Visual Pinwheel Centers Act as Geometric Saliency Detectors
Authors: Haixin Zhong
Mingyi Huang
Wei P Dai
Haoyu Wang
Anna Wang Roe
yuguo yu
Venue: NeurIPS 2024 poster (2024)
Keywords: Visual Contour Saliency
Orentation Map
Population Coding
Hebbian Learning
Primary area: neuroscience_and_cognitive_science

Abstract: During natural evolution, the primary visual cortex (V1) of lower mammals typically forms salt-and-pepper organizations, while higher mammals and primates develop pinwheel structures with distinct topological properties. Despite the general belief that V1 neurons primarily serve as edge detectors, the functional advantages of pinwheel structures over salt-and-peppers are not well recognized. To this end, we propose a two-dimensional self-evolving spiking neural network that integrates Hebbian-like plasticity and empirical morphological data. Through extensive exposure to image data, our network evolves from salt-and-peppers to pinwheel structures, with neurons becoming localized bandpass filters responsive to various orientations. This transformation is accompanied by an increase in visual field overlap. Our findings indicate that neurons in pinwheel centers (PCs) respond more effectively to complex spatial textures in natural images, exhibiting quicker responses than those in salt-and-pepper organizations. PCs act as first-order stage processors with heightened sensitivity and reduced latency to intricate contours, while adjacent iso-orientation domains serve as second-order stage processors that refine edge representations for clearer perception. This study presents the first theoretical evidence that pinwheel structures function as crucial detectors of spatial contour saliency in the visual cortex.

Visual Pinwheel Centers Act as Geometric Saliency Detectors
Haixin Zhong 1.2
Mingyi Huang 1.3 myhuang20@fudan. edu. en
Wei Dai 1,5 weidai@fudan, edu, cn
hxzhong@fudan. edu. cn
Haoyu Wang
Anna Wang Roe annawangezju. edu. cn
Yuguo Yu 12,3,,,, yuyuguo@fudan edu. cn
haoyuwang180f 18@fguan edu cn
1. Research Institute of Intelligent Complex Systems, Fudan University.
2. State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institutes of Brain Science, Fudan University.
3. Institute of Science and Technology for Brain- Iasi--ns Intelligence, Fudan University.
4. MOE Frontier Science Center for Brain Science and Brain-machine Integration, School of Brain Science and Brain Medicine, Key Laboratory Biomedical Engineering of Ministry Education, College of Biomedical Engineering and Instrument Science, Zhejiang University.
5. Shanghai Artificial Intelligence Laboratory. * Corresponding author.
Abstract
During natural evolution, the primary visual cortex (V1) of lower mammals typ- ically forms salt-and-pepper organizations, while higher mammals and primates develop pinwheel structures with distinct topological properties. Despite the general belief that VI neurons primarily serve edge detectors, the functional advantages of pinwheel structures over satt-and-eeperss are not well recognized. To this end, we propose wwo-dimensional self-evolving spiking neural network that integrates Hebbian-like plasticity and empirical morphological data. Through extensive exposure to image data, network evolves from salt-and- and--eed-eepeers pinwheel structures, with neurons becoming localized bandpass filters responsive various orientations. This transformation accompanied by increase in visual field overlap. Our findings indicate that neurons in pinwheel centers (PCs) respond more effectively complex spatial textures in natural images, exhibiting quicker responses than those in salt-and-pepper organizations. PCs act as first-order stage processors with heightened sensitivity and reduced latency intricate contours, while adjacent iso-orientation domains serve as second-order stage processors that refine edge representations for clearer perception. This study presents the first theoretical evidence that pinwheel structures function crucial detectors of spatial contour saliency in the visual cortex.
peppers
1 Introduction
The seminal work of Hubel and Wiesel revealed orientation-sselctiv columns in the visual cortex of higher mammals [1 In higher mammals' primary visual cortex (V1), neurons cluster into "pinwheel" structures around singularities (3), unlike in some mammals like rodents, which display salt-and-pepper" organizations 4 or mini-columns [5]. While there are established theories and
experiments for studying the formation topological organization maps in the visual cortex 7 10 [ the functional significance of pinwheel-like columnar organization remains an unresolved
question and even debated 12
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Sophisticated visual analyses, such as image pattern extraction [4], pattern symmetry [5] material properties [T6]. and textures [17] are crucial for understanding complex visual inputs. Imaging and electrophysiological studies have shown that iso-orientation domains (IODs) undergo cross- orientation suppression [18] reducing a neuron's 's response to its preferred orientation when another orientation is also present in the stimulus [13] [9 20]. This indicates IODs encoding the linear oriented stimuli, which is crucial for detecting edges and contours 22). Cross-orientation suppression is believed to facilitate the detection of local discontinuities, such as orientation discontinuities [23 24
25I. leading to perceptual "pop-out" effects and the perception of illusory contours [24] 26 27 In
contrast, neurons at pinwheel centers (PCs) exhibit greater selectivity for cross-orientation stimuli This indicates that PCs respond more effectively to multi- oulli-orientation patterns, such as pattern symmetry symmetryyy than IODs [12] This indicates PCs may contribute to encode more complex contour features. However, PCs are less selective but have longer response latency than IODs for stimulus orientation in the hierarchy process within OPMs when it comes single stimulus orientation Some studies indicate that colors [29]. textures [30, darks and lights [1., luminance 32 and mirror symmetry
12 [3]
13
19 28)
(15) play role in salient visual processing. Despite these insights, the functional implications of how neurons within IODs and PCs of pinwheels process complex contour stimuli--otentiall affecting stimulus salience for both IODs and PCs-from bottom-up visual inputs remain poorly understood, particularly from a temporal-spatial neural dynamics standpoint.
In response to these challenges, our research contributes the following:
We propose novel 2D self-evolving spiking neural network (SESNN) model that investi- gates the spiking mechanisms behind orientation preference maps (OPMs), spanning from salt-and-peye pepper organizations in mice to pinwheel structures in cats and macaques. The SESNN uniquely produces sparse codes through local synaptic plasticity during natural image learning, establishing a new benchmark for neural coding strategies.
PCs act as first-stage processors, detecting natural images and initiating spiking waves to neighboring IODs, which then process as second-stad neurons. This indicates that early processing involves complex contours, not just edge detection.
PCs react faster to variety of orientation features than IODs, indicating their function in detecting complex orientations and serving as geometric saliency detectors. This suggests PCs have an evolutionary advantage due to self-organized pinwheel structures, which improves their ability to process complex contours.
2 Results
2.1 Visual overlap underlying pinwheels emergence
Our SESNN model generates diverse OPMs. from salt-and-peppers to pinwheel structures, by adjusting the visual overlap metric s. This metric, crucial for the variety visual topologies across species, is shown in Fig. Ta to produce pinwheel structures at high overlap, akin to those in cats and macaques, while low overlap results in salt-and- and-pepper organizations, typical of mice or rats. High overlap also enables cortical neurons to sample natural scenes more frequently, aiding in generating high-resolution images during decoding (3].
Fig. [h shows how visual input overlap levels from 9 to 15 pixels affect V1 orientation selectivity maps the model. The top panel illustrates a higher overlap (15 pixels), and the middle, lower overlap (12 pixels). This comparison reveals the impact of stimulus overlap on pinwheel density and layout in the visual cortex. Below the threshold (10 pixels in our case), salt-and-pepper patterns form, as the bottom panel indicates. Thus, pixels of overlap are excluded from pinwheel analysis, as shown in Fig. Dp-d.
We quantitatively analyze the OPMs shown in Fig. Dh with several metrics
Pinwheel counts, defined as the number of PCs, can be measured by 2D fast Fourier transform 35). which are located at the intersection of the real and imaginary components that equal (34 exhibits decreasing trend as the visual input overlap increases (illustrated in Fig. [p). suggesting that a greater overlap in the visual field may lead to reduction the number of discrete pinwheel structures.

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Overapp degree
Stimitus
OPM
Number stwwhols
Hepercouumn ean (Inr))
100
0.3
100
0.6
SESNN post traininn
02
Ulimukus
OPPM
0.4
Visual Inous overiop (C)
Visaal inou overiop (C)
Vicua mortee (4)
ovariap degres At +0
post post-traiming
SESNN vs, and.omicai data overlap
Antiooicaal IOD size vs. visual fold
Salt -an---nd--- pap--papp meap
Araitrn data coattag
100
Stimuluus
R²- 0.97
100 (ere/
0.91
86
y
57
0.01'' 2.43
SESNN post training
1 mm
90
70
80
100
140
150
100
200
SESAN model overiep
Visual feeld (degree)
Visual Input
Figure Receptive field (RF) visual overlaps underlying the emergence of OPM and the salt- and-peppers revealed via SESNN model. Modifying the overlap parameter (e) among neighboring neurons receiving (16 x 16 pixels) visual inputs from natural images influences the dimensions (e.g., b. Pinwheel counts, Nearest-neighbor pinwheel distance, d. Hypercolumn size) of pinwheel structures and salt-and-pepper organizations. (Lines: mean. Shaded area: SD.) e. Comparing the SESNN model overlap percentage (- x 100%) with actual anatomical data overlap percentages (5 (egeeeentag)) in various species (mice, cats, and macaques). f. Relationship between the IOD size and the extent of the visual field in anatomical data (mice, cats, and macaques).
The nearest-neighbor pinwheel distance (NNPD) in millimeter (mm) unit is defined as the distance between the two nearest PCs. The increasing trend of visual input overlap expands the distance between neighboring pinwheels (Fig. [T.).
The size of hypercolumns (mm) is defined with periodicity measured by 2D fast Fourier transform and also increases with the visual input overlap (shown in Fig. [t). This paper does not account for left- and right-eye dominance columns, so the hypercolumn size is defined as the full 180 cycle of repeating column spacing (A) (mm).
