TS-LIF: A Temporal Segment Spiking Neuron Network for Time Series Forecasting
Authors: FENG SHIBO
Wanjin Feng
Xingyu Gao
Peilin Zhao
Zhiqi Shen
Venue: ICLR 2025 Poster (2025)
Keywords: spiking neural network
time series forecasting
Application
Primary area: learning on time series and dynamical systems
TL;DR: We proposed a Temporal Segment Spiking Neuron Network (TS-LIF) for multivariate time series forecasting, supported by stability analysis and frequency response analysis to demonstrate its effectiveness and efficiency.

Abstract: Spiking Neural Networks (SNNs) offer a promising, biologically inspired approach for processing spatiotemporal data, particularly for time series forecasting.
However, conventional neuron models like the Leaky Integrate-and-Fire (LIF) struggle to capture long-term dependencies and effectively process multi-scale temporal dynamics.
To overcome these limitations, we introduce the Temporal Segment Leaky Integrate-and-Fire (TS-LIF) model, featuring a novel dual-compartment architecture.
The dendritic and somatic compartments specialize in capturing distinct frequency components, providing functional heterogeneity that enhances the neuron's ability to process both low- and high-frequency information.
Furthermore, the newly introduced direct somatic current injection reduces information loss during intra-neuronal transmission, while dendritic spike generation improves multi-scale information extraction.
We provide a theoretical stability analysis of the TS-LIF model and explain how each compartment contributes to distinct frequency response characteristics.
Experimental results show that TS-LIF outperforms traditional SNNs in time series forecasting, demonstrating better accuracy and robustness, even with missing data.
TS-LIF advances the application of SNNs in time-series forecasting, providing a biologically inspired approach that captures complex temporal dynamics and offers potential for practical implementation in diverse forecasting scenarios.

Published as a conference paper at ICLR 2025
TS-LIF: A TEMPORAL SEGMENT SPIKING NEURON NETWORK FOR TIME SERIES FORECASTING
Shibo Feng : Wanjin Feng" Xingyu Gao Peilin Zhao Zhiqi Shen
shibo001 @ntu. edu. sg: (rengwanjing geox inguj e meme... a ac. en Nanyang Technological University" University of Chinese Academy of Sciences?
Tencent AI Lab Webank-NTU Joint Research Institute on Fintech, NTU, Singapore
ABSTRACT
Spiking Neural Networks (SNNs) offer a promising, biologically inspired ap- proach for processing spatiotemporal data, particularly for time series forecast- ing. However, conventional neuron models like the Leaky Integrate-and-Pe (LIF) struggle capture long-term dependencies and effectively process multi- scale temporal dynamics. To overcome these limitations, we introduce the Tem- poral Segment Leaky Aitegrate-and-Firg (TS-LIF) model, featuring novel dual- compartment architecture. The dendritic and somatic compartments specialize in capturing distinet frequency components, providing functional heterogeneity that enhances the neuron's 's ability to process both low- and fighffreueecy informa- tion. Furthermore, the newly introduced direct somatic current injection reduces information loss during intra-neuronal transmission, while dendritic spike gen- eration improves multi-scale information extraction. We provide a theoretical stability analysis of the TS-LIF model and explain how each compartment con- tributes to distinct frequency response characteristics. Experimental results show that TS-LIF outperforms traditional SNNs in time series forecasting, demonstrat- ing better accuracy and robustness, even with missing data. TS-LIF advances the application of SNNs in time-series forecasting, providing biologically inspired approach that captures complex temporal dynamics and offers potential for practi- cal implementation in diverse forecasting scenarios. The source code available at lhttts:: thub... com/ com/kkking-kk/IS--L
INTRODUCTION
Spiking Neural Networks (SNNs) have garnered significant attention due to their biological plau- sibility and unique capacity to process spatiotemporal information (Hu et al., 2024). Unlike tradi- tional artificial neural networks (ANNs), which rely on continuous activations, SNNs utilize discrete spikes as their primary communication mechanism (Wang et al., 2024). This event-driven nature al- lows SNNs to operate efficiently, only processing information when necessary, making them highly suited for tasks involving sparse, time-dependent data (Gast et al. 2024). By encoding information through the precise timing of spikes, SNNs achieve fine temporal resolution. providing significant advantage in applications requiring both temporal and spatial accuracy (Zhu et al.) 2024). Moreover, the asynchronous processing of SNNs closely mimics biological neurons, enabling
computation (Ganguly et al. 2024 Bellec al. 2020).
One domain that aligns naturally with SNNs is time series forecasting, which involves predicting future values based on historical observations. It is critical in various domains, including finance, weather prediction, healthcare, and energy monitoring (Lin et al., 2024; llbert et al.) 2024a An- gelopoulos et al.) 2024). The sequential nature of time series data, characterized by time depen- dencies, aligns well with SNNs' temporal processing abilitics. Traditional deep learning models, such Temporal Convolutional Networks (TCNs), and Transformer, have been effective in captur- ing long-term dependencies (Luo & Wang 2024 Wu et al. 2021 llbert et al. 2024b). However,
"Equal contribution. "ooresponniig to: Peilin Zhao (masonzhan@tenceet.cocm and Zhiqi Shen (zqshen @ntu.cdu.sg)

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these models typically require significant computational resources to manage complex temporal re- lationships (Liu et al.) 2023] Feng et al. 2025). In contrast, SNNs, with their event-driven and sparse computational architecture, can offer more efficient solution, particularly for applications that involve sparse temporal events and demand low energy consumption (Ly et al. 2024).
Despite the potential benefits, applying SNNs to time series forecasting has been limited. A notable exception is the work by Lv et al. (2024), which demonstrated that SNNs could achieve competi- tive results in this domain, particularly in terms of efficiency when implemented on neuromorphic hardware. However, broader adoption remains constrained by the limitations of the widely used Leaky sategrate-and-Fiin (LIF) neuron model. While the LIF neuron biologically plausible and computationally efficient, its rapid membrane potential decay impairs its ability to capture long- term dependencies (Wang & Yu (024). Furthermore, it struggles to process multi-timescal information, which is crucial for understanding both short-term fluctuations and long-term trends (Zheng et al., 2024). These challenges restrict the effectiveness of LIF-based SNNs in complex forecasting tasks, where accurate predictions require capturing patterns across multiple temporal scales.
To address these limitations, we propose the Temporal Segment LIF (TS-LIF) Neuron Model, specif- ically designed for time series forecasting. TS-LIF incorporates dual-compartment mechanism to process information across different timescales. This model extends the standard LIF neuron by introducing dendritic and somatic compartments, each responsible for capturing distinct frequency components of the input signal. Furthermore, the addition of direct somatic current injection miti- gates information loss during intra-neuronal transmission, while dendritic spike generation improves the neuron's 's capacity for extracting information across multiple scales. We establish the stability conditions for this dual-compartment model and derive the frequency-domain transfer functions for both the dendritic and somatic compartments. The TS-LIF model was evaluated on four benchmark datasets using CNN, RNN, and Transformer architectures. consistently outperforming previous LIF- based models. Additionally, TS-LIF demonstrates significant advantage in maintaining accuracy under scenarios of missing inputs. Finally, through ablation studies, we show how TS-LIF achieves superior performance by effectively decomposing input signals into different frequency components. In summary, our contributions include:
We propose the Temporal Segment LIF (TS-LIF) model, a dual-compartment neuron with dendritic and somatic branches that effectively captures multi-scale temporal features, en- hancing time series forecasting.
We establish stability conditions for TS-LIF, ensuring robustness, and derive frequency- domain transfer functions that illustrate the distinct contributions of dendritic and somatic compartments to temporal processing.
We validate TS-LIF on four benchmark datasets using CNN, RNN, and Transformer archi- tectures, demonstrating consistent improvements over based SNNs, superior accuracy, and robustness to missing inputs.
2 RELATED WORK
2.1 MODELING LONG-TERM DEPENDENCIES IN SNNS
Early SNN research using the LIF neuron model focused on simulating neuronal dynamics but strug- gled with long-term dependencies, restricting its effectiveness in memory-intensive tasks. (Wang
et al.
2023).
To address this challenge, several advanced neuron models have been proposed.
The Gated Leaky integrate-and-Fir (GLIF) model introduced a gating mechanism to regulate tem- poral information flow, improving long-term sequence modeling while maintaining energy effi- ciency (Yao et al., (022). Similarly, Wang & Yu (2024) explored autaptic connections to enhance long-term dependency processing. Dual-compartment models have also shown promise in improv- ing memory retention. The Two-Compartment LIF (TC-LIF) model divides memory between den- dritic and somatic compartments, enhancing gradient propagation and improving long-sequence retention (Zhang et al.] 2024). Building on this, the Learnable Multi-hierarchical (LM-H) neuron model introduced learnable parameters to dynamically balance historical and current information (Hao et al.) 2024). Additionally. Zheng et al. (2024) proposed a multi nuuli-ccomprrtent neuron model with temporal dendritic heterogeneity, enabling neurons process different time-scale inputs.
