TSkips: Efficiency Through Explicit Temporal Delay Connections in Spiking Neural Networks
Authors: Prajna G. Malettira
Shubham Negi
Wachirawit Ponghiran
Kaushik Roy
Venue: Accepted by TMLR ()

Abstract: Spiking Neural Networks (SNNs) with their bio-inspired Leaky Integrate-and-Fire (LIF) neurons inherently capture temporal information. This makes them well-suited for sequential tasks like processing event-based data from Dynamic Vision Sensors (DVS) and event-based speech tasks. Harnessing the temporal capabilities of SNNs requires mitigating vanishing spikes during training, capturing spatio-temporal patterns and enhancing precise spike timing. To address these challenges, we propose _TSkips_, augmenting SNN architectures with forward and backward skip connections that incorporate explicit temporal delays. These connections capture long-term spatio-temporal dependencies and facilitate better spike flow over long sequences. The introduction of _TSkips_ creates a vast search space of possible configurations, encompassing skip positions and time delay values. To efficiently navigate this search space, this work leverages training-free Neural Architecture Search (NAS) to identify optimal network structures and corresponding delays. We demonstrate the effectiveness of our approach on four event-based datasets:  DSEC-flow for optical flow estimation, DVS128 Gesture for hand gesture recognition and Spiking Heidelberg Digits (SHD) and Spiking Speech Commands (SSC) for speech recognition. Our method achieves significant improvements across these datasets: up to 18% reduction in Average Endpoint Error (AEE) on DSEC-flow, 8% increase in classification accuracy on DVS128 Gesture, and up to  ~8%  and  ~16%  higher classification accuracy on SHD and SSC, respectively.

Published in Transactions on Machine Learning Research (07/2025)
TSkips: Efficiency Through Explicit Temporal Delay Con nections in Spiking Neural Networks
Prajna G. Malettira
pmaletiippurtue.el
Deportment of Electrical and Computer Engineering
Purdue Universily
Shubham Negi
snegi edu
Department Electrical and Computer Engineering Purdue University
Wachirawit Ponghiran
wponghirrBbm..cm
Department of Electrical and Computer Engineering Purdue University
Kaushik Roy
kaushik Spurduce edu
Department of Electrical and Computer Engineering
Purdue Universily
Reviewed on OpenReview: https: // openreview. net/ form?? id= hwz32506G4
Abstract
Spiking Neural Networks (SNNs) with their bio-inspired Leaky Integrate-and-Fire (LIF) neu- inherently capture temporal information. This makes them well-suited for sequential tasks like processing event-based data from Dynamic Vision Sensors (DVS) and event-based speech tasks. Harnessing the temporal capabilities of SNNs requires mitigating vanishing spikes during training, capturing spatio-temporal patterns and enhancing precise spike tim- ing. To address these challenges, we propose TSkips, augmenting SNN architectures with forward and backward skip connections that incorporate explicit temporal delays. These connections capture long-ter apatio-temporal dependencies and facilitate better spike flow long sequences. The introduction of TSkips creates vast search space of possible figurations, encompassing skip positions and time delay values. To efficiently navigate this search space, this work leverages training-free Neural Architecture Search (NAS) identify optimal network structures and corresponding delays. We demonstrate the effectiveness of our approach on four event-based datascts: DSEC-flow for optical flow cstimation, DV$128 Gesture for hand gesture recognition and Spiking Heidelberg Digits (SHD) and Spiking Speech Commands (SSC) for speech recognition. Our method achieves significant improve- ments across these datasets: up 18% reduction in Average Endpoint Error (AEE) on DSEC-flow, 8% increase in classification accuracy DVS128 Gesture, and up to ~ 8% and 16% higher classification accuracy SHD and SSC, respectively.
1 Introduction
Spiking Neural Networks (SNNs) are class of bio-physically realistic models with Leaky Integrate-and- Fire (LIF) (Abbott) 1999) neurons that offer a promising alternative for processing sequential data. By encoding information in the precise timing of spikes, SNNs capture spatio-temporal dependencies (Rathi & Roy 2020 Chowdhury et al. 2021 Wu et al. (2117) through the membrane potential of their LIF neurons.
This intrinsic ability to process temporal information allows SNNs to excel at capturing dynamic patterns, offectively functioning as specialized RNNs (Rathi & Roy 2024
Deng al. 2022) with reduced complexity.

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Pico
Nano
Mini
Micro
Base
The ability of SNNSs to leverage the precise tim- ing of spikes offers a distinct advantage over traditional Artificial Neural Networks (ANNs) for sequential tasks. Note, ANNs are "state- less" in nature (Hagenaars et al.] 2021b) and their reliance on specially curated input en- coding schemes (Zhu et al. 2018b Paredes- Vallés & De Croon 2021) hinder their ability to accurately capture precise timing informa- tion crucial in event streams, as generated by
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Dynamic Vision Sensors (DVS) [Lichtsteiner
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et al.
2008 Brandli et al., 2014). Standard Re-
0.07
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current Neural Networks (vRNNs) Rumclhart
Total Parameters (x109)
eet al. 1986) and Long Short-Term Memory
Figure 1: Model size vs. average endpoint error (AEE) for fully spiking EV--FlowNet architectures (Kosta & Roy 2023) modified with Forward and Backward TSkips on the DSEC- flow dataset (lower AEE is better). Each tick on the hori- zontal axis represents a 3x increase in model size, TSkips achieve an average reduction 15% in AEE and 40.75% in inference energy (E) while maintaining comparable AEE to larger baselines.
(LSTM) networks [Hochreiter 1997 Ponghi-
ran & Roy 2021 Gehrig et al.
2021bb at-
tempt to address this, but remain difficult to train (Pascanu et al. 2013) and computation- ally expensive. Furthermore, transformers and spiking transformers (Li et al.) 2022a Zhou
et al. 2023 Li al.) 2023) excel at sequential processing but come at the cost of significantly
larger models and computational overhead.
Deep SNNs offer the appealing combination of rich temporal information processing and computational efficiency, but training them effectively presents unique challenges (Pfeiffer & Pfeil 2018 Rathi et al. 2021
The combination of multiple time steps with Back Propagation through Time (BPTT), non-differentiabe
spikes and sparse event data can worsen the vanishing spike problem (Hagenaars et. al. 2021a; Neftei et al.
2019). To circumvent this, previous works have proposed adaptive LIF neurons with trainable threshold and
leak Fang et al. 2021b Kosta & Roy 2023 Wang & Li| 2023) and approximate surrogate gradients (Fang
et al.
2021a Neftci el al. 2019p. Other works (Shrestha & Orchard 2018 Sun el. al. 2023b Hammouanri
et al.
2023) have considered synaptic delays as an additional parameter alongside weights, thus offering a
richer representation of the spike patterns present in event data.
In contrast. this work introduces explicit temporal delays in forward and backward skip connections, named
temporal skips (TSkips), for SNNs and hybrid ANN-SNN (Kugele et al.] 2021 Negi et al., 2024) models.
TSkips offer finer control over spike timing, enhance responsiveness to temporal patterns, mitigate vanishing spikes, all while capturing long-term spatio-temporal dependencies for event-based data. In addition, our
method utilizes adaptive LIF neurons Yin et al. 2020 Hagenaars et al. 2021a Kosta & Roy 2023) that
have learnable lcaks and thresholds that capture local temporal patterns.
The next question to address would be, what are the optimal TSkips configurations within the network architecture and what are the corresponding temporal delays associated with them? To efficiently identify optimal TSkips configurations across different architectures and sequence lengths, we leverage training-free Neural Archilecture Search (NAS) tailored for SNNs (Kim et al. 2022). TSkips introduces minimal increase in model size with very few additional trainable parameters, minimal overhead and improves inference event- based tasks. In addition, we have obscrved that training time is faster for the proposed networks compared to standard SNNs, RNNs and LSTMs. The contributions of this work can be summarized as follows:
We introduce TSkips, a novel mechanism that enhances SNNs and hybrid ANN-SNN architectures by enabling direct transmission of spike information between non-adjacent layers with temporal delays, effectively capturing long-term ppatio-temporal patterns. (Soction 3)
We analyzed various TSkips confiuuratios,, revealing the complexities of the search space, partic- ularly the interplay between the temporal delay (At), TSkips position and network depth. This
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complexity motivated the use of NAS to efficiently identify optimal TSkips architectures. (Sec- lion 4.2)
We show that TSkips achieves strong performance across sequential tasks. On the DSEC-flow dataset, they reduce average endpoint error (AEE) and inference energy, up to 18% and 56% re- spectively, as shown in Fig. Furthermore, TSkips achievess significant accuracy improvements on DVS128 Gesture, SHD and SSC dalasets up to 8.3%, 8.6% and 16.04%, respectively. This highlights the scalability and effectiveness of our approach across diverse sequential tasks and archi- tectures. (Section
2
Related Work
This section explores the challenges of training deep SNNs and incorporating delays to capture richer tem- poral dynamics.
2.1 Training Deep SNNs
Early methods to train SNNs relied on ANN-Lo-SNN conversion (Cao et al. 2015 Panda et al., 2020
However, this approach often struggled to match ANN performance on complex sequential tasks (Deng et al. 2020), particularly with event data. To overcome the challenges associated with ANN-to-SNN conversion, Kugele et al. (2020) foeus on converting existing neural network architectures into spiking neural networks using streaming rollouts (Fischer et al., 2018). By temporally unfolding the recurrent structures in the spiking domain the DenseNet skip connections essentially have single step delay, much like vRNNs.
