Original: WaveSense: A Spiking Neural Network Inspired by the WaveNet Architecture for Keyword Spotting
Revised: W AVE S ENSE : E FFICIENT T EMPORAL C ONVOLUTIONS WITH S PIKING N EURAL N ETWORKS FOR K EYWORD S POTTING

Original: Anonymous Author(s)
Revised: Anonymous authors

Original: AfﬁliationAddress email
Revised: Paper under double-blind review

Original: Abstract
Revised: A BSTRACT

Original: Ultra-low power local signal processing is a crucial aspect for edge applications onalways-on devices.
Revised: Ultra-low power local signal processing is a crucial aspect for edge applications on always-on devices.

Original: Neuromorphic processors emulating spiking neural networksshow great computational power while fulﬁlling the limited power budget asneeded in this domain.
Revised: Neuromorphic processors emulating spiking neural networks show great computational power while fulﬁlling the limited power budget as needed in this domain.

Revised: In this work we propose spiking neural dynamics as a natural alternative to dilated temporal convolutions.

Original: In this work we develop a spiking neural network inspiredby the WaveNet architecture which is based on simple neural dynamics, ﬁxedtime-constants and is strictly feed-forward  and hence is particularly well suited fora neuromorphic implementation.
Revised: We extend this idea to WaveSense, a spiking neural network inspired by the WaveNet architecture. WaveSense uses simple neural dynamics, ﬁxed time-constants and a simple feed-forward architecture and hence is particularly well suited for a neuromorphic implementation.

Original: We test the capabilities of this model on severaldatasets for keyword-spotting.
Revised: We test the capabilities of this model on several datasets for keyword-spotting.

Original: The results show that the proposed network beats thestate-of-the-art of other spiking neural networks and reaches near state-of-the-artperformance of artiﬁcial neural networks such as CNNs and LSTMs.
Revised: The results show that the proposed network beats the state of the art of other spiking neural networks and reaches near state-of-the-art performance of artiﬁcial neural networks such as CNNs and LSTMs.

Original:  Introduction
Revised:  I NTRODUCTION

Original: Local signal processing is an important component of the computational pipeline for Internet-of-Things (IoT)14 devices equipped with a range of sensors like audio, video and motion sensing.
Revised: Local signal processing is an important component of the computational pipeline for Internet-ofThings (IoT) devices equipped with a range of sensors like audio, video, and motion sensing.

Original: A signiﬁcant range of thesesensors capture signals comprising temporal features.
Revised: A signiﬁcant range of these sensors capture signals comprising temporal features.

Original: Ideally these features need to be extracted by an on-board16 processor before decision making or relaying the pre-processed information for further processing.
Revised: Ideally these features need to be extracted by an on-board processor before decision making or relaying the preprocessed information for further computation.

Original: Processingtemporal signals is often computationally challenging and requires large amounts of memory and power,18 especially in always-on scenarios.
Revised: Processing temporal signals is often computationally challenging and requires large amounts of memory and power, especially in always-on scenarios.

Original: Neuromorphic [13] processors with spiking-neural networks have shownpromise in this domain as ultra-low power compact solutions [10, 2, 14, 8, 6, 12].
Revised: Neuromorphic (Mead, 1990) processors with spiking-neural networks have shown promise in this domain as ultra-low power compact solutions Indiveri et al. ; Benjamin et al. ; Merolla et al. (2014); Furber et al.

Original:  In this work we propose WaveSense a Spiking Neural Network (SNN) model suitable for efﬁcient neuromorphic21 implementations while retaining high accuracy on temporal data streams.
Revised: ; Davies et al. Liu et al. In this work we propose an elegant way of implementing temporal convolutions in spiking neural networks by leveraging their inherent synaptic and membrane dynamics. Based on this idea we propose WaveSense, a Spiking Neural Network (SNN) model suitable for efﬁcient neuromorphic implementations while retaining high accuracy on temporal data streams.

Original: This work bridges the performancegap between Artiﬁcial Neural Networks (ANNs) and SNNs for temporal tasks.
Revised: This work bridges the performance gap between Artiﬁcial Neural Networks (ANNs) and SNNs for temporal tasks.