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Desditte
Soma
Hil
Halt
kyripss
(b)
High Irqpancy
MMMM
Aom
Originad tre serice
MMMV
Lowe bosparcy
Soria
(4)
(d)
Diagram of Neuronal Signal Processing and Integration: (a) Structural organization of neuronal signal transmission, highlighting axosomatic and axodendritic synapses. (b) A generalized two-compartment spiking neuron model, applicable to TC-LIF or LM-H models, with dendritic (gray) and somatic (orange) compartments. (c) Proposed TS-LIF model with the newly introduced direct somatic current injection and dendritic spike generation (highlighted red). (d) Time series decomposition and spike output generation in the TS-LIF model.
Figure 1:
Despite these advances, current models still fall short in effectively decomposing and integrating features from different time scales within a single input signal, leaving room for further exploration in this area.
2.2 TIME SERIES FORECASTING
Time series refers to sequence of data points recorded over time intervals, which crucial for understanding temporal dynamics in various fields (Wu et al., 2020) Feng et al., 2024: Woo al. 2024). While recent advancements in model architectures have improved forecasting accuracy, bal- ancing performance with computational efficiency remains a challenge.
Traditional models like Recurrent Neural Networks (RNNs), including LSTMs and GRUs, are widely used for sequential data but often struggle with long-term dependencies and inefficiencies on large datasets (Ilhan et al. 2021 Dera et al. 2023). Temporal Convolutional Networks (TCNs) offer a more scalable alternative by capturing long-range dependencies through dilated convolutions, allowing for parallel processing of sequences (Lea al. 2017 Luo & Wang 2024). Transformers, initially designed for natural language processing, have also been adapted for time series forecasting and generation (Ilbert et al. 2024a; Zhang & Yan 2023 Zhicheng et al. (024). Their self-attention mechanism models long-range dependencies effectively, while variants like Informer and Auto- former sparse attention and decomposition techniques to reduce computational demands (Zhou
et al. 2021 Wu et al., (021).
However, the computational requirements of TCNs and Transformers, particularly regarding energy consumption, remain substantial. Implementing these models in resource-come esource-constrained environments still challenging, even with optimizations such sparse attention and hybrid approaches.
3 PRELIMINARIES
3.1 TIME SERIES PROBLEM SETTING
We consider the task of multivariate time series forecasting, where the observations represented as a sequence
{x1, {x1.X2,.... x2,...,,xy. .T) T'C Here, represents the number of time steps, and C' denotes the number of variables. The goal is to learn predictive function that generates future values Y = {x XT XT+1} I LxC for the next time steps.
To achieve this, time series decomposition
be utilized to reveal features across different tem- poral scales, such as short-term variations and long-term trends. These features play a crucial role in developing models that handle both rapid fluctuations and slower patterns in the data. By
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modeling these components individually jointly, the predictive function can better capture the underlying structure of the time series, thereby enhancing forecasting accuracy.
3.2
LIF NEURON MODEL
The Leaky untegrate-and-Fing (LIF) neuron is widely used in SNNs due to its computational simplic- ity and biological relevance. The evolution of the membrane potential in the discrete-time domain expressed as:
(I) where a < 1 is the decay factor, u(t] represents the membrane potential at time step f, and c[t) the input current, The term st 1] accounts for resetting the membrane potential after spike. The spike output is determined by the Heaviside step function H.).. given by:
v[4 = avil 1] c[4 u - 1]:
s|t] H (u(t) Vu)),
where (x) outputs 1 if x 2 0 and otherwise. This function indicates whether the membrane potential has exceeded the threshold Ui. thereby triggering spike.
Assuming the initial membrane potential v/0] O, the evolution of the membrane potential simpli- fies to:
ult + 1]
Σ k=1
a +++++1 c[k]]
Uth Σ <''
(3)
k=
This equation shows that elt 1] is weighted sum of past input currents c[k] and spike output s(k),, with older values decaying exponentially (Wang & Yu (2024). The LIF neuron integrates inputs over a short window, acting like a low-pass filter. Consequently, it primarily responds to recent inputs, making it less effective in capturing long-term dependencies, which limits its use in tasks that require extended memory and complex spatiotemporal processing.
3.3 DENDRITES AND SOMA
Biological neurons often represented with dual-compartment architecture, comprising den- drites and soma, each handling specific signal processing functions, as illustrated Figure Ta). Dendrites receive synaptic inputs and integrate them over time, while the soma acts the central decision-making unit, determining whether to generate a spike based on the accumulated inputs, The dynamics of this system
shown in Figure [b) (Zhang al. 2024
Hao et al. 2024).
mathematically described as:
calf [1] a1 1] + 8,0,5 it- 1| + ctt,,
U. [ = a2v, - 1] 32va[t] - un 1],
(4)
s, [t] H (v.[tt] va.)
Here, va[t] and [t] represent the membrane potentials at the dendrites and soma, respectively. a and 02 are decay factors that modulate the influence of previous membrane potentials, while and B2 signify coossccompartmentall interactions. The soma generates a spike when its membrane potential vz[t] exceeds the threshold Un-
By making minor adjustments to Equation 4 the TC-LIF and LM-H neuron models can be derived. These models can, some extent, mitigate the problem of vanishing gradients by appropriately tuning the decay factors a and cross- cross-compartmental interactions 3, enabling them to better model long-term dynamic relationships. However, these models lack a clear distinction in processing capa- bilities across different temporal scales, such as high and low frequencies, between the dendritic and somatic compartments. Moreover, there is no theoretical validation of their robustness or temporal processing capabilities, limiting their effectiveness in scenarios requiring explicit multi-timescaa feature extraction and reliable long-term memory retention.
METHODOLOGY
4.1 TEMPORAL SEGMENT LIF NEURON
In the dual- coup-coomartmentt model described by Equation 4 the input current c(t) flows through the dendrites before reaching the soma, which can result in information loss during transmission. For
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example, if the dendritic compartment vdd primarily captures the low www-frequeccy features of c(t), it becomes challenging for the somatic compartment V, to recover the original high- frequency com- ponents without direct current imput. This limitation highlights the model's difficulty in effectively handling multi-scale information simultaneously.
Biological neurons contain numerous synapses that function independent pattern detectors (in- cluding identity mapping), ensuring soma receive sufficient information (Hawkins & Ahmad] (016)) However, describing the complete neural dynamics using simple formulas is impractical. To address this, we propose the TS-LIF neuron model, which incorporates shortcut mechanisms. These mech- anisms can be viewed dendritic pathways performing identity mapping or as more direct connec- tions, such as axosomatic synapses (Figure I [a)) and electrical synapses (gap junctions) (Fréal et al., 2023
Tewari et al. 2024 Farsang et al. 2024). The dynamics of this model are defined as:
Mal [t] = anvalt - 1| + 3I 1] + (1 01 )c({] - si - 1],
0s [t] (2uu[[ 1] [2ua((] (4) (1 -a2)c(1) 728.(( 1},
(5)
sali = (u, - vnn);
[x (v, vu.)
In this model, the shortcut is implemented through the term (1 - -x2)c(]] allowing direct current input to the soma as shown in Figure
When is close to 1, the dendritic membrane potential ca[t] acts like moving average, capturing long-term features by focusing on low-frequency components. Conversely, when ag is close to O, the somatic potential v. rapidly adapts to changes in c(t), making the neuron highly responsive to rapid fluctuations. This coml-commat model can therefore effectively handle both short-term and long-term signals, providing a balanced approach to temporal processing.
Both dendritic (s,2) and somatic (s,) compartments can generate spikes, similar biological neu- rons like hippocampal and cortical pyramidal neurons (Muller et al. [2023: Hayashi-Takaan 2023 Narayanan et al.] (0244). The simultaneous firing of multiple types of spikes is also observed multi- compartment neurons and Hierarchical Temporal Memory (HTM) neurons (Payeur al.) 2021 Capone et al.) 2023 Hawkins & Ahmad 2016). 71 and 722 represent adaptive reset mechanisms rather than fixed voltage resets, providing greater flexibility in the neuron's response. Furthermore, the dendritic and somatic compartments can be modeled as two distinct LIF neurons with unique characteristics, interacting and collaborating process signals across different frequencies, such as in the visual and auditory systems (Dallos et al. 1972, Wang & Kefalov (011). The intensity of their interaction is modulated by the parameter /3 which governs the strength of their mutual influence.
