We sincerely thank the reviewer for the valuable comments. In response to the concerns raised, we provide the following detailed replies and additional experiments:

Weakness 1: Insufficient analysis of computational overhead analysis comparing D-RF to conventional spiking neurons.

We compared the computational complexity of the D-RF neuron and the LIF neuron.

Dynamics of the LIF Neuron:

$H[t] = \tau U[t-1] + \frac{1}{\tau} (I[t] - (U[t-1] - V_reset)),$

$S[t] = \Theta(U[t] - V_{th}),$

$U[t] = H[t] (1 - S[t]) + V_reset S[t],$

where $I[t]$ denotes the input current, $V_{\text{reset}}[t]$ represents the reset membrane potential, and $\tau$ is the time constant. For a sequence of length $T$, the computational complexity of the LIF neuron is $\mathcal{O}(T)$.

Dynamics of the D-RF Neuron:

$\mathcal{Z}[t] = \exp \{\delta \mathcal{D}\} Z[t-1] + \Gamma^l \mathcal{I}[t], \quad \mathcal{D} \in \mathbb{C}^{N\times N}, \Gamma^l \in \mathbb{R},^N$

$\mathcal{S}[t] = \Theta (\mathcal{C} \Re \{ Z[t]\} - \sum_{k=1}^T \alpha_k \Theta \left(\Re\{\mathcal{Z}[t-k-1]\} - V_{pre}) - V_{pre}\right), \quad \mathcal{C} \in \mathbb{R}^N,$

$N$ denotes the number of dendritic branches. Therefore, the computational complexity of the D-RF neuron is $\mathcal{O}(NT)$.

Weakness 2 and Question 2: The impact of D-RF's complex number operations on neuromorphic chip deployment remains inadequately discussed by the authors.

As you per, D-RF model introduces additional complex-valued computations. It is worth noting that modern neuromorphic chips already support such operations, such as Loihi2 [1]. This provides hardware-level support for the deployment of the D-RF model.

[1] Efficient neuromorphic signal processing with loihi 2[C]. SiPS 2021.

Weakness 3: The selection of dendritic branch number lacks systematic analysis of the performance-complexity trade-off.

To further address your concern, we conducted ablation experiment on the S-CIFAR10 dataset:

The model reaches 84.3% accuracy at $n=4$, with only 3K more parameters than $n=2$ and a 2.2% accuracy gain. Increasing to $n=8$ brings just a 0.3% improvement over $n=4$. Thus, $n=4$ offers the best trade-off between performance and complexity on the S-CIFAR10 tasks.

Question 1: Does introducing a multi-dendritic structure into LIF neurons enhance their temporal modeling capabilities? The authors are required to conduct experiments to verify this.

As you noted, multi-dendrite modeling significantly enhances the temporal processing capability of neurons. To assess this effect, we replace the D-RF neuron with the LIF neuron and evaluate performance on the S-CIFAR10 task:

Experimental results show that incorporating a multi-dendrite structure significantly improves the modeling capability of the LIF neuron. Based on this, the D-RF neuron achieves an additional 16.2% performance gain, further highlighting the advantage of RF neurons in temporal processing tasks.

Question 3: How to train the RF neuron-based neural networks? The authors should clarify this question.

In this work, we adapt the STBP training method [2] to effectively address the issue of non-differentiable gradients. The weight gradient is defined as follows: $\frac{\partial L}{\partial W } = \sum_t \frac{\partial L}{\partial S[t]} \frac{\partial S[t]}{\partial V[t]} \frac{\partial V[t]}{\partial W},$ $\frac{\partial S[t]}{\partial V[t]}$ denotes the surrogate gradient of the Heaviside function. In this work, we use the arctangent function [3] as the surrogate gradient. $\frac{\partial S[t]}{\partial V[t]} = \frac{\alpha}{2(1+(\frac{\pi}{2}\alpha x)^2))}.$

[2] Spatio-temporal backpropagation for training high-performance spiking neural networks[J]. Frontiers in neuroscience, 2018.