Original: Crucially, the proposed model• accepts spike streams and not ‘buffered
Revised: Crucially, the proposed model

Original:  frames’ as input,• requires no delays in its connectivity,• utilizes a very simple spiking neuron model - Leaky Integrate and Fire (LIF) neuron - without the needof any additional adaptive mechanisms,• does not require recurrent connectivity (recurrent connectivity can often be difﬁcult to tune or train).• produces a high classiﬁcation performance.
Revised: • accepts spike streams and not ‘buffered frames’ as input, • requires no delays in its connectivity, • utilizes a very simple spiking neuron model - Leaky Integrate and Fire (LIF) neuron - without the need of any additional adaptive mechanisms, • does not require recurrent connectivity (which can often be difﬁcult to tune or train), • achieves a high classiﬁcation performance.

Original: Recently several works have shown how to build efﬁcient SNNs with accuracies equivalent to ANNs [7, 18].
Revised: Recently several works have shown how to build efﬁcient SNNs with accuracies equivalent to ANNs Diehl et al.

Original:  In30 these studies, spiking neurons are used in rate mode with equivalent response curves to ReLU activations, totransfer weights from pre-trained ANNs to SNNs
Revised: Rueckauer et al. In these studies, spiking neurons are used in rate mode with equivalent response curves to ReLU activations, to transfer weights from pre-trained ANNs to SNNs.

Original: This approach therefore completely neglects the temporal32 capabilities of spiking neurons
Revised: This approach therefore completely neglects the temporal capabilities of spiking neurons.

Original: On the other hand, surrogate gradient methods enable directly training SNN using 
Revised: On the other hand, surrogate gradient methods enable directly training SNN using Back Propagation

Original: Back Propagation Through Time (BPTT) [
Revised: Through Time (BPTT) Neftci et al.

Original: Shrestha and Orchard [21] for instance show temporal processing on temporal gesture recognition task and show a good performance on a visual task.
Revised: (Shrestha & Orchard, 2018) for instance show temporal processing on temporal gesture recognition task and show a good performance on a visual task.

Original: Similar approaches have35 already been investigated on audio tasks[1, 26, 5]. Bellec et al. 
Revised: Similar approaches have already been investigated on audio tasks Bellec et al. ; Wu et al.

Original: [1] demonstrate classiﬁcation results on TIMITdataset using long time constants, a complex learning strategy (Deep-R) and require signiﬁcant computational37 resources to train.
Revised: ; Cramer et al. (Bellec et al., 2018) demonstrate classiﬁcation results on the TIMIT dataset using long time constants, a complex learning strategy (Deep-R) and require signiﬁcant computational resources to train.

Original: Wu et al. [26] train SNNs for automatic speech recognition tasks in a tandem approach withan ANNs.
Revised: (Wu et al., 2019) train SNNs for automatic speech recognition tasks in a tandem approach with an ANNs.

Original: This training pipeline integrated a language model and pronunciation model which goes beyond the39 capabilities of the neuromorphic system.
Revised: This training pipeline integrated a language model and pronunciation model which goes beyond the capabilities of the neuromorphic system.

Original: The same authors showed in an earlier study the capabilities of a SNNin combination with a self-organized map to learn to recognize digits using the TIDIGIT dataset [25].
Revised: The same authors showed in an earlier study the capabilities of an SNN in combination with a self-organized map to learn to recognize digits using the TIDIGIT dataset Wu et al.

Original: Blouw et al. [3] demonstrate high accuracy in a audio classiﬁcation task using dense networks with spectrograms42 as inputs.
Revised: (Blouw et al., 2018) demonstrate high accuracy in a audio classiﬁcation task using dense networks with spectrograms as inputs.

Original: This approach requires passing the frequency data of previous time steps (deﬁned by the spectrogramtime window) in every sample presentation to the network.
Revised: This approach requires passing the frequency data of previous time steps (deﬁned by the spectrogram time window) in every sample presentation to the network.

Original: Kugele et al. [11] show that by matching ANN44 roll-out delays to the propagation delays in SNN, the resultant networks can demonstrate a high accuracy onvision based spatio-temporal classiﬁcation tasks.
Revised: (Kugele et al., 2020) show that by matching ANN roll-out delays to the propagation delays in SNN, the resultant networks can demonstrate a high accuracy on vision-based spatio-temporal classiﬁcation tasks.

Original: Implementation of delays in neuromorphic hardware requires46 additional memory resources to store and deliver spikes in a delayed fashion and could be potentially quiteexpensive.
Revised: Implementation of delays in neuromorphic hardware requires additional memory resources to store and deliver spikes in a delayed fashion and could be potentially quite expensive.