To leverage multi-scale information, we combine dendritic and somatic spike outputs through a weighted sum:
(6) where controls the balance between dendritic and somatic contributions. This coefficient can adapt across different feature channels, allowing flexible integration of both low- and gegeffrryyncc components, thereby enabling the model to capture richer temporal features and produce more robust representations of input signals. Here, all the coefficients (a, 3, Y, mentioned above are learnable.
5 siix [+] [s + (1 k)s,[t].
4.2 STABILITY ANALYSTS
To ensure the robustness of the proposed LIF model, we perform a stability analysis by focusing on the homogeneous part of the system (Chen 1984). The goal is determine the conditions under which the system remains stable, meaning all solutions remain bounded over time.
Theorem 1.
The system governed by the the following dynamics:
va[t] = valt - 1] + Biva[t -1] [. aguslt - 1] 320a(t],
has eigenvalues:
01 a2 8192 + /ai + 02 31 40x
(8)
2
For the system to remain stable, it is necessary that [I] < 1 for both eigenvalues.
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Proof. We start by representing the system dynamics in matrix form. The system can be expressed
as:
vit] = Avit 1},
(9)
U/ v.
where the state vector v[[]
and the system matrix is:
A
Q1
31
(10)
01
02 +
31
To determine the eigenvalues of the system, solve the characteristic equation:
det( A Al) 0,
(11)
which results the quadratic equation:
x (01 + 02 + 11 + 01002 = 0.
(12)
Solving this quadratic equation gives the eigenvalues:
Q1 + 02 + 31 + / (aa + + 02 + 31,32)² 40000
(13)
2
For stability, both eigenvalues must satisfy ||| < 1, ensuring they lie within the unit circle, thereby guaranteeing the boundedness of the system over time.
L
The stability of the system is governed by the eigenvalues of matrix A. Stability is achieved when both eigenvalues lie within the unit circle, which occurs only if the sum a1 02 81,8 is less than 2. This explains why the TC-LIF model, with a₁ = a2 = 1, requires 31 I to ensure stability (Zhang et al. 2024). Properly balancing the interactions between the dendritic and somatic compartments is crucial to maintaining stability.
4.3 FREQUENCY RESPONSE ANALYSIS
To examine the frequency characteristics of TS-LIF, we derive the transfer functions by applying the Z-transform to the system equations, while ignoring the effects of spike generation and reset mechanisms for simplicity (Chen 1984). The discrete-time system governing the dynamics of the dendritic and somatic potentials is described by:
[altt] a1 aavalt - 1] + BIv,st - 1] + (1-a))dff
(14)
0, [c] a2v, 1] + (2) (1 - [2)c
Applying the Z-transform under zero initial conditions yields:
(1 012 (eaa() = (2))) (1 (1-a))c(2);
(15)
-32 + (1 - 022 ()=(()) = =(1 -02))c((=).
The system can then be expressed as:
Mv(2) = ε(2).
(16)
where
1 012-1
-
[ea()) [2)
(1 an )c(2)
M
v(z)
ē(=)
B2
1 1-azz
(1 c(2
The transfer functions for [t and U/ [t] with respect to the input c(t) are:
va(2)
(1- - a1) a22 11) + B1 (1 - a2)
Ha(z)
c(2)
det(M)
(17)
(2) v2(2)
32(1 01) + (1 (1-012-
012-11111 )) -02
c(2)
det(M)
where the determinant of M is:
det(M) = (on + 02 + B (2)22 01002
(18)
These transfer functions offer insights into how the dendritic and somatic compartments process different frequency components of the input signal. The magnitudes of Hz(z) and H2(x) represent the system's 's gain at specific frequencies, while their phases indicate the delay or shift introduced by the system.

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4.4 EXAMPLE: FREQUENCY SEPARATION IN PRACTICE
To illustrate the system's behavior, we use the following parameter settings: ai = 0.95, which enables low-pass filtering in va[t], 02 0.05, providing high-pass filtering for v,[t], along with 31 = 0 and 32 = 0.9. Under these conditions, the characteristic equation for the system is derived as:
1 À + 0.0475A 0,
(19)
Solving this, we find the eigenvalues A 0.95 and X2 0.05, both of which lie within the unit circle, ensuring system stability. The corresponding transfer functions for the dendritic and somatic compartments are:
0.05 - 0.0025
Ha(z) 1 2-1 0.04752-2
(20)
H=(=) 0.905 0.9025
(21)
0.0475=-2
At low frequencies (w 0), Ha(e²=) indicating that va[t] effectively captures low- oowfrrquency signals, while H, (eJw) R 0.0526, showing minimal response. Conversely, at high frequencies (w т), (eJw)) 0.8829, demonstrating that [2[(] accurately reflects high-frequency components. This example highlights the system's frequency separation properties, where va(t] captures slow- changing signals, and [t is sensitive to rapid changes.
EXPERIMENTS
this section, we present the experimental evaluation of the TS-LIF model across multiple time- series benchmarks. We analyze the model's forecasting performance, its robustness against various prediction settings, and its ability in temporal decomposition.
5.1 TEMPORAL ANALYSIS
Cunent
Dendrise kiit)
Dendritee Volt!
Some V,10
Some V,(0
Time (8)
Time (6)
Figure 2: (a) TC-LIF Model Response
Figure 3: (b) TS-LIF Model Response
Figure 4: Comparison of dendritic and somatic voltage responses between TC-LIF and TS-LIF models with mixed-frequency input current.
We performed temporal analysis to assess the TS-LIF model's ability to decompose input signals into distinct frequency components. To validate this temporal decomposition capability, we fed mixed-frequent input current (blue line) into both TS-LIF and TC-LIF models, as depicted by the blue line in Figure Detailed experimental settings provided in Appendix A.4.
By visualizing the voltage responses of the dendritic (green line) and somatic (red line) compart- ments, observed distinct behaviors between the models. The TS-LIF model effectively separated

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the input signal into its low- and high-frequeney components, with the dendritic compartment retain- ing primarily wwwfrreuenccy information and the somatic compartment focusing on sigh-freuenccy components. In contrast, the TC-LIF model did not demonstrate clear separation, with both compartments reflecting mixed-frequency components. These results emphasize the advantage of the TS-LIF model in managing temporal information, effectively capturing and processing multi- timescale dependencies in time series - an essential capability for handling complex temporal patterns.
5.2
MAIN RESULTS
Forecasting results on four benchmark datasets with different prediction horizons L. Results for our TS-LIF model with TCN, GRU, and Transformer architectures included, while the remaining results are sourced from Lv et al. (2024). The top-perforning and second-best scores are shown in bold and underlined. respectively. Arrows 1 (J) denote whether higher or lower values
Table 1:
are preferred. The Avg. Rank column reflects the average rank of each model across the different
configurations.
Method
Syske
Metro
Mete-lo
Pems-bos
15
Solar
Electricit
Arg.
Arg. Rank.
ARIMA
.373
481
-022
1072
-235
1-1
RSEI
-500
-155
0551
2013
3555
-33
1051
3075
RSE.
775
-563
-210
513
1350
.119
Spik-TTN
RSEJ
.001
1011
.350
TUN
RSF:]
1-1
.150
8556
732
354
1400
.964
1.80
0350
1951
-318
-300
.475
4.6
.150
3311
1:11
3500
2.75
155
753
3661
RSt1
5022
Spiko-CRU1
RSE]
Spike RNN
RSF:
.412
.888
79:
0055
357
505
166
A51
1778
-125
435
.066
1957
286
-595
.551
-503
TS-GRU
RSB1
K'
.412
.848
.188
.61
7750
.410
1552
229
874
.884
742
5530
-587
584
(540
.507
1928
(253
3878
-10
.326
915
772
.127
991
-2.0
200
161
.93
.231
-211
.97g
.778
-101
4.5
4.5
Autooomer
RSEI
.565
.756
.597
J548
ITuasfumer
RSE
200
.400
6645
.75
110
.75
062
.447
.501
783
.584
1071
190
3468
750
448
363
7:5
-350
1070
.00
.85
1715
351
.277
-710
.400
4.7
Sppkffener
RSE,
K'
.176
018
868
752
410
.05
270
070
376
741
396
280
360
204
390
206
200
355
270
.365
750
1.1
821
255
011
171
284
1712
-588
318
361
-710
.170
4.6
TS former
3-1
.16
.867
855
820
445
763
894
255
874
370
785
372
663
860
383
1751
331
886
528
382
774
435
088
197
21.5
985
238
081
977
201
.785
.481
3.5
The proposed TS-LIF model (TS-TCN, TS-GRU, and TS-former) was evaluated on four benchmark
datasets (Metr-la, Pems-bay, Solar, and Electricity), following the setup in Lv et al. (2024), where TS-former represents
iTransformer architecture based TIFLIF (Liu et al. 2024). Hyperpa- rameters were tuned via cross-validation, and performance was assessed using RSE and R² metrics. As shown in Table [T] Our TS-LIF consistently outperforms L.F-based SNN models (Spike- TCN, Spike-GRU, and iSpikeformer) across different metrics, particularly excelling in tasks requiring long-term forecasting. For example, in the Solar dataset, the TS-TCN and TS-former achieved an average improvement of 8% in R² and 16.8% in RSE. Similarly. in the Electricity dataset, TS-GRU GRU and TS-former showed significant improvements in RSE of 43.6% and 25.0%, respectively, for the 96-step prediction length. These results highlight the effectiveness of TS- in capturing long- term dependencies, unlike traditional LIF neurons.
