Retina gap junctions support the robust perception by warping neural representational geometries along the visual hierarchy

Kai Du; Shenjian Zhang; Tiejun Huang; Yang Yue; Yonghong Tian

arxiv: 2604.14200 · v1 · submitted 2026-04-03 · 🧬 q-bio.NC · cs.AI

Retina gap junctions support the robust perception by warping neural representational geometries along the visual hierarchy

Yang Yue , Shenjian Zhang , Yonghong Tian , Kai Du , Tiejun Huang This is my paper

Pith reviewed 2026-05-13 18:23 UTC · model grok-4.3

classification 🧬 q-bio.NC cs.AI

keywords retinal gap junctionsadversarial robustnessneural manifoldsdecision boundariesdeep neural networksG-filtervisual system

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The pith

Retina gap junctions enhance DNN robustness by warping neural manifold geometries along the visual hierarchy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the role of retinal gap junctions in making the human visual system robust to adversarial attacks that fool deep neural networks. By creating a biological hybrid model that adds a G-filter modeling gap junctions to DNNs, the authors show this combination is more robust than other defense strategies and improves further with noise training. Geometric analysis from the manifold perspective reveals the hybrid model has a distinctive highly nonlinear 2D decision boundary with lower curvature. The authors further rewrite the G-filter using neural ODEs to show the boundary evolves gradually to a steady state controlled by gap junction conductance.

Core claim

Incorporating a retina gap junction-based filter into DNNs yields a biological hybrid model with greater adversarial robustness, featuring a unique 2D decision boundary of high nonlinearity and lower curvature on the manifold; this transformation occurs as a gradual process reaching steady state modulated by gap junction conductance.

What carries the argument

The G-filter, an abstract model of retinal gap junctions that warps the geometry of the neural representational manifold and its decision boundary.

If this is right

The biological hybrid model is more robust than other defense methods.
Introducing noise during training can further improve robustness.
The decision boundary of the manifold changes gradually with time to reach a steady state.
Gap junction conductance modulates the evolution and final state of the decision boundary.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This suggests biological early vision mechanisms can be abstracted to improve artificial neural network defenses.
The time-dependent warping may point to dynamic processes in other parts of the visual hierarchy.
Models like this could guide experiments on how gap junctions affect real neural population geometries.

Load-bearing premise

The G-filter accurately captures the denoising role of retinal gap junctions and the observed manifold changes causally explain the robustness gain.

What would settle it

An experiment ablating the G-filter component and measuring the resulting loss in adversarial robustness, or direct observation of manifold curvature in biological visual areas exposed to perturbed stimuli.

Figures

Figures reproduced from arXiv: 2604.14200 by Kai Du, Shenjian Zhang, Tiejun Huang, Yang Yue, Yonghong Tian.

**Figure 1.** Figure 1: Retina gap junctions support the robust perception by warping the manifold along the visual hierarchy. (A) The artificial neural network is significantly less robust against adversarial noise than the human visual system due to the neglect of the retina in the deep neural network architecture. (B-C) This work adopts a G-filter derived from the retinal photoreceptor network as a retinal model and combines i… view at source ↗

**Figure 2.** Figure 2: The gap junction filter improves the DNNs’ robustness to adversarial attacks. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: The G-filter transforms DNN’s 2D decision boundary into a unique circle-like shape. (A) The visualization of CNN’s manifold and its decision boundary (Resnet50). We use the smooth gradient G of the network and a vector h perpendicular to it to project the original gradient g on a 2D plane. The center point of the plane is the input image, and the other points are the positions of the perturbed image. Diffe… view at source ↗

**Figure 4.** Figure 4: The quantitative analysis of the manifold in the high-dimensional space. (A) The first five plots are visualizations of PGD attack trajectories of the CNN (Resnet50) trained with different defense methods, similar to Figure 2E but projected to a 3D space. The origin point of the plot is the original input image. Each axis is a direction chosen by LLE48 that can preserve distances within local neighborhoods… view at source ↗

**Figure 5.** Figure 5: The architecture and workflow of Shallow Retina Block. (A) Mathematical reconstruction of biophysical neurons in the G-filter to recurrent artificial neurons. (B) Expand the recurrent connection of the shallow retina block by time into layers. Each layer represents a timestep. (C) The entire end-to-end network architecture. The peak values of neurons in the shallow retina block are the input to the downstr… view at source ↗