A key obstacle in training deep SNNs is the non-different iable nature of spike activations (Fang et al. 2021a
which prevents the direct application of gradient-based optimization techniques, leading to subpar perfor- mance. To overcome this, approximate surrogate gradients (Fang et al. 2021a Neftci et al.) 2019 Wu et al. 2017) have been proposed, that replace nonfdifferentiable spike activations with smooth gradient approxi- mations, enabling the of BPTT (Werbos) 1990) to train deep SNNs. However, this approach introduces other challenges like vanishing gradients, especially with long sequences and sparse event data. (Hagenaars)
et al. 2021a Neftei et al. 2019), and reduce accuracy compared to ANNs (due to approximate gradients). To address these challenges, previous work has investigated two main avenues: adaptive LIF neurons with learnable thresholds and leaks (Fang et al. 2021b Kosta & Roy 2023 Wang & Li (022), and skip connec- tions in SNNs (Benmeziane et al.j 2023). While adaptive LIF neurons allow for dynamic adjustment and better capture of spatio-temporal pallerns, skip connections can improve accuracy and efficiency, However, neither approach fully addresses the challenges of representing and capturing complex temporal patterns. To achieve this, propose TSkips, incorporating explicit temporal delays into the network architecture with forward and backward skip connections.
2.2 Delays in SNNs
The importance of precise timing information in event-based data, such as that from dynamic vision sensors, has motivated research into effectively capturing temporal dynamics in SNNs (Rathi & Roy 2020 Chowdhury et al., 2021b. SCTT (Soo et al., 2023) explore temporal skips in recurrent networks and are evalauted on cognitive tasks that have long-term temporal dependencies. However, SCTT employs an expensive evaluation strategy to identify optimal delay and temporal skip hyperparameters that involves training several models across multiple tasks to identify optimal connections. TTFS (Kim al., (2024) explore adding delays skip connections by encoding the latency of the first spike emitted by neuron. This encoded delay is then introduced into skip connections in SNNs learnable parameters that promote local path synchronization. However, the evaluation of both these works are limited to simple tasks that are not typically conducive to SNNs. Furthermore, while the spike encoding strategy of TTFS allows for better synchronization of spikes for the model, it does not account for factors such as noise or irregularities in the event stream or long periods sparse events.
Other works have introduced delays alongside the weights in SNNs to offer a richer representation of the spike patterns. For instance, Shrestha & Orchard (2018) introduced fixed delay in SNNs to improve learning of
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temporal complexities, Sun et al. (2023b) extended this by making these delays learnable and introducing layer-specific maximum delay. Hammouamri et al. (002)) further refined this by making the per-layer maximum delay learnable and utilizing Dilated Convolutions with Learnable Spacings (DCLS) (Khalfaoui- Hassani et al. 2023) to capture spatio-temporal patterns. However, learning these delays, as in Sun et al. (2023b); Hammouamri et al. (2023), introduces a new set of paramnterrs with the same dimension as the weights, essentially doubling the number trainable parameters.
In contrast to these methods that rely expensive tempral skip configuration evaluation strategics, estimat- ing delay values for local path synchronization or learning delays, our proposed method introduces explicit temporal delays in SNNs. We explore these delays in both forward and backward temporal skip connec- tions, named TSkips. The use of TSkips coupled with a learnable scaling factor and adaptive LIF neurons effectively captures long-term apatio-temporal patterns with minimal additional computational overhead.
3 Methodology
This section details our methodology, starting with the input representation and the neuron model employed in our SNNs, followed by the proposed method, our NAS search space, and the training process.
3.1 Input Representation and Sensors
For efficient computation, SNNs require data in the form of discrete spikes, mirroring communication in bi- ological neurons. DVS (Lichtsteiner et al. 2008) cameras output asynchronous spikes representing real-time changes in pixel intensity (4)) This eliminates redundant data transmission and achieves higher temporal resolution than traditional brsed cameras or rate coding methods (Cao ot al. 2015). These cameras
trigger events when the log intensity change at a pixel crosses a threshold (0) (Gallego et al. 2022 repre-
sented as [[log(T+) log((=)))] 2 0. Events are encoded in the Address Event Representation (AER) format
representing pixel coordinates, timestamp, and polarity. Similarly, event-based audio datasets (Cramer et al. 2022 mimic human auditory spiking activity, with spikes represented as (z,t) denoting spike unit and timestamp.
as tuples (,,)
3.2 Neuron Model
The fundamental computational unit of SNNs the spiking neuron. We employ Leaky Integrato-and- (LIF) (Abbott, 1999) neurons for their biological plausibility and computational effieiency. The LIF neuron integrates imput spike information over time, accumulating it in its membrane potential. This potential gradually decays, allowing controlled forgetting of less relevant information. The dynamics of the LIF neuron can be described by
Uf = -U-- + WOOL, 1
(1)
where Uf represents the membrane potential of the neurons in layer at time step X is the leak fac- tor, controlling the decay rate of the membrane potential. W₁ is the weight matrix for neurons in layer 1, With is the voltage threshold of layer I and Of is the output generated by layer at time step t.
When the membrane potential surpasses the volt- age threshold, the neuron emits spike. The first term in Eq. ( denotes the leakage in the membrane potential, the second term computes the weighted summation of output spikes from layer (1 11-1) 1) and the third term denotes the reduction in membrane potential when an output spike is generated at layer I. The membrane potential is then reset, either be (hard reset) by subtracting 4ith (soft reset).
0
10
V
O
w 4
U
w $2
Input Events
Weights
LIF Neuron
Output Events
Figure 2: LIF Neuron
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Equation describes the spike generation.
U V
1,
zi
Of
(2)
0,
otherwise
We use hard reset for optical flow estimation and a soft reset for gesture and speech classification. Fig. shows the LIF neuron dynamics.
3.3 Proposed Method
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Backward TSkip
Standard Forward Skip (At=0)
Standard Backward Skip (At=1)
Element
TSkip
Concatenation
Figure 3: Illustration of TSkips in an SNN. (a) A 3-layer SNN with forward and backward TSkips, annotated
with their origin and destination layers and the delay (At). (b) Unrolled SNN with 7- 4 with a forward
TSkips and At compared with a standard skip connection (no delay). (c) Unrolled SNN with T with a backward TSkips and At compared with standard backward connection (At = 1) (Rumelhart
et al. 1986
Efficiently training deep SNNs is often hindered by vanishing gradients (Hagenaars et al. 202 Neftci et al. 2019), which impede accurate spike propagation across time steps. To address this, we propose a novel method that augments skip connections SNNs by introducing explicit temporal delays (At) within the connections. We refer to these augmented skip connections, which can be forward, backward, or a combination of both, TSkips. The duration of these explicit delays is constrained by 0 where is the current time step and T is the sequence length of the data. Specifically, represents the set of all discrete time steps within the sequence, denoted as f = (t,, vi = 0, , This constraint on At ensures that the network does not receive future information.
A/ T.
T).
To illustrate the information flow in a neural network with TSkips, let us consider how they modify the output layer time step f, then a forward TSkips provides input Mi and
of a layer. If hy denotes the input backward TSkips provides input Mig For brevity, we denote these skip inputs as hig where & indicates the layer separation between layer and the source of the skip connection. TSkips can be represented
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M = - ① W. W. (1-A0
(3)
where fi is the affine function of layer 1, θ represents either concatenation (Huang et al. 2017) or element- wise addition (He et al. 2015) and W, is a fixed shortcut path matrix (He et al.) (016) that randomly selects channels in h 1 step L is now influenced by the output of layer + k at time step (L - At). Here, k represents the difference in layer indices between connected layers. For example, if 1 = 4 and k = 2, a forward TSkips connects layers 2 and with delay At.
(F-))) to match the dimensions of hj. Eq. 3 demonstratos that the output of layer I at time
Our method, incorporating TSkips, is illustrated in Fig. Fig. shows a simple 3-yeerr SNN architecture, illustrating both forward and backward TSkips between adjacent layers. Each connection annotated with the origin and destination layers and (At). Fig. B(b) depicts the temporal unrolling of the network over T = 4 time steps. It contrasts standard skip connection (At = 0) and a forward TSkips with At = 3. Fig. ((c) similarly illustrates a backward TSkips with At = 3 and contrasts it with a standard backward connection that has delay of At = 1, typically seen in vRNNS (Rumelhart et al. 1986). This comparison emphasizes that TSkips allow for more flexibility and can thus capture longer temporal dependencies com- pared to standard RNNs. This flexibility comes with minimal overhead, as TSkips are identity mappings that introduces very few additional paramcters and no computational complexity to the network.
TSkips enhance the ability of SNNs and hybrid models to process sparse event streams by facilitating the propagation of temporally relevant information across non-adjacent layers. By capturing these long-term dependencies, TSkips can improve the network's ability to learn complex temporal patterns. Furthermore, the explicit temporal delays in TSkips offer finer control over spike timing within the network. This finer control enhances the network's responsiveness to temporal patterns by allowing it to selectively integrate information from different time steps. Additionally, by enabling the network to access relevant information from the past, TSkips can mitigate the issue of vanishing spikes. To further enhance temporal representation, we introduce a learnable scaling factor, a, that controls the ratio of data at the current time-step (1) and data from the delayed time step (t- At) within the TSkips. This is incorporated into the skip as shown in Eq.
M f( @ Walahfan + +(1 a) a)h ()))
3.4 Exploring the search space
Identifying optimal models with TSkips is challenging due to the vast number of potential architectures and associ- ated TSkips configurations. To manage this complexity, we initialize our search with a backbone network (Cai let al. 2020). This backbone provides a starting point for exploration, reducing the number of possible config- urations and allowing the search to focus on optimizing the specific parameters of our proposed method. How- ever, significant complexity remains due to the numerous choices for At, connection placement, and network depth.
(a)
(b)
L
L
L
L
L
To illustrate this complexity, consider a 3-layer network with the possibility of forward and backward connections between any two layers (Fig. 4]. This simple example results in 12 possible combinations of skip connections. With a sequence length of T 6, this grows to 120 pos- sible delay combinations and 2120 total possible TSkips configurations. This combinatorial problem, grows expo- nentially with the sequence lengths, as each additional time step introduces new TSkips configurations.
Forward TSkip
Backward
Unrolled Timsteps
Tskip
to
Figure 4: Illustration of the NAS Search Space. (a) Example of possible TSkips combinations a 3-layer network with T = 6. (b) Top-rankod forward and backward TSkips with Al 4 and At = 3, respectively, found by (Kim et al. 2022) For visual clarity, the figure depicts the TSkips spanning a single delay window (A(). Here 40 refers to the first time step and T is the sequence length.