It's noteworthy that pinwheel density is not included as metric in our analysis. This omission is because the observed pinwheel density, irrespective of the hypercolumn size, approaches pinwheels/A?, conforming to topological constraints 34 35).
Our findings emphasize the importance of overlap degrees (Fig. Tb). Greater overlap (e.g., = 15 pixels) fosters stronger local clustering, leading to larger hypercolumn sizes, fewer pinwheels, and longer NNPDs, versus lower overlap (e.g., pixels), yields weak clustering, resembling sutt-and--eppee organizations. This suggests that shared input among V1 neurons significantly influences OPM and salt-and- formation. We obtain the anatomical data overlap using Eq. 3 and observe a strong positive correlation (A²2 0.97)
12 pixels). Minimal overlap (e.g.. E3 9
between the SESNN model and species visual RF overlaps (mouse, cat, macaque) (Fig. [T]). This relationship highlights the overlap index's key role in spatial organization within orientation maps. The model's predictions on IOD sizes and visual field extent (Fig. [ align with empirical data 77.. confirming the SESNN model's 's robustness in simulating neuroanatomical organization and the biological development of orientation maps.
2.2 Spatial-temporal distributed spiking waves propagate within pinwheels
VI neurons stimulated by natural images primarily fire within pinwheel structures, particularly within and around PCs (Fig. (b).)). This pattern especially pronounced in higher mammals with large IODs, such as macaques and cats.
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Spatial-temporal response
6
Zoom
Dietance in 2D
Orientation map
180
140
120
Reating neuron
h+1 Response time (ms)
100
Firing
Distanco from nouron to PC
3.5
within piwwhese
20
0
2.5
R' 0.99
Neuronal powitions the box
1.5
0.5
0.4
0.8
f+11 ms
Response Onset Latency (normalized)
Figure 2: Spatial-temporal response pattern within pinwheels. a. This figure displays the neuronal responses on OPM with a large IOD in a pinwheel structure. The neurons that fire at time to are shown as large black dots at PC, and they expand towards the periphery at time to+1, also denoted large black dots. The other small dots represent resting neurons. b. Distance between firing neurons and the PC at time to and fo+1. c. This panel shows the response onset latency of neurons and the mean distance (# SD) between these neurons within a pinwheel. The distance is measured as the Euclidean distance within 2D grid, simulating the structure of 2D V1 area. (Significance: #**0<0001, Mann-Whinne Whimey U test.)
We define the response onset latency as ms for the initial discharge from pinwheel structures, with subsequent firings occurring ms, based on time unit. Stimulated by natural images, the discharges start at the PCs and exhibit pronounced diffusion within the IODs sequentially, depending on their distance from the center, as suggested in Fig. 2
2.3 Visual bottom-up saliency detection: functional role of pinwheel in geometric encoding
In this section, we investigate whether pinwheel structures respond distinctly to salient features in input images. The ground truth boundary from the BSDS 500 dataset (36] used as binary input represents geometric complexity (edges and curves) (Fig. (3a). The complexity is measured by calculating the local pixel entropy using sliding windows, with 15x15 pixel neighborhood assess pixel value dispersion in the binary images. The computation adheres to the following equation:
H(i.j) = Σ p(m=) logz p(me),
where Hii,) denotes the entropy at pixel position (i,j) in the entropy map. I. the count of distinct gray levels within the local neighborhood around pixel (i, and my the kth gray level within this specified neighborhood. A large entropy value reflects great unpredictability pixel values, signifying highly variable pixel value distribution. Conversely, a low entropy value indicates high degree of predictability, less variation, and reduced complexity in the contours of pixel values. addition, the saliency map of images is generated based on the classical methodology 337.
complexity in the
Furthermore, we propose a bimodal ratio analysis compute the orientation bimodal ratio (OBR) to indicate neuron's orientation tuning curve as either unimodal (single peak) or perfectly bimodal (two peaks of equal strength). This analysis focuses on identifying the peaks in the orientation tuning curve and quantifying their relative strengths.
OBR 2 min( (R.. Ra)
Rg + Rg

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BSDS500 image
BSDS500 binary input
BSDS500 saliency vs. complexity
Complexity (pormalized)
0.6
0.2
0.5
0.8
Saliency (normalized)
BSDS500 saliency map
BSDS500 entropy map
Response to complexity of BSDS500
Complesity (normalized))
0.8-
Pinwhoots
Selland--eppers
0.6-
0.4-
0.2
0.4
10
Response onset latency (ms)
Figure 3: Pinwheel structures in V1 exhibit geometric properties. A BSDS 500 grayscale image displays boundaries, saliency, and entropy maps. b. Natural images show a positive correlation between saliency and entropy. c. Neuronal response onset latency from pinwheels and salt-and- peppers relates to structural complexity, measured by local pixel entropy. (Data: mean SD, significance: **#*pc0.0001, Welch's t-test.)
where Ri and R2 represent the normalized firing rates corresponding to the strengths of the two most pronounced peaks the orientation tuning curve. The OBR ranges from 0, denoting unimodality, to indicating perfect bimodality in the neuron's orientation tuning.
positive correlation observed between the saliency map and the geometrical complexity of the BSDS500 dataset (Fig. (3)), demonstrating that higher geometrical complexity correlates with increased saliency. Significantly, in response the stimulus shown in the BSDS500 image (Fig. 3p), pinwheel structures primarily activate in areas of high contour complexity (regions with the highest saliency this binary image), which is response pattern have not been observed salt-and-peppers (Fig. 3)).
To confirm the disparity in contour complexity responses between pinwheel and salt-and- salt-and-pepper pepper organizations, we design a star-like binary imput (depicted in Fig. 44), including four identical entities negate the impact of neuronal positioning within the SESNN model. This approach reaffirms the correlation (Fig. 4b) and the priority of pinwheel activation over aalt-and-eepeer in response to heightened complexity (Fig. 46).
Findings show that PCs exhibit enhanced saliency detection and significantly faster response times than IODs, indicating that PCs respond more quickly and sensitively to geometrically complex stimuli, while 1ODs are slower and react to simpler geometrical stimuli (see Fig. 4t. Both saliency and latency measurements normalized to 0-1 scale for comparison.
The enhanced saliency detection of PCs is due to the complex orientation preference in RFs. As addressed in Fig. 4e. the ordinate represents the OBR, reflecting that neurons PC generally exhibit bimodal orientation tuning curves with near-equal peak strengths while there is primary peak and secondary peak at relatively far position from PC (z 2). And the secondary peak is nearly absent at the IODs level (x = 3), leading to an OBR close to O. Salt-and Salt-and-peppers, however, show less variation, maintaining consistent OBR.
In conclusion, PCs demonstrate selectivity for more intricate orientations. This is experimentally supported by 13 38 who suggest that PCs are particularly sensitive to specific geometric configura- tions, such as T junctions. Characterized by multiple orientations and OBR nearing (Fig. 4 these neurons tend to initiate action potentials in response complex orientations. Consequently,
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a
b
Star-like binary input
Star-like shape saliency vs. complexity
Response to complexity of star-like shape
Complesity Complexilynoommaaat (normalize))
Complexity (normalized)
Pinsheels
Sak and poppors
0.0-
0.5-
0.2
2" 200
0.6
Sallendy (normalized)
Response ansot latency (ms)
d
Star-iike entropy map
Response sallency of star-like shape
Bimocial tuning cortical
Salency Salency (parmalize))
CeR
0.5-
Finwhee's Sullvend-peppers
0.5
0.2 0.4
0.8
2
3
Latency (normalized)
corical (M.A.)
Figure 4: Geometric properties emergence in PCs of V1 star-like patterns. We introduce artificial star-like patterns to assess neural response to complexity. b. Star-like images show a link between saliency and entropy. Neuron response times in PCs and halt-and-peppers reduce with lower entropy. d. The analysis compares PCs and IODs for saliency and response to star-like patterns; the inset details saliency and latency. e. OBR varies across cortical distance; the red line marks pinwheels, and the black line, sall-and-peppers (an arbitrary point for salt-and-peppers). (Data: mean SD, significance: **pc0.01, ***p<0.001, **#*p<0.0001, Welch's 's t-test.)
this leads to pinwheels being the first to respond. In contrast, neurons in salt-and- do not exhibit a similar responsiveness to complex orientations as observed in pinwheels.
3 Methods
3.1
The architecture of SESNN model
Our SESNN model a two-dimensional network of excitatory (B-) and inhibitory (I-) leaky integrate- and-fire neurons (LIF) (5) stimulated by whitened natural images to mimic the LGN's functions of contrast normalization and edge enhancement without complex modeling
43
44 45
We use
160 whitened natural images as the training dataset, normalized to zero mean and uniform variance,
derived from 20 base images (512x512 pixels) 45 46). To capture orientation details, each of the base images undergoes 90-degree clockwise rotation and flip, creating 8 variations per original.
The configuration features E- and I- neurons in recurrent networks with periodic boundary conditions (PBCs) (Fig. (5)). simulating a continuous 2D cortical surface. The neural connectivity at initialization depicted in Fig. 5 (see Eq. [Tp. Moreover, the connection strengths in the well rell-trained model align closely with the experimental finding ((47)). Under natural image stimuli, the SESNN forms single neuron RFs and population-level pinwheel structures the OPM (Fig- 5e-f). To validate the model, we compare its evolution from randomness to organized states against biological data from macaque pinwheel structures and a baseline model [42] using metrics such as pinwheel density (pinwheels/
A),, NNPD (mm), and hypercolumn size (mm) 34 35 (Fig. and Table
Table 1: SESNN pinwheels (mean + SD) vs. macaque pinwheels.