Original: Yin, Corradi, and Bohté [27] use a Spiking Recurrent Neural Network (SRNN) architecture and48 demonstrate that by utilizing adaptive LIF neurons and learning the time constants, these networks can performtemporal classiﬁcation tasks in a sequential manner fairly well.
Revised: (Yin et al., 2020) use a Spiking Recurrent Neural Network (SRNN) architecture and demonstrate that by utilizing adaptive LIF neurons and learning the time constants, these networks can perform temporal classiﬁcation tasks in a sequential manner fairly well.

Original: The authors demonstrate the effective use of50 spiking neural networks and show a signiﬁcant increase in power efﬁciency.
Revised: The authors demonstrate the effective use of spiking neural networks and show a signiﬁcant increase in power efﬁciency.

Original: Unfortunately, having ﬁne tunedtime constants in low-power neuromorphic hardware can often be challenging especially while using ﬁxed52 precision numerical representations and computations.
Revised: Unfortunately, having ﬁne tuned time constants in low-power neuromorphic hardware can often be challenging especially while using ﬁxed precision numerical representations and computations.

Original: We propose a novel network architecture for SNN that does not require buffering or delays and can directly54 process  spiking data from event-based sensor using simple LIF neurons.
Revised: We propose a novel network architecture for SNN that does not require buffering or delays and can directly process temporally varying streams of spiking data from event-based sensors using simple LIF neurons.

Original: Our architecture is derived from ﬁrstprinciples and inspired by the WaveNet [16] architecture that does not necessitate learning the time constants of56 the system but could be deﬁned as the task demands.
Revised: Our architecture is derived from ﬁrst principles and inspired by the WaveNet van den Oord et al. (2016) architecture that does not necessitate learning the time constants of the system but could be deﬁned as the task demands.

Original: In addition we also propose an efﬁcient training strategyand a corresponding loss-function that is suitable for streaming based models, in particular models that could be58 run in real-time with neuromorphic hardware.
Revised: In addition we also propose an efﬁcient training strategy and a corresponding loss-function that is suitable for streaming based models, in particular models that could be run in real-time with neuromorphic hardware.

Original: The ﬁrst key aspect of the WaveNet architecture is the use ofa multi-layer causal dilated convolutions.
Revised: The ﬁrst key aspect of the WaveNet architecture is the use of multi-layer causal dilated convolutions.

Original: The60 causal refers to the use of data from the past, dilated refers to a sparse kernel and the convolution is along thetime axis.
Revised: The causal refers to the use of data from the past, dilated refers to a sparse kernel and the convolution is along the time axis.

Original: Stacking such convolutional operations along multiple layers enables the network to have a long62 temporal memory.
Revised: Stacking such convolutional operations along multiple layers enables the network to have a long temporal memory.

Original: A second aspect is that it eliminates the need for sliding window based inference/predictionand minimizes the number of computations within the network when operating on a continuous stream of data.
Revised: A second aspect is that it eliminates the need for sliding window based inference/prediction and minimizes the number of computations within the network when operating on a continuous stream of data.

Original: The WaveNet architecture is very amenable to general purpose micro-processors and micro-controllers
Revised: The WaveNet architecture is very amenable to general purpose micro-processors and micro-controllers

Original: but it still65 requires a reasonable amount of memory and non-linear computations such as tanh and sigmoid which arefairly complex (within the context of ultra-low power devices) and this inturn requires higher engergy and power67 requirements.
Revised: but it still requires a reasonable amount of memory and non-linear computations such as tanh and sigmoid which are fairly complex (within the context of ultra-low power devices) and this in turn requires higher energy and power requirements.

Original: Neuromorphic technology promises to bring the energy required for these tasks down by utilizing SNNs to perform ultra-low power computation.
Revised: Neuromorphic technology promises to bring the energy required for these tasks down by utilizing SNNs to perform ultra-low power computation.

Original: So far, while neuromorphic devices have been demonstrated to69 operate atan extremely low power, they have fallen short in demonstrating computational performance that ison-par or comparable to state of the art ANNs for temporal tasks, most prominently in the audio domain.
Revised: So far, while neuromorphic devices have been demonstrated to operate at extremely low power, they have fallen short at demonstrating computational performance that is on-par or comparable to state-of-the-art ANNs for temporal tasks, most prominently in the audio domain.