This large search space necessitates an efficient explo- ration method to identify optimal architectures. To ad-

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dress this, we leverage NASWOT-SAHD Kim et al. 2022 a training-free NAS method tailored for SNNs. NASWOT-SAHD scores networks at initialization using the Sparsity Aware Hamming Distance (SAHD); which quantifies the dissimilarity in spike patterns between different layers. By favoring networks with diverse spiking activity, SAHD acts as a proxy for identifying optimal sub networks of the backbone archi- tecture augmnented with TSkips. Specifically, (Kim al.) 2022) performs random search for archilectures with optimal At, TSkips positions (origin and destination) and network depth.
3.5 Training with Explicit Temporal Delays
Training SNNs and hybrid models with gradient descent requires addressing the non-differentiable nature of spike activations (Fang et al., 2021a] in LIF neurons. We employ adaptive LIF neurons (Kosta & Roy 2023) with learnable leaks and thresholds, and use the ArcTangent (Fang et al. 2021a) surrogate gradient approximate the derivative of the spike activation function. To capture precise spike timing and spatio- temporal dependencics,
unroll the network in time. This, combined with adaptive LIF neurons and TSkips, allows for explicit representation of the network's temporal evolution, capturing both long-term and local temporal patterns. We then use back propagation through time (BPTT) (Werbos) 1990) for gradient
propagation and Batch Normalization Through Time (BNTT) (Kim & Panda 2021 for improved training stability.
4 Experiments
4.1 Experimental Setup
DSEC-Flow The DSEC-Flow dataset (Gehrig et al. 2021a) consists of 24 challenging driving sequences with varying lighting conditions, fast motion, and occlusions. To assess our models on unseen data, we created a custom test set by splitting the training set, following the approach in Ponghiran et al. (2023). To evaluate the accuracy of the predicted optical flow, we use average end point error (AEE) (Zhu et al. 2018a which measures the average Euclidean distance between the predicted and ground truth flow vectors.
AEE = 1 Σ (1(,, u) u) - (u, u) gelll
(5)
n
For experiments on DSEC-flow [Gehrig et al. 2021a), we use a fully spiking (Kosta & Roy| 2023) and hybrid (Negi et al. 2024 multi-scale encoder-decoder network inspired by EV-FlowNet (Zhu et al. 201 Sa) our backbone archilecture. We augment this architecture by integrating TSkips into the existing skip connections between the encoder and decoder blocks, as depicted in Fig. 5 Due to the inherent structure of our backbone, the search space for optimal TSkips configurations is relatively small, focusing primarily on sclecting which existing skip connection to modify and determining the appropriate temporal dclay (At).
DVS128-Gesture The IBM DVS128 Gesture dataset (Hu et al. 2022) contains 1342 instances of 11 hand gestures, captured with a DVS128 [Lichtsteiner et al. 2008) camera. For experiments on DVS128 Gesture, we use a ResNet18 (He et al. 2015) backbone architecture (Cai et al. 2020) and explore various configurations by modifying its basic blocks. This scarch includes modifying the input and output channels of each layer, kernel sizes, stride, and network depth. To integrate TSkips in the backbone, we remove the original ResNet18 skip connections and search for optimal TSkips placement and corresponding At.
For optical flow estimation and gesture recognition, we introduce a learnable scaling factor, a, within the TSkips to further enhance temporal processing (detailed in Section, 3.3
SHD and SSC The SHD (Cramer et al.) 2022 dataset comprises 10,000 recordings of spoken digits (zero to nine in English and German), while the larger SSC (Cramer et al. 2022) datasct contains 100,000 recordings of spoken words from various speakers. These datasels present challenges for audio classification, requiring the network to capture and process subtle temporal patterns within spike trains that encode spoken sounds. We focus on the top-one classification task for all classes in SSC and all 20 classes in SHD. For our experiments on speech recognition, we use fully connected Multi Layer Perceptron(MLPP (Rumelhart) et al. 1986) backbone architecture. We explore various MLP configurations by adjusting the input
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Figure 5: Fully spiking EV-FlowNet Zhu et al. 2018a architecture with forward and backward TSkips. Each TSkips replaces pre-existing skip connection between the encoder and decoder. Although shown together conciseness, forward and backward connections are evaluated independently. In practice, when used together, they connect different encoder-decoder layers. This architecture can be modified to be a hybrid ANN-SNN model, by replacing the LIF neurons with ReLU activations.
and output features of each layer, the overall network depth, and the placement and AL of TSkips. In these experiments, omit a used in the EV-FlowNNe and DVS128 Gesture TSkips architectures.
augment the training sets for DVS128 Gesture, SHD and SSC with channel jitter and random noise (Shen el al. 2023 We use sequence lengths (T) of 10, 30, and 99 for DSEC-flow, DVS128 Gesture, and SHD/SSC, respectively. All models are trained on an NVIDIA A40 GPU using the Adam optimizer (Kingma & Ba 2014). For DSEC-flow, we use a multi-step learning rate scheduler (initial
To improve generalization,
rate: 10 scaled by 0.7 every 10 epochs) and the supervised mean squared error (MSE) loss (Kosta &
Roy 2023 Negi et al. 2024) for 200 epochs. For all other datasets, we use Cosine Annealing Learning Rate Scheduler (Loshchilov Hutter 2017) (initial rate: 0.001, minimum rate: 10-6, updated every 10 iterations) for 100 epochs.
Details on the constraints the search parameters and TSkips configurations for DSEC-flow, DVS128 Gesture, SHD, and SSC can be found in Appendix D.I
4.2 Ablation Study
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Figure 6: Ablation study results on the SHD dataset. demonstrating the impact of varying the (a) temporal
delay (At), (b) TSkips position and (c) network depth on classification accuracy.
As detailed in Section 3.4 the search space of possible TSkips configurations is exponentially large. To effectively navigate this complex search space, we performed an ablation study on an 8-layer MLP baseline found using Kim al. (022)) on the SHD datasct. We varied the temporal delay (At), TSkips position and network depth using concatenation-basee (Huang al. 2017) TSkips for our analysis (see Appendix C.6 for detailed baseline network configuration).

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Impact of Temporal Delay (At): We investigated the impact of varying At for both forward and backward TSkips (Fig- a.)). Forward connections connected the input data to the second layer, while backward connections connected the final output to the seventh layer, with a delay of At. Varying At significantly influenced accuracy, with larger delays generally leading to better classification. This highlights the importance of optimizing AL relative to the sequence length (T), as both excessively small and large delays can hinder performance.
Impact of TSkips Position: Next, we investigated the impact of TSkips position on classification accu- 11=6,, 16, we varied the destination layer of both forward and backward connections. Forward connections originated from the imput data, while backward connections originated from the final output. Our analysis revealed that connecting TSkips to deeper layers consistently improved accuracy. This suggests that propagating temporal information to deeper layers is crucial for enhancing model performance. Note, the optimal placement varies based on forward or backward TSkips.
racy (Fig. bb).. Fixing A/ =
Impact of Network Depth: We analyzed the impact of TSkips on models of varying depth (Fig. 6 with forward connections originating from the input and backward connections originating from the linal output with At 16. Our analysis revealed that deeper networks benefited more from forward connections, while shallower architectures favored backward connections. This suggests the optimal configuration of TSkips and network depth are intertwined.
These findings underscore the complex interplay between Al, TSkips position (origin and destination layers), and network depth, which we set as our search parameters. For the results presented in the following sections, we leveraged Kim et al. (2022) to identify optimal baseline and concatenation based (Huang et al., 2017) TSkips architectures (see A Appendix C.5 for comparisons with addition-based TSkips), constraining the architecture search by the number of parameters.
4.3 DSEC-Flow Results
(a) GT
(b) Mini Baseline
(c) Mini F TSkip
(d) Mini TSkip
(e) Base Baseline
Figure 7: Qualitative results on the DSEC-flow dataset. (a) Ground Truth (GT) mask, (b) Mini (3.4M) SNN
baseline model mask, (c) Mini SNN (3.4M) with forward (F) TSkips, (d) Mini SNN (3.4M) with backward (B) TSkips, and (e) Base (13M) SNN baseline model mask. As observed, the Mini model that 3.8x smaller than Base model performs just as well qualitatively when TSkips are incorporated.
Incorporating TSkips into the fully spiking and hybrid EV-FlowNet architectures (Kosta & Roy significantly lowers AEE the DSFCCfllow datasel. (Table Across both fully spiking and hybrid architectures, TSkips consistently yielded an average reduction in A ABE of 14% and 9.5%, respectively. Notably, these improvements are achieved with models 3x smaller than baselines with comparable AEE. Although SOTA methods such as E-RAFT (Gehrig et al. 2021b) and E- FlowFrrmer (Li et al., 2023) achieve 6% and 10% lower AFE. respectively, these reductions come at the cost of increased complexity. E-RAFT, for example, while being 3x smaller than our best model, relies on complex processing of event data before its gated recurrent unit (GRU) update. These processing operations involve converting each event to voxel grid, extracting features using CNNs and building correlation volume. These dense kernel operations are computationally expensive during both training and inference, architecture which
2023 Negi
et al. 2024), as detailed in Section 4.1
as they must be performed for every event sample. E-FlowFormer is a transformer- relies on dense MAC operations in it's self and cross attention blocks. These event processing steps lead TSkips architectures, which take advantage of the inherent sparsity
to higher inference energy compared and driven nature of SNNs, performing computationally cheaper sparse AC operations. Additionally, Former is trained on large custom dataset and DSFC-flow, which introduces significant increase
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in computation power and memory during training. Fig. provides qualitative analysis of how the 3x larger baselines perform compared to the smaller TSkips variants which highlights the efficiency of TSkips in allowing accurate temporal processing without increasing model complexity. Hyper parameters and a detailed analysis convergence and inference energy for TSkips on DSEC-flow models are in Appendix
Table AEE on DSEC-flow (lower is better). Bost performing SNN and hybrid basclines and for- ward/backwer backward TSkips models highlighted in bold.
AEE
Architecture
# Params (M)
SNN Hybrid
EV-FlowNNet Geerii al. 2021b
13.04
2.32
LSTM-FlowNG Ponghran ct al. 2023
N/A
1.28
E-RAFT Gchrig ct al. 2021b
5.3
0.79
E-FlowFormer Li al.