Metric
E-I baseline
SESNN model
Macaque
Pinwheel density (pinwheels/A3)
2.941
3.175 + 0.397
3.327
NNPD (mm)
N/A
0.277 = 0.043
~ 0.244
Hypercolumn size (mm)
N/A
0.839 + 0.054
0.760

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SESNN model
Periedic boundary conditions
Neural connecivitt
d
connection stringths
Post-trairing
512-612-160
imge
szze:
connections
Connection
streigth
Exchatory
Connection strengh gtt
10'
connection
Fewdfforoent
Inbibiory connection
connection Aatin
101
Gog
loj
Swiect 100 potches
Single neuron RF emergence
Populational spatial sett organizttion
190 ma Leternl connection up
Randomness
SEBNN
Macarue pinwheeels
[llazelino model)
www-baded model
Randomness
training
VHO
0
Exteuroo
Excilatory cornecttion
and UM rulle
RF everlap
Neuron groups
Tenerron
Figure Architecture of proposed SESNN model. The SESNN model comprises 4,900 E-
and 1,225 I- neurons [3 40 41
It processes 160 natural images (100 patches each), presenting
each 512x512 pixel patch to E-neurons for 100 ms with input overlap. The Feed-forward and E-E
connections adhere to the Hebbian-Oja (HO) rule; others follow the Correlation Measuring (CM) rule. and I-neurons are spatially arranged with periodic boundaries, sharing coordinates with connected boundaries as per diagram arrows. Identical connections are marked by same-color arrows. Initial weights are Gaussian distributed. Post-training connection strengths are depicted, with medians in red. RF emerges after training. f. Post-training spatial organization is compared among the SESNN model's OPM, macaque VI, and an SNN-based model [42), with color bars for orientation and I mm scale bar on the cortical surface.
3.2 Experiment-daat--usttfedd overlapping visual fields among nearby neurons
In each trial, E-neuron processes 100 different 16x16 patches for 100 milliseconds each, randomly selected from the training dataset to serve as RFs (see Fig. 5 middle and right panels). It is assumed that these visual inputs overlap on the retina (Fig. 5p. middle panel and its inset). To reflect biological conditions, we perform a statistical analysis based on data from cats, macaques, and mice (Table 2 calculating average overlaps of 99.90% for cats, 99.98% for macaques, and 97.23% for mice using (Eq. 3). These results closely align with our SESNN model's 's configurations (refer to Fig. [T]. RF size in VI is more related to resolution than orientation map formation. In macaque V1, RF size increases more than tenfold from fovea periphery, while orientation map properties show little variation 48 49 Our study does not focus on RF size variations across the retina, as we expect minimal effects from these shifts across species, provided the overlap remains constant. Since the fovea is key for detailed visual information, we use V1 RFs in the area centralis to modeling.
We propose the visual input overlap metric percentage which is defined as follows:
V Suni
Lani M Ser VPviSumi -
x 100%
(3)
percentage
where Suni represents the unit cortical area mm² SEE denotes the size of the RF in VI with unit in degrees, pvi represents the density of neurons in V1, Lunit represents the unit of cortical spacing length in unit of mm, and M refers to the cortical magnification factor (CMF) (mm//eereee) We consider only an effective cortical layer composed of output neurons. This is because the apparent overlap within vertical cortical column primarily contributes to intermediary processing stages for the same input. Therefore, such overlaps should not be conflated with overlaps in the input space.
3.3 Neural dynamics
E-neurons receive stimuli from natural images as well as noise (0, 0.04) from other brain areas (noise term). I-neurons indirectly receive natural image stimuli by adjusting E-neurons. The neural spiking dynamics are modeled using biologically inspired LIF neurons, incorporating refractory
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Table 2: Comparative anatomical data of the retina and VI across three species. a. This table includes three diverse species, encompassing both primates (e.g., macaques) and non- con-primates (e.g., mice and cats). b. V1 neuron density (neurons/ mm²) within 2D surface. Size of V1 RF in area centralis (deg). d. Peak CMF (mm/deg) of V1 in area centralis.
(A)SPECIES (B)VI NEURON DENSITY
(C)VI RF SIZE
(D)PEAK CMF
CAT
99, 200
33
1.0
50
1.90
[
MACAQUE
243, 000
13
~ 0.2
52
18. 18
(52
MOUSE
86, 600
33
4.0
53
0.03
[54]
periods and adaptive firing thresholds
153 The neural dynamics are iteratively formulated as follows:
u;
(K)
(t (t+1) - u; (t)e dkt +hk(
(K)
FF fimage++B +E)
Xj
Σ
B1 [K) w -K)
(1)) noise,
[1, if is an E-neuron IDD
hg (1)
(5)
0, if is an I-neuron ID,
kk x pi(2; (k") 1) (K)
(6)
where i 1,2, Nth (the neuron IDs of E-neurons and I-neurons).
In neural dynamics equation, u; (K) (1) denotes the membrane potential of neuron i time i, applicable to neurons of class K, which includes E- and neuron groups. The membrane time constant, symbolized by the resistor-capacitor circuit, governs the decay rate of the membrane potential in individual neurons. Notably, inhibitory neurons are configured to fire more rapidly than excitatory neurons 44 [66] This setup reduces reconstruction error and hastens system convergence, leading to a more efficient and accurate representation of input stimuli. See the section A.2 for detailed neural dynamics.
3.4 Hebbian Learning in SESNN
The learning rules consist of the HO rule
4K for input weight adjustments and the CM rule 44 451 for
intra-network weight changes (Fig- 5a-c). These facilitate adaptive synaptic weight adjustment based on firing pattern correlations, emulating a key learning mechanism in biological neural networks.
The formula for these adjustments is given by:
HO AW (K- x yız v w. (K--KK
CM : AW. (K*-K) x yay - (yi) (zz) (1+ W w.(
(8)
1)
where x, denote the spike rates of presynaptic and postsynaptic neurons, respectively, with (.) denotes the lifetime average. After each stimulus presentation of 100 neuronal instantaneous spike rates using exponential moving averages (EMAs), which aggregate spikes over time to reflect recent activity (see section A.I Lifetime averages, also computed as EMAs, are crucial for homeostatic stability, helping to modulate neuronal properties or synaptic strengths for consistent activity. See the section A.2 for the hyperparameters.
calculate the network's
Our SESNN model reflects experimental findings [57 by representing VI pyramidal neurons with weaker synaptic strengths, essential for preventing over-excitation and maintaining neural balance. We apply the HO rule 43 to E-E connections with a normalization factor to keep synaptic weights between 0 and while stronger lateral E-I connections under the CM rule lack this normalization Post-training synaptic strengths are depicted in Fig. 51. Stabilizing neural network training requires careful learning rate adjustment. A slower rate for E-E connections compared to others is crucial to prevent E-neuron over-excitation, aligning with empirical data [57 47 [58).
45 44
The HO and CM rules facilitate LTP and LTD mechanisms, common in rate learning rules that do not require precise spike timing. We selected these rules for their ease of tuning and ability to stabilize recurrent excitation.
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4 Related works
Functional roles of pinwheel structure can be revealed by SESNN model The classical self-
organizing map model [8] and other computational approaches like on-off models [6
7
g [5]]
and
related ANNS [10 60 61 lack the dynamic and temporal fidelity needed to realistically simulate the
emergence of pinwheel structures in the visual cortex. To address these shortcomings, we propose the
novel SESNN model, integrating retinotopy data [33 50 [2 (33, detailed morphological data [62]
63 [64 and CMF [21 [54] to enhance biological fidelity. The SESNN model effectively simulates macaque cortical organization and pinwheel development within OPMs (Fig. 55D Furthermore, our
investigations reveal that the degree of everlap-reflecting similar feed-forward inputs from identical RGCs to neighboring caurooss-psitivved correlates with the retino-cortical mapping ratio 6 aiding in distinguishing between different V1 organizational patterns.
PCs and IODs in neural processing hierarchies Our findings show that PCs and IODs exhibit distinct neural activity waves, leading varied responses to contour complexity from spatial-temporal dynamics: PCs react first to complex contours, having more multi-orientation selective neurons (Fig. fe. x 1) before activity spreads to IODs, which process simpler edges (Fig. 41 and e, = 3). PCs display a stronger correlation with contour saliency, indicating a heightened role in processing visual stimuli over IODs. In rodents with salt-and -epperr organizations, contour saliency is less pronounced (Figs. 3 and 4p.. While PCs are thought to indicate higher-order processing due to delayed response [13 28 this is likely due to the nature of the stimuli. Studies reveal IODs show cross-orientation suppression under complex stimuli [2),, unlike PCs with broader tuning. The SESNN model illustrates preference for complex stimuli in PCs and simple stimuli in IODs, with activity propagating from PCs to IODs upon encountering complex contours (Fig. 41 and e).
PCs as geometric saliency detectors The SESNN model reveals PCs have broader orientation tuning and less selectivity for complex contours, unlike IODs, which show sharper tuning and cross- orientation suppression, preferring simpler edges (x 3 in Fig. (b)) [12)
65 66 67). PCs' excitation leads to reduced cross-orientation suppression. With binary input, PCs correlate more positively with contour complexity than IODs (Figs. 3 and (p), making them more salient in processing visual stimuli. This differs from rodents with salt-and-pepper organizations that lack distinct contour complexity saliency (Figs. 33 and 4p). Prior studies 1 28 suggest PCs have delayed response latency, indicative of higher-order processing. This arises from using drifting grating stimuli that activate IODs more readily. Koch et al. [12] note that IODs show cross-orientation suppression under complex stimuli, narrowing their tuning, unlike PCs. However, these studies omit temporal neural data within pinwheel structures. The SESNN model supports physiological findings that IODs and PCs favor single and complex orientation stimuli, respectively.
