A Chaotic Dynamics Framework Inspired by Dorsal Stream for Event Signal Processing

We sincerely appreciate your thorough evaluation and valuable feedback on our paper. We are pleased that our chaotic dynamical framework and experimental results have been recognized, and we are grateful for the insightful questions that have helped us further improve the paper. In response to your comments, we have made the necessary revisions, and we believe these improvements will enhance the quality and impact of our work. Below, we address each of your comments in detail, providing clarifications and additional analyses where necessary.

A1: Thank you for the reminder. The annotations in Figure 1(a) highlight the superiority of the event representation generated by our framework. While the pyramid in the original image shows numbers 1-6, our framework clearly restores their contours, unlike event representations from end-to-end networks, which fail to preserve these details.

A2: The chaotic dynamic framework proposed in this paper includes CCNN, CWT, and LPF. CCNN is a network inspired by the primary visual cortex (V1) of the brain. After the event signals are processed by CCNN, they are further analyzed and extracted using CWT and LPF for dynamic object detection, which corresponds to the brain's processing from V1 to MT.

A3: The unconnected CCNN comprises modulated input $U(k)$, continuous output $Y(k)$, and dynamic threshold $E(k)$. When $U(k)>E(k)$, the output is $Y(k) = \frac{1}{1+e^{-(U(k)-E(k))}}$, indicating excitation. After stimulation, $E(k)$ increases, requiring a stronger stimulus for the next output, mimicking the neuronal refractory period. Siegel observed chaotic behavior in the primary visual cortex of cats under periodic stimulation [1]. Similarly, CCNN exhibits periodic signals under constant stimulation and chaotic signals under periodic stimulation, adhering to this biological constraint.

[1] Siegel, R. M. Non-linear dynamical system theory and primary visual cortical processing. Physical D: Nonlinear Phenomena, 42(1-3):385–395, 1990.

A4: Thank you for your reminder. The testing has been conducted on a local workstation, and the experimental results demonstrate the model's potential for real-time applications. Future work will focus on further validation in real-world scenarios.

A5: Hyperparameters include batch size 16, cross-entropy loss, Adam (lr=1e-4), 40% Dropout before FC layers, and early stopping. A smaller batch size aids generalization, cross-entropy improves accuracy, Adam ensures stable convergence, and Dropout with early stopping prevents overfitting. The appendix and open-source code include the parameter settings, facilitating reviewers and readers in reproducing and improving this work.

A6: The model was tested on a workstation with an Intel Core i9 CPU, NVIDIA RTX 4060 GPU (8GB VRAM), and 16GB RAM. Training on a small dataset (N-Caltech101/N-CARS, ~50,000 samples) took 12-18 minutes, while a large dataset (N-MNIST/ASL-DVS, >200,000 samples) took 30-60 minutes. To optimize for resource-constrained environments, techniques like pruning, quantization, knowledge distillation, lightweight architectures, and mixed-precision training can be used to reduce computational demands and improve efficiency.

A7: The chaotic dynamic framework proposed in this paper processes event signals to obtain a general event representation, which can be extended to other tasks. We also plan to apply this event representation method to more event-based tasks in future work.

A8: Parameter count affects memory and training time but not inference speed. PointNet++ runs slower due to costly neighborhood queries, while dense CNNs benefit from optimized parallelism. Our method (21.9M params) achieves 2.1ms inference on an RTX4060 via a regularized convolutional design (MACs = 3.7G, 7.5% lower than PointNet++) and PyTorch + TensorRT optimizations.

A9: We propose a hybrid CCNN-SNN framework that replaces the ResNet-34 classifier with SNNs to reduce computational energy consumption. By integrating the STDP mechanism, this architecture achieves adaptive learning capabilities while enhancing biological plausibility and interpretability. Future investigations will prioritize systematic evaluation of its low-power computing performance and neuro-inspired operational principles.

A10: We acknowledge EvT's strengths in global spatiotemporal modeling but exclude it from comparisons due to its computational inefficiency with high-resolution event data. Our current focus on efficiency-generalization trade-offs motivates the proposed CCNN-Transformer hybrid architecture for enhanced event representation in complex scenarios.

A11: We have not yet conducted systematic small-sample learning experiments, but CCNN’s chaotic dynamics allow it to maintain good generalization with limited data. Future research will include small-sample experiments and explore combining CCNN with meta-learning to enhance adaptability in low-data scenarios.