2023
N/A
0.76
Our Models
Base Baseline
13.04
1.35
0.96
Base Forward TSkips
1.12
0.86
Base Backward TSkips
1.13
0.84
Mini Baseline
3.41
1.65
1.11
Mini + Forward TSkips
1.44
1.02
Mini Backward TSkips
1.46
1.01
Micro Bascline
0.93
1.80
1.22
Micro + Forward TSkips
1.57
1.12
Micro + Backward TSkips
1.56
1.09
Nano Baseline
0.27
2.17
1.47
Nano + Forward TSkips
1.86
1.37
Nano Backward TSkips
1.77
1.35
Pico Baseline
0.092
2.57
2.02
Pico Forward TSkips
2.19
1.78
Pico Backward TSkips
2.28
1.81
4.4 DVS128-Gesture, SHD and SSC Results
Using TSkips in ResNet18 and MIP backbone architectures, as detailed in Section 4.1 consistently improved the classification accuracy of SNNs across the DVS Gesture, SHD, and SSC datasets (Tables and
On the DVS Gesture dataset, incorporating TSkips resulted in a significant 8.37% improvement accuracy over the bascline model, convolutional SNN found by Kim et al. (2022). Importantly, our approach achieved this with significantly smaller models compared to SOTA, including spiking transformer (Qin & Liu 2024) demonstrating the efficiency of proposed method. Furthermore,
method outperformed several other approaches, including spiking RNNs (Xing et al. 2020), methods incorporating learnable delays (Shrest.ha & Orchard 2018). and methods using specialized LIF neurons or spatio-temporal feature extraction (Jiang & Zhang 2024 Samadzadeh et al. 2023 This highlights the effectiveness of our approach in capturing and leveraging temporal dependencies for improved gesture recognition.
On the SHD dataset, TSkips achieved an average accuracy gain of 8.6% over the 4-layer baseline (Baseline 1) and 8.31% over the 8-layer baseline (Baseline- 2). Our approach also outperformed various recurrent architectures (vRNNs, spiking RNNs, and LSTMs) by substantial margins. Similarly, the SSC dataset, TSkips yielded an average accuracy gain of 14% over Baseline 1 and 16.04% over the 8-layer Baseline 2, again surpassing the performance of recurrent architectures.
N/A not reported #Params
2 Backward skips are added baseline layers with At
Zhou (0023 evaluated on SHD and SSC with minimal updates the architecture and tuned learning rate.
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Table 2: Classification accuracy on DVS-Gesture. Comparisons between forward/backward TSkips and
SOTA models. Best models in bold.
Method
Base Model
#arrams (M)
Accuracy (%)
SLAYER Shresthh & Orchard 2018
SNN (8 layer)
N/A
93.6
KLIF (J Jiang & Zhang 20224
VGG-11
N/A A
93.75
DECOLE Kaiser et al.) 2020
Custom
N/A
95.2
SNN-Skip Benmezianc et al. 2023
ResNet18
N/A
95.43
Streaming rollout SNN Kugole et al.
2021
DenseNet
0.8
95.56
SCRNN (Xing et al. 2020)
Custom
N/A
96.59
STS-ReeNet (Samadzadehi et al. 2023
ResNet11
N/A
96.7
Mamba-Spike QQnn Liu 2024
Mambda
6.1
97.8
Our Models
Bascline
0.30
88.75
vRNN2
8
0.30
89.12
Forward TSkips
Backbone
0.42
94.82
Backward TSkips
0.38
95.97
Forward + Backward TSSips
0.55
97.52
Table 3: Classification accuracy on SHD and SSC datascts. Comparisons between forward, backward and a combination of both TSkips against. SOTA models and two baseline models: shallow 4-layer MLP network (Baseline- 1) and deep 8-layer MLP (Baseline 2). Best models with single and two TSkips in bold.
#Params (M) Accuracy (%)
Method
SHD
SSC
SHD
SSC
SOTA Models
LSTM-LIF Zhang et al.
2023
0.14
0.11
88.91
63.46
SRNN Yin et al 2021 DL256-SNNN--LOO
N/A
N/A
90.4
74.2
2023a
0.14
92.56
SpikGRU Dampfhofter et al 2022
0.28
77.00
radLIF (Bittar & Garner 2022
3.9
3.9
94.62
77.40
Spikinglormer (Zouu 20235
2023
1.98
1.99
82.68
72.43
DCLS-Delays
(Sun et al.
0.21
2.5
95.07
80.69
Our Bascline MLPs
Baseline
0.16
0.12
84.32
64.19
Baseline
1.04
1.04
86.42
67.54
Our MLP Models with TSkips
vRNN2 Forward T'Sipss
0.16
0.12
68.50
71.20
0.24
0.42
92.32
76.50
Backward T'Siiss- Forward + Backward TSkips
0.19
0.24
93.64
79.87
0.20
0.54
93.01
78.64
vRNN2
1.04
1.04
71.35
72.24
Forward TSkips 2
1.12
1.08
94.15
78.98
Backward TSkips
1.16
1.14
93.86
79.65
Forward + Backward TSkips 2
1.28
1.42
94.73
80.23
While TSkips achieves accuracy within 0.34% SOTA model JCLS-Delays (Hammouamri et al. 2023) on SHD and 0.46% on SSC, offers several distinct advantages. Specifically, the architectural constraint of DCLS-Delays to feedforward networks highlights key area where TSkips provides a complementary alternative. Furthermore, TSkips architectural addition coupled with NAS allows for modifications
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to various network architectures, as shown in Section 4.3 and also offers efficiency due to very few new trainable parameters coupled with strong performance. In particular TSkips achieves accuracy comparable to Hammouumri et al. (2023) on the SSC dataset with 44% smaller model.
These improvements can be attributed to the ability TSkips to capture long-tem term temporal dependencies, facilitated by the unrolled network structure, detailed in Section 3 Our method improves both the accuracy and convergence rate of the models by mitigating vanishing spikes and enabling more efficient gradient propagation during training. The analysis presented in Appendices A and [ consumption and faster convergence compared to standard SNNSs and recurrent architectures. Additionally, we show that incorporating TSkips in ANNs and hybrid models significantly improves speech classification (Appendix C.4.
demonstrates lower energy
Input
Baseline
FTSkips
no skip
BTSkips
B no skip
0.5
Average Spilke
Average Spikes
0.4
0.3
0.2
0.1
0
50
100
0
50 Timestep
100
Timestep
Timestep
Timestep
Timestep
Timestep
(a)
(c)
0.4
0.5
Average Spikess
Average Spiies
0.4
0.3
0.2
0.1
0.
0.0
50
100
100
130
50
100
Timestop
Timestop
Timestep
Timestep
Timestop
Timestep
(b)
(d)
Figure 8: Trained network's response to temporal patterns at inference, visualized by average spiking activity.
For two randomly sampled SHD event streams ((a) and (b)), we compare the true event activity against that of baseline MLP, a forward TSkips (FTSkipps) network, the FTSkips network with the skip removed (F no skip), backward TSkips (BTki)ss)) network, and the BTSkips network with the skip removed (B no skip). Sub-figures (c) and (d) show the average spiking activity specifically within the forward and backward TSkips, demonstrating spike generation aligned with the specified delay window. All plots normalized by the 700-dimensional input feature representation.
4.5 Observations
To empirically validate our claim that TSkips enhance the network's responsiveness to temporal patterns, we analyze the spike representations of trained models at inference. Fig. g compares the average spiking activity of trained models with and without TSkips against the true event stream for two randomly sampled SHD data points. The TSkips models without temporal skip have zero tensor passing through the TSkips connection to ensure the model being evaluated does not. undergo any modifications. Figures 8(a) and 8(b) show that the average spiking pattern of the trained models (even after removing the TSkips, called F/B no skip) aligns more closely with the ground truth average spike distribution compared to the baseline network. Removing TSkips during inference reduces the average spike rate and memory requirements, and the qualitative results validate that the TSkips model has learned the input event distribution and captures the input dynamics better than the baseline. We attribute this to TSkips aiding the adaptive LIF parameters and weights to learn more effectively during BPTT.
Furthermore, Fig. c)) and (d) isolate the average spiking activity within the forward (F) and backward (B) TSkips connections themselles. These plots reveal two key observations: first, spike generation within the TSkips aligns with the specified temporal delay (At), and second, the activity mirrors a scaled version of the original input distribution. This provides strong empirical evidence that TSkips propagates relevant temporal information from the past. Furthermore, Figs. ([a) and (b) validate that TSkips improve learning rather than acting additional connections. The distinct characteristics of F and B TSkips also evident.
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F TSSiss exhibit more distributed spike patterns and higher variability, likely due to processing denser latent representations from earlier network stages. The smaller and sparser activity in B TSkips might facilitate more nuanced error correction during BPTT. Crucially, both types of TSkips demonstrate sensitivity to the entire event stream, inchuding the sparse tail end, as seen in Figures 8(a) and (b). The sustained activity in Fig 8 a) and (b) during the later, sparser parts of the sequence both /TShips/no TSkips) model evaluations at inference indicates integration of information from carlier, denser time steps.
This ability of TSkips to integrate information across different temporal contexts allows the network to build richer latent representations. This mechanism is particularly important for mitigating vanishing gra- dients/spiker during BPTT, as TSkips establish direct pathways for information and gradients across long temporal distances, ensuring learning even when events are sparser over the sequence length. We provide quantitative results on these 'no skip' models for the DSEc-flow and SHD datasets in Appendixes B.2 and
4.6 Scalability of TSkips
To assess the scalability of TSkips to deeper architectures and more complex visual tasks, we evaluated our method on the CIFARIO-DVS (Li et al. 2017) dataset. While the DSEC-flow results (Section 4.3) demon- strated the effectiveness TSkips on a complex real-world task, the underlying EV-FlowNet architecture is custom-designed To further validate that TSkips works on standard, widely adopted architectures in more complex event-based setting, applied our method to larger models like spiking ResNet18 and VGG11, incorporating the NDA data augmentation technique (Li et al. 2022b) as our baseline. The results presented in Table 4 consistently demonstrate that TSkips improve accuracy over baseline models in these dcoper networks.