[3 19 58
5 Conclusion and limitations
The advantages of pinwheel structures in visual representation and encoding are not fully understood. To address this, we develop a two-dimensional SESNN model that incorporates Hebbian- like plasticity and empirical morphological data. This model evolves to function as localized, bandpass filters, enhancing its responsiveness to range of orientations and complex spatial textures in natural images. Our findings reveal that neurons within pinwheel structures respond more effectively to these textures, with stronger and quicker reactions than those in -nd-pppeeppp configurations. Specifically, PCs act as first-order stage processors with heightened sensitivity and reduced response latency to intricate contours, while IODs function as second-stage processors, refining edge representation for greater clarity. This advanced processing capability of pinwheel structures, particularly in detecting spatial contour saliency, not only deepens our understanding of visual processing in higher mammals but may also inform new strategies for visual saliency algorithms in computational models.
Using sliding windows, local entropy assesses variation and complexity in spatial distributions by capturing local intensity changes, indirectly reflecting geometric complexity through edges, corners, and patterns. Since this method cannot directly measure geometric shapes, we verify the use of the Doaer-DDogllaaeaa
algorithm to approximate and directly measure geometric structures (refer to section (A55) [68. This algorithm simplifies shape contours by reducing vertices while preserving the overall form. The resulting polygon will allow us to calculate the distribution of edge lengths and angles, with geometric entropy defined as the sum of these entropy values. future studies, we will utilize the Ramer-Douglas Peeckkrr algorithm to enhance geometric analysis by identifying

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and measuring the complexity of specific structural features, such as junctions, sharp corners, and textures, which are essential in complex visual scenes.
Acknowledgments
We gratefully acknowledge the support from the Science and Technology Innovation 2030 Brain Science and Brain- Inspieed Intelligence Project (2021ZD0201 the National Natural Science Foundation of China (U20A20221, 12201125, 12072113), the Shanghai Municipal Science and Technology Committee of Shanghai outstanding academic leaders plan (21XD1400400), the Yang Fan plan (22YF1403300), and the China Postdoctoral Science Foundation (2023M740724).
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A Appendices
A.1 Exponential moving average
We compute the network's neuronal instantaneous spike rates as exponential moving averages (EMAs), which accumulate spikes over time (see Eq. ( EMAs are utilized to track recent neuronal activity levels. Concurrently, lifetime average values are also calculated using EMAs, which are crucial for maintaining homeostatic stability. This method helps stabilize the neural network by adjusting neuronal properties or synaptic strengths to sustain consistent activity levels over time.
2y(t) = (1 - ()x,(t)
Ç (t),
(9)
where 1=1-e- to indicating that the 10 ms is temporal window of the moving average weighted with exponential decay. The initialization of æ; is O. The exponential moving average calculated dynamically and updated along with synaptic weights.
(1z) (1 { (m,) T.
(10)
where ç = -- It is dynamically updated to ensure the sum of the weights remains constant over time.
A.2 Detailed parameters and connectivity settings for the model
Detailed neural dynamics: The feed-forward connection, labeled Fry (inggee++)) links pixel Xj of the whitened image patch excitatory (E-) neuron i. W w:KK--K) signifies the synaptic weight from neuron of neuron class K to neuron of neuron class K, with its sign determined by the connection type, described as 3 (K) neuron receives E-connections, set as +1; conversely, the neuron
receives inhibitory (I-) connections, the sign set as -1). 2j (K") (t) indicates the spike output of
neuron j at time r. Upon reaching the spike threshold 0 (initialized as 2), spike emitted, 2 ((K) (t)
set to then the membrane potential is reset O mV, remaining so until the refractory period (3
ms) concludes. Within primary visual cortex (V1), homeostatic plasticity (34(55) [55 ensures neural
activity stability by dynamically adjusting the firing threshold 0. This adjustment is based on the
deviation of the current firing rate p; (t) from the target rates p; (pi = 2, p()) = 4), as outlined
(K)
in Eq. 555 We assign 7(E) = 10 ms for E-neurons and -(1) = ms for I-neurons. To enhance
computational efficiency, set the time step to 1 ms.
Hyperparameters: For the synaptic plasticity, learning rates are F/FF = 0.2 (image to E-ncurons), Me = 0.01 (E- to E-neurons), VæI = 0.7 (I- to E-neurons), 7/1 1.5 (I- to I-neurons), and ThE 0.7 (E- to I-neurons), while the neural connectivity parameters are Olmax.E 1.0 (E- max weight), 0 0.5 (I- max weight), dEg 3.5 (E-E coupling range), σы 2.9 (E-I coupling range), Ois = 2.6 (I-E coupling range), and σn = 1 (I-I coupling range).
Neural connectivity within 2D cortical area: E- and I- neurons are arranged symmetrically on a wwo-dimensional lattice, as illustrated in Fig- 5p. Periodic boundary conditions are employed to mimic the large number of neurons in the actual V1 cortical surface. Specifically, neurons at the boundary are connected to neurons at corresponding symmetric positions on the opposite boundary. The initial connection weights between neurons modeled by Gaussian function of their distance (see Fig. 5b), which can be expressed as:
(1,
W + (i.j) = ag- x exp
(11)
20k=² 2
In this equation, d(i,j) represents the Euclidean distance from neuron i neuron j in grid, a determines the maximum connection weight, which is set to agE 1, agı 1, arE = 0.5, an = 0.5, and a governs the rate at which the weight decays with distance. The synaptic types predominantly determine the parameters for this connection weight distribution function. To accurately replicate the neuronal architecture of V1 in macaques. The connectivity radiuses, denoted by a, are set to оEE = 3.5, dgi 2.9, dIE 2.6, Tn 2.1. These values are based on anatomical data indicating that the axon length scales of E- and I-neurons are approximately 200 ym and 100 yim, respectively, while the dendrite length scales are around 150 pm for E-neurons and 75 um for I-neurons in the V1
62 63 64] We prune any connection strengths below threshold of 0.01 to maintain computational
efficiency and biological plausibility.
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A.3
Anatomical data integration
Neural connection data
The experimental subjects include six adult cats with unknown genders, with data sourced from research by Armen Stepanyants et al. [3];; and eight macaques, aged 5-11 years, including six males and two females, with data sourced from research by Joseph Amatrudo et al. 664
Neuronal synaptic plasticity
The subjects are rats aged 14-16 days, with unknown gender and quantity, with data sourced from research by Holmgren et al. [57]: transgenic mice, with unknown quantity and gender, with data sourced from research by Hofer et al. 47
Retinal-V1 topological projection data
Receptive field (RF) data: V1 neuron counts for macaques, cats, tree shrews, ferrets, mice, rats, and gray squirrels respectively come from Tehovnik et al. [69] (subjects: 3 macaques, unknown gender and age), Scholl et al. [50] (subjects: cats, unknown gender and age). Veit al. (7) (subjects: male and 7 female tree shrews, aged 3-8 years), Huberman et al. [ (subjects: 8 ferrets. unknown gender and age). Niell et al. (53) (subjects: mice, aged 2-6 months, unknown gender), Foik al. [72 (subjects: 21 rats, unknown gender and age), and Hall et al. [73) (subjects: 17 gray squirrels, unknown gender and age). VI neuron density: Neuron density data for macaques, cats, mice, rats, and gray squirrels come from Srinivasana et [5. (subjects: unknown gender and age); tree shrew, ferret, and gray squirrel density data respectively come from Weigand al. al.
Cortical magnification factor
Cortical magnification factor (CMF) data for macaques, cats, tree shrews, ferrets, mice, rats, and gray squirrels are sourced from Tehovnik al. [69] (subjects: macaques, unknown gender and age), Veit et al. [7] cats, unknown gender and age), Bosking et al.[48) (subjects: tree shrews, unknown gender and age), Rockland et al. 775 (subjects: ferrets, female, unknown age). Beest al. (54) (subjects: 28 mice, 11 males and 17 females, ages 2-14 months), Keller et al. (76) (subjects: male rats, age 3 months), and Hall al. 73 (subjects: 17 gray squirrels, unknown gender and age).
Additionally, the anatomical data concerning inter-ocular distances are obtained from Najafian et al.
A.4 Unveiling species-specift factors distinguishing pinwheels and salt salt-and
A.4.1 Anatomical data suggests RF's density underlying V1 organizations
Table 3: Comparative anatomical data the retina and V1 across species.
d. V1 neurons density (neurons/mm"
e. V1 RF size in area centralis (deg)
RFD
a. Species
Retina (mm²)
c. VI size (mm?)