**Figure 6.** Figure 6: The unique 2D decision boundary is gradually formed through the information integration of gap junctions. (A) We visualized the evolution of decision boundaries from two SRBlocks with the maximal gap junction conductance of 5 nS and 0.5 nS at different time steps. (B) Plots of gravity index (top row) and dispersion index (bottom row) of the decision boundaries of two SRBlocks with the maximal gap junction … view at source ↗

read the original abstract

Deep Neural Networks (DNNs) are vulnerable to elaborately designed adversarial noise, although they have achieved extraordinary success in many tasks. Compared with DNNs, the human visual system is highly robust. However, it is unclear how the human visual system defends against adversarial attacks, especially the role of the early visual system and its influence on the brain manifold. Due to retina gap junctions being crucial for the denoising function in the early visual system, we combine a retina gap junction-based filter, G-filter, with DNN as an abstract human visual system model called the biological hybrid model. We adopt this model to study the defense performance of retina gap junctions and their impact on the brain manifold. Compared with other defense methods, the biological hybrid model is more robust and can be further improved by introducing noise during training. Next, we analyze the manifold and its decision boundary of the biological hybrid model from a geometry perspective. The results show that the biological hybrid model has a unique 2D decision boundary with high nonlinearity and a lower curvature of the decision boundary of the manifold compared to other defense methods. The transforming manifold may account for the high robustness of the biological hybrid model. Finally, to dissect G-filter and clarify its internal mechanism, we borrow the Neural Ordinary Differential Equation (ODE) concept and rewrite G-filter into an equivalent recurrent neural network. The results show that the decision boundary of the model's manifold will gradually change with time and eventually reach a steady state, which is modulated by gap junction conductance, revealing the influence of retina gap junctions on the brain manifold is a gradually evolving process.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adds a gap-junction filter to DNNs, reports better adversarial robustness, and ties it to lower manifold curvature via an ODE rewrite, but the geometry-robustness link stays observational.

read the letter

The main takeaway is that prepending a simple gap-junction filter to a DNN produces a hybrid model that the authors say is more robust to adversarial attacks than standard defenses, with the gain linked to a lower-curvature, highly nonlinear decision boundary on the manifold. They also rewrite the filter as a Neural ODE to show the boundary evolving to a conductance-dependent steady state. That modeling step is the clearest addition here. The biological starting point is reasonable—retinal gap junctions do perform local denoising—and turning that into a front-end filter plus a geometric analysis gives a concrete example that is not just another generic defense trick. The ODE rewrite is useful because it makes the time-dependent effect explicit and connects back to the conductance parameter. Those pieces are done cleanly enough to be worth noting. The soft spots sit in the causal story and the missing numbers. The abstract claims the manifold changes account for the robustness, yet the comparison across models is observational; nothing isolates whether the curvature reduction itself drives the gain or whether any denoising front-end would produce similar results. No quantitative robustness deltas, curvature values, or error bars appear in what we have, so the size and reliability of the effect cannot be judged yet. The stress-test note is accurate on this point. If the full paper supplies proper ablations, statistical controls, and independent tests that the geometry is doing the work, the claim strengthens; without them the central argument remains correlational. This is for people working on biologically motivated robustness or manifold geometry in vision models. A reader already thinking about early visual system mechanisms or ODE-style dynamics would find the specific construction and the time-evolution analysis useful to discuss. It deserves peer review because the modeling idea is substantive and the geometric framing is worth testing properly, even if the current evidence needs tightening on causality and quantification.

Referee Report

3 major / 1 minor

Summary. The paper proposes a biological hybrid model combining a retina gap junction-based G-filter with DNNs as an abstract model of the human visual system. It claims this hybrid is more robust to adversarial attacks than other defenses (and can be further improved by noise-augmented training), exhibits a unique 2D nonlinear decision boundary with lower curvature, and that rewriting the G-filter as a Neural-ODE RNN reveals a time-evolving manifold that converges to a conductance-dependent steady state, suggesting the transforming geometry accounts for the robustness.

Significance. If the geometric properties are shown to be causal rather than merely correlated with robustness, the work could link early visual biology to adversarial robustness and offer a mechanistic account of how gap junctions shape representational manifolds. The Neural-ODE reformulation is a useful modeling device for dissecting the filter, but the absence of quantitative metrics and causal interventions limits the immediate impact.

major comments (3)

[Abstract / Manifold analysis] Abstract and results on manifold analysis: the central claim that the hybrid model possesses a unique 2D decision boundary with lower curvature that accounts for robustness is presented without any numerical values, error bars, statistical tests, or baseline comparisons, preventing assessment of whether the reported geometric differences are reliable or load-bearing.
[Results on robustness and geometry] Results on robustness and geometry: the paper reports correlations between manifold curvature/nonlinearity and robustness gains across models, yet provides no ablation, intervention, or counterfactual test (e.g., fixing the denoising operation while altering geometry) that would establish whether the measured geometric features causally drive the robustness improvement rather than being a side-effect.
[Neural-ODE rewriting] Neural-ODE rewriting section: while the reformulation of the G-filter as an equivalent RNN is technically interesting, the manuscript does not supply an independent falsification experiment that would distinguish the geometric explanation from simpler accounts based on the denoising computation itself.

