HetSyn: Versatile Timescale Integration in Spiking Neural Networks via Heterogeneous Synapses
Authors: Zhichao Deng
Zhikun Liu
Junxue Wang
Shengqian Chen
Xiang Wei
Qiang Yu
Venue: NeurIPS 2025 poster ()
Keywords: Spiking Neural Networks
Synaptic Heterogeneity
Multi-Timescale Integration
Neuron Modeling
Primary area: neuroscience_and_cognitive_science
TL;DR: We propose a SNN modeling framework that incorporates synaptic heterogeneity, an essential property largely overlooked in previous studies, and demonstrate its computational advantages and generalizability.

Abstract: Spiking Neural Networks (SNNs) offer a biologically plausible and energy-efficient framework for temporal information processing. However, existing studies overlook a fundamental property widely observed in biological neurons—synaptic heterogeneity, which plays a crucial role in temporal processing and cognitive capabilities. To bridge this gap, we introduce HetSyn, a generalized framework that models synaptic heterogeneity with synapse-specific time constants. This design shifts temporal integration from the membrane potential to the synaptic current, enabling versatile timescale integration and allowing the model to capture diverse synaptic dynamics. We implement HetSyn as HetSynLIF, an extended form of the leaky integrate-and-fire (LIF) model equipped with synapse-specific decay dynamics. By adjusting the parameter configuration, HetSynLIF can be specialized into vanilla LIF neurons, neurons with threshold adaptation, and neuron-level heterogeneous models. We demonstrate that HetSynLIF not only improves the performance of SNNs across a variety of tasks—including pattern generation, delayed match-to-sample, speech recognition, and visual recognition—but also exhibits strong robustness to noise, enhanced working memory performance, efficiency under limited neuron resources, and generalization across timescales. In addition, analysis of the learned synaptic time constants reveals trends consistent with empirical observations in biological synapses. These findings underscore the significance of synaptic heterogeneity in enabling efficient neural computation, offering new insights into brain-inspired temporal modeling. Code available at: https://github.com/dzcgood/HetSyn.

HetSyn: Versatile Timescale Integration in Spiking Neural Networks via Heterogeneous Synapses
Zhichao Dengl.22 Zhikun Liu
Junxue Wang Shengqian Chen 1,2,, Xiang Wei Qiang Yu 'ccooo of Artificial Intelligence, CCA Lab, Tianjin University, Tianjin, China CCollege of Intelligence and Computing, Tianjin University, Tianjin, China School of Computer Science and Technology, Tianjin University, Tianjin, China {dengzhichao, 2k_1iu813, wangj unxue, yuqiang) @tju. edu. cn
Abstract
Spiking Neural Networks (SNNs) offer biologically plausible and energy-efficient framework for temporal information processing. However, existing studies over- look fundamental property widely observed biological neurons neurons-synaptie synaptic heterogeneity, which plays crucial role in temporal processing and cognitive capabilities. To bridge this gap, we introduce HetSyn, a generalized framework that models synaptic heterogeneity with synapse-speeific time constants. This design shifts temporal integration from the membrane potential to the synaptic current, enabling versatile timescale integration and allowing the model capture diverse synaptic dynamics. We implement HetSyn as HetSynLIF, an extended form the leaky integrate-and-fi fire (LIF) model equipped with synapse-specis decay dynamics. By adjusting the parameter configuration, HetSynL.IF can be specialized into vanilla LIF neurons, neurons with threshold adaptation, and neuron-level heterogeneous models. We demonstrate that HetSynL.IF not only improves the performance of SNNs across variety of tasks- tasks-including pattern generation, delayed match-to-sample, speech recognition, and visual recognition- also exhibits strong robustness noise, enhanced working memory performance, effi- ciency under limited neuron resources, and generalization across timescales. In addition, analysis of the learned synaptic time constants reveals trends consistent with empirical observations in biological synapses. These findings underscore the significance of synaptic heterogeneity enabling efficient neural computation, offering new insights into brain-inspired temporal modeling. Code available at: https:/ggghub..om/dggggoo//////
Introduction
Spiking Neural Networks (SNNs) have been widely studied as a promising and energy-efficient alternative to conventional artificial neural networks (ANNs), offering biologically plausible computing paradigm characterized by sparse, event-driven signaling and inherent capability for temporal processing [ 3 However, due to the complex dynamical characteristics of spiking neurons, effectively training SNNs and improving their performance remain major challenges in the field. This calls for new learning paradigms, either by adapting established methods from ANNs [4]
6. 8 9
10 or by drawing inspiration from biological mechanisms [I] 13
14 15 16].
While ANN-derived methods have led to notable progress, we instead focus on strengthening the biological foundations of SNNs by revisiting fundamental neurobiological mechanisms, which
"quual contribution.
CCorrepoondigg author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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remain underexplored and hold great potential for enabling more versatile timescale integration in spiking systems. This capability particularly important, effective timescale integration is central to temporal cognition, and many real-world tasks-such as working memory, speech neural systems to operate across multiple timescales [17] 18 20]. Achieving such multi-timescal, processing requires neural models to incorporate diverse temporal dynamics across different input pathways. To this end, various forms of temporal heterogeneity have been introduced in SNNs to enhance their capability to represent and integrate information across multiple time constants, such as ALIF (1)). PLIF [2T], neuron heterogeneity [22], and dendritic heterogeneity (3). Although these approaches provide valuable insights, they remain limited to the neuron level or sub-neuronal level, where temporal dynamics are uniformly applied across aggregated inputs. This restricts their ability to assign distinct temporal responses to different synaptic pathways, limiting performance on tasks with complex temporal structure.
recognition, and sequential pecision-making--eeeeee
In contrast, numerous neuroscience studies have shown that synapses vary substantially across brain regions and cell types [24, 225, giving rise to diverse temporal basis that supports multi-timescale integration and cognitive abilities 126 27 (see Fig. T B). This diversity, known as synaptic heterogeneity, constitutes fundamental biological principle that plays crucial role in shaping neural computation. Despite its biological significance, synaptic heterogeneity has rarely been incorporated into the design of spiking neural networks. Its computational potential remains largely unexplored, in part due to the challenges modeling fine-graine graggrrined synapse-specifee temporal dynamics.
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Figure 1: (A) Distributions of synaptic time constants (T₃) extracted from human (left, 194 pairs) and mouse (right, 1213 pairs) cortex, shown as histograms with overlaid KDE curves (green). The broad, long-tailed (7a 2 500 ms) profiles reflect substantial synaptic heterogeneity. (B) Postsynaptic membrane potential traces under different synaptic time constants (T, 20, 50 ms. from second to fourth row) in response to a regular spike train (first row). (C-D) Schematic of HetSyn, in which afferent spikes are integrated via synapses with heterogeneous decay dynamics.
To bridge this gap. take first step toward incorporating synaptic heterogeneity into SNNs and introduce HetSyn by focusing on one key aspect: the diversity of synaptic time constants, motivated by our analysis of the raw data from the Allen Institute's recently released Synaptic Physiology

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Dataset 28
which reveals that synaptic time constants follow nor-normal distribution across populations, providing direct empirical support for synapse-specific time constants (Fig. [A). As illustrated in Fig. [3, synapses with longer time constants are able to retain input-driven activity over extended periods, whereas those with smaller time constants respond more transiently and can effectively filter out noise irrelevant fluctuations. This functional diversity lays the foundation for versatile timescale integration, enabling neural models to process information across both long and short temporal windows.
Furthermore, instead of relying on a single membrane time constant, HetSyn computes the membrane potential by aggregating synaptic currents, each governed by synapse-specific decay factor. This synapse-driven formulation allows temporal integration arise from the diverse dynamics of individ- ual synapses, rather than being uniformly controlled at the neuron level (Fig. (F. D). We instantiate HetSyn as HetSynI.IF and demonstrate that it subsumes several representative spiking neuron models as special cases through parameter configuration (see Methods).
Our contributions are as follows:
We propose HetSyn, the first modeling framework to explicitly explore synaptic heterogene- ity in SNNs, offering a biologically plausible yet computationally powerful approach for versatile timescale integration.
We demonstrate that HetSyn serves unified and extensible framework, capable of representing wide range of existing spiking neuron models.
We instantiate HetSyn as HetSynLIF and demonstrate its effectiveness across multiple temporal tasks, with consistently strong performance. Notably, we achieve 92.36% accuracy on the SHD dataset, which is, to the best our knowledge, the best-reported accuracy among models with similar network structures.
2 Related Work
2.1 Training methods
There are two primary approaches for training SNNs: ANN-to-SNN conversion (ANN2SNN)
29
30 31 32 33 (4 and direct training using surrogate gradient methods [10 35 36
RSI 39 The ANN2SNN method first trains a conventional ANN and then maps its parameters to an SNN, where the firing rates of spiking neurons used to approximate the continuous activations of the original ANN. However, it often suffers from accuracy degradation due to the approximation process. In comparison, surrogate gradient methods approximate the non-differentiable spiking function with a surrogate, thus enabling direct end-to-end training of SNNs via backpropagation through time (BPTT). This approach forms the basis of modern surrogate- turoogate-rradiett based training frameworks for SNNs, such as centool Backpropagation (STBP) (35) and Slayer [36]. In this paper, we adopt the surrogate gradient method to enable efficient training of the HetSynI.IF model.
37
2.2 Heterogeneity in SNNs
Recent studies have highlighted the significance of heterogeneity in SNNs, exploring its impact on network performance and temporal processing from various perspectives. For instance, neuron-level heterogeneity has been shown to enhance the stability and noise robustness of SNNs. Perez-Nieves al. (22 show that networks with membrane time constants drawn from Gamma distribution better capture complex temporal patterns, outperforming homogeneous networks in tasks with rich temporal structure. In addition, PLIF [21] learns a shared membrane time constant for each layer, which can be interpreted as introducing heterogeneity at a coarser granularity. Another source of heterogeneity arises from the spiking history of a neuron [1]. Firing thresholds that evolve over time based on recent spiking activity introduce form of adaptive, history-dependent threshold heterogeneity. Furthermore, heterogeneity has also been explored at the level of neural dynamics and plasticity mechanisms. Chakraborty et al. [40] investigate the effects of heterogeneity in LIF and wrike-tining-deeeddenn plasticity (STDP) parameters. Additionally, the temporal heterogeneity of dendritic branches 23 has been integrated into SNNs. While considerable work has explored heterogeneity in SNNs, synapse-level heterogeneity remains largely underexplored. In contrast, our HetSyn introduces synapse-specific decay factors, embedding heterogeneity directly at the synaptic
3