Original:  WaveSense model proposed here aims to bridge this gap.
Revised: The WaveSense model proposed here aims to bridge this gap.

Original: For the results in this work, we focus on audio tasks as72 spatio-temporal tasks without loss of generality.
Revised: For the results in this work, we focus on audio tasks as spatio-temporal tasks without loss of generality.

Original: Sec.
Revised: Sec.

Original: 2 details all the methods used for audio data pre-processing,conversion to spikes and the details of the network architecture.
Revised: 2 details all the methods used for audio data pre-processing, conversion to spikes and the details of the network architecture.

Original: In Sec.
Revised: In Sec.

Original: 3 we demonstrate the computational74 capability of this network over several audio datasets for key-word spotting task.
Revised: 3 we demonstrate the computational capability of this network over several audio datasets for key-word spotting tasks.

Original: We compare our results tothestate of the art SNNs and ANNs.
Revised: We compare our results to the state-of-the-art SNNs and ANNs.

Original: We conclude in Sec.
Revised: We conclude in Sec.

Original: 4 where we discuss the implications and impact of this76 work and potential areas where this work could be utilized.
Revised: 4 where we discuss the implications and impact of this work and potential areas where this work could be utilized.

Original: Most importantly all the code used to generate the reported results have been made open-source and can be found78 at http://XXXXXXXXXXXXXX .
Revised: Most importantly all the code used to generate the reported results have been made open-source and can be found at http://XXXXXXXXXXXXXX .

Original: We believe this will enable the research community to explore other avenuesthat could take advantage of our work.
Revised: We believe this will enable the research community to explore other avenues that could take advantage of our work.

Original:  Materials and Methods2.1 Neuron Model
Revised:  M ATERIALS AND M ETHODS 2. D ILATED T EMPORAL C ONVOLUTIONS

Original: In this work we used Leaky Integrate and Fire (LIF) neuron model with synaptic time constant τ s and membrane 83 time constant τ v . The sub-threshold dynamics of this neuron are described below. [Equation]

Original: where v is the membrane potential, i s is the synaptic current, w the synaptic weight and s is the input spike train.

Original: In-order to optimize simulation time and computational efﬁciency, we make some alterations.

Original: Unlike a traditional 86 LIF which resets to a resting potential upon reaching threshold θ , we subtract a ﬁxed value θ from the membranepotential.

Original: Further more, if the membrane potential increases beyond Nθ , where N is an arbitrary positive integer, 88 then this neuron produces N spikes, and proportionally Nθ is subtracted from the membrane potential.

Original: [Equation]

Original: The use of a mechanism for generating multiple spikes enables the computation to be more robust to the choice 90 of simulation time steps.

Original: This enables us to choose a relatively large time step for our simulations.

Original: In practicewe observe that some neurons occasionally do produce multiple spikes.

Original: (Producing multiple spikes in a single 92 simulation time-step is not necessary if one chooses a small enough time step.)

Original: For further simulation efﬁciency the LIF neurons were simulated using the Spike Response model (SRM) [9].

Original: [Equation]

Original: 4) where [Equation] [Equation] [Equation]
Revised: d = 1 d =dt t au = 1 t au =

Original: [Equation]

Original: We use exponential kernels for synaptic (cid:15) s ( t ) and membrane dynamics (cid:15) v ( t ) and derive the Post Synaptic 96 Potential (PSP) kernel (cid:15) ( t ) .

Original: The refractory kernel ν ( t ) is also a negative exponential kernel with the same timeconstant τ v

Original: as the membrane potential.

Original: The symbol ∗ denotes a convolution operation.

Original: As spike generation is non-differentiable, we use a surrogate gradient [15].

Original: Several proﬁles for the surrogate 99 gradients have been proposed in literature.

Original: We use a modiﬁed exponential kernel for the surrogate gradientfunction.

Original: In order to accommodate the multi-spike behavior of the neuron, we choose a periodic exponential 101 function (Figure 1) as the surrogate gradient.

Original: This function peaks as the membrane potential approaches multiplesof neuron spiking threshold θ .

Original: Intuitively, this gradient function maximizes the impact of a parameter when the 103 neuron is close to spiking or has just spiked and is a variant of the exponential gradient function.

Original: An extremesimpliﬁcation of the periodic exponential would be a Heaviside function 1 .

Original: [Figure]

Original: The simulations were run with the library ‘sinabs’ [19] 2 using an adaptation of SLAYER [21].