For RNN-based models, our TS-LIF achieved superior performance in both R² and RSE metrics compared to based and original ANN models. Even for TCN and Transformer models, which inherently possess cross-time-scale capabilities, TS-LIF aslo provided noticeable improvements, resulting in higher average rankings across metrics. This suggests that the integration of dendritic and somatic components in the TS-LIF framework enables the model to capture richer multi-scale temporal features, leading to improved predictive accuracy.
5.3 MODEL ANALYSIS
This section assesses model robustness in the presence of missing values, evaluates the impact of training timesteps, and examines the effectiveness of different types of LIF neurons.
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Table 2: Experimental performance of the TS-LIF model compared the vanilla LIF the Elec- tricity dataset, evaluated under different ratios of missing values in the historical inputs. Model_* indicates backbone model with prediction length of *, and Transformer. represents the Trans- former architecture with prediction length of 6.
Missing Ratio
10%
20%
40%
60%
80%
Metric
R't
RSEJ
R²t
RSEJ
R't
RSEJ
R²t
RSEJ
R²t
RSE.
iSpikformer
0.977
0.265
0.976
0.266
0.974
0.269
0.971
0.271
0.964
0.275
Transformer.6
TS-former
0.987
0.199
0.987
0.200
0.987
0.206
0.986
0.207
0.983
0.211
Promotion
1.0%
24.9%
1.1%
24.8%
1,3%
23.4%
1.5%
23.6%
1.9%
23.2%
iSpikformer TS-former
0.962
0.344
0.962
0.346
0.957
0.358
0.953
0.368
0.947
0.376
Transformer 96
0.977
0.263
0.976
0.262
0.974
0.270
0.971
0.274
0.971
0.279
Promotion
1.5%
23.5%
1.4%
24.2%
1.7%
24.5%
1.8%
25.5%
2.4%
25.7%
Spike-GRU TS-GRU
0,873
0.774
0.842
0.749
0.771
0,851
0.758
0.874
0.745
0.897
GRU
0.986
0.235
0.983
0.242
0.979
0.256
0.965
0.328
0.939
0.438
Promotion
12.9%
69.6%
16.7%
67.6%
26.9%
69.9%
27.3%
62.4%
26.0%
51.1%
Spike-GRU
0,842
0.693
0.827
0.729
0.803
0.789
0.783
0.828
0.760
0.871
GRU-96
TS-GRU
0.975
0.268
0.973
0.324
0.970
0.303
0.956
0.367
0.922
0.489
Promotion
15.7%
61.3%
17.6%
55.6%
20.7%
61.5%
22.0%
55.6%
21.3%
43.8%
Spike-TCN TS-TCN
0.971
0.341
0.970
0.347
0.967
0.352
0.960
0.361
0.954
0.369
TCN.6
0.980
0.263
0.979
0.266
0.976
0.272
0.973
0.280
0.967
0.291
Promotion
0.9%
22.8%
1.0%
23.3%
1.0%
22.7%
0.7%
22.4%
1.3%
21.1%
Spi TS-TCN
0,953
0.390
0.952
0.394
0,948
0.409
0.942
0.418
0.937
0.426
TCN_96
0.962
0.361
0.961
0.364
0.958
0.370
0.956
0.375
0.952
0.389
Promotion
1.0%
7.4%
0.9%
7.6%
1.0%
9.5%
1.4%
10.2%
1.6%
8.6%
5.3.1 ROBUSTNESS EVALUATION
To verify the robustness of the proposed TS-LIF model, we evaluated its performance on the Elec- tricity dataset under different ratios of missing values in the historical inputs, comparing it to the vanilla Llsed models. The models were assessed under missing data ratios 10%, 20%, 40%, 60%, and 80%. The results are presented in Table
The experimental results indicate that TS-LIF consistently outperforms the vanilla LIF models across different missing value scenarios, as evidenced by higher R values and lower RSE scores. Compared to the LIF-based models. TS-LIF shows significantly smaller reduction in prediction accuracy as the missing data ratio increases, particularly GRU-based models. Since GRU inher- ently has weaker capability to capture long-term dynamics compared to TCN and Transformer, the enhancements introduced by TS-LIF greatly improve its temporal feature extraction ability. Specifi- cally, TS-LIF improves R² by approximately 20% and reduces RSE by around 50% compared to the bascline based models. These improvements highlight the effectiveness of TS-LIF in captur- ing complex temporal dependencies and maintaining robustness under challenging conditions with substantial data loss.
5.3.2 TRAINING TIMESTEPS
Figure 5 iillustrates the forecasting performance of our TS-LIF model, evaluated using TCN, GRU, and Transformer architectures over different training timesteps (24, 96, and 168) for the Solar and Electricity datasets. For each architecture, the TS-LIF model consistently improves performance as the training timesteps increase from 24 to 168. This trend is evident from the rising R2 values and decreasing RSE scores, indicating enhanced accuracy with more extended training. Notably, the most substantial improvements observed in the transition from 24 to 96 timesteps, showcasing the model's capability to leverage longer training periods to capture complex temporal patterns more effectively.

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1.0
Timestop Evaluation
Timestop Evaluation
1.000
Timestop
0.5
Timestop Evaluation
TSTCh
TSTCH
TS-TCH
15 10:
15iomer
0.45
15 dRU
15/trmer
0.975
15 tommr
15-0Nu
2
&
0.35
0.925
TSTEH
0.3
0.7
0.900
0.2
Timesteps
Timesteps
Timestops
Timestaps
Figure 5: Impact of Training Timesteps Forecasting Performance of TS-LIF Model Across Dif- ferent Architectures. Solar dataset with prediction length of and Electricity dataset with a prediction length of 96. We plot mean and std for each experiment over 3 different random seeds.
5.3.3
LIP NEURONS
R Evaluation Sollar4
RSE Evaluation-Soler21
Evalustion Eloctricity24
RSE Evaluation-llectictttz2
1.00
0.5
1.00
0.5
2 0.90
0.3
0.90
0.3
0.85
6AU
TCN
iTonsforte
GRU
TCN
lTFanffrmeer
GAU
TCN
iTansformer
GAU
TCN
ITaasformer
Figure 6: Forecasting Accuracy Comparison of TS-LIF and TC-LIF Neurons Solar and Electric- ity datasets with a prediction length 24.
In this section, we evaluate the accuracy of the proposed TS-LIF model compared to the dual- compartment TC-LIF model. shown in Figure TS-LIF consistettl outperforms TC-LIF across all three architectures and both datasets. The Ra values for TS-LIF are significantly higher, partic- ularly with GRU and TCN, demonstrating improved predictive accuracy. The corresponding RSE scores also confirm this trend, with TS-LIF showing consistently lower errors, indicating better fit and reduced prediction errors. These improvements highlight TS-LIF's superior capability to cap- ture underlying temporal patterns and effectively manage multi-scale information in the datasets.
CONCLUSION
In this work, we introduced the Temporal Segment Leaky Integrate-and-Fir (TS-LIF) model, a novel spiking neural network (SNN) neuron architecture designed specifically for time series fore- casting. The TS-LIF model features a dual-compartment structure, with dendritic and somatic compartments processing different frequency components, allowing for effective multi-timescall information integration. This compartmentalizzatoon enables TS-LIF to enhance both low- and high- frequency signal processing, addressing key limitations of traditional Leaky Integrate-and-Fing (LIF) neurons in capturing long- term dependencies and multi-scale dynamics.