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level. This fine-gn tine-grained design enables HetSyn to integrate temporal information over broader range of timescales, thereby enhancing both computational flexibility and biological plausibility.
Methods
3.1 Vanilla LIF
Spiking neurons are the fundamental computational units in SNNs, enabling the modeling of temporal dynamics through biologically inspired mechanisms. Among various neuron models, the LIF neuron one the most widely adopted for its balance between computational efficiency and biological plausibility. It captures essential neuronal properties such as membrane potential leakage, input integration, and spike emission. The dynamics of the LIFF neuron can formulated as follows:
dV dt
=
V rest
Σ 1
w; . (t (t-
Σ (t-
(1)
Tm
where is the membrane potential, Vrest is the resting potential, and 7m represents the membrane time constant. of and i denote the timing of the j-th input spike from the i-th presynaptic neuron and the j-th output spike from the postsynaptic neuron, respectively. The term wy denotes the synaptic efficacy of the i-th afferent, / denotes the firing threshold and 6(-) represents the Dirac delta function. We set Veest 0 in this paper, and an equivalent continuous-time solution to Eq. ① is then given by:
V
Σ Wt Σ
(t-
0 Σ (t 12)
where V is the membrane potential at time t. The term &
- = exp(- t for to > t2. is the
synaptic kernel induced by the j-th spike of the i-th afferent. It describes the resulting postsynaptic potential (PSP), which decays exponentially at rate governed by the membrane time constant Tm. In practice, simulations typically adopt a discrete-time formulation, which is given by:
V = Vt-L 1 + Σ Wi 2
- -
(3)
z' = H(H 0)
(4)
where exp( At) denotes the membrane decay factor, with At representing the discrete timestep. The output spike 2" is computed using the Heaviside step function H(-).
3.2 LIF-based spiking neuron with HetSyn
We apply the HetSyn principle to the vanilla LIF neuron and propose HetSynLIF, variant that incorporates synaptic heterogeneity. In HetSynLII, the traditional membrane time constant is replaced by synapse-specific time constants. Instead of applying uniform temporal filter to all inputs, each synaptic input is individually integrated through its own exponential decay, resulting in heterogeneous synaptic currents. This design shifts temporal integration from the membrane dynamics to the synaptic dynamics, reproducing synaptic diversity in biological systems. Moreover, we model the reset mechanism as a negative current injection. The neuron then accumulates these individually filtered synaptic currents and subtracts the reset current to update its membrane potential. The dynamics of HetSynLIF can be derived from Eq. (2) yielding:
Vt Σ 1
j
(5)
dIj
11
+
Σ
Wi ( (t-tf)
(6)
dt
Tsa
dJ
J
TJ +
Σ
0 (t-
where T denotes the synaptic current from the i-th afferent at time I, governed by its own synapse- specific time constant Ts. thereby capturing the heterogeneity in synaptic temporal dynamics. J

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denotes the reset current, neuron-level term that models the effect of spike-triggent triggered reset and decays with time constant Ty. The discrete-tine timeete-tmmeeee formulations of synaptic and reset currents are given by:
T ri 1 wi J - 1. 2
(9)
where r; exp(- At) and K exp(-xp ) are the decay factors for the i-th synaptic current and the reset current of the neuron, respectively.
3.3 Generalize to other spiking neurons
Equipped with HetSyn, our HetSynLIF model is highly flexible and can be generalized wide range of spiking neuron models. To distinguish between variants, we use the prefixes "HomNeu" and "HetNeu" to denote homogeneous and heterogeneous configurations at the neuron level, respectively, Under this notation, HetSynLIF can reduce vanilla LIF neurons (HomNeuLIF), neurons with threshold adaptation (HomNcuALIF), and neuron-level hetcrogeneous models (HetNeuLIF)) This flexibility stems from the incorporation of synapse-specific time constants, which enable HetSynLIF to modulate temporal dynamics at a finer granularity. By analyzing the synaptic dynamics from a presynaptic neuron i postsynaptic neuron j. demonstrate how HetSynLIF generalizes to other neuron models under specific conditions. See Appendix [A for detailed proof.
all synaplic decay factors ri and the reset current decuy factor Ki are identical and equal to a shared value p. Le., rji Kj = for all i. then the HetSynl. model reduces the HomNeuLIF model. Under this condition, the membrane potential of the postsynaptic neuron j at time in HetSynLIF simplifies to:
Proposition 1
V =- Σ Wie 2/ -
(10)
The resulting equation matches Eq. (3), which suggests that the vanilla LIF model emerges special case of HetSynLIF when all synaptic and reset decay factors are identical.
Based on Proposition if we further decompose the reset current into a standard component and an additional adaptation current triggered by chhracccharaterrize by decay factor Pa and a scaling coefficient a then HetSynLIF generalizes the HomNeuALIF model. Under this condition, the membrane potential of postsynaptic neuron j at time in HetSynLIF can be transformed into:
Proposition 2
V p p.
Σ Wy 2/ J
2
(11)
This indicates that HetSynLIF effectively reproduces the adaptive dynamics of the HomNeuALIF model proposed by [41] through structural modification of the reset current, demonstrating its flexibility in modeling neuron dynamics beyond ixed-threshold designs.
Proposition For each postsymaptic neuron j. if all synaptic decay factors Tú and the reset current decay factor K2 identical and equal neuron-specific membrane decay factor Pj. i.e., Ty = Ki = Pj for all then HetSynLIF generalizes to the HetNeuLIF model. Under this condition, the membrane potential of postsynaptic neuron time in HetSynL simplifies to:
V Pj V V--1+ Σ Wi 2 0-
(12)
In this case, each postsynaptic neuron evolves according to its own membrane decay factor Pj. which reflects neuron-leve heterogeneity (22). This shows that HetSynLIF encompasses neuron-level heterogeneity a special case by assigning shared decay dynamics per neuron.
4 Experiments
As detailed Section 3.3
HetSynI.IF can reduced HomNeul.IF, HomNeuAL.P and HetNeul.1F through appropriate parameterization. In this section, we conduct systematic comparison of the four
5

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variants and further evaluate HetSynLIF against previous state-of-the-arr methods. All variants are implemented within our unifted framework to ensure theoretical equivalence, controlled ablation. fair comparison, and architectural consistency, enabling us to isolate the specific contribution of synapse- level heterogeneity. For clarity, we prefix feedforward and recurrent SNN implementations with "F-" and "R-", respectively. Further experimental and training details are provided in the Appendix.
4.1 Versatile Timescale Integration in Pattern Generation Task
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Figure 2: Pattern generation task. (A) An input spike pattern with a fixed Poisson generated template (10 Hz, black dots) and superimposed noise spikes (2 Hz, red dots). Repeating features are marked by shaded gray regions (Top). Output traces of four FSNN variants (middle) and four RSNN variants (bottom) in response the same input pattern. (B-C) Normalized distances between output traces at the 2nd vs. 1st and 3rd vs. 2nd occurrences of the repeating input segments for FSNNs (B) and RSNNs (C). Higher means better; see Appendix B (D) Mean squared error over training iterations for four FSNN variants. (E-F) Mean squared error of FSNN variants (E) and RSNN variants (F) under different noise levels. Data in B-F are averaged over runs and reported as mean s.d.
We first evaluate HetSynLIF and three variants using lny-layer FSNN and RSNN architectures a more complex version of the pattern generation task, compared to the setups used in previous works 13 [4], where the network is trained reproduce target trace in response to structured input spike patterns that consist of repeated segments embedded in Poisson noise, with no input provided between the segments (Fig. [A; see Appendix for details). We reveal that our HetSynLIF exhibits the fastest convergence and lowest mean squared error (MSE). In contrast, both HomNeuLII and HomNeuALIF produce near- zero outputs during the input-free intervals between repeated segments, regardless of whether the network is an FSNN or an RSNN. This suggests their limited ability to learn time constants long enough to bridge these temporal gaps (Fig. 2 and Appendix Fig. AT). We then compute normalized distances between outputs corresponding to repeated input segments (Fig. 2 for FSNNs, Fig. 2 for RSNNs, see Appendix B). where larger distances indicate stronger ability to generate target-aligned outputs for identical input segments. HomNeuLIF

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shows consistently low distances, indicating nearly identical responses, while HomNeuALIF and HetNeuLIF show slight improvements in FSNNs and modest gains in RSNNSs, benefiting from recurrent connections. Nevertheless, all three are inferior to HetSynLII in performance, which consistently achieves the highest distances across both architectures. Additionally, under varying levels of input noise, HetSynL.IF maintains the lowest MSE, while other models exhibit greater degradation (Fig. 2 F). Finally, we show that HetSynLIF is also capable generating multiple larget patterns simultaneously (Appendix Fig. A2
4.2 Versatile Timescale Integration in Delayed Match-to-Sample Task
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Figure 3: Delayed match-to-sample task. (A) Schematic diagram of sample mismatch trial with two cues separated by an 800 ms delay (Top). Spiking activity of hidden layer neurons (Second). Membrane potential and spike activities (red dots) of a sample neuron (Third). Softmax outputs of neurons representing match and mismatch (Bottom). (B) Learning curves of four FSNN variants with 100 hidden neurons. (C) Task accuracy under different synaptic time constant masking ratios. (D) Success and failure rates across neuron numbers and FSNN variants. Each grid cell corresponds to different hidden neuron count (5, 20, 50, 100), containing four centered bars for the four FSNN variants. Each bar is split vertically into a success segment (opaque, above) and a failure segment (transparent, below); trials with accuracy 2 90% color scheme as B. (E) Overall task accuracy of four FSNN variants under varying neuron counts. (F-G) Same D-E, but for RSNN variants. Data in B-G are averaged over 50 runs and reported as mean s.d.
considered successful. D-G follow the same
To assess the ability of HetSynLIF to capture celti-timmescae dependencies essential for working memory, we adopt the delayed match-to-sample task-a widely used paradigm in neuroscience [2]
43 44 45
The network must judge whether two temporally separated cues belong to the same category (i.e., left right), requiring short-term processing at cue onset and long-term retention across the delay (Fig. 3A; see Appendix for details). As the pattern generation task, we compare the performance of eight variants four FSNNs and four RSNNs acrosss multiple metrics. Fig, 3
7

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presents the learning curves of the four FSNN variants, showing that F-HetSynLIF converges fastest and achieves the highest accuracy among FSNN variants. To assess the functional importance of synaptic heterogeneity, we progressively mask a fraction of the synaptic time constants in R- HetSynI.IF, rendering them non-trainable. Results show that even with 80% of synapses masked, the model maintains 100% accuracy, highlighting the critical role of heterogeneous temporal integration in sustaining memory over delays (Fig. 3C). We further analyze how performance scales with network size (Fig. 3D-G). Both F-HetSynLII and R-HetSynLIF consistently achieve higher success rates (defined as accuracy 2 90%) across varying numbers of hidden neurons, remaining effective even with five neurons, which highlights computational efficiency of synaptic heterogeneity in resource- constrained scenarios. Besides, R-HetSynLIF maintains 100% accuracy even at a 2500 ms delay, with no notable increase in iterations to reach 95% accuracy, and retains nearly 80% accuracy under noise of 20 Hz, demonstrating both stable training efficiency and strong robustness (Appendix Fig. A3)
4.3
Versatile Timescale Integration in Speech Recognition
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Figure 4: Speech recognition and robustness analysis. (A) Learning curves of four RSNN variants on the SHD dataset. (B) Spike inputs under deletion noise ratios of 0.00, 0.32, and 0.64 (top to bottom), where each ratio denotes the probability of deleting a spike. (C) Test accuracy under varying deletion noise ratios. (D) Distribution of synaptic time constants for connections from the last hidden layer to the output layer, before (top) and after (bottom) training. (E) Spike inputs under time warp conditions with log,- factors of -0.5 (compressed), 0.0 (original), and 0.5 (stretched), top to bottom. (F) Test accuracy under log,
log,-scaled -caledd time warp factors. Data in A, C, and F are averaged over 10 runs.
We then evaluate the speech recognition capability four RSNN variants mentioned above on the SHD[46] dataset, using a two-layer recurrent architecture. As shown in Fig. 4M, HetSynL consis- tently achieves the highest accuracy and fastest convergence, followed by HetNeuLIF, HomNeuALIF, and HomNeuLIF. This result underscores the superior modeling capacity of synapse heterogene- ity. While neuron heterogeneity also improves performance, assigning distinct time constants to individual synapses offers finer temporal resolution. In contrast, threshold adaptation yields limited gains and remains less effective than neuron heterogeneity. To understand how temporal dynamics evolve during learning, analyze the distribution of in the final hidden-to-outpe layer (Fig. 4D).
8