Table Classification accuracy on the CIFARIO-DVS dataset, comparing the performance of baseline spiking ResNet18 and VGG11 models against their TSkips-augmented counterparts, illustrating the scalability of our approach. We use the NDA (Li et al. 2022b spiking ResNet18 and VGG11 models as our baselines.
Method
Base Model #Params (M)
Accuracy (%)
SOTA Models
Spikingformer
Single-stage
2.57
81.3
Zhou et al.
2023
VIT
SSA
Multi-stage ViT
1.54
82.24
Xiao al. 2025
SpikingRess Restormer
ResNet+
35.52
84.8
Shi et al.
2024
Basline Models
Baseline
ResNet18
11.700
78.00
(NDA [Li et al. 2022b
Baseline
VGG11
132.86
81.70
(NDA Li et al.
2022b
TSkips Models
F FTSkips
Res Net 18
11.708
81.08
B TTSkip
Net
12.224
82.93
TSkips 2
VGG11 VGG11
134.04
82.56
BTSkips 2
134.04
83.01
The CIFAR1O-DVSS dataset (Li et al. 2017 provides a valuable test case, showing that TSkips can provide accuracy gains even for event data with artificially generated temporal information from repeated closed-loop movements. These results offer insight into the effectiveness of TSkips in challenging vision/awe /audio tasks that possess rich temporal dynamics, detailed in Sections 4.3 and 4.4 demonstrating their ability to improve
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performance in deeper large-scale networks event data. However, it is important to consider that smaller transformer models, such as Zhou et al. (2023); Xiao et al. 2025 Shi et al. (2024) can achieve similar or better performance with significantly fewer parameters.
Beyond specific task performance, the vast search space for optimal TSkips configurations (temporal delay (At) and skip positions) is a recognized challenge. This motivated our use of training-free NAS for efficient exploration. As detailed in Section 3.4 the NASWOT-SAHID (Kim et al. (022) proxy inherently guides this search by favoring networks with high linear separability in LIF activations across time steps, suggesting robustness beyond just favorable initializations. To confirm that TSkips consistently provide performance improvements over strong basclines identified by NAS, we analyzed the best-found bascline and their TSkips augmented variants across three random seeds. These results for DSEC-flow (Gehrig et al.) 2021a) are provided in Appendix D.2] Table 12 further validating the consistent improvement in inference with TSkips.
5
Discussion
While our approach demonstrates promising results, several avenues for future investigation remain. En- hancing the energy efficiency of discovered architcctures is one key area, potentially through energy-basod regularization within a training-free NAS proxy. Furthermore, mitigaling the increase in memory usage associated with TSkips and temporal unrolling requires exploring memory-efficiet training techniques alternative architectures. Future research could also investigate making the temporal delays learnable/ dynamically changing and inference energy optimization techniques to further refine the efficiency of our method.
Implementing TSkips in neuromorphic or biological systems presents distinct challenges. The storage of historical neural states to enable connections across time steps necessitates memory allocation, which can be a significant constraint on neuromorphic hardware with limited on-chip resources. TSkips can be implemented standard hardware by storing and retrieving past layer states, incurring memory and energy costs for simulation. The analysis in Sec. 4.5 provides a promising solution to this problem, where the trained models can be deployed without hidden state storage and passing mull input through the TSkips. On neuromorphic hardware, TSkips can be realized through direct routing with delays, where information from an carlier layer is directly routed to a later layer with a controlled temporal delay. This can be achieved using physical delay lines or digital buffers within the chip's archilecture, potentially offering energy efficiency by bypassing computations in intermediate layers. Importantly, our findings in Section 5 show that trained TSkips models can perform well even without explicitly using the temporal skip at inference, reducing hardware memory and energy requirements. Biologically, analogies might be found in short-term memory mechanisms or axonal delays that could bridge temporal gaps in information flow. Overcoming connectivity and communication latency limitations in neuromorphic hardware will also be crucial for realizing flexible temporal skips. Balancing the performance gains of TSkips with these hardware costs will guide future work exploring memory-efficiett encoding of historical states, incorporating hardware constraints into the NAS process, and investigating how to mitigate the inherent hardware delays using TSkips.
6 Conclusion
In conclusion, this work demonstrates the potential of incorporating temporal delays in forward and backward skip connections across SNNs and hybrid architectures. Our proposed method, optimized through training- free NAS, enhances accuracy, temporal representation, and efficiency while maintaining small model sizes, shown by our results on the DSEC-flow, DVS128 Gesture, SHD, and SSC datascts. Furthermore, our ablation studies reveal the importance of understanding the interplay between network depth, temporal delays, and connection placement in optimizing SNN performance. Overall, this work demonstrates a promising direction for the dcvelopment of efficient and accurate SNN architectures, achieving competitive performance with reduced complexity, thus offering a compelling alternative for real-world applications requiring fast and accurate processing of temporal information.
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Acknowledgment
This work was supported by, the Center for the Co-Design of Cognitive Systems (COCOSYS), DARPA- sponsored JUMP 2.0 center, the Semiconductor Research Corporation (SRC), and the National Science Foundation.
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A Inference Energy Estimation
To validate the observation that TSkips exhibit reduced energy consumption compared to baseline SNNs and standard recurrent methods (vRNNs (Rumelhart al.) 1986) and LSTMs (Hochreiter) 1997)) for various tasks (Sections 4.3 and 4.4], estimate inference energy. These estimations are made using the method
from Rueckauer et al. 20170: b Lee et al. (2021), which considers the energy required for sparse accumulate (AC) operations in SNNs (EAC = 0.9pJ) and dense multply-anddaccummiaa (MAC) operations in ANNs (EMAC = 4.6pJ) based on 45mm CMOS technology (Horowitz) 2014). We calculated the total inference energy (Erotat) as:
#OPSSNN x FAC,
for SNNs
Etotal
(6)
#OPSANN EMAC, for ANNs
where #OPSSNN and #OPSANN represent the layer-wise synaptic connections in SNNs and ANNs, re- spectively, caleulated as:
#OPSSNN T X #OPSANN N x.
Here, T is the sequence length, N is the number of neurons in the layer, C the number of synaptic connections per neuron, and M is the average spike rate over T.
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Baseline
Forward TSkip
Backward TSkip
1.8
1.8
1.8
(m)))
1.2
E 1.2
1.2
0.6
0.6
0.6
0
0
6
16
24
32
1
2
4
5
4
5
6
7
(a) Temporal Delay (At)
(b) TSkip Position
(c) Network Depth
Figure 9: Ablation study on the SHD dataset demonstrating the impact of varying the (a) temporal delay
(At), (b) TSkips position and (c) network depth on inference energy.
A.1 Inference Energy Ablation Study
Building upon our ablation study in Section 4.2 we further investigated the impact of different TSkips configurations on inference energy, estimated using Eq. 0 Specifically, we explored the impact of varying temporal delay (At), TSkips position, and network depth on an 8-layer multilayer perceptron (MLP) bascline model with concatenation- based TSkips, found using the Neural Architecture Search (NAS) framework (Kim) et al. 2022). This analysis is erucial because TSkips increases the average spike rate within the network, potentially leading to higher inference energy consumption.
Impact of Temporal Delay (At): We investigated the impact of varying At for both forward and backward TSkips inference energy (Fig. ga)).. Forward connections originated from the input data and terminated at the second layer, while backward connections originated from the final output and terminated at the seventh layer. Our analysis revealed that varying At significantly influenced inference energy. Larger delays resulted in lower energy consumption, likely because fewer (but more temporally relevant) spikes were propagated through the connections.
Next, we investigated the impact of varying TSkips placement on inference energy (Fig. (()).. With a fixed Al = 16, we varied the destination layer of both forward (originating from the input data) and backward (originating from the final output) connections. While no clear trend emerged, terminating both forward and backward TSkips at deeper layers generally resulted in lower inference energy consumption.
Impact of TSkip Position:
Impact of Network Depth: Finally, we analyzed the impact of TSkips on inference energy across models of varying depth (Fig, [(c)). Forward connections originated from the imput, and backward connections originated from the final output, with At = 16. Our analysis revealed that increasing the number of layers led to a significant increase in inference energy.
This analysis of inference energy with varying TSkips parameters further emphasizes the complex interplay between At, TSkips position, and network depth. It highlights the importance of using methods like Kim et al. (0222 to find optimal network architectures and TSkips configurations. While Kim et al. (2022) does not explicitly optimize for minimal energy consumption, it prioritizes networks with diverse spiking activity by quantifying the dissimilarity between spiking patterns. As result, the identified configurations often utilize TSkips with larger At values, enabling our networks to efficiently capture long-term patterns while maintaining low energy consumption.
B Additional Results DSEC-flow
B.1 Inference Energy Analysis
As demonstrated in Section TSkips reduce average endpoint error (AEE) without increasing model complexity or energy consumption for optical flow estimation on the DSEC-flow dataset. To further analyze this, we evaluated the inference energy of our fully spiking EV-FlowNet architectures augmented with TSkips using Eq. t
Table
demonstrates the effectiveness of incorporating TSkips into fully spiking EV-FlowNet architec- Kosta & Roy 2023). By efficiently utilizing temporal information, our approach achieves comparable
tures
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Table 5: Comparison of inference energy (Frotat) using Eq. for fully spiking DSFC-flow models with and
without forward/backward backward TSkips across all scales.
# Params
#OPSsNN (x10º)
Spike Rate (mJ)
Etota!
Model
(x10%) (N)
Variant
(M)
Baseline Forward TSkips
25.9
45.83
23.3
Basc
13.04
32.7
57.8
29.4
Backward TSkips
30.7
54.32
27.6
Baseline
9.71
45.15
8.75
Mini
3.41
Forward TSkips
11.7
54.23
10.5
Backward TSkips
11.4
53.21
10.3
Baseline
5.81
61.9
5.25
Micro
0.93
Forward TSkips
6.14
65.4
5.52
Backward TSkips
5.86
62.4
5.27
Baseline
2.67
55.55
2.40
Nano
0.27
Forward TSkips
2.81
58,47
2.53
Backward TSkips
2.71
56.3
2.44
Baseline
2.11
74.12
1.90
Pico
0.092
Forward TSkips
2.29
80.6
2.07
Backward TSkips
2.25
78.9
2.02
AEE to baseline models 3x larger, while significantly reducing inference energy. This improvement stems from TSkips ability to enhance spike propagation with minimal added parameters. While adding TSkips increases the average spike rate, the resulting models achieve comparable AEE to larger basclines (Table 1 with substantially lower energy consumption. This highlights the polential of our method for accurale, robust, and efficient optical flow prediction.