We sincerely appreciate your thorough evaluation and valuable feedback on our manuscript. We are also grateful for the constructive suggestions, which have helped us further refine the theoretical derivations, experimental design, and analysis in our paper. In response to your comments, we have revised and supplemented our manuscript, including providing a more detailed description of the biological background, conducting a more rigorous dynamic characteristics analysis (such as Lyapunov exponent analysis), and offering further clarification on key equations and experimental parameters. We believe these improvements enhance the clarity, completeness, and impact of our work. Below, we provide detailed responses to each comment and explain the corresponding revisions.

W1: The author does not adequately describe the dynamic visual pathways of the real brain, which limits the reader's understanding of the paper. In the dynamic analysis section, the author only provides phase space plots and equilibrium point analysis, and lacks more rigorous analysis methods such as Lyapunov exponents.
A1: Thank you for your valuable feedback. We have supplemented the discussion on the dynamic visual pathways of the brain to enhance the understanding of the biological visual system. Additionally, we have incorporated discussions and calculations of the Lyapunov exponent to provide a rigorous mathematical analysis of the dynamic characteristics of CCNN neuron.

A1: The chaotic dynamic framework proposed in this paper includes CCNN, CWT, and LPF. The CCNN is a brain-inspired network based on the primary visual cortex V1. After processing the event signals with CCNN, CWT and LPF are applied for analysis and extraction, enabling the detection of dynamic objects. This process corresponds to the brain's processing from V1 to MT.

A2: In Equation (4), $U(k)$ represents the modulation input, $Y(k)$ is the continuous output, $E(k)$ is the dynamic threshold, and $e^{-\alpha_f}$, $e^{-\alpha_e }$ denote the exponential decay factors that record the previous input states. $V(e_k)$ represents the input event signal data.

A3: The polarity of the event signal is a Boolean value that can only be 0 or 1. Therefore, the output periodic signal generated by the event data through the CCNN is constant.

A4: Thank you for your valuable suggestions. We will remove the transient time periods in Figures 4(d) and (e), keeping only the steady-state behavior to display the dynamic characteristics.

A5: Thank you for your suggestion. This paper performs a Taylor expansion of $e^{-(U(k)-E(k))}$, retaining only the first two terms, where $x$ refers to $–(U(k)-E(k))$. We will revise the explanation in the paper accordingly.

A6: Thank you for your reminder. This is a detail expression error in the paper. It should be revised to 'In this case, $E(k)$ can be expressed as...'. The magnitude of $E(k)$ cannot be determined.

A7: To analyze the stability of the equilibrium point, we need to compute the Jacobian matrix of the equation $E(k)^2-(U(k)-2)E(k)-\frac{V_E}{1-e^{-\alpha_e }} =0$, that is, by differentiating $F(E):J=\frac{dF}{dE}=\frac{d}{dE}(E^2-(U(k)-2)E-\frac{V_E}{1-e^{-\alpha_e }})$. The derivative is $J=2E-(U(n)-2)$. The Jacobian matrix at the equilibrium point $E^\ast$ is:$J(E^\ast )=2E^\ast-(U(n)-2)$. When $E^\ast=\frac{U(k)-2-\sqrt{(U(k)-2)^2+4V_E (1-e^{-\alpha_e} )}}{2}, J(E^\ast)<0$, indicating that the equilibrium point is stable (attractive point); when $E^\ast=\frac{U(k)-2+\sqrt{(U(k)-2)^2+4V_E (1-e^{-\alpha_e} )}}{2}, J(E^\ast)>0$, indicating that the equilibrium point is unstable (possibly a saddle point).

A8: Parameters of the CCNN model: $\alpha_f = 0.1, \alpha_e = 1.00, V_e = 50, U(0) = 0, E(0) = 0, Y(0) = 0$. Parameters of the CWT: 'gaus1' is used as the base wavelet, with a scale range of 10. Training parameters: The data is split into training, validation, and test sets in a 3:1:1 ratio, with the random seed set to 2024. The model was trained for 5 epochs, with a batch size of 16. During optimization, the cross-entropy loss function was used, and the Adam optimizer was applied with an initial learning rate of 1e-4. To alleviate overfitting, a Dropout layer was added before the fully connected layers, and early stopping was incorporated during training.