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Initialized from (5, 20) ms, shifts toward lower values, with 2.0% exceeding 20 ms, forming mild long-tail that may support slow-varying temporal encoding, loosely resembling biological patterns in Fig. [A. Similar trends are observed across other layers (Appendix Fig. A5 We further assess robustness under deletion noise and time warp, both of which are introduced only during testing (i.e., trained on clean data and tested with deletion noise time-want warped inputs). In deletion noise, each spike is independently removed with a fixed probability (Fig. 43). Although performance degrades with increasing noise, the accuracy ranking remains unchanged (Fig. 4C). Notably, when the noise ratio increases from 0.32 to 0.64, HetSynLIF maintains relatively stable, while others drop sharply, demonstrating the strong resilience of synapse heterogeneity to input disruptions. A similar trend holds under time warp distortions (Fig. 4 F), where HetSynLIF consistently achieves higher accuracy across varying timescales (see Appendix D and Fig. A4 for more details).
4.4 Comparison with Existing Works
We compare our proposed HetSynL.IP model with other existing works on the SHD, S-MNIST 47
TiDigits (48), and Ti46-Alpha [49 datasets, and report the results in Table T Notably, our two- layer RSNN architecture achieves 92.36% accuracy on the SHD dataset, which, to the best of our knowledge, the highest reported accuracy among models with similar architectures. In addition, the HetSynLIF model demonstrates outstanding performance on the other three datasets as well, consistently outperforming prior methods, highlighting its effectiveness processing multi-timescale temporal dynamics across both speech and visual recognition tasks.
Table Accuracy comparison SHD, S-MNIST, TiDigits, and Ti46-Alpha datasets
Dataset
Method
Acc
Dataset
Method
Acc
DH-SFNN Nat. Commun24
23
92.1
BPT-SNN 50
98.1
DH-SRNN Nat. Commun24
23
91.34
M-STIP TNNLS22
51
98.1
SRN21
52
91.19
MPD-AT AAALI9
53
97.5
SHD
SRNN
54
90.4
TiDigits
BAE-MPDAL
97.4
NeuHee-SRNNN Na Nato
82.7
TDP-DL
97.16
SRNNPNAS22
57
81.6
PESNLR-DW
96.5
HetSynLIF (Ours)
92.36
HetSynLIF (Ours)
98.99
DH-SRNN Nat. Commun24
23
98.87
RSNN 59
96.44
SRNN NM21
98.7
ScSr-SNNs 60
95.9
LSTM ICML16
61
98.2
RSNN NeuriPS9 62
93.5
S-MNIST
LSNN LSNN NewrIPS18
96.4
Ti46
LSM 63
92.3
AHP-SNN
96.0
S S-MLP
64
90.98
HetSynLIF (Ours)
98.93
HetSynLIF (Ours)
96.53
5 Conclusion
In this paper, propose HetSyn, the first modeling framework with synaptic heterogeneity in SNNs that replaces the conventional membrane time constant with synapse-specific time constants. This design enables versatile timescale integration at the synapse level, grounded in biological observations of synaptic diversity. We instantiate HetSyn as HetSynLIF and theoretically show its generalization ability existing models. Through comprehensive experiments, show that HetSynLII consistently achieves high accuracy tasks requiring versatile timescale integration, exhibits strong robustness to noise, and maintains computational efficiency under resource constraints. Furthermore, the learned synaptic time constants exhibit a mildly long-tailed distribution, loosely resembling biological observations and reflecting adaptation to multi-timescale processing. These findings underscore the critical role of synaptic heterogeneity in SNNs, not only in enhancing computational performance, but also in aligning with biological principles. By establishing synapse-level modeling as a viable direction, work points toward promising avenues for advancing brain train-inspired learning systems.

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Future work could explore the combination of HetSyn with other advanced spiking architectures or training strategies for further improvements in versatile timescale integration and task performance.
Acknowledgments and Disclosure of Funding
This work in part supported by the Brain Science and Brain-like Intelligence Technology National Science and Technology Major Project (Grant No. 20252D0215600), the National Natural Science Foundation of China (Grant Nos. 92370103 and 62176179), and in part by the Xiaomi Foundation. We thank the reviewers for their insightful and supportive comments.
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Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Question:
Answer: [NA]
Justification: The core method development in this research does involve LLMs as any important, original, or non-standard components.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to our LLM for what should or should not be described.
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Appendix
A Theoretical Proof
If all synaptic decay factors yi and the reset current decay factor Ki are identical and equal to shared value p. Le., Fji Kij = p.ror all i. then the HetSynL.F model reduces the HomNeuLII model.
Proposition 1
Proof From Eq. 55) and Eq. 8 9). the membrane potential Vj of postsynaptic neuron j at time in the HetSynLIF model is given by:
V Σ TB
+
Σ wy of (xy. JJ + +0.25-1)
(13)
Under the condition that rjt Kiz = p. Eq.
13
simplifies to:
Vs=
Σ p. 1ز
Wyi 2 (D-J5- -0- - Σ
=
Σ
- Jj-1
Σ Wift 2 2. z//1
(14)
Observe that the term Σ, 1 JzJ1 corresponds precisely the membrane potential at the previous time step - 1, as defined in Eq
8
1-1 J5-1 1i
(15)
Substituting Eq.
[4 yields:
V = P- + Σ Wit 2 - 1. 2/-1
(16)
This recurrence relation is identical to the membrane update rule of the HomNeuLIF model, as defined in Eq. (3). Therefore, under the condition т₁ = K2 = p. the HetSynLIF model reduces exactly to the HomNeuLIF model under the specified condition. This completes the proof.
Based on Proposition 1, if we further decompose the resel current into a standard component and an additional adaptation current triggered by charesechaa by decay factor Pa and a scaling coefficient u-then HetSynL.IF generalizes to the HomNeuAL.IF model.
Proposition's 2
Proof Under the condition that the total reset current in the HetSynLIF model consists of two components: standard reset current Jj and an additional adaptation current Jú such that the membrane potential V of postsynaptic neuron j at time t satisfies:
1 -
(17)
The standard reset current J3 follows the dynamics defined in Eq. 99 while the adaptation current JA follows the dynamics introduced in [12]:
d.ft a
J + Σa 8 -1)
(18)
dl
3
J = Pa J a
(19)
where = exp(-Ar) is the decay factor derived from the adaptation time constant Ta. and a is the
adaptation strength. Substituting Eq. (8 into Eq. 17 we obtain:
V = Σ (r3e I Wif 2 K5 J 2.
2 2-1 J
(20)
22

---

Under the condition that ryi Rig = , Eq. 20
simplifies to:
Vj = p: p: V
Σ Ji Jz-1
+ Σ Wij 2
Jn 0 0.2
Σ
W/r
2f
J 1 22
(21)
The recurrence in Eq. 21 is similar as the membrane potential dynamics of the HomNeuALIF model defined in 41 This completes the proof.
Proposition For each postsynaptic neuron j. if all synaptic decay factors Ti and the reset current decay factor Ki are identical and equal to neuron-specific membrane decay factor Pj. i.e., rs Rig = Pj for all then HetSynLIF generalizes to the HetNeuLLF model.
Proof From Eq. 5 and Eq. 88 the membrane potential V of postsynaptic neuron j in the LII model is given by Eq. Under the condition that r' Ki - Pj. substituting this into Eq. 13 we obtain:
Vj Ees Pj
1
Σ Wzi 2
(pz (ps-J) 0- -- 2)-1)
(22)
Rewriting Eq.
22 by extracting Pj as a common factor, we have:
Vj = Pj
Σ p - + Σ Wijs 2/ 0 0 2-1
(23)
Substituting Eq.
15 into Eq. 23 yields:
Vj = Pj
+ Σ myy of
0 0.25-1 2
(24)
This update rule corresponds to the membrane dynamics of the HetNeuLIF model, in which each neuron has its own membrane decay factor Pj. Thus, under given condition, the HetSynLIF model reduces to the HetNeul.IF model. This completes the proof.
B Details of the Pattern Generation Task
Task Deseription In this task, network is trained to reproduce a continuous target trace in response to structured input spike patterns. Each input consists of 100 afferent channels spanning 2000- ms window. A single 500-ms spike segment is first generated using a 10 Hz Poisson process and then embedded three times within the input window, evenly spaced and separated by 250-ms silent intervals (i.e., periods with no input spikes from the structured segment, though background noise may still occur). To perturb the input structure, global background noise is superimposed across all channels, and regenerated independently at each training iteration. In our experiments (Fig. (Fig.RE. F), evaluate noise levels with rates of 1, 3, and 4 Hz examine the model's robustness under increasing perturbation. The target trace is constructed as the sum of five cosine components with a base frequency of 0.5 Hz, with each component modulated by random amplitude sampled from 2(00 1) and a phase sampled from (1,0 2T). The resulting signal is then normalized to the range [-1,
Loss Function We train the network using loss that combines task-specific term and a reg- ularization term. The task loss is defined as the mean squared error (MSE) between the network output (3/") and the target trace (1, averaged over all timesteps. The regularization term penalizes deviations of each neuron's 's firing rate from a target rate of 10 Hz, computed as the mean squared relative error across neurons. The two terms are weighted using a fixed coefficient of 0.01 for the regularization.
23