B.2 Inference Accuracy Analysis
As detailed in Sec. 1.5 the trained TSkips models were evaluated inference after removing the temporal hidden state propagation through the TSkips. We provide qualitative results for these models in Table s and see that the DSEC models retain performance even without explicitly storing temporal states at inference. We attribute this to the learnable scaling factor (a) within the 7Skips as detailed in 3.3. This (a) dynamically determines the weighted contribution of both the current timestep's information and the information from the delayed past timestep propagating through the skip connection. For our "no TSkips' inference analysis on DSEC, we used the learned a to control how much of the past hidden state's contribution was zeroed out in the skip connection, allowing the model to still leverage the learned weighting of the current timestep's information.
Table 6: Comparison of AEE (lower is better) DSEC-flow across baseline architectures, models with forward (F)/ backward TSkips and models no TSkips.
Arch
Baseline
F TSSkip
TSkips
BTSkips
B no TSkips
Base
1.35
1.12
1.13
1.13
1.13
Micro
1.65
1.44
1.44
1.46
1.47
Mini
1.80
1.57
1.58
1.56
1.56
Nano
2.17
1.86
1.86
1.77
1.77
Pico
2.57
2.19
2.20
2.28
2.30
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B.3 Convergence Analysis
As discussed in Section incorporating TSkips lead to easier training and faster convergence for both fully spiking (Kosta & Roy 2023 and hybrid NNgii et al. 2024 EV-FlowNet architectures. To validate this, we analyzed the convergence behavior of our DSEC-flow models across different scales. Fig. I0 shows that both our largest. (Base vs. Mini with 7Skips) and smallest (Nano vs. Pieo with TSkips) models exhibit faster convergence when incorporating TSkips, for both fully spiking and hybrid variants. This faster convergence can attributed to TSkips ability to mitigate vanishing spikes and enhance gradient flow throughout the network, enabling quicker optimization and improved learning dynamics. Additionally, by facilitating the propagation of temporally relevant. information, TSkips can help the network learn important temporal dependencies more efficiently, leading to faster convergence. This consistent trend across different model sizes highlights the benefits of TSkips in facilitating fast, efficient and effective training.
Baseline
Forward TSkip
Backward TSkip
AEE
AEE
30
80
120 Epochs
160
200
30
80
120
160
200
Epochs
(a) SNN Nano Baseline
(b) SNN Baseline
Pico F/B Tskip
Mini - F/B Tskip
5
AEE
AEE
3
1
80 120 Epochs
200
30
80
120 Epochs
160
200
(c) Hybrid Nano Baseline vs
(d) Hybrid Base Baseline vs
Pico F/B Tskip
Mini F/B Tskip
Figure 10: Convergence analysis of fully spiking (Kosta & Roy 2023 and hybrid (Negi et al. 2024 EV-
FlowNet architectures on the DSEC-flow dataset. The plots compare the convergence behavior of baseline models (Base and Nano) with their smaller forward (F) and backward (B) TSkips -augmented counterparts (Mini and Pico, respectively).
B.4 Hyper parameters for DSEC-flow
Table 7 specifies the TSkips configurations used to replace existing skip connections in the fully spiking (Kosta) & Roy 2023) and hybrid (Negi et al., 2024) EV-FlowNet architectures. Here, "TSkips Position' indicates the targeted connection, with 'I' representing the longest skip (between the first encoder and last decoder blocks) and '3' the shortest (between the last encoder and first decoder blocks), see Fig.
C Additional Results DVS128 Gesture, SHD and SSC
C.1 Inference Energy Analysis
As demonstrrted in Section 4.4 TSkips improves classification accuracy for speech recognition compared to standard recurrent models (vRNNs and LSTMs). Additionally, we state that TSkips also reduce inference energy compared these models. This energy efficiency further confirmed by the estimations presented in Table & for both shallow (4-layer) and deep (8-layer) MLP (Rumelhart et al., 1986) networks on the SHD Cramer al. 2022 dataset. These estimations calculated using Eq. 6 which considers the
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Table 7: TSkip parameters used for fully spiking and hybrid DSEC-flow models.
SNN
Hybrid
Architecture
At
TSkip Pos At
TSkip Pos
Base + Forward TSkips
3
1
Base
Backward TSkips
4
i
Mini
Forward TSkips
3
4
2
Mini
Backward TSkips
3
1
Micro + Forward TSkips
4
2
3
Micro + Backward TSkips
3
3
Nano + Forward TSkips
3
2
Nano +
Backward TSkips
4
2
Pico + Forward TSkips
4
1
Pico + Backward TSkips
3
2
energy consumed by both sparse accunulate (AC) operations in SNNs and dense mullipl--and-acccmmulaee (MAC) operations in ANNs.
For comparison, the vRNNs in Table are our baseline SNNs with backward skip connections added every layer with AL The LSTMs are implemented ANNs, with the 0.2 x 10 and 1.1 x 10 parameter models having 700 input channels and hidden sizes of 75 and 400, respectively.
The observed reduction in energy consumption can be attributed to several key factors. Firstly, TSkips introduce limited number of additional synaptic connections (C) compared to the densely connected nature of RNNs and LSTMs. Secondly, they promote sparse spiking activity by selectively propagating information across time steps, leading to lower energy consumption than the dense computations inherent in recurrent layers. Finally, the explicit temporal delays in TSkips enable the network focus on the most relevant information from previous time steps, thereby reducing unnecessary computations and further improving energy efficiency.
Table 8: Inference enorgy (Erotal) best-performing models on the SHD dataset. Energy is calculated using Eq.
# Params (x10%) (N)
Spike Rate (x10*) (M)
#OPS (x10²2)
Etotal (mJ)
Model
Baseline vRNN
0.16
0.0083
3.16
7.52
0.16
0.213
38.08
192.41
LSTM
0.2
0.016
74.63
Forward TSkips -1
0.24
0.038
5.62
34.79
Backward TSkips
0.19
0.022
4.95
20.37
Forward + Backward TSkips-
0.20
0.032
7.42
29.06
Baseline - vRNN
1.04
0.815
7,63
734.26
1.04
10.854
58.23
9768.88
LSTM
1.1
1.196
5505.28
Forward TSkips 2
1.12
1.204
8.21
1083.90
Backward TSkips
1.16
1.213
8.23
1091.87
Forward + Backward TSkips 2
1.28
1.761
9.13
1585.70
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Table 9: Comparison accuracy on SHD for two baseline models, forward (F)/ backward TSkips and no
TSkips.
Model
TSkips
TSkips
Baseline
84.32
FTSkips
92.32
90.71
BTSkips 1
93.64
92.78
F+B TSkips
93.01
91.76
Baseline
86.42
FTSkips
94.15
92.32
BTSkips 2
93.86
93.18
F+B TSkips
94.73
92.34
C.2 Inference Accuracy Analysis
As detailed in Sec. 1.5 the trained TSkips models were evaluated at inference after removing the temporal hidden state propagation through the TSkips. We see that the SHD models without the TSkips have a slight decrease in inference accuracy. We attributc this slight decrcase less information being propagated to the later layers of the network through the TSkips. However, the models continue to perform better than the baselines, thus validating that TSkips helped to improve learning during training.
C.3 Convergence Analysis
100
80
Accuracy
Baseline 1
40
T5kip
Tskip
20
vRNN 1
LSTM
100
Epochs
Figure 11: Test accuracy convergence on the SHD dataset, comparing the best-performing models with TSkips (from Table 3 to vRNN and LSTM with 0.2 x 106 parameters.
As discussed in Sections 3 and 4.4 incorporating TSkips can lead to easier training and faster convergence compared to recurrent models like vRNNs and LSTMs, as demonstrated in Fig. II for 4-layer MLP network on the SHD dataset. This accelerated convergence can be attributed to several factors: improved gradient flow by mitigating the vanishing gradient problem, efficient information propagation by facilitating the access to temporally relevant information, and reduced computational complexity compared the dense connectivity of recurrent networks. These factors, combined with the ability of TSSips capture long-term temporal dependencies, contribute to the improved training efficiency observed in our experiments.
C.4 TSkips in ANNs and Hybrid Models
As discussed in Section 4.4 incorporating TSkips into ANNs and hybrid ANN-SNN models can lead to improved classification accuracy. Table 10 presents these results, demonstrating the effectiveness of TSkips in enhancing both ANN and hybrid model performance, surpassing the performance of vRNNs and LSTMs, respectively.
This improvement can be attributed to the ability of TSkips to facilitate more effective temporal processing, By incorporating explicit temporal delays, these connections allow the network to access and integrate information from past time steps, which can be crucial for understanding complex temporal patterns. This enhanced temporal awareness enables the network to make more accurate predictions, leading to improved
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Table 10: Classification accuracy of ANN and Hybrid ANN-SNN models on the SHD and SSC datasets. We compare the 4-layer MLP bascline (Baseline-1) with backward TSkips.
Accuracy (%)
Method
# Params (x108)
ANN Hybrid
SHD
Baseline
0.16
49.95
74.11
vRNN
0.16
60.51
67.45
Forward TSkips
0.24
69.08
84.54
Backward TSkips
0.19
73.45
86.02
Forward Backward TSkips
0.20
73.25
85.74
LSTM
0.20
80.54
SSC
Baseline
0.12
55.41
59.61
yRNN
0.12
68.29
71.43
Forward TSkips
0.42
71.19
73.48
Backward TSkips
0.24
70.23
72.87
Forward + Backward TSkips
0.54
71.09
74.96
LSTM
0.20
72.3
classification accuracy. Furthermore, TSkips can mitigate the vanishing spikes problem often encountered in deep networks, by providing more direct pathways for gradient flow during training. This improved gradient propagation can lead to more stable and efficient training, further contributing to the enhanced performance observed ANNs and hybrid models.