minor comments (1)

[Abstract / Methods] The abstract and methods would benefit from explicit statements of the exact network architectures, training hyperparameters, and the precise definition of the 2D decision boundary used for curvature calculations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive comments, which highlight important opportunities to strengthen the quantitative and causal aspects of our claims. We agree that adding numerical metrics, statistical tests, and targeted interventions will improve the manuscript's rigor. We outline our responses and planned revisions below.

read point-by-point responses

Referee: [Abstract / Manifold analysis] Abstract and results on manifold analysis: the central claim that the hybrid model possesses a unique 2D decision boundary with lower curvature that accounts for robustness is presented without any numerical values, error bars, statistical tests, or baseline comparisons, preventing assessment of whether the reported geometric differences are reliable or load-bearing.

Authors: We agree that the manifold analysis section would benefit from explicit quantitative support. In the revision we will report mean curvature and nonlinearity values (with standard deviations across 5 independent runs), include error bars on all relevant figures, and add statistical comparisons (paired t-tests and effect sizes) against the baseline defense methods. These numbers and tests will be inserted into both the abstract and the results text to allow direct evaluation of the geometric differences. revision: yes
Referee: [Results on robustness and geometry] Results on robustness and geometry: the paper reports correlations between manifold curvature/nonlinearity and robustness gains across models, yet provides no ablation, intervention, or counterfactual test (e.g., fixing the denoising operation while altering geometry) that would establish whether the measured geometric features causally drive the robustness improvement rather than being a side-effect.

Authors: We acknowledge that the current evidence is correlational. To establish causality we will add two new experiments: (1) an ablation in which gap-junction conductance is varied while the denoising kernel is held fixed, and (2) a counterfactual comparison that applies the same denoising operation but with geometry-altering perturbations (e.g., post-hoc manifold smoothing). Robustness will be re-measured under these controlled conditions and reported with the same metrics used for the main results. revision: yes
Referee: [Neural-ODE rewriting] Neural-ODE rewriting section: while the reformulation of the G-filter as an equivalent RNN is technically interesting, the manuscript does not supply an independent falsification experiment that would distinguish the geometric explanation from simpler accounts based on the denoising computation itself.

Authors: We agree that an independent test is required. In the revision we will introduce a static steady-state control: the G-filter is replaced by its converged conductance-dependent equilibrium applied once, removing the temporal evolution while preserving the denoising effect. Adversarial robustness and manifold geometry will be compared between the full time-evolving model and this static control; any additional gains attributable to the dynamics will be quantified and discussed. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper constructs a hybrid model by combining an externally motivated G-filter (based on retinal gap junctions) with DNNs, then performs empirical robustness comparisons and geometric measurements of the resulting manifold and decision boundary. The Neural-ODE rewriting is presented as an interpretive tool borrowed from existing literature to analyze dynamics, not as a derivation that reduces the claimed robustness or manifold transformation back to the model inputs by construction. No load-bearing step equates a prediction to a fitted parameter, invokes a self-citation uniqueness theorem, or renames a known result as novel unification. The geometric account is offered as a possible explanation supported by observed correlations, without circular reduction to the input definitions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on the assumption that gap junctions act primarily as a denoising filter whose effect can be captured by a simple convolutional or recurrent module. No free parameters are explicitly listed in the abstract, but the gap-junction conductance is described as a modulator, implying at least one tunable scalar.

free parameters (1)

gap junction conductance
Described as modulating the steady-state manifold; its value is not derived from first principles and must be chosen or fitted.

axioms (1)

domain assumption Retina gap junctions perform a denoising function that can be abstracted into a filter G-filter.
Stated in the opening sentence of the abstract as the biological premise for the model.

pith-pipeline@v0.9.0 · 5598 in / 1452 out tokens · 30735 ms · 2026-05-13T18:23:10.908866+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We rewrite G-filter into an equivalent recurrent neural network... decision boundary... gradually change with time and eventually reach a steady state, modulated by gap junction conductance
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

biological hybrid model has a unique 2D decision boundary with high nonlinearity and a lower curvature of the decision boundary of the manifold

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

[1]

ShallowRetinaBlock (SRBlock)

Introduction A fundamental question in systems neuroscience is how different sensory processing stages are orchestrated to produce robust perceptual behaviors. As the first stage of visual processing, the retina is an essential part of the biological visual system. The retina has been shown to contain rich circuit structures and perform complex visual com...

work page
[2]