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Computation of the Normalized Distances In Fig. 2 and C, we quantify the model's ability to generate temporally distinct outputs for repeated input segments by computing the normalized distance between the output traces corresponding to different occurrences of the same structured input. Specifically, for any two repeated segments (e.g., the first and second), we compute the mean squared difference between their output traces, and normalize it by the corresponding difference between the target traces:
E, (1hnd Vist!
)
dist(2nd, 1st)
=
(25)
(Vind
x,6
V/st/ v.1)
Here, a higher distance indicates that the model produces differentiated outputs for repeated inputs. suggesting alignment with the target trace rather than generating identical responses to identical stimuli. Conversely, a lower value implies that the model outputs remain nearly the same across repetitions.
Experiment Settings We adopt 100-100-1 network architecture for all models, comprising 100 input channels, 100 hidden neurons, and a single leaky-integrate readout neuron. The synaptic time constant T3 is fixed 20 ms for HomNeuL.IF and HomNeuALIF, and initialized by sampling from N (20, 5) ms for HetNeuLIF and HetSynLIF. The reset time constant is uniformly set to 20 ms across all models. For HomNeuALIF, the adaptation time constant and adaptation strength are set to Ta 500 ms and a = 0.01, respectively. All decay factors are constrained to the range [0, 1] during training. For the surrogate function, we use a triangular-shaped derivative defined as ae
Training is performed using the Adam optimizer with StepLR learning rate scheduler, where the learning rate is initialized at 1e-3 and decayed by a factor of 0.8 every 100 iterations. All models are trained for 1000 iterations with a batch size of 1.
.V = 7 max (0, (
)) we set y = 1 and Ç
C Details of the Delayed Match-to-Sample Task
Task Description In this task, the network is required to determine whether two temporally sepa- rated cues belong to the same category (i.e., left or right). There are four possible cue combinations: left-left, left-right, right-left, and right-right. The left-left and right-right conditions are labeled as "match", while the remaining consists of 30 channels, divided equally into left-cue, right-cue, and noise channels (10 each). Each cue is delivered through either the left right group using independent Poisson spike trains at 40 Hz. The first cue begins at 50 ms and lasts for 100 ms, followed by an 800 ms delay. The second cue then appears, also lasting 100 ms. Throughout the entire 1050 ms input window, continuous background noise is added on the noise channels using a 10 Hz Poisson process. To evaluate the model's s ability retain the first cue and compare to the second after a long delay, we compute the decision by comparing the membrane potentials of two output neurons- corresponding to "match" and "mismatch" -t the final millisecond of the second cue (1050 ms), and the class associated with the higher membrane potential is selected as the predicted label.
are considered "mismatch". The input
Loss Function Similar to the pattern generation task, the network is trained using a loss func- tion composed of a task-specific term and a regularization term. The regularization term remains unchanged and penalizes deviations of each neuron's 's firing rates from target of 10 Hz. The task- specific loss is defined as the cross cross-entropy between the predicted class probabilities and the target labels.
Experiment Settings In this task, the synaptic time constant т, is fixed at 40 ms for HomNeuLIF and HomNeuALIF, and initialized by sampling from (40, 4) ms for HetNeuLIF and HetSynLIF. The reset time constant is uniformly set to 40 ms across all models. For HomNeuALIF, the adaptation time constant and adaptation strength are set to T. = 800 ms and a 0. 15, respectively. All decay factors are constrained to the range [0, 1] during training. A simulation timestep of A/ = 5 ms is used to reduce computational overhead. We use the same surrogate function in the pattern generation task and set y 1 and < 1. Training is performed using the Adam optimizer with StepLR
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learning rate scheduler, where the learning rate is initialized at 5e-3 and decayed by a factor of 0.8 every 100 iterations. All models are trained for 1000 iterations with a batch size of 32.
D Details of the Speech Recognition Task
SHD Dataset and Preprocessing The SHD dataset comprises 10,420 high-quality audio samples of spoken digits (0-9) in English and German. It includes 12 speakers- 6 female and 6 male- aged between 21 and 56, with each speaker contributing approximately 40 utterances per digit for each language. The dataset is divided into training and testing sets, containing 8, 1,156 and 2,264 samples, respectively. Before feeding into neural networks, we first align all audio recordings to a fixed duration of 1000 ms by trimming or zero-padding, and then sample the resulting spike trains using 4 ms time bin, yielding a 250 x 700 input matrix per recording (250 timesteps x 700 input channels).
Deletion Noise Spiking systems deployed in real-world scenarios often face partial signal loss sensor failures, making robustness to missing inputs a critical property. To assess this capability, we evaluate performance under deletion noise, which simulates missing input events by independently removing each spike with a fixed probability p. Specifically, for each spike input (i.e., binary value 1), it is retained with probability - p and set 0 with probability p. We test seven noise levels with p E {0.0, 0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.64), corresponding to 0.01 x 2 for n = 0 to 6, plus clean condition.
Temporal scaling Temporal scaling is fundamental aspect of sensory processing, as biological systems such as the auditory and motor systems are capable of recognizing patterns across wide range of speeds. To test whether SNNs equipped with HetSyn exhibit similar robustness, we simulate temporal variability by scaling each spike time with a global warping factor. That is, each spike time is multiplied by constant factor a, resulting in globally compressed or stretched spike sequence. Accordingly, the total number of timesteps changes proportionally to the warping factor. We evaluate 20 different warping conditions, with factors sampled as log2
4150.5, 0.5), covering both temporal compression (log, a < 0) and dilation (log, a > 0) at varying scales.
neurons for the readout layer to decode the output of the network, where the predicted possibility for class is obtained by summing the normmax-normalized membrane potential of the output neuron over time, i.c., 9: L, softmax(Va.)) For better performance, we use multi-Gaussinn and train the network using the standard cross-entropy loss. The synaptic time constant T₃ is fixed at 20 ms for HomNeuLII and HomNeuALIF, and initialized by sampling from (5, 20) ms for HetNeuLIF and HetSynLIF. The reset time constant Ty is uniformly set to 20 ms across all models. For HomNeuALIF, the adaptation time constant and adaptation strength are set to T, 100 ms and a = 0.05, respectively. All decay factors are constrained to the range [0, 1] during training. The model is optimized using the AdamW with a learning rate of 2e-3 and weight decay of 4e-3. We apply a cosine annealing schedule with 5% warm-up. computed per batch, and fix the learning rate after 40 epochs.
Experiment Settings As in 23 54 we adopt
curve as surrogate function,
E Datasets and Configurations
SHD Same Appendix D
S-MNIST Sequential MNIST (S-MNIST) is a sequential version of the standard MNIST dataset, where each 28 28 image is reshaped into sequence of 784 inputs. At each timestep, a single pixel is presented to the model in a row-wise scan from top-left to bottom-right. The MNIST dataset consists of grayscale images of handwritten digits (0-9), with 60,000 training and 10,000 test samples. We follow the original train/test split in our evaluation.
TiDigits We use the adults subset of the TiDigits dataset, which comprises isolated utterances of the 11 English digit classes ("zero"""nine" and "oh"), with standard training and testing splits of 2,464 and 2,486 speech samples. We use threshold crossing encoding method proposed by Gutig (65) to encode TiDigits into spikes, with 51f 16 Mel filters from 8600 Hz, and 15 thresholds
25

---

per channel for crossing. We use the first 200 timesteps of each sample, yielding an input of shape 200 500 (timesteps channels).
Ti46-Alpha Ti46-Alpha, consisting of the 26 English alphabet letters, subset of the Ti46-Wor dataset. We apply the same encoding method as in TiDigits, yielding input representations of size 200 500.
Experiment settings All experiments conducted using NVIDIA RTX 4090 and Tesla V100- PCIE-16GB GPUs. We employed a cosine-annealing learning rate scheduler applied at each batch step. For S-MNIST, classification is based on spike counts from the output layer neurons, whereas for all other datasets, predictions are derived from temporally integrated outputs, as previously described for SHD. A detailed overview of the experimental settings and hyperparameter configurations is provided in T
Table Experiment settings and hyperparameter configurations for different datasets
Dataset
SHD
S-MNIST
TiDigits
Ti46-Alpha
learning rate
2e-3
le-3
2e-3
4e-3
dropout rate
0.2
0
0.5
0.2
epochs
100
150
50
50
batch size
32
256
32
32
warmup ratio
0.05
0.05
0.05
0.05
optimizer
AdamW
Adam
AdamW
Adam
weight decay
4c-3
lc-2
4c-3
architecture
SRNN
SRNN
SRNN
SRNN
hidden neuron number
[128, 64)
[64, 64]
[64, 32]
[128, 128]
0
1.0
1.0
1.0
1.0
At
le-3
le-3
1e-3
le-3
TJ
20e-3
20e-3
20e-3
20e-3
initialization of T.
U(Se-3, 20e-3)
U(Se-3, 20e-3)
U((e-3, 20e-3)
U(Se-3, 20e-3)
Model Complexity Analysis
We conduct a comparative analysis of model parameters across several representative SNN models with distinct neuronal dynamics. The models considered include four FSNN variants, four RSNN variants, and two dendritic heterogeneity models (DH-SFNN and DH-SRNN (23). For clarity, we assume that each layer consists of N neurons and receives M inputs, with D representing the number of dendritic branches per neuron. The theoretical results are summarized in Table
The analysis indicates that HetSynLIF introduces a moderate increase trainable model parameters under identical architectural configurations and neuron counts. Intriguingly. HetSynLIF achieves comparable or even superior performance with significantly fewer neurons and faster convergence (Fig. 22. B. A and Appendix Fig. AT], suggesting that the increased per-unit complexity effectively offset and may even constitute an advantage in terms of overall training efficiency. Given the notable performance gains and the promising potential of synaptic heterogeneity in SNNs, additional per-unit complexity represents a reasonable trade-off this early stage, which natural and biologically grounded, as synapses greatly outnumber neurons in the brain. Future studies may further mitigate the computational complexity of HetSynI.IF by exploring sparse synaptic connectivity and lightweight architectural designs, inspired by [2] 22).
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Table Comparison of trainable model parameters
Models
Synaptic Parameters
Neuron Parameters
Total Parameters
I-HomNeuLII
MN
0
MN
F-HeiNeuLIF
MN
N
MN N
F H-HoNeLALLF
MN
0
MN
F-
2MN
0
2MN
DH-SFNN
MN
N + ND
MN + (D + 1)N
HImNeuLLI
MN + NNN
0
MN NN
R-HetNeul.IF
MN NN
N
MN NN +N
R-HomNeuALIF
MN + NN
0
MN + NNN
R-HetSynLIF
2MN 2NN
0
2MN + 22NN
DH-SRNN
MN + NN
N + ND
MN NN + DD+ 1)N
G Evolution of Synaptic Time Constants During Training
The DMS task inherently relies on both short-term and long-term memory capabilities: long-term memory enables the model to retain cue information (c.g., "left" or "right") across the delay period, while short-term memory helps suppress irrelevant noise. During training, the time constants in the cue-related pathways tend to increase toward the delay duration to sustain relevant information, while those in related pathways decrease to promote rapid forgetting.
To demonstrate this, we initialize the time constants т from Gaussian distributions with means E {100, 200, 400) ms and standard deviations of 0.1pu Each configuration is trained for five independent runs, and the averaged results in indicate constants between the cue and noise pathways. In addition, approximately 5-6% of synapses develop time constants comparable the task delay, and resetting these synapses their initial mean values leads to substantial decrease in accuracy. These results demonstrate the task-aligned functional specialization of synaptic time constants, and further support the effectiveness of HetSyn versatile timescale integration by adaptively tuning synaptic dynamics to input characteristics during training.
expected divergence of learned time
Table 4: Analysis of time constant statistics
Initialization
NV000 10?)
N2000 20
NV400,402)
Cue-channel (after training)
154.38 (+54.38%)
252.43 (+26.22%)
430.70 (+7.68%)
Noise-channel (after training)
85.59 (-14.41%)
181.93 (-9.04%)
382.29 (-4.43%)
Synapses with 700
5.25%
6.05%
5.80%
Accuracy
99.97%
100.00%
99.87%
Accuracy (reset long T)
75.68% (-24.29%)
76.47% (-23.53%)
77.15% (-22.72%)
H Discussion
Broader impacts By introducing synaptic heterogeneity into SNNs, our work advances the model- ing of biologically inspired temporal dynamics and enhances the computational performance of SNNs. This has the potential to improve both learning performance and energy efficiency in neuromorphic computing systems, contributing to the development of low-power, event-driven Al applications. Furthermore, our study purely computational and does not involve sensitive data human subjects, and we anticipate adverse societal environmental impacts of out study.
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Limitations This work provides a step toward understanding the role of synaptic heterogeneity in SNNs while introducing additional per-unit complexity and increased training cost. Future work will explore approaches for reducing computational complexity, such as sparse synaptic connectivity and lightweight architectuall designs. Moreover, as this work focuses on a subset of synaptic properties, broader range of other synaptic features and more sophisticated architectures remain to be explored.
I Supplementary Figures
A
Learning Rate 1e-4
B
Learning Rate 5e-4
0.2
0.2
MSE
0.15
MSE
HetSynLiF
0.1
HetNeuLIF
0.1
0.05
HomNcuUF
0.05
100
Training iterations
Training Iterations
C
Learning Rate 1e-3
D
Learning Rate 5e-3
0.25
0.2
0.2
MSE
0.15
MSE
0.15
0.05
0.05
50
100
200
500
1000
50
100
200
500
1000
Training Iterations
Training Iterations
Figure Al: Convergence speed evaluation of four FSNN variants on the pattern generation task, trained with learning rates le-4 (A), 5e-4 (B), 1e-3 (C), 5e-3 (D). The curves show the mean squared error (MSE) over training iterations.
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Iteration 10
Iteration 100
Iteration 1000
50
target
Ourpir
barget
Curput
barget
Ourp
Outputt
Outpur2
-1
Output3
0-
500
1000
2000
1000
1500
2000
500
1000
1500
2000
Time
(ms)
(ms)
Figure A2: Dynamics of F-HetSynLIF during training on the pattern generation task with simultane- ous generation of three output patterns. From left right: network dynamics at 10, 100, and 1000 training iterations. Each column shows spike activity of hidden neurons (top), followed by predicted traces (colored lines) and targets (black dashed lines) for the three outputs.
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1000
1000
100
100
90
Training iterations
90
Training lterations
Test Acc 1%)
Test Acc (%)
80
600
80
600
70
400
70
400
60
60
200
200
50
50
1000
1500
2000 2500
3000
5
15
Delay (ms)
Noise (Hz)
Figure A3: Performance and training efficiency of R-HetSynLIF on the delayed satcc-ttossmpll task under varying delays and noise levels. Left: Test accuracy (solid line, left y-axis) and training iterations required to reach 95% accuracy (boxplot, right y-axis; window size 10) across different delay durations. Right: Same metrics evaluated under varying levels of addition noise (Hz).
30