[3] Temporal efficient training of spiking neural network via gradient re-weighting[C]. ICLR, 2022.

Weakness 1: The modifications to RF are in the spirit of functions that are known to work well on LIF neurons, so the novelty could be dismissed as obvious.

The proposed adaptive threshold mechanism fundamentally differs from spike frequency adaptation [1–2] in both implementation and computational complexity, despite their conceptual similarity.

Implementation-wise: The adaptive threshold mechanism employs causal convolution to efficiently integrate historical spikes during inference, whereas spike frequency adaptation relies on a sequential adjustment strategy, which limits its ability to parallelize.

Computational Complexity: The adaptive threshold mechanism achieves $\mathcal{O}(L \log L)$ complexity during training, significantly more efficient than the $\mathcal{O}(L^2)$ complexity of spike frequency adaptation.

Experimental results demonstrate that for sequences of length 4096, the adaptive threshold mechanism yields a 148× improvement in training efficiency over traditional approaches.

[1] Spike frequency adaptation: bridging neural models and neuromorphic applications[J]. Communications Engineering, 2024.

[2] Advancing spatio-temporal processing through adaptation in spiking neural networks[J]. Nature Communications, 2025

Weakness 2: The datasets used are not especially "long" when compared to the things that are used for LLMs nowadays. The LLM state of the art is well advanced whereas this is much more speculative.

As you per, current ANN-based LLMs are capable of processing sequences ranging from 16K to 1M tokens [3–4]. However, such performance gains largely rely on complex architectural designs and large parameter scales, leading to significant computational overhead. We solve the problem from the perspective of neural dynamics, with the goal of enhancing memory and temporal processing at the neuron level. This enhancement is intended to enable a better trade-off between energy efficiency and performance, particularly under smaller model scales.

D-RF model provides a viable component for building low-power SNN-based LLMs. Future work will further investigate its modeling capability on large-scale language tasks.

[3] GPT-4 Technical Report. OpenAI, 2023.

[4] Qwen2.5 Technical Report. Qwen, 2024.

Weakness 3 & Question 1: One assumes (perhaps wrongly) that the original RF neuron was based on observation of biology. To what extent do the proposed modifications retain (or not) that biological plausibility?

The proposed D-RF neuron is inspired by two key neurobiological observations: the Multi-dendritic Structure of cortical neurons and their inherent Resonance Characteristics.

Multi-dendritic Structure: Neuroscientific research shown that cortical neurons are primarily composed of dendritic cells, accounting for approximately 80% of all neurons, and their complex dendritic arborizations play a crucial role in information processing [5–6].

Resonance Characteristics: Biological studies demonstrate that resonance is an intrinsic property of neurons, characterized by subthreshold membrane potential oscillations that enable selective responses to inputs at specific frequencies [7–8].

Design of D-RF Neuron: The D-RF neuron serves as a computational abstraction of these two biological mechanisms, aiming to maintain biological plausibility while enhancing computational efficiency. Each dendrite is modeled as a damped oscillatory dynamic, enabling efficient extraction of frequency-specific features. Additionally, the multi-dendrite and soma architecture mimics the parallel processing ability of biological neurons, allowing the model to capture multi-band information from input signals. This design achieves a favorable trade-off between biological fidelity and computational simplicity, supporting scalable deployment in large-scale neural networks.

[5] Pyramidal cell types drive functionally distinct cortical activity patterns during decision-making[J]. Nature neuroscience, 2023.

[6] Brain-wide presynaptic networks of functionally distinct cortical neurons[J]. Nature, 2025.

[7] Oscillations emerging from noise-driven steady state in networks with electrical synapses and subthreshold resonance[J]. Nature communications, 2014

[8] Resonance with subthreshold oscillatory drive organizes activity and optimizes learning in neural networks[J]. PNAS, 2023.

Question 2: How does the sequence length compare with current long NLP baselines? Speech input (at ~100 Hz sample rate) or repeated sampling of static examples surely represent long inputs, but how long is long?