Results Figure 1: Retina gap junctions support the robust perception by warping the manifold along the visual hierarchy. (A) The artificial neural network is significantly less robust against adversarial noise than the human visual system due to the neglect of the retina in the deep neural network architecture. (B-C) This work adopts a G-filter derived fr...

work page
[3]

VOneNets

Discussion In this work, we combine retina gap junction- based G -filters with several classical machine learning architectures to slightly mimic the human visual system, called the biological hybrid model, and evaluate the impact of retina gap junctions on the robustness to adversarial attacks. G -filter significantly improves the neural network's defens...

work page
[4]

Methods Gap junction Filter (G-filter) Based on retina gap junction network, we have developed a G-filter for facilitating blind denoising and classification in the visual hierarchy in our previous work23. The G-filter only keep passive leak channel and gap junction connections, which can be described as the follows: 𝐶𝐶𝑚𝑚 𝑑𝑑𝑣𝑣𝑚𝑚 𝑑𝑑𝑑𝑑= −𝑔𝑔𝑙𝑙𝑙𝑙𝑔𝑔𝑙𝑙(𝑣𝑣𝑚𝑚− 𝑒𝑒...

work page
[5]

self-to-self weight 𝑊𝑊𝑙𝑙, which can be denoted as: 𝑊𝑊𝑙𝑙 = 𝐺𝐺𝑙𝑙I where I is the identity matrix and 𝐺𝐺𝑙𝑙= −1.4𝑒𝑒−9

work page
[6]

self-to-neighbor weight 𝑊𝑊𝛼𝛼. Here we adopt a hyper -parameter λ to describe the connection strength, then 𝑊𝑊𝛼𝛼 can be denoted as: 𝑊𝑊𝛼𝛼 = 𝜆𝜆 (𝑊𝑊𝐴𝐴− 𝑊𝑊𝐷𝐷) where 𝑊𝑊𝐴𝐴 denotes the adjacency matrix of RNN, and 𝑊𝑊𝐷𝐷 denotes a diagonal matrix, whose main diagonal element in each position is the number of neighbor neuron in this position. According to Eq. 3, at ...

work page doi:10.1101/2020.06.16.154542 2016

[1] [1]

ShallowRetinaBlock (SRBlock)

Introduction A fundamental question in systems neuroscience is how different sensory processing stages are orchestrated to produce robust perceptual behaviors. As the first stage of visual processing, the retina is an essential part of the biological visual system. The retina has been shown to contain rich circuit structures and perform complex visual com...

work page

[2] [2]

Results Figure 1: Retina gap junctions support the robust perception by warping the manifold along the visual hierarchy. (A) The artificial neural network is significantly less robust against adversarial noise than the human visual system due to the neglect of the retina in the deep neural network architecture. (B-C) This work adopts a G-filter derived fr...

work page

[3] [3]

VOneNets

Discussion In this work, we combine retina gap junction- based G -filters with several classical machine learning architectures to slightly mimic the human visual system, called the biological hybrid model, and evaluate the impact of retina gap junctions on the robustness to adversarial attacks. G -filter significantly improves the neural network's defens...

work page

[4] [4]

Methods Gap junction Filter (G-filter) Based on retina gap junction network, we have developed a G-filter for facilitating blind denoising and classification in the visual hierarchy in our previous work23. The G-filter only keep passive leak channel and gap junction connections, which can be described as the follows: 𝐶𝐶𝑚𝑚 𝑑𝑑𝑣𝑣𝑚𝑚 𝑑𝑑𝑑𝑑= −𝑔𝑔𝑙𝑙𝑙𝑙𝑔𝑔𝑙𝑙(𝑣𝑣𝑚𝑚− 𝑒𝑒...

work page

[5] [5]

self-to-self weight 𝑊𝑊𝑙𝑙, which can be denoted as: 𝑊𝑊𝑙𝑙 = 𝐺𝐺𝑙𝑙I where I is the identity matrix and 𝐺𝐺𝑙𝑙= −1.4𝑒𝑒−9

work page

[6] [6]

self-to-neighbor weight 𝑊𝑊𝛼𝛼. Here we adopt a hyper -parameter λ to describe the connection strength, then 𝑊𝑊𝛼𝛼 can be denoted as: 𝑊𝑊𝛼𝛼 = 𝜆𝜆 (𝑊𝑊𝐴𝐴− 𝑊𝑊𝐷𝐷) where 𝑊𝑊𝐴𝐴 denotes the adjacency matrix of RNN, and 𝑊𝑊𝐷𝐷 denotes a diagonal matrix, whose main diagonal element in each position is the number of neighbor neuron in this position. According to Eq. 3, at ...

work page doi:10.1101/2020.06.16.154542 2016