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95
HetSynLIF
HomNeuALIF HomNeuLIF
HetNeuLIF
I
90
I
Test Acc (%)
85
I
80
75
70
Baseline
Noise Ratio 0.32 Time Scale = 0.25, logz
Figure A4: Bar plots show test accuracy of four RSNN variants on the SHD dataset under three conditions: baseline (left), deletion noise ratio 0.32 (middle, from Fig. 4C), and time warp scale 0.25 (log2, right, from Fig. 4F). Error bars represent standard deviation over 10 runs.
31

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Before Training
B
Before Training
2000
Court
Count
250
0
5
10
15
20
5
10
15
20
After Training
After Training
Count
5000
12 3%
20
Count
1000
5
15
0
10
20
Ty (ms)
T, (mst
Before Training
D
Before Training
Count
Court
100
0
15
10
20
After Training
After Training
Count
500
20 8%
Count
12 5%
20
10
T, (ms)
T, (ms)
Figure A5: Distributions of synaptic time constants (rz) across all connection types in the two-layer R-HetSynLIF. From (A) (D): input hidden layer 1, recurrent connections within hidden layer 1, hidden layer to hidden layer 2, and recurrent connections within hidden layer 2. Each subplot shows the distribution of T3 before training (top) and after training (bottom).
32


Reviews:
[{"review_id": "dUcZsoxQ0L", "reviewer": "Reviewer_auyx", "summary": "The author proposes a framework HetSyn for modeling prominent heterogeneity by combining the widely observed but underutilized characteristic of synaptic heterogeneity in biological neurons. This framework combines synaptic specific time constants to reflect synaptic heterogeneity and is instantiated through HetSyn LlF, achieving time integration across different time scales at the synaptic level. This model takes several existing types of neurons (such as Alif, heterogeneous LIF) as special cases and evaluates them on multiple tasks, including pattern generation, delayed matching samples, samples, speech recognition (SHD), and visual recognition.", "questions": "1. Can author quantify training costs (such as power consumption, memory, time) and comparing them with existing work.\n2. Can the authors either provide preliminary results on event-driven benchmarks or clearly justify why these were excluded? Would the model need adaptation to handle asynchronous input?", "limitations": "The Limitation section is brief. It is recommended to discuss potential limitations, such as introducing time constants for each synapse, which significantly increases the optimization dimension and may lead to gradient instability or slow convergence.", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. Introducing synaptic heterogeneity to achieve versatile timescale integration of SNNs, based on empirical neurobiological evidence. This contributes to computational neuroscience and neuromorphic computing.\n2. Comprehensive evaluation, spanning multiple tasks and datasets. The design of ablation research and robustness testing (noise, time distortion, resource constraints) is reasonable.\n3. The paper provides theoretical analysis for the proposed method.          \n\nWeaknesses:\n1. Introducing trainable specific synaptic time constants can significantly increase the number of parameters and may increase the complexity of optimization. Suggest quantifying training costs (such as power consumption, memory, time) and comparing them with existing work.\n2. This paper lacks an evaluation of event based datasets in the real world, such as DVS Gesture or DVS-CIFAR10. Given that the model emphasizes the temporal dynamics of synapses, testing it on asynchronous, event driven data will better demonstrate its practicality and robustness.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you for your thoughtful feedback and hope that the responses below could address your concerns.\n\n---\n>**Weakness 1:** Introducing trainable specific synaptic time constants can significantly increase the number of parameters and may increase the complexity of optimization. Suggest quantifying training costs (such as power consumption, memory, time) and comparing them with existing work.\\\n**Question 1:** Can author quantify training costs (such as power consumption, memory, time) and comparing them with existing work?\n\n**WA1 & QA1:** Thank you for this thoughtful and comprehensive comment. We agree that introducing trainable synaptic time constants may increase the model complexity, and it is indeed important to quantify the associated training costs. Motivated by this valuable suggestion, we conducted both a theoretical analysis and an additional set of experiments to evaluate the training cost, and we report the results below. We hope these analyses help clarify the impact of our design and address your concern.\n\n**Theoretical Analysis:** Following the methodology of [1], we conducted a theoretical comparison of the number of parameters and operations (multiplications and accumulations) across several models, based on the neuronal dynamics that define their computation processes. These include:\n- vanilla SNNs (denoted as HomNeuLIF)\n- dendrite heterogeneity models (DH-SFNN and DH-SRNN [1])\n- neuron heterogeneity models (HetNeuLIF [2])\n- neuron with threshold adaptation (HomNeuALIF [3])  \n- our proposed synaptic heterogeneity model (HetSynLIF)\n\nFor consistency, we assume each layer contains $N$ neurons and receives $M$ inputs, with average input and output spike rates denoted as $r_{\\text{in}}$ and $r_{\\text{out}}$, respectively. $D$ represents the number of dendritic branches per neuron, as used in [2].\n\n|Models|Synaptic parameters|Neuronal parameters|Total parameters|Total multiplications/timestep|Total accumulations/timestep|\n|:-:|:-:|:-:|:-:|:-:|-|\n|F-HomNeuLIF|$MN$|0|$MN$|$N$|$MNr_{in}+Nr_{out}+N$|\n|F-HetNeuLIF|$MN$|$N$|$MN+N$|$N$|$MNr_{in}+Nr_{out}+N$|\n|F-HomNeuALIF|$MN$|0|$MN$|$N$|$MNr_{in}+Nr_{out}+N$|\n|F-HetSynLIF|$2MN$|0|$2MN$|$MN+N$|$MNr_{in}+Nr_{out}+N$|\n|DH-SFNN|$MN$|$N+ND$|$MN+(D+1)N$|$(2D+2)N$|$MNr_{in}+Nr_{out}+(2+3D)N$|\n|R-HomNeuLIF|$MN+NN$|0|$MN+NN$|$N$|$MNr_{in}+NNr_{out}+Nr_{out}+N$|\n|R-HetNeuLIF|$MN+NN$|$N$|$MN+NN+N$|$N$|$MNr_{in}+NNr_{out}+Nr_{out}+N$|\n|R-HomNeuALIF|$MN+NN$|0|$MN+NN$|$N$|$MNr_{in}+NNr_{out}+Nr_{out}+N$|\n|R-HetSynLIF|$2MN+2NN$|0|$2MN+2NN$|$MN+N$|$MNr_{in}+NNr_{out}+Nr_{out}+N$|\n|DH-SRNN|$MN+NN$|$N+ND$|$MN+NN+(D+1)N$|$(2D+2)N$|$MNr_{in}+NNr_{out}+Nr_{out}+(2+3D)N$|\n\n**Experimental Analysis:** We then conducted an empirical evaluation using the DMS task as a representative benchmark. Specifically, we measured the training time for 1000 iterations, the maximum GPU memory usage, and the final accuracy on a single NVIDIA RTX 4060 GPU. The results are summarized in the table below. \n\n|n_hid=20|F-HomNeuLIF|F-HetNeuLIF|F-HomNeuALIF|F-HetSynLIF|R-HomNeuLIF|R-HetNeuLIF|R-HomNeuALIF|R-HetSynLIF|\n|-|-|-|-|-|-|-|-|-|\n|Training Time(s)|96.4|106.36|111.26|136.24|110.11|124.11|124.47|176.02|\n|Peak GPU Memory(MB)|19.56|19.82|19.56|20.78|19.57|20.34|19.57|31.92|\n|Accuracy(%)|~50|~50|~65|~100|~50|~70|~100|~100|\n\n|n_hid=50|F-HomNeuLIF|F-HetNeuLIF|F-HomNeuALIF|F-HetSynLIF|R-HomNeuLIF|R-HetNeuLIF|R-HomNeuALIF|R-HetSynLIF|\n|-|-|-|-|-|-|-|-|-|\n|Training Time(s)|96.78|110.1|112.5|139.22|111.24|124.97|125.84|180.6|\n|Peak GPU Memory(MB)|22.50|23.84|22.51|50.15|22.57|25.23|22.57|118.75|\n|Accuracy(%)|~50|~60|~70|~100|~50|~75|~100|~100|\n\n|n_hid=100|F-HomNeuLIF|F-HetNeuLIF|F-HomNeuALIF|F-HetSynLIF|R-HomNeuLIF|R-HetNeuLIF|R-HomNeuALIF|R-HetSynLIF|\n|-|-|-|-|-|-|-|-|-|\n|Training Time(s)|96.11|105.51|111.96|140.86|119.54|138.07|123.53|194.16|\n|Peak GPU Memory(MB)|27.57|30.14|27.58|99.13|27.79|32.9|27.8|379.05|\n|Accuracy(%)|~50|~70|~75|~100|~50|~90|~100|~100|\n\nTheoretical and empirical results indicate that HetSynLIF indeed introduces a slight increase in training cost when evaluated **under identical architectures and neuron counts**. Given the notable performance gains and the potential of synaptic heterogeneity in SNNs, we consider the added training cost a reasonable trade-off at this early stage. This complexity is expected and biologically plausible, as synapses greatly outnumber neurons in the brain.\n\nMoreover, HetSynLIF achieves comparable or even superior performance with significantly **fewer neurons**. For example, as shown in the above table, **F-HetSynLIF (20 neurons) outperforms R-HetNeuLIF (100 neurons) with lower memory and time costs**. Additionally, Fig. 2D, Fig. 3B, Fig. 4A, and our response to Reviewer L2NP (WA2 & QA1) demonstrate that HetSynLIF **converges faster**, requiring **fewer training iterations**. Together, these findings suggest that **the increased per-unit complexity is effectively offset and may even serve as an advantage in overall training cost**.\n\nIn future work, we plan to explore methods to reduce the computational complexity of HetSyn, such as incorporating sparse connectivity and low-complexity designs in [1, 3]. We will also explicitly discuss this limitation and potential future directions in the revised manuscript. \n\n---\n>**Weakness 2:** This paper lacks an evaluation of event based datasets in the real world,..., event driven data will better demonstrate its practicality and robustness.\\\n**Question 2:** Can the authors either provide preliminary results on event-driven benchmarks or clearly justify why these were excluded? Would the model need adaptation to handle asynchronous input?\n\n**WA2 & QA2:** We sincerely thank you for highlighting the importance of evaluating our method on real-world, event-based datasets such as DVS Gesture and DVS-CIFAR10. Below, we first explain why these datasets were not included in the original submission and then present preliminary results on DVS Gesture dataset in response to your insightful suggestion.\n\nIn this work, we focus on exploring the potential of synaptic heterogeneity in versatile timescale integration. For this reason, we prioritize tasks that involve **longer temporal dependencies**, where the benefits of synaptic heterogeneity can be more effectively observed. While DVS datasets are indeed event-driven and asynchronous, their temporal windows are typically short (often **fewer than 20 timesteps** in common configurations). Given that the membrane time constant of a standard LIF neuron is commonly set to 20 ms, it is typically sufficient to capture the temporal structure within these brief input windows. As a result, these datasets may not fully exploit the diverse temporal integration capabilities that HetSyn is designed to provide. In contrast, Pattern Generation (2000 timesteps) and Delay Match-to-Sample (1050 timesteps), along with datasets such as SHD (250 timesteps, **which is also an event-based dataset**) and S-MNIST (784 timesteps), offer richer temporal dynamics over longer time scales, making them more suitable for evaluating the advantages of HetSyn.\n\nNevertheless, in full respect of the your valuable suggestion, we conducted preliminary experiments on the DVS Gesture dataset to assess the generality of our approach. We adopted a 5Conv+1FC architecture, with HetSyn incorporated into the FC layer. The model achieved **96.18%** accuracy, compared to **95.49%** for the baseline HomNeuLIF configuration. This result demonstrates that even in a limited application setting, HetSyn can improve performance on event-driven data.\n\n|Model|DVS Gesture|\n|:-:|:-:|\n|F-HomNeuLIF|95.49%|\n|F-HetSynLIF|96.18%|\n\nDue to time constraints, we did not extensively optimize the architecture or hyperparameters; with further tuning and broader integration of HetSyn, the results may be even better. That said, our primary contribution lies not in achieving state-of-the-art accuracy on specific benchmarks, but in proposing a general and biologically inspired mechanism to enable more flexible and effective temporal integration in SNNs. We appreciate your feedback and plan to explore broader architectural integration and evaluate HetSyn on additional datasets in future work.\n\n---\n>**Limitation 1:** The Limitation section is brief. It is recommended to discuss potential limitations, such as introducing time constants for each synapse, which significantly increases the optimization dimension and may lead to gradient instability or slow convergence.\n\n**LA1:** Thank you for pointing out this important issue. As discussed in **WA1 & QA1**, we are aware of introducing synapse-level time constants in our model inevitably increases training cost. We acknowledge that these practical limitations are indeed important considerations.\n\nIn the revised manuscript, we have included a more detailed discussion of these challenges in the **Limitation** section, and additionally outlined potential directions for addressing them in future work. To provide a clearer and more complete view of the resource demands associated with our approach, we also include the theoretical and empirical training cost analyses from WA1 & QA1 in the Appendix.\n\nAs for the potential concern regarding slow convergence, we are surprised to observe that HetSynLIF in fact converges faster in practice (Fig. 2D, Fig. 3B, Fig. 4A). Due to space limitations, we kindly refer you to our response to **Reviewer L2NP (WA2 & QA1)** for detailed empirical evidence.