We theoretically proved the stability conditions for the TS-LIF model, ensuring robustness across wide range of temporal inputs. Through frequency response analysis, we demonstrated how the den- dritic and somatic compartments contribute efficient temporal decomposition. Our empirical eval- uation on four benchmark datasets showed that the TS-LIF model consistently outperformed con- ventional LIF-based SNNs as well as artificial neural networks, particularly long-term forecasting scenarios. Moreover, the TS-LIF model showed resilience under missing input data, maintaining perior accuracy compared to baseline models. The proposed model advances the state-of-the-e art in SNNs for time series forecasting by combining biologically inspired design with computational ef- ficiency, providing a promising solution for applications requiring robust temporal processing in resource-constrained environments.
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7 ACKNOWLEDGMENT
This research is supported by the Joint NTU-WeBank Research Centre on Fintech, Nanyang Tech- nological University, Singapore.
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A APPENDIX
A.1 EXPERIMENT SETTINGS FOR MAIN RESULTS
In this section, we outline the experimental setup used to evaluate the performance of the proposed TD-LIF model. We conducted experiments several benchmark time series datasets, including Metr-LA (Li et (017), which records average traffic speed on highways in Angeles County; Pems-Bas Bay (Li et al. 2017). capturing traffic speed data in the Bay Area; Electricity (Lai et al.) 2018 which tracks hourly electricity consumption in kWh; and Solar (Lai et al., 2018). detailing solar power production. Preprocessing steps were applied to ensure consistency across datasets, standardizing input dimensions, sampling rates, and data normalization.
The TS-LIF model framework implemented in line with the approach in Lv et al. (2024), in- corporating CNN-based TCNs (Bai et al.] 2018), RNN-basee GRUs (Chol 2014). and Transformer- based models such as Autoformer (Wu et al.] (2021) and i'Transformer (Liu et al. 2024). As for the SNN-based structure, we introduce the TCN, RNN, GRUs, and Transformer models the SNN format from Lv feature-mixing weights, were optimized through cross-validation. We employ two statistical met- rics: the Root Relative Squared Error (RSE) and the coefficient of determination (R²) followed by the Lv et al. (2024) settings. Detailed descriptions of the experimental settings and hyperparameter configurations are provided in the appendix.
(2024). Hyperparameters, including learning rate, timestep intervals, and
A.2 DATASET AND METRIC DETAILS
Datasets. The details of the datasets used the main experiment are shown in Table S In the
experimental partitioning of datasets Metr-la and Pems-bay, adopted train-validation-tess ratio of 0.7, 0.2, and 0.1, respectively, while for datasets Solar and Electricity, we used ratios of 0.6, 0.2, and 0.2. The settings for history and prediction lengths in the experiments followed those in the paper by Ly et al. (2024), except that for the history length datasets Metr-la and Pems-bay, we added setting of 168 to further improve experimental performance.
Table 3: Properties of the datasets in experiments
DATASET
Dimension
Domain
Freq
Samples
Context Length
Pred Length
Metr-la
207
g+
30-min
34,272
{12, 168}
{6, 24, 48, 96}
Pems-bay
325
R+
30-min
52,116
{12, 168)
{6, 24, 48, 96}
Solar
137
R+
Hourly
52,560
168
{6, 24, 48, 96]
Electricity
321
R
Hourly
26,304
168
{6, 24, 48, 96]
Metrics. To comprehensively evaluate our model's performance, we employ two statistical metries: the Root Relative Squared Error (RSE) and the coefficient of determination (R?).. The RSE mea- sures the relative discrepancy between the predicted and actual values, while the R. indicates the proportion of variance in the dependent variable that is predictable from the independent variables. These metrics are calculated as follows:
EM
Ym
RSE
Y
112
(22)
M C
L
(Y Y
R MCL ΣΣΣ
(ym Y2.)²
where M denotes the number of samples the test set, C represents the number of channels or variables, and L is the prediction horizon. The true values for the m-th sample are denoted by Y and their average over all samples is Y. Specifically, Y represents the /-th future value the c-th variable for the m-th sample, with its mean across all samples given by Y.,. The predicted values corresponding to these true values are denoted by m' and ÿ.m respectively.
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A.3 IMPLEMENTATION DETAILS
In this section, we summarize the detailed experiment setup of our TS-LIF. 4 show the hyperparameters of our overall structure in three types of backbones (TCN, GRU, Transformer). As for the timesteps in the SNN structures, we align them with the history length in each setting. The threshold of the TS-LIF is set 1.0.
Table Hyperparameters of different backbones (TCN, GRU, Transformer) used for each dataset
Datesets
TCN Layers
TCN Kemels
GRU Layers
Transformer Layers
Attention Heads
Attention Dim
Metr-la
3
2
8 256
Pems-bay
3
16
2
8
512
Solar
8
Electricity
8
Table 5: Training details of different backbones (TCN, GRU, Transformer) used for each dataset
Datesets
TCN Hidden
TCN Dilation
GRU Hidden
Transformer d_f
Learning Rate
Batch Size
Metr-la
64
2
128
1024
{,001,, .0005)
{32. 64
Pems-hay
64
2
128
2048
[,000,.00055 .0005}
{32, 64
Solar
64
2
128
2048
.0001
64
Electricity
64
2
128
1024
.0001
64
A.4 EXPERIMENT SETTINGS FOR TEMPORAL ANALYSIS
The injected current, I(t), consists of two sinusoidal components: cow-frequency component, How freq. with an amplitude of and a frequency of 0.5 Hz, and a high-frequency component, Lnggh freq- with an amplitude of 5 and frequency of 4 Hz. This combination represents complex input environment with both slow and rapid variations, simulating mixed-frequency stimuli.
For the TCLIF model, adopted parameters 01 02 1, -0.5, and B2 0.5, suggested in Zhang et al. (2024). In contrast, the TS-LIF model was set with a = 0.95, and B2 0.9, which corresponds the parameter settings used in the frequency response analysis in the previous subsection. These values were selected to facilitate low-pass filtering in the dendritic compartment (ualt)) and high-pass filtering in the somatic compartment (u,[t)).
0.05, 31 = 0,
A.5 THEORETICAL ENERGY CONSUMPTION CALCULATION
The theoretical energy consumption for each layer during inference is determined based the operations performed by spiking neural networks (SNNs) and artificial neural networks (ANNs)
Yao et al. 2023
For SNNs, the energy required by layer calculated as:
(nergy(() = EAC x SOPs((),
where SOPs(() is the number of spike-based accumulate (AC) operations, and ÉAC represents the energy per AC operation.
For ANNs, the energy consumption for layer b is:
(nergy(b) EMAC FLOPs(b).
where FLOPs(b) refers to the number of floating pooaingg-poitt multiply-and-acee accumulaeee (MAC) opera- tions, and E is the energy per MAC operation. The constants are set as EMAC 4.6 pl and EAC = 0.9 pJ. assuming operations are performed on 45nm hardware.
For SNNs, the number of synaptic operations in layer is further estimated SOPs(I) T x y x FLOPs(I).
where T the number of timesteps required in the simulation, and 7 is the firing rate of the input spike train for layer
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Table 6: Energy consumption per sample of the Electricity dataset during inference. "OPs" includes
SOPs for SNNs and FLOPs for ANNs. "SOPs" refers to synaptic operations in SNNs, and "FLOPs" denotes floating-poin operations in ANNs.
Model
Param(M)
OPs (G)
Energy (m.J)
Energy Reduction
Train/Infer Time (8)
R²
TCN
0.460
0.14
0.64
21.34/1147
.973
Spike-TCN
0.461
0.15
0.23
63.60% +
306.91 /27.85
.963
TS-TCN
0.465
0.19
0.25
60.93% J
308. 26.26//28.
.911
GRU
1.288
1.32
6.07
37.73/7.35
.922
Spike-GRU
1.289
1.63
1.51
75.05% +
235.46/ 115.46/10.0 10.05
.944
TS-GRU
1.291
1.67
1.58
73.80%
246.23/9.76
.911
iTranfformer
1.634
2.05
9.47
7.24/6.38
.977
iSpikformer
1.634
3.55
3.19
66.30% 4
49.84/8.69
.974
TS-former
1.640
3.59
3.22
65.99%
50.36/ /8.72
.985
Table 7: Performance of our TS-former with SparseTSF and SAMformer of 3 prediction lengths (24, 48, 96) on the Metr-la and Electricity datasets. SparseTSF* replace the ReLU function of SSF with our TS-LIF. Bold numbers represent the best outcomes.