Original: [Figure]

Original: of membrane potentials gradient levels

Original: GNU AGPL

Original: 2.2 Network description

Original: We take inspiration from the work of Coucke et al.

Original: [4] who uses the WaveNet architecture [16] for classiﬁcation 108 of continuous audio streams.

Original: The WaveNet architecture provides a prescription for distributing temporal memoryand computation across layers without repeated presentation of previous input data.d = 1 d =dt t au = 1 t au =

Original: dt output hiddenhiddenhiddeninput d= d= d= d= time
Revised: dt output hiddenhiddenhiddeninput d= d= d= d= time

Original: A
Revised: A

Original: B time time C
Revised: B time time C

Original: The original ANN WaveNet model comprises of a few different computational building blocks. We translate 111 each of these building blocks to SNNs as follows. Dilated Temporal Convolutions are the crux of what makes WaveNets efﬁcient.
Revised: Temporal convolutions enable a layer of neurons to integrate information from the past.

Original: The dilation enables convolu- 113 tion over a large time window (or sample length) while still only using a small number of parameters.
Revised: The dilation enables convolution over a large time window (or sample length) while still only using a small number of parameters.

Original: Theseconvolutions perform a weighted-accumulation of information from different points in time, separated by the115 dilation parameter.
Revised: Temporal dilated convolutions therefore, perform a weighted-accumulation of information from different points in time, separated by the dilation parameter.

Original: This is done by storing previous activations in ANNs, and naively, this could be mimickedby replacing it by  synaptic transmission delays.
Revised: This is done by storing previous activations in ANNs. Naively, the equivalent could be achieved in SNNs by utilizing synaptic transmission delays.

Original: In this work, we observe that neuron and synaptic dynamics117 could be seen as proxies for temporal convolutional processing as shown in Figure 2.
Revised: In this work, we observe that neuron and synaptic dynamics could be seen as proxies for temporal convolutional processing as shown in Figure 1.

Original: Figure 2B shows thecontributions of each projection with a kernel size 2would look like when realized with delays.
Revised: Figure 1B shows the contributions of each projection with a kernel size 2 when implemented with delays.

Revised: Implementing synaptic transmission delays in real-time neuromorphic hardware incurs a steep overhead in terms of memory and computational resources and only a limited number of neuromorphic devices support them.

Original: Alternatively, if 119 we choose an appropriate set of synaptic time constants τ s , this is shown in Figure 2C. While quantitatively,these are different, qualitatively both these approaches provide the ability to transform and project information121 in the temporal domain [20].
Revised: We instead propose to use an appropriate set of synaptic time constants τ s as shown in Figure 1C. While quantitatively, these are different, qualitatively both these approaches provide the ability to transform and project information in the temporal domain Sheik et al.

Original: This is the key insight we leverage to design our ﬁnal model.
Revised: This is the key insight we leverage to design our ﬁnal model.

Revised: 2. N ETWORK DESCRIPTION

Revised: We take inspiration from the work of (Coucke et al., 2018) who uses the WaveNet architecture van den

Revised: Oord et al.

Revised: for classiﬁcation of continuous audio streams.

Revised: The WaveNet architecture provides a prescription for distributing temporal memory and computation across layers without repeated presentation of previous input data.

Original:  Rectiﬁed Linear Unit (ReLU) activations can be approximated by spiking neurons because a spiking neuron123 can only produce spikes if the membrane potential crosses a threshold and is silent otherwise [7].
Revised: The original ANN WaveNet model comprises of a few different computational building blocks. We translate each of these building blocks to SNNs as follows. Dilated Temporal Convolutions as mentioned above are implemented by synaptic projections with multiple time constants. Rectiﬁed Linear Unit (ReLU) activations can be approximated by spiking neurons because a spiking neuron can only produce spikes if the membrane potential crosses a threshold and is silent otherwise Diehl et al.

Original: Non-linear activations like tanh and sigmoid cannot be efﬁciently translated to SNNs.
Revised: Non-linear activations like tanh and sigmoid cannot be efﬁciently translated to SNNs.

Original: So we choose to125 replace these activations with SNNs activations (potentially ignoring the beneﬁts of ﬁltering and gating).
Revised: So we choose to replace these activations with SNNs activations (potentially ignoring the beneﬁts of ﬁltering and gating).

Original: In theoriginal model, these two activations are preceded by two sets of weights, where as in our SNN we only use one127 weighted projection.
Revised: In the original model, these two activations are preceded by two sets of weights, where as in our SNN we only use one weighted projection.