Compare with long NLP baseline: We surveyed commonly used text benchmarks, including GLUE, WikiText-103, and WikiText-2. A summary is provided in the table below:

Therefore, the sequence length used in this work is comparable to that of existing NLP benchmarks, indicating its potential for effective language modeling.

how long is long: Due to the inherent training challenges of SNNs—such as gradient approximation and the instability introduced by BPTT—most existing models adopt 4 to 8 timesteps to maintain a balance between performance and training stability. Within this constraint, tasks like S/PS-MNIST (784 steps) and S-CIFAR10 (1024 steps) are commonly regarded as long-sequence benchmarks. In this context, the proposed D-RF model further demonstrates its capability to model extended sequences, achieving effective performance on the LRA benchmark with 1K–4K time steps.

Paper Formatting Concerns

Thank you for the correction. Reference [23] will be revised accordingly.

[23] Higuchi S, Kairat S, Bohté S M, et al. Balanced resonate-and-fire neurons[C]//Proceedings of the 41st International Conference on Machine Learning. 2024: 18305-18323.

Thank you for your valuable suggestion. To address your concern, we have conducted additional experiments.

W1: PathX is missing from the LRA Benchmark

Some existing SNN-based sequence models, such as Spiking LMUFormer [1] and PRF [2], encounter training difficulties or fail to converge on the Path-X task. To ensure a fair comparison, we only report results on the commonly tasks. Nevertheless, to address your concern, we conduct additional evaluations on the Path-X task:

[1] Lmuformer: Low complexity yet powerful spiking model with legendre memory units[C]. ICLR 2024.

[2] PRF: Parallel Resonate and Fire Neuron for Long Sequence Learning in Spiking Neural Networks.

[3] Learning long sequences in spiking neural networks[J]. Scientific Reports, 2024.

W2: The eigen-frequencies of the dendrites are fixed to the freq. bins of the input FFTs; in other words, depends on the discrete time delta. Would be interesting if these frequencies could be learned as well.

It is important to clarify that both the frequency bands and discrete time parameters of the D-RF neuron are learnable. Specifically, for the D-RF neuron:

$\mathcal{Z}[t] = \exp \{\delta \mathcal{D}\} Z[t-1] + \Gamma^l \mathcal{I}[t], \quad \mathcal{D} \in \mathbb{C}^{N\times N}, \Gamma^l \in \mathbb{R}^N,$

$\mathcal{S}[t] = \Theta (\mathcal{C} \Re \{ Z[t]\} - \sum_{k=1}^T \alpha_k \Theta \left(\Re\{\mathcal{Z}[t-k-1]\} - V_{pre}) - V_{pre}\right), \quad \mathcal{C} \in \mathbb{R}^N,$ where $\delta$ and $\mathcal{D}$ are learnable parameters, enabling the D-RF neuron to more effectively capture information from the input signal.

W3: Neither hyperparameters nor the architecture of the models trained are mentioned in detail on the appendix or in the supplementary material; especially for S/PS-MNIST and SHD.

We adopt a residual block-based network architecture, where each block consists of: "D-RF Module – 1×1 Convolution – Spiking Neuron – 1×1 Convolution." The detailed configurations for each task are as follows:

W4: (maybe too small a point to mention) Inconsistent number of parameters for S-CIFAR10 on Tables 7 and 8.

Thank you for your correction. After recalculation, the parameter count for the S-CIFAR10 task is 216K. We will further revise the manuscript accordingly.

Q1: How does the summation of dendritic signals at the soma contribute to frequency selectivity, given that the signals are merged before thresholding? How are multiple selected frequencies still reflected in the output spikes?