\n\n---\n**References**\n\n[1] Nicolas Perez-Nieves, et al. Neural heterogeneity promotes robust learning. Nature communications, 12(1):5791, 2021.\n\n[2] Hanle Zheng, et al. Temporal dendritic heterogeneity incorporated with spiking neural networks for learning multi-timescale dynamics. Nature Communications, 15(1):277, 2024.\n\n[3] Guillaume Bellec, et al. Long short-term memory and learning-to-learn in networks of spiking neurons. Advances in neural information processing systems, 31, 2018."}, {"review_id": "PjHxI80OJx", "reviewer": "Reviewer_L2NP", "summary": "This work proposes HetSyn, a variant of a spiking neural network where the synaptic time constant of each synapse is treated as an independent trainable parameter. The authors applied the proposed model to four different tasks and demonstrated that it outperforms the model where only the neuron-level membrane time constant is trainable and models without plastic decay time constants.", "questions": "Have you compared the proposed model with the previous models where synaptic delays are trained? In what kind of tasks do you think the proposed model performs better?\n\nRefs: \n\nZhang, Malu, et al. \"Supervised learning in spiking neural networks with synaptic delay-weight plasticity.\" Neurocomputing 409 (2020): 103-118.\n\nYu, Qiang, et al. \"Improving multispike learning with plastic synaptic delays.\" IEEE Transactions on Neural Networks and Learning Systems 34.12 (2022): 10254-10265.", "limitations": "Please see the comments above", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength: \n\nThe numerical experiments clearly demonstrate the advantage of the proposed model against the model with adaptive membrane time constant in pattern generation, working memory, and speech recognition tasks.  \n\nGiven the popularity of the membrane time constant adaptation in spiking neural network literature (e.g., Fang et al., ICCV 2021), I thought trainable synaptic time constant has also been implemented before, but I couldn’t find a previous work that specifically implements this variant. Several works previously introduced trainable synaptic delays (see the reference below), but these mechanisms are mathematically distinct from trainable synaptic time constant introduced here.\n\nWeakness: \n\nThe data analysis presented in Fig. 1A is misleading from a neuroscience perspective. In excitatory synapses in the cortex, there are two neuro-transmitter types: AMPA and NMDA, having different decay timescales. AMPA decays fast in a few milliseconds, while NMDA decays slowly in the order of 100 milliseconds. Fig. 1A shows a bimodal distribution which presumably corresponds to AMPA and NMDA components. The claim of ‘mildly long-tailed distribution’ is somewhat odd, given this underlying biology. Additionally, the importance of having these two neurotransmitters with different timescales has been studied extensively in computational neuroscience literature (e.g., Brunel and Wang, J Comp Neurosci, 2001; Panzeri et al., Trends Neurosci 2010).     \n\nSome of the comparisons are not well controlled. For instance, in Fig. 2D, the authors claim that the HetSynLIF model converges faster than the other models. However, the comparison was performed at a single learning rate; thus it does not rule out the possibility that this particular learning rate is optimized for HetSynLIF over others. To claim faster convergence, the hyperparameters of each model should be optimized individually for their best performance for a fair comparison.", "was_revised": true, "final_justification": "The rebuttal effectively addressed my concerns regarding the relationship with previous related works and hyper-parameter issues. While their claims about the long-tailed synaptic time constant distribution in the brain are somewhat exaggerated, the argument is sufficiently sound to serve as motivation for artificial spiking neural networks training. Overall, I believe the manuscript meets the criteria for acceptance.", "rebuttal": "We sincerely thank you for your thoughtful feedback and hope that the responses below could address your concerns.\n\n---\n**Weaknesses**\n>**Weakness 1:** The data analysis presented in Fig. 1A is misleading from a neuroscience perspective. ... Fig. 1A shows a bimodal distribution which presumably corresponds to AMPA and NMDA components. The claim of 'mildly long-tailed distribution' is somewhat odd, given this underlying biology.\n\n**WA1:** Thank you for the insightful and biologically grounded comments relevant to Fig. 1A. We apologize for the insufficient explanation in the original manuscript and provide further clarification below.\n\nTo the best of our knowledge, AMPA and NMDA are receptor types rather than neurotransmitters. Both are ionotropic glutamate receptors, and glutamate is the primary excitatory neurotransmitter in the cortex. As you rightly noted, biological neurons express various receptor types beyond AMPA and NMDA, each mediating post-synaptic currents with distinct decay timescales. However, our model does not aim to explicitly capture neurotransmitter- or receptor-level mechanisms. Instead, we work at a higher level of abstraction(the synapse level) and use the **effective synaptic time constant**, which refers to the characteristic timescale over which a post-synaptic response decays from its peak back to baseline. This effective timescale typically reflects the combined influence of multiple biophysical processes, such as neurotransmitter release and clearance, receptor kinetics (e.g., AMPA, NMDA), among others.\n\n**Regarding the bimodal distribution shown in Fig. 1A:** We would like to clarify that it does **not** correspond to AMPA and NMDA components. As discussed above, the distribution represents the effective synaptic time constant, not receptor-specific dynamics. The data were obtained without any modification from a published dataset (Campagnola L, et al., Science, 2022 [1]), which reports empirically measured values of effective synaptic decay time constants across biological synapses. Notably, since long-tailed distributions of synaptic time constants are commonly observed in biological systems, the dataset applied a clipping procedure by setting all values above 500 ms to 500 ms. As a result, some data points accumulate at 500 ms, giving rise to an artificial secondary peak at that point. Thus, supported by biological evidence, the dataset structure, and the distribution in Fig. 1A, our description of it as a 'mildly long-tailed distribution' is appropriate and consistent with the data. To avoid potential misunderstanding, we will revise the figure in the updated manuscript by using a distinct color for the final histogram bin and excluding it from the KDE fit.\n\n---\n>**Weakness 2:** Some of the comparisons are not well controlled. For instance, in Fig. 2D, ..., the hyperparameters of each model should be optimized individually for their best performance for a fair comparison.\n\n**WA2:** We appreciate your concern regarding the fairness of the convergence comparison in Fig. 2D, and we would like to clarify our motivation and provide further evidence to support our findings.\nIn pattern generation task, we used a fixed learning rate of 1e-3 and kept all training settings identical across models except for their architectures to ensure fair and consistent comparisons. We emphasize that this learning rate was not selected to favor HetSynLIF. Instead, it's the default setting of the Adam optimizer in PyTorch and is widely adopted. Furthermore, we observe that many prior studies (e.g., [2, 3]) also adopt the same learning rate across models when evaluating convergence speed, suggesting that our setup is consistent with common practices in related work.\n\nNevertheless, we have carefully considered your suggestion and found it necessary to include additional experimental results to further support our conclusions. However, due to time and computational resource constraints, we were unable to conduct an exhaustive grid search across all models. To address this concern, we evaluated all models mentioned in Fig.2D under four different learning rates uniformly sampled between 1e-4 and 5e-3, and we present the corresponding MSE with respect to training iterations for each model in the table below. The results show that, under identical training iterations, HetSynLIF consistently demonstrates the fastest convergence and the lowest final MSE, suggesting that it completes the task more effectively than its counterparts. We will revise the manuscript to better clarify this point and include these additional results to strengthen the experimental rigor.\n\n|Training Iteration (lr = 1e-4)|50|100|200|500|1000|\n|---|---|---|---|---|---|\n|F-HomNeuLIF|0.282|0.264|0.244|0.225|0.222|\n|F-HetNeuLIF|0.277|0.251|0.220|0.201|0.192|\n|F-HomNeuALIF|0.261|0.244|0.232|0.224|0.221|\n|F-HetSynLIF|**0.254**|**0.227**|**0.214**|**0.160**|**0.125**|\n\n|Training Iteration (lr = 5e-4)|50|100|200|500|1000|\n|---|---|---|---|---|---|\n|F-HomNeuLIF|0.217|0.211|0.208|0.207|0.206|\n|F-HetNeuLIF|0.216|0.211|0.201|0.167|0.145|\n|F-HomNeuALIF|0.234|0.224|0.223|0.219|0.218|\n|F-HetSynLIF|**0.211**|**0.196**|**0.134**|**0.059**|**0.041**|\n\n|Training Iteration (lr = 1e-3)|50|100|200|500|1000|\n|---|---|---|---|---|---|\n|F-HomNeuLIF|0.213|0.208|0.206|0.205|0.204|\n|F-HetNeuLIF|0.213|0.206|0.181|0.141|0.137|\n|F-HomNeuALIF|0.224|0.220|0.218|0.211|0.207|\n|F-HetSynLIF|**0.209**|**0.178**|**0.139**|**0.048**|**0.021**|\n\n|Training Iteration (lr = 5e-3)|50|100|200|500|1000|\n|---|---|---|---|---|---|\n|F-HomNeuLIF|0.219|0.215|0.214|0.214|0.214|\n|F-HetNeuLIF|0.215|0.193|0.187|0.163|0.162|\n|F-HomNeuALIF|0.218|0.217|0.215|0.209|0.213|\n|F-HetSynLIF|**0.167**|**0.161**|**0.157**|**0.119**|**0.015**|\n\n---\n**Questions**\n>**Question 1:** Have you compared the proposed model with the previous models where synaptic delays are trained? In what kind of tasks do you think the proposed model performs better?\n\n**QA1:** We sincerely thank you for the insightful comments and for recognizing the novelty of our proposed approach. To the best of our knowledge, we are the first to incorporate synaptic heterogeneity into SNNs, which offers a biologically plausible yet computationally powerful approach for versatile timescale integration.\n\nWe appreciate you for pointing out the two excellent works [4, 5] on synaptic delays. These studies highlight the potential of synaptic delays to enhance SNN performance, which aligns well with our motivation as stated in the introduction: *\"This calls for new learning paradigms, either by adapting established methods from ANNs or by drawing inspiration from biological mechanisms.\"* Synaptic delay is indeed a crucial biological feature at the synapse level and clearly falls into the latter category. **Based on this, we believe it is necessary to cite these two works in our paper.** We will include the aforementioned delay-based studies in the revised manuscript and acknowledge their relevance in the *Introduction* section.\n\n**The first part of this question:** While we did not explicitly discuss synaptic delays in the main text, we did include one representative delay-based method (corresponding to the first work mentioned by the reviewer) in our empirical comparisons in Table 1. We did not initially elaborate on this comparison because synaptic delays and our proposed method reflect different biological properties and address distinct aspects of temporal processing, although both operating at the synaptic level.\n- Synaptic delays primarily facilitate spatial-temporal **synchronization** by shifting spike timings, thereby aligning neural activity across channels. However, they do not alter the intrinsic temporal dynamics of individual synapses.\n- In contrast, our trainable synaptic time constants enable **versatile timescale integration** by dynamically adjusting how long past information is retained, allowing the model to better capture temporally diverse input patterns.\n\nAs a quick empirical comparison, we observed that both referenced works and our proposed model have been evaluated on the TiDigits dataset, where our model achieves higher accuracy than the delay-based models. We include this result to offer a reference point, but we emphasize that it does not constitute the core of our contribution. Our main contribution lies in introducing synaptic heterogeneity as a novel biologically inspired mechanism for SNNs, and demonstrating its effectiveness in versatile timescale integration. This expands the design space of SNNs and strengthens the link between biological plausibility and computational capability.