((c) (d)/(b)
(mean)
(RFs/mm²
Macaque
636 6
1,090 33
243,000
0.2
416.462.26
Cat
510 6
6 33
99,200
1.0
73,913.73
Tree shrew
122
77
6 33
192,800 74
2.0
115,363.93
Ferret
83 6
75
78(33
95,813 74
3.0
90,041.13
Mouse
15 6
2.5
86,600
4.0
14,433.33
Rat
52 6
78
7.1 33
90,800 33
3.0
12,397.69
Gray squirrel
205
32
84,213
2.0
13,145.44
We analyzed anatomical data from seven species, including primates (e.g., macaques) and non- primates (e.g., mice, rats, cats, tree shrews, gray squirrels, and ferrets), as detailed in Table 3 We first find that V1 RFs density (RFD) (PRF) acts linear classifier (y 4.42 10*z), effectively distinguishing species with pinwheel structures from those with salt-and-pepper organizations. In this classifier, species like macaques, cats, tree shrews, and ferrets, which have higher RFD,
17

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Ri's density dessifer
Species dasssiieed by V1 neurone-relina size reñi
Salt and peoper organ.cations
Pinwheed structures
10
Number ofV1 nouron
10"
Mouse
Cat
Spaciess
Pinwheel structures
Gray equiree
10
y
4.422010's
Forrot
10
aall-ad
Macaque
10"
10"
10
16"
RF dorsity Per (RFaimm")
Retina size (mmn"
Figure 6: A linear classifier based on RED (y = 4.42 x 10¹x;) effectively differentiates species with aetpper organizations (rats, mice, gray squirrels) from those with pinwheel structures (macaques, ferrets, cats, tree shrews). a. This classifier reflects variations in VI organizations across species. b. plot categorizing species by the ratio of V1 neuron number retina size acts divider, implying a critical ratio for the formation of pinwheel structures.
associated with pinwheel structures (light red area in Fig- 66 and exceed the classification threshold. In contrast, species with lower RFD, such as mice, rats, and gray squirrels, are linked to salt-and- pepper organizations (light blue area in Fig- ( Thus, VI RFD serves as a predictive metric for V1 organizational patterns across species. The PRF is calculated as follows:
n' PRF
(12)
st [[SRF =) =) (Vn- SRE]"
where n' denotes the total number of neurons in V1, s/ indicates the retinal surface area. We have n' = 8y1 x Pr1. where 8v1 corresponds to the V1 2D surface area, and fvi signifies the neuronal density within V1. The variable quantifies the degree of visual input overlap among adjacent neurons, n denotes the total number of neurons, and SRF represents the RF size in the self-evolving spiking neural network (SESNN). Referring to Eq. and anatomical data (Table 3. the overlap positively correlates to VI RFD PRF and is main factor influencing V1 RFD. We discuss the overlap the variable of V1 organizations in the main text.
A.4.2 SESNN reveals neuronal connection range influencing V1 clusters
The anatomical data in Table 3 for seven species show variability in V1 neuronal density (Pv1), which influences nntrrnn spacing and connection strength. We explore how V1 cortical orientation patterns form by adjusting the lateral connection range, impacting axon reach among E- and I-neurons, depicted in Fig. 7 We modulate axonal arborization through parameter to adjust the connection range, allowing us to simulate neuronal connections areas with varying densities. This setup enables the SESNN model to predict changes in cortical patterns (Fig. 77. Our observations indicate that increasing axon lengths, thereby extending the connection range, enlarges hypercolumn sizes within pinwheel structures (Fig. 7d), reduces the overall number of pinwheels (Fig. ()) and increases the nearest- neigest pinwheel distance (NNPD) (Fig. 77.. These findings underscore the critical role of neural synaptic connection range organizing orientation maps.
A.5 Relationship between maximum values of local pixel entropy and local geometrical entropy for various shapes
To address the limitations of using local pixel entropy (LPE) with sliding windows alone to capture complex geometric properties, we conduct new analysis comparing the maximum values LPE with local geometrical entropy (LGE) across various shapes. These shapes include lines, angles, and junctions (L-, T-, X-junctions), as well as jagged edges. Both LPE and LGE values were normalized to the range [0,1] for consistency.
Let P {u1, u/,,.., Un) be polygon with vertices e; = (x,, y:), where = -1,2,... n. The edges of the polygon are the line segments between consecutive vertices, denoted e || v/]l.
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Neuronal connectin range
Neuronnal connactinn
Pinwhaels
Pinutheeis
range
Increase the connection range
1.7
Numbar of pimetuals
200
0.35
150
0.3
100
0.2
0.8
088
3.5
2.0
Neuronal connection range (o)
Neuronal connection range (1)
Neuronal connection range (0)
Figure 7: Neuronal connection range within VI contributes to the formation of pinwheel structures. Modifying the synaptic connection range reshapes the dimensions of pinwheel structures. b-d. The relationship between the synaptic connection range (o) and the number of pinwheels, NNPD (mm), and hypercolumn size (mm). The scale bar: mm cortical surface. Color scheme: orientation preference. Lines; mean. Shaded area: SD.
where || represents the Euclidean distance. The angle 0; between two consecutive edges and 6441 can be computed using the dot product:
8, cos ( c++1
(1e
(13)
With the of edge lengths {er, 62, en) and angles (01, Oz,... 0n). we calculate the entropy for both distributions. The entropy H of discrete distribution X with probability mass function p(z) given by:
H(X) = Σ p(x) logp(x). {()))o)p(()) TEX
(14)
For the edge lengths and angles, the probability mass function is estimated by normalizing the frequency occurrence of each unique edge length and angle polygon:
H (Lengthh))
Σ
p(es) logp(e;),
(15)
H ((Anlees) =
Σ p(0)) logp(0.))
(16)
To enhance the sensitivity of geometrical entropy to structural complexity, particularly in differen- tiating shapes that have similar edge lengths and angles but different structural arrangements, we introduce scaling factor based the logarithm of the number of vertices The defined geometrical entropy (GE) with the scaling factor is thus defined as:
GE = (Hennt)))) + H (Angles)) x log(n).
(17)
19

---

This modification allows GE to capture additional complexity arising from intersections and the global arrangement of vertices, providing more comprehensive assessment the shape structural intricacies.
Our results, summarized in Table show that while LPE reflect the complexity of certain patterns, it does not fully capture the geometric variations seen in more intricate shapes. For instance, the LPE values for line structures remain relatively low compared to those for jagged edges, which have the highest LPE and LGE values due to their high structural complexity. This comparison highlights the added value of incorporating LGE to better characterize local geometric structures, providing more nuanced measure of complexity that includes both intensity distribution and spatial organization.
Table 4: Relationship between maximum values of LPE and LGE for various shapes. Both metrics are normalized to the range [0,1].
Various shapes
Max local pixel entropy
Max local geometrical entropy
Line I
0.56
0.43
Line 2
0.56
0,43
Angle |
0.81
0.87
Angle 2
0.79
0.86
Angle 3
0.77
0.87
L-junction
0.78
0.74
T-junction
0.78
0.64
X-junction
0.78
0.84
Jagged edges
1.00
1.00
A.6
Pinwheel centers response to different orientation bandwidths
Probabilty distribution preferred adjusted acule
b
Ablation study
angles PCs
D.5
Complexity (nommlizee)
1.0
Pinwheels: control group
Interchange neurons' feedforward connection (FF)
Probabiity
0.3
Shuffle lateral connections
0.2
Interchange FF, shuffle conneciions
Shuffle FF
80
Shuffle all connections
Adjusted angle (degrees)
Response ansot latency (ms)
Figure 8: PCs in VI prefer orientations and ablation study. a. Probability distribution of preferred acute angles in PCs. b. Ablation study on normalized complexity across response onset latencies. Data: mean + SD.
Understanding the tuning of pinwheel centers (PCs) in V1 to edges, corners, and junctions essential. In Fig. c. we show that PCs exhibit broader orientation tuning curves than IODs when using star-like patterns as stimuli, potentially enabling the detection of T-junctions and corners, as demonstrated by Li al. [3] and Koch et al. [12]. We further examine the distribution of PCs' tuning curves using gratings as inputs, specifically analyzing acute angles formed by the primary and secondary peaks (Fig. Ba). This analysis reveals that PCs are more frequently associated with larger acute angles, closer to orthogonal (90"), suggesting a preference for orthogonal junctions. However, this result does differentiate between L- and T- junctions based solely on angle. We propose that such high-order feature extraction be deferred to higher visual cortices, like V2 and V4, which are involved texture detection, as noted by Wang et al. (79 and Roe al. 80
A.7 Ablation study
We present mechanism of multiple orientation tuning that is essential for processing complexity. Our analysis of PCs' preferred acute angles (Fig. ( suggests that their broad tuning enables the detection
20

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of complex junctions, such as T- and L-junctions, likely due to variations in local connectivity within and between iso-orientation domains.
To test this, we conduct an ablation study by disrupting local connectivity and shuffling the spatial arrangement of orientation-tuna RFs in the pinwheel orientation map, while keeping other properties constant (Fig. Sp) The control group (red) maintains higher complexity over time, whereas shuffling in decline in complexity. This
connections especially both feed-forward and highlights the importance of structured connectivity in preserving complex neural responses in VI and supports the conclusion that structured connectivity underlies enhanced saliency detection by pinwheels.
A.8 Computing infrastructure
Table Computing infrastructure
CPU
Intel Xeon Gold 6348 CPU @ 2.60GHz
GPU
A100
Memory
512 GB
Operating system
Ubuntu 20.04.6 LTS
Simulation platform
MATLAB R2023a and Python 3,9
The simulations and analyses in this study are performed on a tructure to ensure efficient processing of large datasets and complex models. The system powered by an Intel@ Xeon@ Gold 6348 CPU running at 2.60 GHz and an NVIDIA A 100 GPU, providing robust computational power for intensive tasks. The system includes 512 GB memory, which supports handling memory-intent -iiteneiiiteeivveeeeeee applications and large- scale simulations. The operating system used is Ubuntu 20.04.6 LTS, known for its stability and compatibility with scientific software. The simulations are conducted using MATLAB R2023a and Python 3.9, both of which are widely used in scientific computing and neural modeling, enabling effective implementation and analysis of the models presented in this study.
computing infras-
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should be clear whether the error bar is the standard deviation the standard error of the mean.
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It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of enrors is not verified.
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For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of exccution) needed to reproduce the experiments?