A9: Let $F(x,y)$ be the generative function of the event representation. The input $S_{ij}$ is the sum of the real part of the coefficient matrix, corresponding to different types of event sequences. It is convolved with the low-pass filter $H(f)$, and the coordinate points corresponding to event sequences where $S_{ij} >0$ are assigned a value of 255, while others are assigned a value of 0, enabling the detection of moving objects.

we would like to express our sincere gratitude for your in-depth review of our paper and your valuable feedback. We greatly appreciate your recognition of the proposed method and experimental results, and we also thank you for raising some important questions that will help us further improve the quality of the paper. In response to your comments, we have made several revisions and additions to the manuscript, and we provide detailed answers to the concerns you raised below. We believe that, with your feedback, the paper will be further enhanced.

W1: The author did not explain some of the parameters in the brain-inspired model, especially certain setting parameters in the CCNN, which play an important role in understanding the brain's visual mechanisms.
A1: The unconnected CCNN comprises modulated input $U(k)$, continuous output $Y(k)$, and dynamic threshold $E(k)$. The terms $e^{-\alpha_f}$ and $e^{-\alpha_e}$ denote exponential decay factors that record the previous input states. $V_E$ is the weight factor for adjusting the neuronal potential. When $U(k)>E(k)$, the output is $Y(k) = \frac{1}{1+e^{-(U(k)-E(k))}}$, indicating excitation. After stimulation, $E(k)$ increases, requiring a stronger stimulus for the next output, mimicking the neuronal refractory period. Siegel observed chaotic behavior in the primary visual cortex of cats under periodic stimulation [1]. Similarly, CCNN exhibits periodic signals under constant stimulation and chaotic signals under periodic stimulation, adhering to this biological constraint.

[1] Siegel, R. M. Non-linear dynamical system theory and primary visual cortical processing. Physical D: Nonlinear Phenomena, 42(1-3):385–395, 1990.

C1: In Figure 4, the x-axis labels for subfigures (a), (b), and (c) should be corrected from ‘Iterations’ to ‘Iterations’. Additionally, in Table 3, the value in the second row, fifth column should be changed from ‘70000’ to ‘100000’.
A1: Thank you for your careful review. We have revised the x-axis labels in subfigures (a), (b), and (c) of Figure 4 as suggested and corrected the value in the second row, fifth column of Table 3 to ensure accuracy. These changes have been incorporated into the revised manuscript.

A1: Thank you for your reminder. In Equation (4), $U(k)$ represents the modulation input, $Y(k)$ is the continuous output, and $E(k)$ is the dynamic threshold. The terms $e^{-\alpha_f}$ and $e^{-\alpha_e}$ denote exponential decay factors that record the previous input states. $V_E$ is the weight factor for adjusting the neuronal potential.

A2: When the modulation input $U(k)$ exceeds the dynamic threshold $E(k)$, the output $Y(k)$ is given by $\frac{1}{1+e^-(U(k)-E(k))}$, which corresponds to the neuron generating an excitatory potential in response to sufficient stimulation. Upon the next stimulus, the dynamic threshold increases, and the model requires a stronger input to produce an output, mimicking the refractory period of biological neuronal cell membranes.

A3: In Equation (7), $k$ is a parameter that controls the input. When the event signal input follows the periodic sequence {0,1,0,1,$\cdots$,0,1}, its equivalent formula is $\sin(\frac{k\cdot \pi}{2})$, where $k$={0,1,2,$\cdots$, n}.

A4: Both $E(0)$ and $V_E$ can affect the period of the output signal. However, the setting of these parameters does not impact the results, as long as the CCNN output is a periodic signal when the input polarity of the event signal remains constant.

A5: Under the stimulation of periodic signals, the CCNN exhibits complex chaotic dynamic characteristics. This paper discusses its equilibrium state, where a balance point exists in the output, such that $E(k+1)=E(k)$.

A6: This section discusses the equilibrium point of the CCNN neuron. When $V_E >0$, $\alpha_e >0$, and $4\frac{V_E}{1-e^{-\alpha_e}}>0$, with $\Delta>0$, the equation has a solution, and an equilibrium point exists. This discussion does not affect the computational results.

A7: Gaussian wavelets are widely used in time-frequency analysis due to their smoothness and good time-frequency locality. They are well-suited for analyzing periodic and chaotic signals generated by CCNN neurons.

A8: The heatmap of the output sequence is a visualization of the sequence after CWT waveform analysis, showing the value distribution of the real part of the coefficient matrix. The sum of the real part of the coefficient matrix for chaotic sequences is an integer, while for periodic sequences, the sum is negative. A low-pass filter is then applied to extract the coordinate points of the periodic sequence.