For the D-RF neuron, its dynamics can be expressed as follows:

$\mathcal{Z}[t] = \exp \{\delta \mathcal{D}\} Z[t-1] + \Gamma^l \mathcal{I}[t], \quad \mathcal{D} \in \mathbb{C}^{N\times N}, \Gamma^l \in \mathbb{R}^N,$ $\mathcal{S}[t] = \Theta (\mathcal{C} \Re \{ Z[t]\} - \sum_{k=1}^T \alpha_k \Theta \left(\Re\{\mathcal{Z}[t-k-1]\} - V_{pre}) - V_{pre}\right), \quad \mathcal{C} \in \mathbb{R}^N.$ The learnable dendritic parameters $\mathcal{D}$ and $\delta$ determine the neuron's response to specific frequency bands, enabling frequency-selective filtering. The parameter $\mathcal{C}$ adjusts the relative weighting of each frequency band. The soma integrates the weighted dendritic inputs and generates sparse spikes through an adaptive threshold mechanism. During training, all parameters are optimized via gradient-based methods to achieve task-specific frequency selection.

Question 2: What are the frequency initialization for the 8 dendrites that are shown in Figure 4 (c)? How is it possible to obtain enough information about the input signal with only 4-8 eigen-frequencies?

The eight dendrites are initialized using a linear distribution. For the $k$-th input, the initial frequency is defined as follows:

Thank you for your clarifications, they address most of my questions and concerns. However, I feel that Question 2 has not been fully answered on a theoretical level, though I appreciate the empirical results. Overall, I still consider the paper a valid contribution. That said, I increasingly feel that, methodologically, it represents only a modest increment over the PRF work. The main difference appears to be the structural composition that merges RF and ALIF units.

Thank you very much for your valuable comments. We will further clarify and supplement the explanation to address your concerns.

W1: The Computational Overhead of D-RF Neuron.

Answer: As you per, D-RF neuron exhibits more complex dynamics, which significantly enhance the temporal processing capability of SNNs. On the S-CIFAR10 dataset, our method achieves an accuracy of 84.3%, representing a 39.23% improvement over the 45.07% achieved by the LIF neuron. Notably, current neuromorphic chips such as Loihi2 [1] supports complex-valued computations.

W2 & Q1: Evaluation on Speech and Neuromorphic Datasets.

Answer: To evaluate the generalizability of the proposed method, we further conducted experiments on the Speech Dataset (GSC) and the neuromorphic dataset (CIFAR10-DVS). The results are presented as follows:

Q2: Algorithmic of D-RF Neuron.

To facilitate understanding and reproducibility, we provide both the parallel training and serial inference algorithms of the D-RF neuron.

Q3: Analysis of Model Complexity and Performance.

To further justify the choice of dendritic branch number, we analyze both the computational complexity and model size of the D-RF neuron. Computational Complexity: Dynamics of the D-RF neuron is as follows:

$\mathcal{Z}[t] = \exp \{\delta \mathcal{D}\} Z[t-1] + \Gamma^l \mathcal{I}[t], \quad \mathcal{D} \in \mathbb{C}^{N\times N}, \Gamma^l \in \mathbb{R}^N,$ $\mathcal{S}[t] = \Theta (\mathcal{C} \Re \{ Z[t]\} - \sum_{k=1}^T \alpha_k \Theta \left(\Re\{\mathcal{Z}[t-k-1]\} - V_{pre}) - V_{pre}\right), \quad \mathcal{C} \in \mathbb{R}^N.$

Therefore, the computational complexity of the D-RF neuron is $\mathcal{O}(NL)$, where $N$ denotes the number of dendrites and $L$ is the sequence length. The complexity increases linearly with the number of dendrites.

Model Size: We evaluated the model’s accuracy on the S-CIFAR10 task under different numbers of dendrites.

As shown in the table, the D-RF model achieves an accuracy of 84.3% with 216K parameters when the number of dendrites is set to 4. Compared to $n=1$, this setting adds only 3K parameters while providing a 2.2% improvement in accuracy. In contrast, increasing to $n=8$ yields only a 0.3% gain in energy efficiency. Therefore, we choose $n=4$ as the optimal dendrite number for the S-CIFAR10 task, offering the best trade-off between model complexity and accuracy.