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Answer: [Yes]
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Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics
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Reviews:
[{"review_id": "R5jj40scwf", "reviewer": "Reviewer_TFr2", "summary": "This paper uses a self-evolving spiking neural network model to investigate why some visual systems develop pinwheel structures while others have salt-and-pepper organization of orientation tuning. The simulation shows that the organization depends on the amount of receptive field overlap between neighbouring neurons. Experiments on the trained network show that pinwheel centers respond more efficiently to complex edge structure in images than salt-and-pepper neurons.", "questions": "Do the pinwheel centers show faster responses to regions of the image that are ground-truth boundary vs. other regions of the image? (If a BSDS image is input to the model, do the pinwheel centers respond differently to the pixels which are 1 in the edge map than those which are 0?) This might show an advantage for these cells in boundary detection or figure-ground analysis.\n\nAre pinwheel centers tuned for particular types of edge structure (for example, giving a different response for T-junctions than other types of junctions)?", "limitations": "Not applicable", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "+The findings relating orientation tuning organization to receptive field overlap are quite interesting and seem novel.\n+The modelling approach seems well-designed and has a lot of potential to investigate the evolutionary advantages of different types of organization for different images/tasks.", "weaknesses": "- The experiments seem to use binary edge map images only, if I’ve understood them correctly. No visual system evolved to process these kinds of binary images, so it’s unclear what conclusions we should draw from these experiments. It would be much more useful to show experimental results for real images.\n- Entropy in a local region of the edge map is used as a proxy for geometric complexity, but this just measures the proportion of pixels in a local part of the edge map which are white vs. black.  A little patch of random noise (50% white and 50% black pixels) would have maximum entropy but no geometric information. From the experiments, it’s hard to tell what aspect of the high-entropy regions the pinwheel centers are more responsive to – would they respond highly to random noise? Or are they responding to edge intersections? Corners? Textures? Given that the input to the model is a binary edge map, there are many ways the edges could be characterized to better understand the tuning.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Rebuttal for Reviewer TFr2\nThank you for your detailed feedback on our paper. We appreciate your recognition of the novelty in our approach and the potential of our modeling technique.\n## Points Raised:\n### 1. Use of Binary Edge Maps:\n**Response:** We indeed used whitened natural images to train the model and tested with binary image map. We used binary edge maps as an initial test to isolate the geometric complexity of natural images while eliminating the influence of luminance and contrast variations. By using binary images, we ensure that the model focuses on detecting complex features inherent in natural scenes, rather than being influenced by luminance differences and thus explicitly demonstrate that pinwheel centers respond more efficiently to complex edge/contour structures. Luminance and contrast are important elements for saliency, complementing complexity saliency. In this case, we will further consider natural images to validate our model's performance in more realistic scenarios. Future experiments will involve testing with real-world images to validate our model's performance in more realistic scenarios, particularly in boundary detection and figure-ground separation. As addressed in Fig.S1(a) in supplemental PDF, we indeed observe PC's significantly shorter latency in response to edges than other regions of the BSDS500 natural images. \n### 2. Entropy as a Proxy for Geometric Complexity:\n**Response:** The concept of using entropy in a local region of the edge map as a proxy for geometric complexity can be encapsulated by the following equation which is derived from the idea of Shannon's mutual information[1]:$$H = H_{Geometric\\ Complexity} + H_{Noise}$$\nThis equation suggests that the entropy of an image region is composed of both geometric information and noise. In our current approach, we hypothesize that the noise level in the edge maps (artificial star-like binary images and BSDS 500 groundtruth in Figs. 3 and 4) is negligible, allowing us to consider entropy as a direct measure of geometric complexity. By assuming that noise is zero, we can simplify our analysis and use entropy to reflect the structural information within the image accurately. \nHowever, we acknowledge the potential influence of noise on entropy measurements. To address this, we plan to include a noise term in our study soon, which will help us differentiate between random noise and true geometric complexity, ensuring a more robust and accurate assessment of image structure.\n1. Shannon, C. E. (1948). “A Mathematical Theory of Communication.” Bell System Technical Journal, 27(3), 379-423. \n### 3. Pinwheel Centers' Response to Ground-Truth Boundaries and Specific Edge Structures:\n**Question1:** Do the pinwheel centers show faster responses to regions of the image that are ground-truth boundary vs. other regions of the image? \n**Response:** Our model demonstrates that pinwheel centers respond faster to binarized boundaries, indicating their role as saliency detectors without the influence of other elements. We consider additional tests using diverse datasets to provide a comprehensive evaluation of our model's functionality toward edge detection in non-binarized original images, and indeed observed statically significant speed advantage of PC in detection of edges (>5 ms) than other regions (~10ms) as illustrated in Fig.S1(a), Supplemental PDF file.\n**Question2:** Are pinwheel centers tuned for particular types of edge structure? \n**Response:** Understanding the tuning of pinwheel centers to various edge junctions and textures is crucial. Pinwheel centers have the broadest orientation tuning curves, as verified by Fig. 4e. They significantly contribute to detecting T-junctions and corners, as shown by citation 7 in our paper[1]. Additionally, textures are detected in V4, as demonstrated by Tianye Wang et al. in their 2024 Nature Communications article. Due to time limitations, we will provide the new results during our discussion period. Thank you for understanding.\n1.Wang, T., Lee, T.S., Yao, H. et al. Large-scale calcium imaging reveals a systematic V4 map for encoding natural scenes. Nat Commun 15, 6401 (2024).\n## Conclusion:\nWhile we acknowledge the limitations highlighted in the review, we believe that our initial findings provide a strong foundation for future research. We appreciate the opportunity to improve our work and are confident that these enhancements will demonstrate the robustness and applicability of our model in understanding visual processing.  We have made every effort to address the Reviewer TFr2's concerns and kindly urge you to reconsider the score in light of our clarifications. We remain available to provide further explanations if there are any additional questions. Thank you for your valuable feedback.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RRTqrB9C1o", "reviewer": "Reviewer_Boae", "summary": "The authors present a comprehensive model of the primary visual cortex adapted for various mammalian species, demonstrating its ability to reproduce orientation maps and compatibility with experimental data across different factors such as neuron density or RF overlap. Importantly, they provide evidence in their model that pinwheel centers act as saliency detectors.", "questions": "In the computation of entropy, why use luminance values instead of that of the (whitened) images used during the training? Also the numbers used in the paper and synthesized in table 2 are given following previous papers, bt it is not said at what eccentricity they are computed. Could you please provide this information? How do you justify that the emergence is uniform while retinotopic space is not (certainly thanks to the fact that RF size is function of eccentricity, as well as the RF density, but this is not discussed in the paper as far as I could read)?", "limitations": "The main result is figure 3, and to better the mechanisms leading to this result, an ablation study would be an asset to the paper. Minor: in Figure 4c, your error bar escapes the imit of valid values (normalized entropy higher than 1). Use quantile regression to estimate the 95% confidence interval?", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "While the result put forward by the paper may seem intuitive, as a PC contains in a close neighborhood cells selective to different orientations, and thus may be a good candidate for a saliency detector, yet this model gives some interesting quantitative predictions.", "weaknesses": "Given the link with neuroscience, more links with behavioural data would be beneficial: are animals without PCs less efficient in detecting saliency? Is the density of PCs compatible with the \"resolution\" of the saliency map? In general, this feature of PCs as detecting features containing multiple orientations should be more broadly tested, for instance by using existing results on textures with different orientation bandwidths. such work could help better undertand the underlying principles which give rise to that particular feature.  (The link to https://github.com/HenryGithub1?tab=following (and to its followers) may reveal the authorship, which may be a problem for NeurIPS. Use anonymous links instead. There is a strong overlap with submission 16614, most certainly from the same authors.)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Rebuttal for Reviewer Boae\nThank you for your insightful feedback and constructive comments on our paper.\n## Points Raised:\n### 1. Behavioral Data and Saliency Detection:\n**Question1:** Are animals without PCs less efficient in detecting saliency?\"\n\n**Response:** We acknowledge the importance of behavioral data, yet we didn't identify existing research that can explicitly prove with behavioral data that animals lacking well-defined pinwheel centers (PCs) in their visual cortex may indeed be less efficient in detecting saliency compared to species with distinct pinwheel organizations. However, we do expect so as PCs are critical for integrating information from surrounding iso-orientation domains (IODs), allowing for enhanced sensitivity to complex visual features like edges and textures[1]. Since most related experiments didn‘t focus on this address, which is the novelty point of our work from the perspective of computational models, we'll try to launch behavioral experiment evidence soon by cooperating with experimentalists.\n\n**Question2:** Is the density of PCs compatible with the 'resolution' of the saliency map?\n\n**Response:** If we understand correctly, the 'resolution' of the saliency map should be referring to resolution of image. Then, the density of PCs within the cortex correlates with the resolution of the saliency map, where higher densities typically enable finer discrimination of visual stimuli. In general, comparative neuroanatomy studies across species have shown that variations in PC density and organization impact visual processing capabilities, influencing the ability to detect and respond to salient visual cues[2]. \n\n1. Bosking, W. H., Zhang, Y., Schofield, B., & Fitzpatrick, D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. The Journal of Neuroscience, 17(6), 2112-2127.