A9: The Low-pass Filter is a module proposed in this paper's chaotic dynamic framework and is not directly related to the brain-like mechanism of the CCNN. It is used to extract the coordinate points corresponding to the constant polarity event sequences, enabling the detection of moving objects.

We sincerely appreciate your time and effort in reviewing our paper. We are grateful for your constructive feedback and insightful questions, which have helped us refine our work and clarify its contributions. We acknowledge your concerns regarding the theoretical foundations, biological plausibility, and certain experimental analyses, and we appreciate the opportunity to further elaborate on these aspects. In this response, we address each of your comments in detail, providing clarifications, additional discussions, and further justifications where necessary. We hope that our responses effectively resolve your concerns and further demonstrate the significance and robustness of our proposed framework.

A1: The CCNN simulates the encoding mechanism of primary visual cortex neurons. The proposed chaotic dynamics framework, consisting of three modules—CCNN, CWT, and LPF—mimics the dorsal stream's function in extracting dynamic object location information.
Experimental Evidence: Siegel observed complex electrical signal fluctuations in the primary visual cortex neurons of cats under periodic signal stimulation, revealing the presence of chaotic behavior in the mammalian primary visual cortex [1]. Building on this, Liu further modified the dynamic threshold adjustment mechanism of PCNN and proposed CCNN [2]. This model exhibits periodic signals under constant stimulation and chaotic signals under periodic stimulation, aligning with findings from biological experiments.

[1] Siegel, R. M. Non-linear dynamical system theory and primary visual cortical processing. Physical D: Nonlinear Phenomena, 42(1-3):385–395, 1990.

[2] Liu, J., Lian, J., Sprott, J. C., Liu, Q., and Ma, Y. The butterfly effect in primary visual cortex. IEEE Transactions on Computers, 71(11):2803–2815, 2022.

A2: The period $k$ has no physical relationship with the event stream (such as velocity or direction) and cannot be used to improve classification performance. The derived period $k$ is used to demonstrate that the CCNN generates periodic signal outputs when subjected to constant stimuli.

A3: The Gaussian wavelet is widely used in time-frequency analysis. Compared to the Morlet wavelet, it offers superior smoothness and better time-frequency localization, making it particularly suitable for analyzing periodic and chaotic signals generated by CCNN neurons.

A4: This design does not lead to information loss. Setting negative values to 255 is intended to extract the coordinates of event signal points with constant polarity, thereby detecting moving objects. A more refined threshold design will be presented in future papers.

A5: As event density increases, the proposed framework captures finer textures, improving IoU. While denser events enhance performance, the framework is not dependent on them. For sparse events, effective denoising and enhancement techniques may be needed to optimize IoU.

A6: Our model uses ResNet-34 with 21.9M parameters, more than EV-VGCNN (0.8M), but parameter count mainly affects memory usage and training time, not inference speed. The faster inference is due to: (1) Efficient 3×3 convolutions and residual connections optimizing computation flow; (2) GPU-optimized deep learning frameworks (cuDNN) accelerating ResNet inference; (3) Convolutional optimizations like Winograd transformations reducing computational complexity. In contrast, EV-VGCNN's fully connected layers may limit parallelism, leading to slower inference.

A7: The LIF method suppresses many event points due to an unreasonable threshold, leading to an incomplete event pattern. The Time Surface captures motion trajectories but introduces redundancy, affecting IoU detection. Event Count maps event accumulation to pixel values, causing inconsistencies that impact pattern integrity. This paper proposes a framework that converts events with constant and periodic polarity changes into periodic and chaotic signals via CCNN, then processes them using CWT and LPF. Event coordinates with constant polarity are set to 255 to extract valid event signals effectively.

A8: Dataset size and category count significantly impact classification performance. N-MNIST, N-CARS, and ASL-DVS, with fewer categories and high intra-class similarity, enable effective feature learning and high accuracy. In contrast, N-Caltech101's limited samples, diverse categories, and large intra-class variation increase training difficulty and lower accuracy. This study introduces a chaotic dynamic framework inspired by the dorsal visual pathway, generating robust event representations. Combined with lightweight ResNet34, it achieves high accuracy across all four datasets.

A9: The appendix and open-source code provide the full CCNN implementation, including network architecture and hyperparameters. This documentation enables readers to reproduce results with high confidence in their reproducibility.