Datasets
Metr-la
Electricity
Lengths
96
Metrics
1²t
RSEJ
R²t
RSE
R²t
RSEJ
R
RSEJ
R²t
RSE
R²1
RSEJ
SparseTSF
0.576
0.681
0.427
0.792
0.253
0.916
0.991
0.167
0.986
0.195
0.982
0.232
SparseTSF=
0.580
0.692
0.426
0.801
0.247
0.924
0.990
0.177
0.985
0.201
0.982
0.234
SAMformer
0.549
0.739
0.401
0.863
0.219
0.965
0.983
0.218
0.980
0.239
0.978
0.257
TS-former
0.620
0.655
0.445
0.763
0.283
0.874
0.985
0.215
0.981
0.234
0.977
0.261
A.6 PERFORMANCE COMPARISON ON SOTA TIME SERIES FORECASTING METHONS
compares the performance of our TS-former with SparseTSF (Lin et al. 2024). Sparse (where ReLU is replaced by TS-LIF), and SAMorrrr (Ilbert al. 2024a) on the Metr-la and Electricity datasets for prediction lengths of 24, 48, and 96.
On the Metr-la dataset, TS-former achieves the best results across all metrics and prediction lengths, demonstrating its ability to effectively capture complex temporal dependencies. For example, at prediction length of 24, our TS-former achieves an R² of 0.620 and RSE 0.655, outperforming both SSF and SAMformer. On the Electricity dataset, SparseTSF achieves slightly better performance in some cases, such as an R² of 0.991 and RSE of 0. 067 at a prediction length of 24. However, TS-former remains competitive, delivering consistent and robust results across different prediction lengths. These results highlight the effectiveness of TS-LIF Sparse and the overall robustness of TS-former in time series forecasting tasks.
A.7 COMPARISON OF TS-LIF WITH OTHER LIF NEURONS
Table 8 compares the performance of TS LIF with TC-LIF, LM-H, and CLIF in the GRU back- bone on the Metr-la and Electricity datasets for prediction lengths 6, 24, and 96. TS-LIF con- sistently outperforms the baseline methods across all metries and prediction lengths. For example, on the Metr-la dataset, TS-LIF achieves the highest of 0.848 and the lowest RSE of 0,412 at prediction length of Similarly, the Electricity dataset, TS-LIF achieves R2 of 0.991 and RSE of 0.216 at the same prediction length, demonstrating its robustness and effectiveness in mod- cling temporal dependencies. These results highlight the superiority of TS-LIF over existing LIF structures, making it strong choice for time series forecasting tasks.
A.8 ROBUSTNESS ANALYSIS ON THE METR-LA DATASET
To further verify the robustness of the proposed TS-LIF model, we evaluated its performance on the Metr-la dataset under different ratios of missing values in the historical inputs, comparing it the
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Table 8: Performance of our TS-LIF with other LIF neurons (TC-LIE, LM-H, and CLIF) in the GRU backbone. Bold numbers represent the best outcomes.
Datasets
Metr-la
Electricity
Lengths
96
96
Metrics
R²
RSE.
R²1
RSEL
R
RSEL
R
RSE.
R²*
RSE
R²
RSEJ
TC-LIF
0.828
0.453
0.594
0.673
0.259
0,956
0.978
0.263
0.976
0.257
0.941
0.503
LM-H
0.812
0.464
0.570
0.719
0.246
0,973
0.971
0.269
0.969
0.280
0.936
0.512
CLIF
0.837
0.429
0.606
0.667
0.271
0.930
0.973
0.259
0.972
0.276
0.954
0.376
TS-LIF
0.848
0.412
0.618
0.651
0.329
0.853
0.991
0.216
0.981
0.240
0.976
0.271
vanilla LIF-based models. The models were assessed under missing data ratios 10%, 20%, 40%, 60%, and 80%. The results are presented in Table
Table 9: Experimental performance of the TS-LIF model compared to the vanilla LIF on the Metr-la dataset, evaluated under different ratios of missing values in the historical inputs. Model_* * indicates backbone model with prediction length of and Transformer 6 represents the Transformer architecture with a prediction length of
Missing Ratio
10%
20%
40%
60%
80%
Metric
RSFL
R²
RSF.
R²1
RSFL
R²1
RSF4
R²1
RSF,
iSpikformer
0,815
0,479
0.813
0.486
0.809
0.488
0.804
0.492
0.802
0.496
Transformer.6
TS-former
0,843
0,419
0.842
0.421
0.838
0.430
0.835
0.436
0.831
0.440
Promotion
3.43%
14.3%
3.56%
15.4%
3.58%
13.4%
3.86%
12.8%
3.61% %
12.7%
iSpikformer TS-former
0,270
0.915
0.254
0.926
0.230
0.935
0.204
0.948
0.194
0,959
Transformer.90 96
0.277
0.907
0.263
0.911
0.238
0.92 7
0.212
0.936
0.205
0.945
Promotion
2.59%
0.88%
3.54%
1.65%
3.47%
0.86%
3.92%
1.28%
5.67%
1.48%
Spike-GRU TS-GRU
0.830
0.429
0.819
0.440
0.771
0.497
0.746
0.522
0.743
0.530
GRU.6 6
0.843
0.417
0.839
0.414
0.834
0.425
0.823
0.435
0.792
0.473
Promotion
1.50%
2.40%
2.50%
5.90%
8.10
16.9%
10.3%
20.0%
6.50%
12.1%
Spike-GRU TS-GRU
0.243
0.924
0.240
0.919
0,213
0.932
0.191
0.944
0.171
0.970
GRU 96
0.342
0.857
0.341
0.860
0.338
0.863
0.319
0.869
0.294
0.878
Promotion
40.7%
7.80%
42.0%
6.86%
58.7%
7.99%
67.0%
8.63%
71.9%
10.4%
Spike-TCN TS-TCN
0.774
0,509
0.765
0.521
0.757
0.549
0.742
0,570
0.731
0.596
TCN.6
0.792
0.469
0.781
0.493
0.773
0,512
0.756
0.538
0.744
0.562
Promotion 2.33%
8.53%
2.1%
5.84%
1.1
7.23%
1.89%
5.94%
1.78%
6.05%
Spike-TCN 0.315
0.884
0.307
0.914
0.248
0,936
0.214
0.973
0.202
0.996
TCN_96
TS-TCN
0.323
0.870
0.319
0.883
0.276
0,914
0.256
0.925
0.228
0.970
Promotion
2.54%
1.61%
3.91%
3.52%
11.3%
2.41% 1%
19.6%
5.19%
12.9%
2.68%
A.9 STANDARD DEVIATION ANALYSIS
Table 10 shows the standard deviation of lt2 and RSE metrics over three runs with different random seeds for TS-GRU and TS-former on the Metr-la and Electricity datasets, across prediction lengths of 6, 24, 48, and 96. Both models exhibit low standard deviations, demonstrating their stability and robustness. These results confirm the reliability of TS-GRU and TS-former under varying random seeds.
A. AVERAGE POWER SPECTRUM ANALYSIS
To gain deeper understanding of how TS-LIF processes temporal features, we analyze the average power spectrum of dendritic and somatic voltages after the first encoder layer of TS-former. Fig- ure vre7illlon illustrates the power distribution of voltage signals from dendrites and soma across different frequency ranges.
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Table 10: The standard deviation of 3 runs with different random seeds with our TS-former and TS-GRU on Metr-la and Electricity datasets.
Flectricity
Lengths
24
48
96
24
48
96
Metrics
RSE]
RSEI
RS1
RSE,
R²1
RSE,
R21
RSE.
R²t
RSE
TS-GRU (ours)
.002
.055
004
906
002
.011
004
.009
000
002
001
000
002
004
.001
008
TS-former (ours)
.088
.02
9006
0055
0013
.002
.10
.011
.03
.001
.033
001
.005
.001
.007
The analysis reveals distinet frequency response characteristics between dendritic and somatic com- partments. These different roles allow TS-LIF to encode diverse temporal features effectively, con- tributing to its superior performance on time series forecasting tasks.
Irequeiicy Spectrur Ehergy of Dendrite
Frequnscy Spectiuen dneapy Soms
Smoutred Spects
Shoathee Sancion
102
M Mo
42-
spy and Annt anndde And A
Horrlbee Fressercy
Torm wwwaliaedooooo Prequenes
Olie of Sociiom
Seignel Sectioes
19
Mo and A
46-
30
82
64
0.8
Trepancc Spactrurr Energe Dencrite
Tragpency Specctuem Energy Some
Seacched Seecie
A-2
214
M Vad JoMter
Pregenia
Figure 7: Average power spectrum analysis of dendritic and somatic voltages. The figure illustrates the power distribution of voltage signals from dendrites and soma across different frequency ranges, providing insights into neural signal processing mechanisms.
A.11 EVALUATING LONG-TERM DEPENDENCY CAPTURE WITH DELAYED SPIKING XOR PROBLEM
To further evaluate the ability of spiking models to capture long-tern dependencies, conducted experiments using the delayed spiking XOR problem. This task tests the model's 's capacity retain and process information extended periods. The task involves three stages: initial
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spike imput, delay period with noisy spikes, and second spike input. The model computes XOR operation between the first and final inputs based on their firing rates.