\n2. Angelucci, A., & Rosa, M. G. (2015). Resolving the organization of the third tier visual cortex in primates: A hypothesis-based approach. Visual Neuroscience, 32(E010). \n### 2. Testing on Textures with Different Orientation Bandwidths:\n**Response:** We agree that such work could help better undertand the underlying principles which give rise to that particular feature and will incorporate results from textures with different orientation bandwidths to validate our model further. This will help clarify the underlying principles governing the observed features in PCs.\n\n### 3. Computation of Entropy using luminance values:\n**Response:** With our definition of saliency, we want to control other saliency components like contrast, and use binarized luminance value to isolate the effect of geometric complexity. \n### 4. Uniform Emergence and Retinotopic Space:\n**Question1:** \"The numbers used in the paper and synthesized in table 2 are given following previous papers, but it is not said at what eccentricity they are computed. Could you please provide this information?\"\n\n**Response:** For mouse[1] and cat[2], the receptive field eccentricity ranged from 0 to 90°, and the corresponding level used here is around 0°. For macaque[3], the eccentricity ranges from 0 to 15°. Here we all used data corresponding to lowest eccenctricity level at 0°.\n1. van Beest, E.H., Mukherjee, S., Kirchberger, L. et al. Mouse visual cortex contains a region of enhanced spatial resolution. Nat Commun 12, 4029 (2021).\n2. Wilson, J. R., & Sherman, S. M. (1976). Receptive-field characteristics of neurons in cat striate cortex: changes with visual field eccentricity. Journal of neurophysiology, 39(3), 512-533.\n3. Tehovnik, E. J., & Slocum, W. M. (2007). Phosphene induction by microstimulation of macaque V1. Brain Research Reviews, 53(2), 337–343.\n**Question2:** How do you justify that the emergence is uniform while retinotopic space is not?\n\n**Response:** The uniform emergence of orientation maps in the visual cortex, despite non-uniform retinotopic space, underscores the sophisticated self-organizing principles governing neural development, and is primarily facilitated by receptive field (RF) size with eccentricity and the density of RFs across the visual field[1]. Neurons in the visual cortex adaptively adjust their RF sizes according to their distance from the fovea, ensuring optimal sensitivity to visual features at different spatial resolutions[2]. Additionally, the density of RFs compensates for variations in retinal input, with higher eccentricity regions exhibiting smaller, densely packed RFs[3]. \n### 5. Limitations:\n**Question1:** Ablation study.\n\n**Response:** We ablate the local connectivity of trained pinwheel orientation map while keeping other properties. This result indicate the structured connectivity from pinwheel may be the underlying mechanism for its better saliency. Due to time limit we're not able to conduct more detailed ablation studies, however we thank your suggestions and will furnish our word with more ablation studies soon.\n\n**Question2:** Minor correction in Figure 4c.\n\n**Response:** Thanks for the suggestion, to address this question we now use boxplot to show the trend and statistical features as provided in  supplemental PDF file.\n\n### 6. Anonymous Links and Overlap with Submission:\n**Response:** We will replace the GitHub link with anonymous references and clearly distinguish any shared content with submission 16614 through proper citation and differentiation.\n\n## Conclusion:\nYour feedback has been invaluable in identifying areas for enhancement. Thank you once again for your thorough review and constructive suggestions. We are committed to refining our work to contribute effectively to the field of visual processing and the role of pinwheel centers.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WWjxmHmhBo", "reviewer": "Reviewer_FA4k", "summary": "This paper introduced a novel spiking neural network (SNN) to investigate the functional roles of pinwheel structures in the primary visual cortex of higher mammals and primates. By adjusting a visual RF overlapping parameter, their model can produce the salt-and-pepper and pinwheel organizations observed in lower (rodent) and higher (macaque and cat) mammals. Their results suggest neurons in pinwheel centers are more responsive towards complex geometry and spatial textures than those in the iso-orientation domains.", "questions": "- One of the main claims is the differences in neuronal response time with respect to the complexity of the visual scene between salt-and-pepper and pinwheel organizations. Based on Figure 3c, other than the initial time point (1 ms), the two structures seem to have similar response ranges and a downward trend as latency increases. Can the author comment on that?\n- In Table 1, the authors compare a baseline model and the SESNN model against the experimental data obtained from macaques. Can the authors clarify why the NNPD and hypercolumn size are “N/A” for the baseline model? Without a proper baseline, it is difficult to evaluate how well the proposed model is performing in this specific task. \n  - Moreover, can the authors clarify why the pinwheel density is omitted as a metric in Section 2.1, though it is included in Table 1?\n  - Finally, I believe a brief description of the baseline model, and how it differs from SESNN, should be added to the main text.\n- I believe the analysis would be more complete if the authors could add the pinwheel data from rodents and cats in Table 1 to compare the performance of the proposed model against the baseline.", "limitations": "I strongly suggest the authors discuss the limitations of this work and potential future research direction in the paper.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- This paper investigates the important problem of salt-and-pepper vs pinwheel structure observed in the mammalian visual cortex. Their model shows that visual overlap can influence the topological organization in V1 is interesting, and that the resulting orientation preference maps match experiential data obtained from rodents, macaques, and cats.\n- The paper is very well-written. Moreover, analysis of the spatial-temporal response pattern and response time with respect to the complexity of the visual scene is novel and interesting.", "weaknesses": "- The paper lacks a comparison with previous work or verification with experimental data. For instance, only one metric from the baseline model is reported in Table 1. Please see points 2 and 3 in “Questions”. \n- The SESNN model shows a rippling effect/pattern (Figure 2) and a heightened response with high contour complexity (Figure 3) in pinwheel centers, it is unclear whether or not this is indeed the case in the visual cortex without validation/comparison with experimental data.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Rebuttal for Reviewer FA4k\nThank you for your thorough review and valuable feedback on our paper. We appreciate your recognition of the strengths of our model and its presentation.\n## Points Raised:\n### 1. Neuronal Response Time to Complexity of Visual Scene:\n**Response:** Based on our findings, pinwheel centers (PCs) exhibits quicker and stronger neuronal responses to complex spatial textures in natural visual scenes. This contrasts with neurons organized in salt-and-pepper configurations, which generally exhibit slower responses to such stimuli. Though the downward trends look similar in both structures the slope is higher for pinwheels and demonstrate a clear preference for more complex inputs by responding quicker.\n\n### 2. Comparison with Previous Model:\n**Question1:** I believe a brief description of the baseline model, and how it differs from SESNN, should be added to the main text.\n\n**Response:**  We investigated previous model and found that the \"baseline\" model's performance in generating a complete pinwheel structure, crucial for validation by our metrics, did not meet our criteria, leaving NNPD and hypercolumn size not available for calculation. Therefore, \"N/A\" was appropriately indicated in Table 1. However we may have misused the word \"baseline\", \"a previous model\" is more appropriate.\nSpecificaly, the mentioned model[1] is a spiking neural network model simulating the formation of orientation and ocular dominance maps in the visual cortex. In contrast, the SESNN model in the current study not only forms orientation and ocular dominance maps but also involve both salt-and-pepper clusters and pinwheel structures. SESNN overtakes the baseline model in generation of Pinwheel structures, and shows that Pinwheel centers act as first-order processors with heightened sensitivity and reduced latency to intricate contours. This advancement underscores the SESNN model’s ability to better mimic the functional advantages observed in the visual cortex of higher mammals, providing a significant improvement over previous approaches.\n1. Srinivasa, N., & Jiang, Q. (2013). Stable learning of functional maps in self-organizing spiking neural networks with continuous synaptic plasticity. *Frontiers in Computational Neuroscience, 7*, 10.\n\n**Question2:** Can the authors clarify why the pinwheel density is omitted as a metric in Section 2.1, though included in Table 1?\n\n**Response:** In a paper published in 2010[1], it was established that pinwheel density is approximately 3.14, which is considered a reliable metric for assessing the quality of pinwheel structures. Our model also measured pinwheel density, consistently finding it around three, aligning well with experimental evidence. In Figure 2, we varied the overlap size, and given our earlier analysis, the density remains around three in our model with reasonable change in overlap (as long as it does not cause a transition to salt-and-pepper structure). Therefore, it wasn't necessary to use pinwheel density to measure the impact of overlap. However, we included pinwheel density in Table 1 because it is a crucial benchmark for comparing the quality of pinwheel structures across different models, including our baseline model and real animal data.\n1. Kaschube, M., Schnabel, M., Löwel, S., Coppola, D. M., White, L. E., & Wolf, F. (2010). Universality in the Evolution of Orientation Columns in the Visual Cortex. Science, 330(6007), 1113-1116. doi:10.1126/science.1194869​\n\n### 3.  Include Experimental Data to Compare: \n**Response:** \nWe acknowledge the importance of experimental data and did extra investigation on the experimental data from rodents and cats[1-3] and will add into the revised manuscript. This addition will provide a broader comparative analysis and strengthen the validation of our model across different mammalian species. Yet we didn't identify existing research that can explicitly address our conclusion. However, this is the novelty point of our work from the perspective of computational models, we'll try to launch behavioral experiment evidence soon by cooperating with experimentalists.\n1. Stryker, M. P., Sherk, H., Leventhal, A. G., & Hirsch, H. V. Physiological consequences for the cat's visual cortex of effectively restricting early visual experience with oriented contours. Journal of Neurophysiology 1978, 41(4), 896-909.\n2. Tanaka, S., Miyashita, M., Wakabayashi, N., O’Hashi, K., Tani, T., & Ribot, J. (2020). Development and reorganization of orientation representation in the cat visual cortex: Experience-dependent synaptic rewiring in early life. Frontiers in Neuroinformatics, 14, Article 41. \n3. Vita, D. J., Orsi, F. S., Stanko, N. G., et al. Development and organization of the retinal orientation selectivity map. Nat Commun 2024, 15, 4829.\n### 4. Discussion of Limitations and Future Work\n**Response:** We recognize the need to discuss the limitations of our work more comprehensively and outline potential future research directions in the paper. This will ensure transparency and guide further advancements in this area of study. Several limitations should be considered, including potential oversimplification of biological neural networks, and the exclusive focus on functions of spatial aspects of the saliency map. Future research could focus on empirically validating these findings using neurophysiological techniques in biological models, developing dynamic computational models that can address more apects of saliency comprehensively to broaden our understanding of neural network functionality and advance applications in neuroscience and artificial intelligence.