\n\n|Methods|Accuracy|\n|---|---|\n|ReSuMe-DW[4]|92.45%|\n|PBSNLR-DW[4]|96.50%|\n|TDP-DL[5]|97.16%|\n|**HetSynLIF(Ours)**|**98.99%**|\n\n**The second part of this question:** Based on the aforementioned differences between synaptic delays and our proposed method, we believe that our proposed model is especially beneficial in tasks that involve rich or diverse timescale structures, such as speech recognition, working memory–dependent tasks, and complex spatio-temporal information processing.\n\n---\n**References**\n\n[1] Campagnola L, et al. Local connectivity and synaptic dynamics in mouse and human neocortex[J]. Science, 2022, 375(6585): eabj5861.\n\n[2] Fang W, et al. Incorporating learnable membrane time constant to enhance learning of spiking neural networks[C]//Proceedings of the IEEE/CVF international conference on computer vision. 2021: 2661-2671.\n\n[3] Liu F, et al. STNet: A novel spiking neural network combining its own time signal with the spatial signal of an artificial neural network[J]. Frontiers in Neuroscience, 2023, 17: 1151949.\n\n[4] Zhang M, et al. Supervised learning in spiking neural networks with synaptic delay-weight plasticity[J]. Neurocomputing, 2020, 409: 103-118.\n\n[5] Yu Q, et al. Improving multispike learning with plastic synaptic delays[J]. IEEE Transactions on Neural Networks and Learning Systems, 2022, 34(12): 10254-10265."}, {"review_id": "ucf52Qc0jb", "reviewer": "Reviewer_5HJ5", "summary": "The authors propose the use of spiking neural networks (SNNs) for classification or temporal signal generation tasks, enhanced by introducing heterogeneity in synaptic time constants. They demonstrate that these networks outperform conventional networks lacking this variability.", "questions": "When training your network on the delayed match-to-sample task, can you interpret the parameters obtained post-training? Specifically, in the distribution of time constants, do you observe values on the order of the delay duration (around 800 milliseconds)?\n\nThe state-of-the-art performance for the SHD dataset has been achieved using spiking neural networks with delays. Do you believe it would be feasible to combine these two approaches to further enhance performance?", "limitations": "A limitation of this work is its relatively incremental progress compared to existing research, particularly citation 22.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "One of the notable strengths of this paper is its foundation in physiological data, illustrating how such biological inspiration can enhance the performance of spiking neural networks. The performance improvements are evident across the tasks presented, with classification results that surpass those of similar networks (RSNNs) without heterogeneity. The application to a delayed match-to-sample task is particularly compelling.\n\nA limitation of this study is its incremental nature compared to previous work that has explored variability in SNNs, such as citation 22. Additionally, the paper lacks an interpretation of the parameters obtained after training, which could provide insights into the underlying mechanisms driving the improved performance.", "was_revised": true, "final_justification": "The response to my comments were encouraging, however, I will not raise my score and keep it to 4.", "rebuttal": "We sincerely thank you for your thoughtful feedback and hope that the responses below could address your concerns.\n\n---\n>**Weakness 1 & Limitation 1:** A limitation of this study is its incremental nature compared to previous work that has explored variability in SNNs, such as citation 22. \n\n**WA1 & LA1:** We appreciate your concern regarding the contribution of our work in comparison to prior studies, and your thoughtful engagement with the relevant literature. While we respectfully disagree with the assessment that our work is relatively incremental progress, we appreciate the opportunity to clarify its contributions and highlight the key distinctions between our approach and prior efforts, particularly citation [22].\n\nAs we stated in the introduction, we focus on strengthening the biological foundations of SNNs by revisiting fundamental neurobiological mechanisms. Specifically, we focus on synaptic heterogeneity, a well-established phenomenon in neuroscience known to support versatile timescale integration and cognitive functions. Despite its recognized importance in biological systems, its computational potential in SNNs remains largely unexplored and highly promising. To the best of our knowledge, our work is **the first** to investigate this direction and is fundamentally different from existing approaches. We believe this represents a meaningful and impactful contribution to the field, which we summarize below.\n\n1. **Bio-Grounded Design:** Drawing on biological evidence, HetSyn is the first SNN modeling framework to incorporate synaptic heterogeneity for versatile timescale processing.\n\n2. **Detailed Theoretical Proof:** We provide a theoretical analysis demonstrating HetSyn’s generalization capacity with diverse spiking neuron models.\n\n3. **Strong Empirical Results:** We instantiate HetSyn as HetSynLIF and demonstrate its competitive performance across multiple tasks and benchmarks.\n\n4. **Parameter Insight:** We provide analysis of the learned time constants, offering interpretability and task-aligned insights (see Fig. 4D, Fig. A4, and our responses to Weakness 2 and Question 1).\n\nWe greatly appreciate the valuable insights provided by citation [22] on heterogeneity in SNNs, which we regard as an important step toward understanding diversity in neural computation. Nonetheless, our work differs in several important ways and provides a complementary perspective to prior work, as detailed below.\n\n1. **Finer Level of Heterogeneity:** While citation [22] investigates **neuron-level** heterogeneity by varying membrane properties across neurons, our work focuses on the more fine-grained and biologically fundamental **synapse-level** heterogeneity.\n\n2. **Different Core Objectives:** Citation [22] emphasizes neuron-level variation for improving **robustness**, while our work centers on synaptic-level mechanisms to support **versatile timescale integration**.\n\n3. **Broader Experimental Validation:** In addition to the robustness and timescale generalization tests conducted in [22], we further evaluated our model on working memory and limited-resource scenarios, thereby providing a more comprehensive validation of its capabilities.\n\nNotably, other reviewers have also acknowledged the originality and value of our contributions. That said, we recognize that the initial manuscript may not have been sufficiently clear, and we have carefully revised the manuscript to present our ideas more clearly. Again, we sincerely thank you for your thoughtful review and we hope this clarification helps address your concerns regarding the scope and contribution of our work. \n\n---\n>**Weakness 2:** Additionally, the paper lacks an interpretation of the parameters obtained after training. \\\n**Question 1:** When training your network on the delayed match-to-sample task, can you interpret the parameters obtained post-training? Specifically, in the distribution of time constants, do you observe values on the order of the delay duration (around 800 milliseconds)? \n\n**WA2 & QA1:** We thank you for this insightful question regarding the interpretability of learned time constants in the delayed match-to-sample (DMS) task. Motivated by your comment, we have conducted an additional analysis to explore this question in greater depth. We hope this new experiment addresses your concern, and we sincerely thank you for bringing up this important point.\n\nThe DMS task inherently requires both short-term and long-term memory mechanisms: long-term memory is needed to retain cue information (e.g., \"left\" or \"right\") across the delay period, while short-term memory helps to suppress irrelevant noise. Ideally, training encourages the cue-channel $\\tau$ to increase toward the delay duration (~800 ms), while the noise-channel $\\tau$ decreases to promote fast forgetting. \n\nTo test this hypothesis, we initialized $\\tau$ from Gaussian distributions with means $\\mu \\in \\\\{100,200,400\\\\}~\\text{ms}$ , where the standard deviation was set to $0.1\\mu$, and trained the model. For each setting, we conducted 5 independent runs, and reported the averaged results in the table below. \n\n|Initialization|Cue-channel(after training)|Noise-channel(after training)|Synapses with $\\tau$ > 700 ms (after training)|Accuracy|Accuracy(masked long $\\tau$)|\n|:---:|:---:|:---:|:---:|:---:|:---:|\n|$\\mathcal{N}(100,~10^2)$|154.38(+54.38%)|85.59(-14.41%)|5.25%|99.97%|75.68%(-24.29%)|\n|$\\mathcal{N}(200,~20^2)$|252.43(+26.22%)|181.93(-9.04%)|6.05%|100.00%|76.47%(-23.53%)|\n|$\\mathcal{N}(400,~40^2)$|430.70(+7.68%)|382.29(-4.43%)|5.80%|99.87%|77.15%(-22.72%)|\n\nWe observed consistent trends across all initialization settings, with the learned $\\tau$ values exhibiting a clear divergence between input pathways.\n\n- For synapses receiving cue signals, the mean $\\tau$ increased significantly, enabling long-term information retention required for task completion.\n\n- For synapses receiving noise inputs, the mean $\\tau$ decreased notably, suggesting a functional adaptation to suppress irrelevant temporal integration.\n\nWe further analyzed the distribution of $\\tau$ after training, and **observed values on the order of the delay duration** (around 800 ms). Specifically, we used $\\tau\\ge 700~\\text{ms}$ as the statistical criterion and found that approximately **5-6% of synapses** exhibited time constants in the same order of magnitude as the delay duration. \n\nWe hypothesize that **this small subset of $\\text{long-}\\tau$ synapses plays a critical role** in solving the task. To verify this, we masked these $\\text{long-}\\tau$ synapses by resetting their $\\tau$ values to their original initialization means, and re-evaluated the model. The results showed a significant drop in accuracy after masking, supporting the importance of these long-timescale synapses.\n\nIn summary, we analyzed and interpreted the $\\tau$ obtained after training and demonstrated the task-aligned functional specialization of synaptic time constants. These results further support the effectiveness of HetSyn in handling versatile timescale integration by adaptively adjusting $\\tau$ values based on input characteristics. We sincerely thank you for raising this insightful and technically relevant question. We will include the above analysis and results in the appendix of the revised manuscript.\n\n---\n>**Question 2:** The state-of-the-art performance for the SHD dataset has been achieved using spiking neural networks with delays. Do you believe it would be feasible to combine these two approaches to further enhance performance?\n\n**QA2:** We thank you for highlighting the success of delay-based SNNs on the SHD dataset. Indeed, recent works [1, 2] have demonstrated that incorporating synaptic delays can significantly improve task performance in temporally complex datasets like SHD. In recognition of their relevance and contributions, we believe it is necessary to cite these works in the revised manuscript.\n\nAlthough both synaptic delays and our proposed method operate at the synaptic level, they reflect different biological properties and address distinct aspects of temporal processing and may complement each other.\n- Synaptic delays primarily facilitate spatial-temporal **synchronization** by shifting spike timings, thereby aligning neural activity across channels. However, they do not alter the intrinsic temporal dynamics of individual synapses.\n- Our trainable synaptic time constants enable **versatile timescale integration** by dynamically adjusting how long past information is retained, allowing the model to better capture temporally diverse input patterns.\n\nWe believe that combining delays with HetSyn is not only feasible but potentially beneficial. While delays enhance spatial-temporal synchronization by aligning spikes across input channels, HetSyn enables fine-grained control over information retention across versatile timescales. Together, these mechanisms may allow SNNs to handle both precise spike timing and temporally diverse patterns more effectively, potentially leading to improved performance on complex temporal tasks. We consider this an exciting direction for future work, and we are interested in exploring how the synergy of delay-based alignment and versatile timescale integration can further enhance performance on temporal tasks.\n\n---\n>**Paper Formatting Concerns:** some minor typos : \"The results of the experiments shows significant improvement.\" - ...\n\n**Response to Paper Formatting Concerns:** We are encouraged that you took a close interest in our work, and we greatly appreciate your careful reading and attention to detail. We have carefully reviewed the manuscript for any potential typos or clarity issues.\n\n---\n**References**\n\n[1] Hammouamri I, et al. Learning delays in spiking neural networks using dilated convolutions with learnable spacings[J]. arXiv preprint arXiv:2306.17670, 2023.