Our experimental setup follows the parameters described in (heng et al. 2024). Specifically, employed a two-layer MLP with only 20 hidden neurons, where the imput feature size was set to 20. The results, measuring prediction accuracy under different delay timesteps and activation functions (ReLU, LIF, and TS-LIF), are summarized Table 11
Table 1: Prediction accuracy of the delayed spiking XOR problem under different delay timesteps and activation functions.
Delay timesteps
ReLU
LIF
TS-LIF
10
0.5
0.748
0,994
20
0.5
0.504
0.977
30
0.5
0.504
0.791
40
0.5
0.500
0,585
50
0.5
0.500
0.585
The results demonstrate that TS-LIF significantly outperforms both ReLU and standard LIF across all tested delay timesteps, particularly excelling at shorter and moderate delays. While the perfor- mance of LIF degrades as delay increases, TS-LIF retains higher accuracy, showcasing its enhanced capability for capturing long-term dependencies. This improvement can attributed to the distinct processing mechanisms of dendritic and somatic compartments. which allow TS-LIF to maintain more robust temporal memory compared to traditional spiking and non-spiking activation functions.
TS-LIF
Recurrent renteeett Call
Element-wise Add
Blecs x N
x
BN
Batch Normalization
BN
Conv2d
Conv2d
Linear
Linear
TSSA
Temporal spiking Self Attention
TSSA
(a) TS-TCN
(b) TS-RNN
(c) TS-Transformer
Figure & An illustration of our proposed TS-LIF based spiking structure in three models (TCN, RNN and Transformer).
A. TEMPORAL ALIGNMENT AND SPIKE ENCODER
To utilize the intrinsic nature of SNN its best, it's crucial align the temporal dimension between time-series data and SNNs. Our central concept is to incorporate relevant finer information of the spikes within the time-series data at each time step. Specifically, we divide time step AT of the time series into T. segments and each of them allows firing event for neurons whose membrane potentials surpass the threshold, i.e., AT T,AL
This equation bridges between a time-series time step AT and an SNN time step At. As result, the independent variable t time-series (X((t) and in SNN (U),,, [t),, ((t) are now sharing the same meaning. To this end, the spiking encoder, responsible for generating the first spike trains moating-oinntioo based on the floating point inputs, needs to calculate T, x T x C possible spike events. The most straightforward non non-paramttric approach is to consider each data point in the input time series the current value and replicate it T, times. However, this approach can disrupt the continuous nature of the underlying X (t) hypothesis. Therefore, we seek parametric spike encoding techniques.
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Given the historical observed time-series X RTxC, we feed it into convolutional layer followed by batch normalization and generate the spikes as:
SNN (BN (Conv (X))).
(23)
Where SNW is the TS-LIF neuron, by passing through the convolutional layer, the dimension of the spike train S is expanded to T, x T x C. Spikes at every SNN time step are generated by pairing the data with different convolutional kernels.
The convolutional spike encoder capture internal temporal information of the input data, i.c., tempo- ral changes and shapes, respectively, contributing to the representation of the dynamic nature of the information over time and catering to the following spiking layers for event-driven modeling. Also the pipeline of spiking based TCN, RNN-based models and Transformer streuture are show in the
A.13 LIMITATIONS AND FUTURE WORK
Limitations. In multivariate time series forecasting, modeling the correlations between variables is crucial for improving prediction accuracy. Current SNN-based models for time series forecasting primarily focus temporal modeling and lack explicit mechanisms for capturing inter-variable correlations. For instance, explicitly computing cross-variable correlations, as shown in works like Ilbert al. (2024a) and /Zhag & Yan (2023), can effectively model multivariate relationships. We intend to explore how SNN filtering mechanisms can efficiently model cross-variable relationships further enhance predictive performance.
Future Work. Future research directions include: (I) designing an efficient and effective SNN mechanism for capturing cross-variable correlations in multivariate time series, and (2) developing more generalized SNN structures for comprehensive time series analysis tasks, such as anomaly detection, time series generation, and classification.
21


Reviews:
[{"review_id": "MMKxJJptNW", "reviewer": "Reviewer_fwe4", "summary": "This paper introduces TS-LIF, a novel dual-compartment spiking neuron model for time series forecasting. The authors argue that traditional LIF models struggle to capture long-term dependencies and multi-scale temporal dynamics. Their proposed TS-LIF model incorporates dendritic and somatic compartments to process different frequency components, aiming to improve the accuracy and robustness of time series forecasting.", "questions": "- Have you explored the computational efficiency of TS-LIF compared to traditional ANNs, particularly in terms of energy consumption?\n\n- Are there specific types of time series data or forecasting tasks where TS-LIF might be particularly well-suited or, conversely, might struggle?\n- How does the choice of the weighting parameter κ in the mixed spike output affect the model's performance? Is there an optimal way to determine this parameter?\n\n- I suggest to include those references on spiking networks that are relevant for the topic. [1] is a biologically implementation of RFLO in spiking networks, [2] discuss learning temporal sequences leveraging multi-compartment neurons and local errors, [3] discuss learning in deep architectures thanks to multi-compartment neurons.\n\n[1] Bellec, Guillaume, et al. \"A solution to the learning dilemma for recurrent networks of spiking neurons.\" Nature communications 11.1 (2020): 3625.\n\n[2] Capone, Cristiano, et al. \"Beyond spiking networks: the computational advantages of dendritic amplification and input segregation.\" Proceedings of the National Academy of Sciences 120.49 (2023): e2220743120.\n\n[3] Payeur, Alexandre, et al. \"Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits.\" Nature neuroscience 24.7 (2021): 1010-1019.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. **Novelty**\n\nThe introduction of the TS-LIF model with its dual-compartment architecture (and signal decomposition), together its application to series forecasting is a novel contribution to the field of spiking neural networks .\n\n2. **Placement**\n\nThe relationship of the work as respect to previous ones is well discussed.\n\n3. **Performance Improvement**\n\nThe experimental results demonstrate clear improvements over traditional LIF-based SNNs and even some ANNs on standard benchmark datasets.\n\n4. **Robustness**\n\nThe model shows good robustness in the face of missing data, which is a common challenge in real-world time series data.", "weaknesses": "1. **Limited Biological Plausibility? **\n\nWhile the authors claim biological inspiration, the specific implementation of the dual-compartment model may not have direct biological correlates.\nE.g. I like the idea of decomposing of the input signal in different frequencies. (Maybe Hierarchical temporal memory could referenced here). Can the authors discuss more on the biological plausibility of this phenomenon?\n\n2. ** Over-Reliance on Benchmark Comparisons** \n\nThe paper heavily focuses on comparing TS-LIF with existing models on benchmark datasets. While this demonstrates performance improvements, it doesn't provide a deep understanding of the model's behavior. A more in-depth analysis of the model's inner workings, including how the dendritic and somatic compartments interact and contribute to the final prediction, would be beneficial.\n\nIt would be nice to some example of the network dynamics in response to data input, for different dataset, before and after training, while forecasting, populations analysis (such as the average power spectrum for different compartment over many realizations of the experiment).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "mwAQmfp4tP", "reviewer": "Reviewer_nqfP", "summary": "This article improves the dynamical characteristics of the LIF neuron and proposes a TS-LIF model for time series forecasting, incorporating interactions between dendrites and soma. The authors analyze the robustness and functionality of the improved dynamical system's different components and validate through experiments that TS-LIF outperforms the standard LIF on time series prediction benchmarks.", "questions": "Please see weaknesses above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* The analysis of the improved model is quite thorough.  \n* Experiments demonstrate that it outperforms previous SNN-based methods.  \n* The writing is clear and easy to understand.", "weaknesses": "The main issue with this article is the somewhat unclear connection between the motivation and contributions. I believe the authors need to clarify their motivation for using a spiking model for time series tasks. \n\nIf the goal of using a spiking model is to achieve better performance, the following points should be addressed:\n\n* If the spiking model is used to improve performance, it should be compared with the latest state-of-the-art methods, such as [1] and [2].\n* In the introduction, it states, \"In contrast, SNNs, with their event-driven and sparse computational architecture, can offer a more efficient solution, particularly for applications that involve sparse temporal events and demand low energy consumption.\" If the motivation for using a spiking model is to achieve low energy consumption, then additional experiments on hardware platforms should be provided to verify the model's energy efficiency, including specific tests on platforms like FPGA, GPU, and neuromorphic chips [3] to support this claim.\n* The authors improved the model by introducing input stimuli into the soma, achieving a symmetric dynamical form. While this improvement indeed enhances performance, it also introduces additional computational overhead. I believe it would be beneficial to compare this model to others in terms of parameter count, training time, and FLOPs to illustrate the advantages of using a spiking model.