boththe feedback and feedforward model parameters.

Original: Figure 2A shows the information, information per spike, and the average ﬁring rate when λ rangesfrom 0 .
Revised: Figure 2A shows the information, information per spike, and the average ﬁring rate when λ rangesfrom 0 .

Original: 75 to 1 .The information per spike with feedback achieves its maximum of 7154 for λ = 0 .
Revised: 75 to 1 .The information per spike with feedback achieves its maximum of 7154 for λ = 0 .

Original: This is greater than the maximum achieved without feedback by approximately %14 .
Revised: This is greater than the maximum achieved without feedback by approximately %14 .

Original: The learnedfeedback weights for λ = 0 .
Revised: The learnedfeedback weights for λ = 0 .

Original: 988 show a pattern of connection that is aligned with the V1 RF(Figure 2B).
Revised: 988 show a pattern of connection that is aligned with the V1 RF(Figure 2B).

Original: In other words, feedback excites the ON(OFF)-center LGN cells that overlap the
Revised: In other words, feedback excites the ON(OFF)-center LGN cells that overlap the

Original: ON(OFF) region of the V1 receptive ﬁeld.
Revised: ON(OFF) region of the V1 receptive ﬁeld.

Original: The feedback weights have a small inhibitory impact onthe phase reversed cells.
Revised: The feedback weights have a small inhibitory impact onthe phase reversed cells.

Original: Those are the ON(OFF)-center cells on the OFF(ON) regions of the V1receptive ﬁeld.
Revised: Those are the ON(OFF)-center cells on the OFF(ON) regions of the V1receptive ﬁeld.

Original: Another signature of the feedback pattern is a general inhibition of the LGN cells in aneighborhood of the V1 cell RF elongated in the preferred orientation of the cell.
Revised: Another signature of the feedback pattern is a general inhibition of the LGN cells in aneighborhood of the V1 cell RF elongated in the preferred orientation of the cell.

Original: This can explainthe impact of this feedback on stimuli integration, which is explored in section 3.1.
Revised: This can explainthe impact of this feedback on stimuli integration, which is explored in section 3.1.

Original: 3.1 Impact of feedback on RF properties
Revised: 3.1 Impact of feedback on RF properties

Original: To investigate the impact of the feedback on LGN RF properties, we computed the area summationcurve for ON and OFF-center LGN cells with and without feedback.
Revised: To investigate the impact of the feedback on LGN RF properties, we computed the area summationcurve for ON and OFF-center LGN cells with and without feedback.

Original: These curves are computed bymeasuring the peak response of the LGN cell to a windowed moving sinusoidal grating as the size ofthe window increases from zero to a few multiples of the LGN RF size.
Revised: These curves are computed bymeasuring the peak response of the LGN cell to a windowed moving sinusoidal grating as the size ofthe window increases from zero to a few multiples of the LGN RF size.

Original: Figure 2C shows the areasummation curves for spatial freq = 

Revised: Figure 2C shows the areasummation curves for spatial freq =

Original: (light spot for ON-center cell, dark spot for OFF-center cell),0.02 and 0.04 (cycles / pixel).
Revised: (light spot for ON-center cell, dark spot for OFF-center cell),0.02 and 0.04 (cycles / pixel).

Original: In all three cases, feedback increases the peak ﬁring rate for smallwindows and decreases the ﬁring rate for large window sizes.
Revised: In all three cases, feedback increases the peak ﬁring rate for smallwindows and decreases the ﬁring rate for large window sizes.

Original: This is in agreement with experimentalresults in [7], which show a similar feedback effect on stimuli integration in LGN.
Revised: This is in agreement with experimentalresults in [7], which show a similar feedback effect on stimuli integration in LGN.

Original: 3.2 Phase-aligned vs phase-reversed
Revised: 3.2 Phase-aligned vs phase-reversed

Original: Our model suggests a phase-aligned feedback arrangement for the LGN cells directly overlappingthe V1 RF consistent with results in [7, 24].
Revised: Our model suggests a phase-aligned feedback arrangement for the LGN cells directly overlappingthe V1 RF consistent with results in [7, 24].

Original: In [33], by measuring the burst-to-tonic ratios for LGNcells after feedback deactivation, the authors deduce a phase-reversed arrangement for LGN cells thatdirectly overlap the V1 cell RF.
Revised: In [33], by measuring the burst-to-tonic ratios for LGNcells after feedback deactivation, the authors deduce a phase-reversed arrangement for LGN cells thatdirectly overlap the V1 cell RF.

Original: In [18], A computational model based on predictive coding has beensuggested to account for this.
Revised: In [18], A computational model based on predictive coding has beensuggested to account for this.

Original: In a recent work, Lian et al propose a model of V1-LGN pathway basedon efﬁcient coding that learns the feedback weights using an anti-Hebbian rule [21].
Revised: In a recent work, Lian et al propose a model of V1-LGN pathway basedon efﬁcient coding that learns the feedback weights using an anti-Hebbian rule [21].

Original: This makesthe feedback weights converge to the negative of feedforward weights, resulting in a phase-reversed pattern.
Revised: This makesthe feedback weights converge to the negative of feedforward weights, resulting in a phase-reversedpattern.

Original: However, there is overwhelming evidence that feedback impact goes beyond the receptiveﬁeld of the V1 cell [30, 32].
Revised: However, there is overwhelming evidence that feedback impact goes beyond the receptiveﬁeld of the V1 cell [30, 32].

Original: We believe more comprehensive experiments are required to resolvethese conﬂicting results.
Revised: We believe more comprehensive experiments are required to resolvethese conﬂicting results.

Original: ON weightsOFF weights
Revised: ON weightsOFF weights