C.5 Comparison between TSkip Operators
To further analyze the impact of different TSkips connection types, we compared the performance of concatenation-base based and addition-based TSkips the 4-layer and 8-layer baselines (Table 3
Table 11: Comparison of classification accuracy on SHD and SSC datasets with concatenation- based (C) and addition based (A) forward forward/backwark backward TSkips on a 4-layer (Baseline -1) and 8-layer (Baseline 2) MLP network.
# #aarmss (x109)
Accuracy (%)
Method
SHD
SSC
SHD
SSC
Baseline
Baseline
0.16
0.12
84.32
64.19
Forward TSkips C
0.24
0.42
92.32
76.5
Backward TSkips C
0.19
0.24
93.64
79.87
Forward + Backward TSkips C
0.20
0.54
93.01
78.64
Forward TSkips A
0.19
0.37
87.65
72.13
Backward TSkips
0.11
0.21
87.54
73.15
Forward + Backward TShips A
0.11
0.40
88.13
75.12
Baseline
Baseline
1.04
1.04
86.42
67.54
Forward TSkips C
1.12
1.08
94.15
78.98
Backward TSkips C
1.16
1.14
93.86
79.65
Forward + Backward TSkips C
1.28
1.42
94.73
80.23
Forward TSkips
0.99
1.05
86.39
72.15
Backward TSkips
0.97
1.01
87.32
75.53
Forward Backward TSkips A
0.98
1.14
89.45
77.12
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Table 11 demonstrates the superior performance of concatenation-based TSkips over addition-based on the baseline models. Concatenation--usee TSkips consistently outperformed their addition-based counterparts. This can be attributed to the increased representational capacity of concatenation, which expands the feature space by combining information from the skip connection and the destination layer. This richer representation allows the work to learn more complex temporal palterns, particularly crucial in deep SNNs where information is encoded in sparse spike trains and membrane potentials. Furthermore, concatenation preserves information from both sources, preventing potential information loss that can occur with addition.
C.6 Hyper parameters for DVS128 Gesture, SHD and SSC
Table 13 presents the top-ranked network architectures and TSkips configurations identified by NASWOT-
SAHD Kim et al.] 2022). with corresponding results shown in Tables 2 andd The table specifies the following for each configuration:
1. Network architecture:
(a) DVS128 Gesture: 2x 2x represents the input dimensions (polarity 2, 64 64 spike resolution) for all networks. Convolutional layers are represented concisely, for example, 3c80s1 denotes layer with x 3 kernel, 80 output channels, and a stride of 1.
(b) SHD and SSC: Specifies the number of input channels for each MLP layer, including the final fully connected layer. The channels represented as n 2 indicate that concatenation- based TSkips were used, doubling the number of channels (n) in that layer. This representation is used to highlight that the results shown in Table 11 which uses addition-based TSkips, are based on the same underlying network architectures.
2. TSkips parameters: The temporal delay (At) and the origin and destination layers (from - to) for forward (F), backward (B) and combined (F + B) TSkips
3. Other hyper paramcters:
(a) Leak and threshold initialization values for adaplive LIF neurons: 0.6 and 15, respectively.
(b) Dataset-specific dropout rates: 0.4 for SHD and 0.2 for SSC.
D NASWOT-SAHD Validation
D.1 Correlation on TSkips
Baseline
T5kip
TSkip
To validate the offectiveness of NASWOT-SAHD (Kim et al., 2022) in identifying optimal network configurations, we an- alyzed the correlation between the accuracy and score of the identified networks, as shown in Fig. I2 The scores are based on the Spar- sity Aware Hamming Distance (SAHD) (Kim et al., 2002),, and the correlation is sured using Kendall's т. Our bascline models achieved a I correlation of 0.63, consis- tent with the results reported in Kim et al. (2022). How- ever, the forward and back- ward TSkips network searches
Baseline Corr.
Forward T5kip Corr.
Spearman:0.77 77, Kendall=0.63
Speaman=0 63, Ke55
755
Accuracy (%6)
55
45900
2100
2300
2100
2300
2500
2700
Score
Score
Backward TSkip Corr.
Spearman=0 60, K.55
90
Acgurasy
81
2300
2500 Score
2700
Figure 12: Correlation between accuracy and SAHD score for different net- work configurations (baseline, forward TSkips, and backward TSkips).
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resulted in slightly lower cor-
relations of 0.58 and 0.55, respectively. All results reported are for the top-ranked networks identified by NASWOT-SAHD (Kim et al. 2022).
To ensure a focused and efficient search, we introduced several constraints:
1. Temporal Delay (At):
(a) DSEC-flow (T' = 10): 2 2 Af 6
(b) DVS Gesture (T 30): 5 < Al s 14
(c) SHD and SSC (T (9): 10 < A S 45
2. TSkips Position: We constrained connections to not be within the same layer, ensuring that all connections originated from different layer than the destination.
Model Size:
(a) DSEC-Flow: No constraint was applied we directly replaced existing skip connections in the fully Salking(Kosta & Roy 2023) and hybrid (Negi et al. 2024) EV-FlowNet architecture with TSkips, maintaining the original model size.
(b) DVS128 Gesture: 0.6 x 10 parameters
(c) SHD and SSC (Baseline- 1): 0.3 x 10t parameters
(d) SHD and SSC (Baseline-2): 1.3 x 10 parameters
D.2 Robustness across Random Seeds
To validate the robustness of our NAS-identified configurations and the consistent performance enhancement provided by T'Skiss conducted additional experiments the DSEC-flow (Gehrig et al. 2021a) dataset.
Table 12 presents the Average Endpoint Error (AEE) for both baseline models and their variants, averaged across three different random seeds. These results, reported as mean (4) standard deviation (o), demonstrate the stability and reliable improvement offered by our approach.
Table 12: DSEC flow results on performing NAS search for TSkips with multiple random seeds. Presented below is the AEE (mean(μ) + standard deviation(r)) (lower is better) of the models found across random seeds.
Model
At Position
AEE (μ -
Base Baseline
1.38 = 0.09
Base FTSkki
3,2,3
1,1,2
1.16 = 0.10
Base BTSkip
4,3,4
1,2,1
1.14 = 0.13
Mini Baseline
1.72 = 0.07
Mini FTSkip
3,2,2
1,1,2
1.49 = 0.06
Mini BTSkip
3,2,3
2,1,2
1.47 0.07
Micro Baseline
1.97 = 0.11
Micro F'TSkip
4,3.3
2,1,2
1.66 0.10
Micro BTSkipp
3,2,2
3,2,3
1.69 0.15
Nano Baseline
2.23 0.17
Nano FTSkkip 3.3.2
1,1,2
1.85 0.07
Nano BTSkip
4,3,3
2,1,2
1.78 0.13
Pico Baseline
2.64 0.08
Pico F'Skkpp
4,2.3
1,2,1
2.32 0.13
Pico BTSkip
3,2,3
2,1,1
2.28 0.17
27

---

Published in Transactions on Machine Learning Research (07 (075)025)
Table 13: Optimal Parameters for Training MLP Networks with Temporal Skip Connections on SHD and
SSC Datascts.
TSkip Position (from + to)
Delay (At)
Variant
Nctwork
DVS128 Gesture
Baseline
5c86s 5cckk
2x64 (40.