\n\nIn the abstract, the authors mention that the spiking model is a biologically inspired neural network. If the purpose of this work is to validate the biological plausibility of this approach (or if the motivation is computational neuroscience rather than merely solving an engineering problem), then I believe the following points should be further addressed.\n\n* In the proposed dynamic form where input stimuli are added to the soma rather than only to the dendrites, is there evidence that this mechanism is employed in the brain for similar time series forecasting processes?\n* Can dynamics or data similar to TS-LIF be observed in the biological brain, thereby validating that TS-LIF indeed simulates brain mechanisms?\n* It is suggested that the authors theoretically connect \"shortcuts in soma\" to analogous time series prediction processes in the brain, such as through predictive coding, active inference, etc. (This is optional, as it is challenging, but it would greatly enhance the contribution of the paper.)\n\n[1] Lin, Shengsheng, et al. \"SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters.\" arXiv preprint arXiv:2405.00946 (2024).\n\n[2] Ilbert, Romain, et al. \"Unlocking the potential of transformers in time series forecasting with sharpness-aware minimization and channel-wise attention.\" arXiv preprint arXiv:2402.10198 (2024).\n\n[3] Yao, Man, et al. \"Spike-based dynamic computing with asynchronous sensing-computing neuromorphic chip.\" Nature Communications 15.1 (2024): 4464.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XWWoOr6yGy", "reviewer": "Reviewer_a5wF", "summary": "To enhance the ability of SNNs to model long-term dependencies and process multi-scale temporal information, this paper proposes the Temporal Segment LIF (TS-LIF) model, which builds upon the existing Two-Compartment LIF (TC-LIF) model. The two compartments in TS-LIF are specifically designed to process low- and high-frequency signals, respectively. Theoretical analysis demonstrates the stability of the TS-LIF model, and experiments on time series forecasting tasks show that TS-LIF outperforms the standard LIF model.", "questions": "- How many time steps are used in TS-LIF on the time series forecasting tasks?\n\n- What are the specific values of the hyperparameters used in TS-LIF on the time series experiments? Are there established principles for determining these hyperparameters, and what effects do they have on model performance?\n\n- What is the value of the decay factor in the LIF baselines presented in Table 1? Have you examined the influence of the decay factor on performance in these time series tasks?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- Effectively modeling long-range dependencies remains an important yet unresolved challenge in SNNs. \n\n- Using two compartments to separately capture low- and high-frequency information is novel.", "weaknesses": "- The primary concern lies in the experimental design. This paper evaluates the TS-LIF model by integrating it with TCN, GRU, and Transformer architectures on time series forecasting tasks. However, it is questionable whether these setups and datasets effectively assess the ability of spiking neuron models to capture long-term dependencies. Given that GRU, TCN, and Transformers already have strong long-sequence modeling capabilities, the performance of SNNs may not be adequately represented.\n\n- The paper lacks comparisons with existing spiking neuron models such as TC-LIF [1], LM-H [2], CLIF [3], and BHRF [4].\n\n- It is biologically questionable whether the input current can be applied to both the dendrite and soma while producing weighted spikes.\n\n[1] TC-LIF: A Two-Compartment Spiking Neuron Model for Long-Term Sequential Modelling, AAAI 2024\n\n[2] A Progressive Training Framework for Spiking Neural Networks with Learnable Multi-hierarchical Model, ICLR 2024\n\n[3] CLIF: Complementary Leaky Integrate-and-Fire Neuron for Spiking Neural Networks, ICML 2024\n\n[4] Balanced Resonate-and-Fire Neurons, ICML 2024", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HSCCgrRLNB", "reviewer": "Reviewer_toyw", "summary": "The authors propose an extension of the dual-compartment Leaky Integrate-and-Fire model with the aim of improving time-series forecasting, by capturing both low- and high-frequency input in their model. The authors validate the prediction accuracy of their model compared to other models on different datasets and demonstrate that their model performs slightly better.", "questions": "### Questions:\n- What is the reason for introducing equation 3 on page 4? This was not used anywhere else.\n- I am not familiar with the frequency response analysis (Sec. 4.3). Perhaps you could provide more background on what this is measuring, why this was done, and where it is used. For example, how do we interpret the values of H_d(z) and H_s(d)? Shouldn’t the low frequencies and high-frequencies have units Hz (line 341-343)? Also, why is w=pi equal to high-frequency?\n- What are the top row numbers in Table 1? Are these L? If not, what are they and what was L set to?\n- Why does your model outperform the Transformer architecture (e.g. iTransformer)? SNNs do not usually outperform non-spiking neural networks. Please try to discuss this.\n- Can you also discuss why your model might perform better on certain datasets? i.e. how certain frequency information is discarded by the other models.\n- Did you use surrogate gradients for training? \n- In Figure 2, what do training timesteps refer to? Is this the number of training epochs or gradient updates?\n- In the robustness evaluation you only use the Electricity dataset. However, this dataset seems to be “easily solved” using other models under different ratios of missing values, making it hard to infer if your model is better – perhaps you could run your analysis on a harder dataset (e.g. Metr-la)?\n- What are the main limitations of your work – I would suggest adding a discussion to your paper.\n- Is the code publicly available?\n### Additional feedback to improve your paper:\n- I would suggest moving the Temporal Analysis (Sec. 5.3.1) before the benchmarking section, as this allows the reader to get a better feel for the model early on.\n- If possible, I would include multiple training runs with different random seeds and include some statistical analysis to better compare the results in Table 1, as many of the results are very similar, making it hard to know if this is due to weight initialization or not. Also, what are the shaded regions in Fig. 2 (eg. SD or SEM)?\n- Typo in Fig. 2 plot 2 y-label.\n- Missing reference for iTransformer (line 378).", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The proposed model is interesting, and the paper is generally well-written. In addition, the authors include several lines of analysis and benchmark their model on four different timeseries datasets - the preliminaries section is also well written.", "weaknesses": "I have several concerns regarding the work.\n\n1. **Questionable biological realism.** The proposed idea of modeling the voltage of the dendrites and soma separately is interesting (although not new [1]). However, adding the dendritic and somatic spike outputs using a weighted sum (Eq. 6) is biologically questionable, as the outputs of the units now become graded and are no longer spiking. How is this modeling step reconciled in biology?  If the model is intended to capture the biology, then I would expect to see more comparisons to actual electrophysiological recordings of neurons.\n\n2. **Is the model more efficient than other neural networks?** You state that TCNs, Autofromers, and Transformers require more memory and computational resources (stated on line 49 and 145-148). Does your model overcome this issue? I would assume that your model would also incur significant resource demands during training. Furthermore, it is not clear how your model could be ported to a neuromorphic computer for inference, as the output is not strictly spiking.\n\n3. **Missing controls.** The author's motivation for the work is that spiking neurons struggle to capture long-term dependencies in temporal input. However, they do not mention (or compare to) works using trainable membrane time constants [2] or trainable adaptive firing rates [3], which have been shown to significantly improve SNN performance on different time-series datasets. Simply making membrane time constant trainable can even make single-spike SNNs outperform standard multi-spike LIF-SNNs on complex temporal datasets [4]. I would suggest the authors compare their model to models in which the membrane time constant and adaptive firing rates are learned.\n\n4. **Confusion regarding the analysis.** In the stability analysis (Sec. 4.2) the authors use the equations of the dual comportment model (Eq. 4) rather than their model (Eq. 5). Why was this done? Furthermore, the analysis was only conducted on the homogenous part of the equations, please explain why this assumption can be made. I am also unsure why this analysis was done, as – unlike standard artificial neural networks – the output of spiking neurons is bounded, so why would we need to analyze these conditions? Lastly, where did you utilize this analysis in your work (e.g. for setting hyperparameters or initial weights)?\n\n[1] Gerstner, W., Kistler, W.M., Naud, R. and Paninski, L., 2014. Neuronal dynamics: From single neurons to networks and models of cognition. Cambridge University Press.\n\n[2] Perez-Nieves, N., Leung, V.C., Dragotti, P.L. and Goodman, D.F., 2021. Neural heterogeneity promotes robust learning. Nature communications, 12(1), p.5791.\n\n[3] Yin, B., Corradi, F. and Bohté, S.M., 2021. Accurate and efficient time-domain classification with adaptive spiking recurrent neural networks. Nature Machine Intelligence, 3(10), pp.905-913.\n\n[4] Taylor, L., King, A. and Harper, N., 2022. Robust and accelerated single-spike spiking neural network training with applicability to challenging temporal tasks. arXiv preprint arXiv:2205.15286.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)