\n\n[2] Baronig, M., et al. Advancing spatio-temporal processing through adaptation in spiking neural networks. Nat Commun 16, 5776 (2025)."}, {"review_id": "JKJP3el1z7", "reviewer": "Reviewer_2fHR", "summary": "This paper introduces HetSyn, which incorporates synaptic heterogeneity into spiking neural networks (SNNs) to enable multi-timescale integration. The authors instantiated HetSyn in combination with LIF neurons as HetSynLIF and experimentally validated it in pattern generation, delayed match-to-sample, speech recognition and visual recognition tasks.", "questions": "See weaknesses.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strength:\n1. HetSyn introduces synaptic heterogeneity into the SNN, which is consistent with biological mechanisms.\n2. The authors analyze the proposed HetSynLIF and point out that other LIF neuronal variants that exist can be treated as special cases of HetSynLIF.\n3. The authors demonstrated the effectiveness of the proposed method across multiple tasks.\n\n\nWeakness:\n1. The details of HetSynLIF need to be described in more detail, such as how the synaptic time constants are set and their impact on performance; if the synaptic time constants are learnable, what is the evolutionary trend during training?\n2. Could the theoretical contribution of HetSynLIF to the spatio-temporal representation performance of SNNs be analyzed in depth?\n3. The authors should analyze the impact of setting up individual time constants for each synapse on the overhead of the SNN, as this incurs a large number of additional parameters.\n4. The experiments in this paper are limited to tiny taskss, making it difficult to demonstrate the effectiveness of the proposed method for challenging tasks and its scalability. Does HetSynLIF work for typical visual recognition tasks, such as CIFAR and ImageNet? Furthermore, [1] achieved significantly better performance on SHD, even with a single-layer SNN. How does this justify the performance advantage of HetSynLIF?\n\n[1] Advancing Spatio-Temporal Processing in Spiking Neural Networks through Adaptation. arXiv. 2024.", "was_revised": true, "final_justification": "Although the author's response indicates that this paper has limited insights into typical static object recognition (such as CIFAR and ImageNet), I maintain my positive score given the paper's other strengths.", "rebuttal": "We sincerely thank you for your thoughtful feedback and hope that the responses below could address your concerns.\n\n---\n>**Weakness 1**: The details of HetSynLIF need to be described in more detail, such as how the synaptic time constants are set and their impact on performance; if the synaptic time constants are learnable, what is the evolutionary trend during training?\n\n**WA1**: We appreciate your attention to the setup and evolutionary trend of synaptic time constants, and provide further clarifications below.\n\nActually, we have included the initialization of synaptic time constants ($\\tau$), along with other task-specific configurations in **Appendices B–E** to ensure reproducibility. Based on our experiments, the initialization of $\\tau$ does not significantly impact performance, as **it is learnable and adjusts according to task requirements**, either increasing or decreasing as needed. Additionally, while we have shown the changes in $\\tau$ before and after learning in **Fig. 4D** and **Fig. A4**, we have carefully considered your feedback and agree that the previous description lacked sufficient detail. Therefore, we conducted an additional experiment to provide a more detailed explanation of its evolution trend.\n\nThe DMS task inherently requires both short-term and long-term memory mechanisms: long-term memory is needed to retain cue information (e.g., \"left\" or \"right\") across the delay period, while short-term memory helps to suppress irrelevant noise. Ideally, training encourages the cue-channel $\\tau$ to increase toward the delay duration (~800 ms), while the noise-channel $\\tau$ decreases to promote fast forgetting. We initialized $\\tau$ from Gaussian distributions with means $\\mu \\in \\\\{100, 200, 400 \\\\} \\text{ms}$ , where the standard deviation was set to $0.1\\mu$, and trained the model using 5 independent runs.\n\n|Initialization|Cue-channel|Noise-channel|\n|:---:|:---:|:---:|\n|$\\mathcal{N}(100,~10^2)$|154.38(+54.38%)|85.59(-14.41%)|\n|$\\mathcal{N}(200,~20^2)$|252.43(+26.22%)|181.93(-9.04%)|\n|$\\mathcal{N}(400,~40^2)$|430.70(+7.68%)|382.29(-4.43%)|\n\nWe observed consistent trends across all initialization settings, with the learned $\\tau$ values exhibiting a clear divergence between input pathways.\n- For synapses receiving cue signals, the mean $\\tau$ increased significantly, enabling long-term information retention required for task completion.\n- For synapses receiving noise inputs, the mean $\\tau$ decreased notably, suggesting a functional adaptation to suppress irrelevant temporal integration.\n\nThe results align with our expectations and validate our hypothesis that $\\tau$ automatically learns and optimizes in the direction required by the task.\n\n\n---\n\n>**Weakness 2**: Could the theoretical contribution of HetSynLIF to the spatio-temporal representation performance of SNNs be analyzed in depth?\n\n**WA2**:  We would like to provide the following analysis of the theoretical contribution of HetSynLIF to the spatio-temporal representation performance of SNNs.\n\nFeaturing synapse-specific decay factors, HetSynLIF effectively represents dynamic spatio-temporal inputs and captures the natural variation in temporal behaviors observed in biological systems. From a biological perspective, synaptic heterogeneity is a crucial factor in enabling neural systems to encode diverse temporal patterns. Our approach leverages these biological principles, applying them computationally to enhance spatio-temporal encoding in SNNs.\n\nEmpirical results show that during training, HetSyn allows each synapse to adapt its $\\tau$ according to task requirements, with synapses for long-term memory increasing $\\tau$ and those for short-term memory decreasing it. Additionally, theoretical proof in Appendix A demonstrates that HetSynLIF generalizes to several models, showing its ability to combine the strengths of these models based on the specific task requirements.\n\nIn summary, these features collectively enable HetSynLIF to excel in spatio-temporal representation performance. Although our primary focus is on its computational potential, we believe that theoretical analysis is also crucial and we will include the above analysis in the revised manuscript.\n\n\n---\n\n>**Weakness 3**: The authors should analyze the impact of setting up individual time constants for each synapse on the overhead of the SNN, as this incurs a large number of additional parameters.\n\n**WA3**: We conducted both a theoretical analysis and an additional set of experiments to evaluate the training cost. **Due to the 10,000-character constraint, please refer to our response to Reviewer auyx (WA1 & QA1) for full table of results**. We summarize the conclusions below and hope these analyses help clarify the impact of our design and address your concerns.\n\nTheoretical and empirical results indicate that HetSynLIF indeed introduces a slight increase in training cost when evaluated **under identical architectures and neuron counts**. Given the notable performance gains and the potential of synaptic heterogeneity in SNNs, we consider the added training cost a reasonable trade-off at this early stage. This complexity is expected and biologically plausible, as synapses greatly outnumber neurons in the brain.\n\nMoreover, HetSynLIF achieves comparable or even superior performance with significantly **fewer neurons**. For example, as the table shown in our response to Reviewer auyx (WA1 & QA1), **F-HetSynLIF (20 neurons) outperforms R-HetNeuLIF (100 neurons) with lower memory and time costs**. Additionally, Fig. 2D, Fig. 3B, Fig. 4A, and our response to Reviewer L2NP (WA2 & QA1) demonstrate that HetSynLIF **converges faster**, requiring **fewer training iterations**. Together, these findings suggest that **the increased per-unit complexity is effectively offset and may even serve as an advantage in overall training cost**.\n\nIn future work, we plan to explore methods to reduce the computational complexity of HetSyn, such as incorporating sparse connectivity designs. We will also explicitly discuss potential future directions in the revised manuscript. \n\n\n---\n\n>**Weakness 4.1**: The experiments in this paper are limited to tiny tasks, making it difficult to demonstrate the effectiveness of the proposed method for challenging tasks and its scalability. Does HetSynLIF work for typical visual recognition tasks, such as CIFAR and ImageNet?\n\n**WA4.1**: Below, we first clarify the rationale behind our task selection and then present preliminary results on an event-based visual recognition task to further support our claims.\n\nOur work aims to explore the computational potential of synaptic heterogeneity for **versatile timescale integration** in SNNs. To this end, we prioritize tasks with rich or extended temporal structures. While HetSynLIF can work with typical visual recognition tasks like CIFAR and ImageNet, these datasets are static and lack meaningful temporal structure. In the SNN field, **such tasks are often handled by repeating the same image over several timesteps, which does not provide meaningful temporal dynamics and is not aligned with our focus on versatile timescale integration**. \n\nNevertheless, we have carefully considered your suggestion and conducted extra experiments on the DVS Gesture dataset, **an event-based and real-world visual recognition task with richer temporal dynamics**, and present preliminary results on the table below. Due to time constraints, we did not extensively optimize the architecture or hyperparameters. However, HetSynLIF outperformed HomNeuLIF in accuracy, which is sufficient to demonstrate the effectiveness of HetSyn in versatile timescale integration.\n\n|Model|DVS Gesture|\n|:-:|:-:|\n|F-HomNeuLIF|95.49%|\n|F-HetSynLIF|96.18%|\n\n\n---\n\n>**Weakness 4.2**: [1] achieved significantly better performance on SHD, even with a single-layer SNN. How does this justify the performance advantage of HetSynLIF?  \n\n**WA4.2**: We apologize for not noticing this timely and insightful work [1] earlier, as it was still under review when we wrote our manuscript. After carefully reading the paper, we find its contributions both insightful and inspiring. **However, we believe that the work presented in [1] does not conflict with our HetSynLIF approach**.\n\nIn SNNs, the dynamics of neuron models are typically represented using differential equations. To simulate these dynamics on digital hardware, they must be discretized into a time-stepped form, with updates occurring at fixed intervals for computationally feasible approximations. A commonly used discretization method is the forward Euler scheme, favored for its simplicity and efficiency. In line with standard practice in the field, our HetSynLIF also adopts this approach. Despite its widespread use, the forward Euler method can have accuracy limitations. The work in [1] rigorously demonstrates the shortcomings of the conventional forward Euler discretization used in the ALIF model and addresses them by adopting the alternative Symplectic Euler discretization approach. \n\n**Therefore, the work in [1] and ours address distinct yet complementary challenges**. While [1] focuses on addressing the stability and parameterization challenges in solving differential equations for SNNs, our work explores the computational potential of synaptic heterogeneity for versatile timescale integration and introduces a new model to leverage this potential. \n \nWe believe that incorporating this advanced discretization technique into HetSynLIF could further improve its performance. This presents a promising direction for future research, and we will cite and discuss this work in the Future Work part of the revised manuscript. We hope this response clarifies the relationship between [1] and our contributions and we welcome further discussion.\n\n\n---\n\n**References** \n\n[1] Baronig M, et al. Advancing spatio-temporal processing through adaptation in spiking neural networks[J]. Nature Communications, 2025, 16(1): 5776."}]

Author rebuttal:

Meta-review: This paper proposes a framework HetSyn for modeling prominent heterogeneity by combining the widely observed but underutilized characteristic of synaptic heterogeneity in biological neurons. This framework combines synaptic specific time constants to reflect synaptic heterogeneity and is instantiated through HetSyn LlF. 

After rebuttal, three reviewers believed that their doubts are fixed well. Although Reviewer auyx keeps a negative score, the weaknesses or suggestions seem to be supported well by the supplementary experiments.
Decision: Accept (poster)