F TSkips
3e91ssl-cc94s1-c332211
5
1+2
B TSkips
5
4 4-3
F + B TSkips
2x661x64--311233-5c11221
F: 6
F: 1 +
B: 8
B: 5
+
SHD
Baseline
200-124-288-144-20
TSkips
700-1244=2-43--115220
24
2
B TSkips
70002-124-111-96-221
14
4 + 2
F +
F: 18
+ 4
700-2-1244144-7222220
TSkips
B: 14
B: 2
+
700-512-288-224
Baseline
192-896-288-20
110-532-288-524
TSkips
192-448*2-288-27
17
2 6
700-321-558*2-332
B TSkips
12
3 + 5
292-452-328-20)
+
100-22--22822-333
F:
2 + 5
TSkips
2
402-4--46-
B: 13
B: 7
- 3
SSC
Baseline
700-124-148-130-35
F TSkips
700-324-2988
15
1
B TSkips
700-184P2--19--23--33
3
+ TSkips
F: 14
1
+ 3
700-3644*2225"22-15555
B:
B: 4
+
700-731-410-340-
Baseline 2
150-184-58-35
700-646-410-400-
F TSkips 2
17
2
250-184*2-135-35
700-663-373*22-337-
B TSkips
15
7
292-182-135-2
F + B TSkips
700 700-674-493
F: 9
F: 1 +
278-192-894
B: 11
B: 7 -
28


Reviews:
[{"review_id": "2mmkQGSQMw", "reviewer": "Reviewer_HneG", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Practical Advantages and Hardware Considerations:\n1. TSkips introduce minimal overhead, with very few additional parameters.\n2. Discusses potential for neuromorphic implementation using delay lines or buffers.\n3. Highlights that TSkips can be disabled at inference time to save memory/energy with minimal performance drop.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces TSkips, a novel architectural mechanism that augments Spiking Neural Networks (SNNs) and hybrid ANN-SNN models with forward and backward skip connections that include explicit temporal delays. The goal is to enhance the ability of SNNs to model long-term spatio-temporal dependencies in event-based data while improving computational efficiency.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Stability Against Perturbations and Hardware Noise: To establish the robustness of TSkips in practical scenarios, we recommend the authors include a stability analysis under the following conditions:\n1. Input perturbations (e.g., noise in event timing or channel jitter),\n2. Internal perturbations (e.g., quantization noise, delayed or dropped spikes),", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "5z4Vig8sD2", "reviewer": "Reviewer_BsKM", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n1. The paper effectively tackles a crucial aspect of SNNs: the temporal domain. The exploration of temporal dependencies through TSkips is a key strength, as it directly enhances the model’s ability to capture spatio-temporal patterns, which is vital for tasks involving event-based data.\n\n2. The application of NAS to explore the vast search space of TSkip.\n\n3. The experimental results demonstrate clear performance improvements in accuracy and energy efficiency across different datasets, including optical flow, gesture recognition, and speech tasks. \n\n## Weaknesses\n1. While TSkips introduce a novel approach, the search space for optimal configurations (skip positions and time delays) is vast and difficult to navigate. The reliance on NAS introduces a dependency on the effectiveness of the search algorithm. This could undermine the novelty of TSkips since its performance is heavily influenced by the NAS method.\n\n2. The method may face challenges when applied to deep SNN architectures with long temporal sequences. The increasing complexity of the skip connection search space with network depth and sequence length can be computationally expensive and difficult to manage.\n\n3. The paper does not provide a detailed analysis on how TSkips contribute to capturing “spatio-temporal patterns” as claimed. Specifically, there is no clear discussion on which connections capture better features and how TSkips enhance this process. A more thorough examination of this aspect would strengthen the claims.\n\n4. The experiments involving parameter reduction (<10M) do not clearly justify the significance of scaling down models for TSkips. The real challenge lies in scaling up models with larger parameters (>50M), which would provide a more rigorous test of TSkip's effectiveness.\n\n5. While the authors conduct experiments across multiple tasks, the difficulty of these tasks is relatively low. For instance, the DVS-Gesture dataset is considered simple, and testing on more challenging datasets such as DVS-Cifar100 or Tiny-N-Imagenet would provide a more robust validation of TSkip's capability.\n\n6. There are instances of subjective claims without sufficient evidence. For example, in the introduction, the authors state: “We posit that these learnable synaptic delays only capture spatio-temporal patterns over a short window of time” without providing empirical or theoretical evidence to support this. These types of statements should be better substantiated to enhance credibility.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces TSkips, a novel mechanism for Spiking Neural Networks (SNNs), which augments the network architecture with temporal skip connections that incorporate explicit temporal delays. TSkips are designed to capture long-term spatio-temporal dependencies by enabling direct transmission of spike information across non-adjacent layers. The authors employ a training-free Neural Architecture Search (NAS) to identify optimal configurations for TSkips, including temporal delays and connection placements, and demonstrate their effectiveness on four event-based datasets.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. A detailed analysis should be included to explain how TSkip connections help capture better spatio-temporal features. It would be beneficial to provide insights on which types of connections work best for capturing long-term temporal dependencies.\n\n2. The experiments should address the scalability of TSkips, especially for deep networks and long temporal sequences. The paper should discuss how TSkips can be effectively used in larger, more complex networks.\n\n3. To demonstrate the full potential of TSkips, the authors should consider testing the method on more challenging datasets. This would provide stronger evidence of the method’s robustness and versatility.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "Ak9LRaGHaX", "reviewer": "Reviewer_caaK", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Strengths\n\n- The paper is well-written: the motivation is clearly stated, the proposed approach is easy to understand, and all important details are clearly explained.\n- The paper includes thorough analyses of how various parameters (temporal delay values, skip connection positions, network depth) affect model performance.\n- The authors test their approach across multiple datasets and tasks (optical flow, gesture recognition, speech recognition), demonstrating the versatility and effectiveness of TSkips.\n\n### Weaknesses\n\nOverall, I do have some concerns about the robustness of the empirical results as well as some about \"physical\" implementations of the proposed mechanism. I provide an overview below and more details in the next section.\n- As far as I can tell the learning rates were not tuned. While this seems to be the case both for the proposed approach and the baselines, I am afraid that this may increase the performance difference between the two.\n- It is not clear to me how much of the performance gain is due to finding \"easy to learn\" initializations thanks to the training-free NAS. One concern would be that TSkips adds some variability to the architecture, which increases the chance that a good initialization exists. It could be that applying the NAS on different seeds for the baselines already boosts performance. Maybe even more when adding more variability, e.g. magnitude of the weights / thresholds... To the best of my understanding, this possibility is partially ruled out by the MLP ablations (as there is not NAS there (?)), but not really in the other experiments.\n- There is no discussion of how physical networks (i.e. neuromorphic hardware / biological networks) could implement these mechanisms. To the best of my knowledge, these are one (if not the) main interests of spiking networks and the proposed mechanism requires some storing mechanisms that at best requires extra memory.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces TSkips, a mechanism that enhances Spiking Neural Networks by incorporating explicit temporal delays in skip connections. The authors propose both forward and backward temporal skip connections that enable direct transmission of spike information between non-adjacent layers and different time steps. The exact skip connections are found using a training-free Neural Architecture Search.\nThe effectiveness of TSkips is evaluated on four event-based datasets: DSEC-flow for optical flow estimation, DVS128 Gesture for hand gesture recognition, and Spiking Heidelberg Digits and Spiking Speech Commands for speech recognition. Results show improvements across all datasets.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Following up on the weaknesses I have mentioned in the previous questions, I would like the following points to be addressed to secure my recommendation for acceptance:\n\n- Can the authors tune the learning rates in their different experiments (for all the results they produce)?\n- Could the authors argue why applying NAS to different initializations would not yield benefits as significant as the ones they found with their method? One experiment to clarify that on, e.g., DSEC-flow would be welcomed.\n- How can the TSkips be implemented on \"physical\" hardware? What are the related extra memory / energy costs? \n\nThe first two points are to the best of my understanding critical to ensure the robustness of the experiments, and the last one is an important consideration to clarify.\n\nLess critical but still important is to include a reference to [1], which studied skip connections through time in rate based recurrent networks (with motivations similar to the ones here). Potentially of interest for my last point above: they removed the skip connection through time after training. Would the same benefits would hold for SNNs? If so, such a result would strengthen the paper: there is no need for extra mechanisms at inference time and the benefits would solely be attributed to learning (and not the addition of new pathways, as it may partially be the case in the current version).\n\n[1] Training biologically plausible recurrent neural networks on cognitive tasks with long-term dependencies, Soo et al.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "UR0k1zwCdm", "reviewer": "Reviewer_edR7", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n-\tThe paper tackles an important problem of how SNNs can learn arbitrary range temporal dependencies that might be required for more accurate performance on event-based datasets, without needing heavy networks (like transformers) or adding too many complications in the network architecture. \n-\tResults on multiple datasets are promising for showing the value of the proposed approach.\n\n**Weaknesses**\n- I found the literature review and the positioning of the paper within the literature to be insufficient. My main concerns are:  \n  - Some important references are missing. I found at least a couple of them that I think are very relevant:  \n    - [Rethinking skip connections in Spiking Neural Networks with Time-To-First-Spike coding](https://doi.org/10.3389/fnins.2024.1346805)  \n    - [Efficient Processing of Spatio-Temporal Data Streams With Spiking Neural Networks](https://doi.org/10.3389/fnins.2020.00439)  \n  - I would want to see a discussion of these, and how the proposed method is different from these methods. I would also like to see a performance comparison.  \n  - A lot of SNN-related references in the paper seem to have the same subset of authors (Rathi, Roy, etc.). This is fine if these are being used as references in addition to other references, but for a lot of the claims in the Intro and throughout the paper, these are the only references. I would like to see a more diverse and wider range of references to substantiate the claims.  \n  - Some of the references do not seem to be relevant to the context in which they are being cited. For example, the paper Cao et al. 2015 is constantly cited to support the statement of vanishing gradients. However, I found no discussion of vanishing gradients in that paper.  \n\n- While the results are promising, I am not convinced that they support all the claims that the authors have made in the paper. For example, the following claims:  \n  - i) Offer finer control over spike timing  \n  - ii) Enhanced responsiveness to temporal patterns  \n  - iii) Even capturing long-range temporal dependencies  \n  These do not have any direct support in the results. The only support for these claims is the improvement in the downstream performance, but these claims are so specific that they will each require a more thorough analysis (similar to ablation) to validate. While it is okay to discuss these as possible reasons for improved performance, claiming that the proposed approach offers these benefits is too strong.  \n\n- There are several issues with experiments and results:  \n  - For the experiments on the DSEC-Flow dataset, E-RAFT gives a similar performance, but the paper says that it relies on complex mechanisms like gated recurrent units. This is too vague—what makes GRU more complex than Tskips + NAS? Likewise, the paper says that E-FlowFormer will “likely lead to higher inference energy than Tskips.” This is a conjecture that is not supported by any results. I would love to see an inference energy comparison of these two architectures. Additionally, what are mini, micro, and pico architectures mentioned in Table 1?  \n  - For DVS Gesture, SHD, and SSC datasets, the paper augmented the training sets with channel jitter and random noise. The paper should clarify if the baselines had the same augmentation too to ensure fair comparison.  \n  - The proposed method performs very similarly to DCLS-Delays, and the paper outlines several advantages of Tspikes over DCLS-Delays, including very few new trainable parameters. However, the total number of parameters of DCLS-Delays is the same as Tspikes and sometimes even less (Table 3) with greater performance. Given the difference in the fundamental components of DCLS-Delays and Tspikes, and the similar or higher performance of DCLS-Delays, I am not sure if Tspikes is a substitute for DCLS-Delays (as the paper indicates) or rather just a complementary approach.  \n\n- I would love to see a discussion of the intuition behind temporal skip connections and why they can enable long-range dependency learning, especially when combined with NAS, which can output skip connections between layers that are not too far from each other (indeed, some of the hyperparameters mentioned in the appendix seem to suggest so).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper proposes a temporal skip connection augmentation to standard SNN architectures, with the idea that it enables learning of long-range temporal dependencies, resulting in improved performance on event-based datasets with smaller architectures.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "See weaknesses", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper presents an interesting architecture that enhances Spiking Neural Networks (SNNs) and hybrid ANN-SNN models. Following the discussion, two reviewers provided positive feedback (Accept, Leaning accept). Although some concerns were raised (e.g., scalability for deep networks, the need for more comparisons with SOTA methods), all reviewers acknowledged the novelty and contributions of the proposed method. The method is expected to attract significant interest from TMLR's readership, and thus I recommend “Accept with minor revision”. For the final version, the authors are required to carefully revise the manuscript and incorporate additional analysis, especially on the scalability of the architecture.
Decision: Accept (poster)