\n## Conclusion:\nYour feedback has been instrumental. By enhancing our comparisons with previous work, providing further validation with experimental data, and addressing the noted limitations, we aim to strengthen the impact and robustness of our study. Thank you once again for your valuable feedback and for the opportunity to improve our paper.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "e3KrGqI5r8", "reviewer": "Reviewer_indp", "summary": "This work aims to explain the origin and functional benefits of pinwheel structures in V1 compared to salt-and-pepper configurations. They use a two-dimensional self-evolving spiking neural network (SESNN) model with Hebbian-like plasticity and empirical morphological data to simulate the evolution from salt-and-pepper clusters to pinwheel structures. Their findings reveal that neurons at pinwheel centers exhibit heightened sensitivity and quicker responses to complex spatial textures in natural images, acting as primary processors for intricate contours, while adjacent iso-orientation domains refine edge representations.", "questions": "- In Related works line 228, when referring to ANN models explaining pinwheels, the lack of temporal processing in these models were mentioned but their ability in connecting these maps to the overall functionality of the network is not discussed. Since the main claim of this paper is about functionality of PCs, I wonder what authors think about the functional role previous work attributed to PCs.", "limitations": "- In the setup, It seems that the difference between receptive filed sizes of monkeys, cats and mice was ignored. In mice receptive fields for V1 are generally much larger than monkeys (>20x, see ref below for example). \n\n- The claim about functionality of pinwheels requires more support: the question whether the differences in responses of PCs and IODs in terms of response latency, etc have a functional role could be verified by using SESNN as a frontend for a simple DNN performing object recognition, motion detection, etc. At this point, it remains a different in response properties.\n\n- Code is not shared at this version.\n\nVan den Bergh G, Zhang B, Arckens L, Chino YM. Receptive-field properties of V1 and V2 neurons in mice and macaque monkeys. J Comp Neurol. 2010 Jun 1;518(11):2051-70. doi: 10.1002/cne.22321. PMID: 20394058; PMCID: PMC2881339.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The question is of high interest: Pinwheel structures amazed experimentalist and theorist alike for decades. This is one of the main hallmarks of difference in sensory processing in primates vs rodents.\n\n- Bioplausibility of the model: use of bioplausible modeling (spiking neurons and learning rules)\n\n- Through citations to previous works", "weaknesses": "- More analyses to support the main claim in needed (see limitations)\n- The use of different learning rules for E>E vs E>I is justified computationally (for stability) but not discussed in terms of bio-plausibility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your detailed review and insightful comments on our manuscript. \n## Points Raised:\n### 1. Bioplausibility of Learning Rules for E>E vs E>I Connections:\n**Response:** We recognize the importance of bioplausibility in modeling neuronal networks. In the context of our SESNN model, biological plausibility in learning rules for E>E and E>I connections is essential for simulating realistic neural behavior. We integrate principles of Hebbian-like plasticity, similar to biological brains, where synaptic connections between neurons strengthen based on their co-activation. E>E connections, according to [1], is set to be weaker than E>I connections. By incorporating these bioplausible learning rules, SESNN models can better balance excitation and inhibition that is crucial for maintaining stable neural activity levels and emulate the complex processing capabilities observed in biological neural networks.\n1. Hofer, S. B., Ko, H., Pichler, B., Vogelstein, J., Ros, H., Zeng, H., … & Mrsic-Flogel, T. D. (2011). Differential connectivity and response dynamics of excitatory and inhibitory neurons in visual cortex. Nature Neuroscience, 14(8), 1045-1052.\n### 2. Functional Role of Pinwheel Centers in Previous Work:\n**Response:** The three cited works provide significant insights into the functional roles attributed to pinwheel centers (PCs) in the visual cortex from different perspectives. One study explores how the retino-cortical mapping ratio influences the organization of visual cortical maps, including columnar structures and salt-and-pepper patterns[1]. Another research[2] investigates how orthogonal tiling projections from the retina to the visual cortex contribute to the formation of visual maps, including the arrangement of pinwheel centers. Also, a study[3] presents a network model that explains the emergence of simple and complex cells in the visual cortex, with PCs playing a pivotal role in this development. Though they haven't consider PCs latency as salieny detector, the three cited works collectively highlighted the multifaceted roles of pinwheel centers in visual processing. \n1. Jaeson Jang, Min Song, and Se-Bum Paik. Retino-Cortical Mapping Ratio Predicts Columnar and Salt-and-Pepper Organization in Mammalian Visual Cortex. *Cell Reports, 30*(10), 3270-3279.e3, March 2020. \n2. Min Song, Jaeson Jang, Gwangsu Kim, and Se-Bum Paik. Projection of Orthogonal Tiling from the Retina to the Visual Cortex. *Cell Reports, 34*(1), January 2021.\n3. Louis Tao, Michael Shelley, David McLaughlin, and Robert Shapley. An egalitarian network model for the emergence of simple and complex cells in visual cortex. *Proceedings of the National Academy of Sciences, 101*(1), 366-371, January 2004.\n### 3. Receptive Field Sizes Across Species:\n**Response:** In our study, we acknowledge the differences in receptive field sizes across species such as monkeys, cats, and mice. The focus of our research is primarily on the overlap and interaction within orientation maps, where we have normalized receptive fields for comparative analysis. The size of receptive field in v1 is more about resolution than orientation map formation, for example theres more than ten times change in the rf size from fovea to peripheral in macaque v1 while very little change in the properties of the corresponding orientation map[1,2]. Therefore we expect little effects from receptive field shift sizes across species as long as the overlap is constant. However, if time permits, we can further verify this in our model during the discussion period.\n1.  Bosking, W. H., Zhang, Y., Schofield, B., & Fitzpatrick, D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. The Journal of Neuroscience, 17(6), 2112-2127.\n2.  Horton, J. C., & Hocking, D. R. (1996). Intrinsic variability of ocular dominance column periodicity in normal macaque monkeys. Journal of Neuroscience, 16(22), 7228-7339. \n### 4. Verification of Functional Claims with Simple DNN:\n**Response:** We designed a Spiking Neural Network (SNN) for classifying the Fashion MNIST (FMNIST) dataset. The images were first processed by the SESNN network, generating a 20ms spike train. This spike train was then fed into a convolutional SNN. The final layers consisted of a flattened layer, followed by two linear layers, leading to the classification output. The network was trained using surrogate gradient methods. For comparison, we also evaluated a version of the SESNN where the neuronal activity was resampled based on firing rates to generate Poisson spike trains, effectively removing latency.\nThe classification accuracy of the SNN with and without latency across different classes of the FMNIST dataset is summarized in the tables below:\n|Dataset Class| Accuracy(%) of Model With Latency| Accuracy(%) of Model Without Latency|\n|-|-|-|\n| T-shirt / top| 86.80 | 85.40|\n|Trouser| 97.30|96.40|\n|Pullover| 83.40| 83.80|\n|Dress| 91.10| 90.30|\n|Coat| 83.60| 81.60|\n|Sandal|96.20|96.80|\n|Shirt|73.20|67.80|\n|Sneaker| 95.40| 95.40|\n|Bag| 97.80| 97.00|\n|Ankle boot|96.10|94.20|\n|**Overall**|**90.09**|**88.87**|\nThis experiment elucidates the functional significance of differences in response latency between pinwheel centers and iso-orientation domains (IODs). We also did decoding and reconstruction part with results addressed in Fig.S(b) of Supplemental PDF File.\n### 5. Sharing of Code:\n**Response:** The code is shared at https://github.com/HenryGithub1?tab=following.\n## Conclusion:\nYour feedback has been invaluable in identifying areas for enhancement. We appreciate the opportunity to improve our paper and are committed to delivering a revised version that meets the standards of thorough evaluation and clarity. Thus, we kindly urge you to reconsider the score in light of our clarifications. We remain available to provide further explanations if there are any additional questions. Thank you once again for your thorough review and constructive input.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We greatly thank the reviewers for their valuable advice and comments, which are very helpful for us to further improve this work. We are especially encouraged by the recognition from the reviewers:
1. The findings are quite interesting and novel. The modeling approach seems well-designed.
2. This work can be a good candidate for a saliency detector and gives some interesting quantitative predictions. 
3. Their model is interesting and matches experiential data across species. The paper is very well-written and their analysis is novel and interesting. The paper solves an interesting problem combined with biophysics and neuroscience. 
4. The question is of high interest. The paper is good for a thorough investigation of previous works and good bio-plausibility of the model.

There were some unclear points in the paper that may have caused confusion. To address these unclear points, we have made thorough revisions. The significant changes are summarized as follows:
1. We have validated the efficiency of PCs in response to edges again by testing with real image data, in accordance with the suggestions of Reviewer TFr2.
2. We have investigated more into the relationship between our model and biological ground truth, following the suggestions of Reviewer Boae.
3. We have verified with experimental data and compared it with previous models to validate our model, as suggested by Reviewer FA4k.
4. We have accomplished a DNN implementation to our model SESNN performing object recognition to elucidate the functional significance of differences in response latency between pinwheel centers and iso-orientation domains (IODs), based on the recommendations of Reviewer indp.

Meta-review: The paper proposes a novel self-evolving spiking neural network (SESNN) that develops either salt-and-pepper or pinwheel organization reminiscent of primary visual cortex. The author propose that pinwheel centers respond more effectively to complex patterns than salt-and-pepper populations. The reviewers recognize the work as novel and innovative, especially the fact that the model replicates the pinwheel structure of monkeys and that it illustrates a functional difference between pinwheel and salt-and-pepper organization. However, the reviewers also criticized the entropy-based measure used for evaluation and this criticism could not be fully resolved during the author-reviewer discussion. Overall, the positives outweigh the negatives and I suggest the paper for acceptance. However, I ask the authors to tune down their claims that rest on the contested metric and add a discussion of its limitations to the final version of the paper.
Decision: Accept (poster)