Original: (See Figure 3)
Revised: (See Figure 2)

Original: Residual connections and summation ( + ) are realized by a synaptic connection.
Revised: Residual connections and summation ( + ) are realized by a synaptic connection.

Original: The WaveSense model is built upon these building blocks as shown in Figure 3.
Revised: The WaveSense model is built upon these building blocks as shown in Figure 2.

Original: It comprises of several ‘blocks’,130 each of which comprises of three spiking neuron layers.
Revised: It comprises of several ‘blocks’, each of which comprises of three spiking neuron layers.

Original: The ﬁrst spiking layer receives inputs ﬁltered by twoseparate synapses with different time constants τ s and weights.
Revised: The ﬁrst spiking layer receives inputs ﬁltered by two separate synapses with different time constants τ s and weights.

Original: The time constants τ s of the slow projections in132 each of these blocks are chosen such that they span a range of values relevant to the task.
Revised: The time constants τ s of the slow projections in each of these blocks are chosen such that they span a range of values relevant to the task.

Original: The number of blocksis chosen such that the sum of all these time constants is proportional to the temporal memory demanded by the134 task.
Revised: The number of blocks is chosen such that the sum of all these time constants is proportional to the temporal memory demanded by the task.

Original: This layer projects to the second spiking layer.
Revised: This layer projects to the second spiking layer.

Original: Additionally a third spiking layer in each of these blocksprojects to a ‘hidden’ layer followed by a non-spiking ‘low pass’ readout layer.
Revised: Additionally a third spiking layer in each of these blocks projects to a ‘hidden’ layer followed by a non-spiking ‘low pass’ readout layer.

Original: The output of this block is the136 summation of its input (residual connection) and the output of the second layer.
Revised: The output of this block is the summation of its input (residual connection) and the output of the second layer.

Original: These ‘blocks’ are connectedin a feed forward manner.
Revised: These ‘blocks’ are connected in a feed forward manner.

Original: The non-spiking ‘low-pass’(LP) layer simply acts as a weighted low pass ﬁlter on138 the spikes of the ‘hidden’ layer.
Revised: The non-spiking ‘low-pass’(LP) layer simply acts as a weighted low pass ﬁlter on the spikes of the ‘hidden’ layer.

Original: This is equivalent to the synapse of a spiking neuron (without the neuron’smembrane potential or the spiking dynamics) and does not require any extra components unavailable to spiking 140 neurons.
Revised: This is equivalent to the synapse of a spiking neuron (without the neuron’s membrane potential or the spiking dynamics) and does not require any extra components unavailable to spiking neurons on a typical neuromorphic platform.

Original: The choice of leaving the output layer to be non-spiking is to enable a smooth, continuous valuedreadout useful for faster learning using BPTT.
Revised: The choice of leaving the output layer to be non-spiking is to enable a smooth, continuous valued readout useful for faster learning using BPTT.

Original: 2.3 Datasets
Revised: [Figure]

Original: In order to evaluate the efﬁcacy of the proposed model, we train and test it against several open-source publicly144 available audio datasets.
Revised: In order to evaluate the efﬁcacy of the proposed model, we train and test it against several open-source publicly available audio datasets [Figure]

Original: 2.3.1 Aloha Dataset
Revised: 2.3. A LOHA D ATASET

Original: The Aloha dataset [3] is a small collection of audio samples containing the keyword ’Aloha’ and several147 distractors such as ’take a load off’.
Revised: The Aloha dataset Blouw et al. (2018) is a small collection of audio samples containing the keyword ’Aloha’ and several distractors such as ’take a load off’.

Original: As the dataset is very small, only ∼ 2000 samples, we augmented thesamples using the MUSAN noise dataset [22].
Revised: As the dataset is very small, only ∼samples, we augmented the samples using the MUSAN noise dataset Snyder et al.

Original: For that end we standardized the sample length of each utterance149 in the training and validation set to ﬁve seconds and added randomly selected background noise data with asignal-to-noise ratio (SNR) of 5 dB to the training data.
Revised: For that end we standardized the sample length of each utterance in the training and validation set to ﬁve seconds and added randomly selected background noise data with a signal-to-noise ratio (SNR) ofdB to the training data.

Original:  The ’Hey Snips’ dataset [4] for wake phrase spotting distinguishes between two classes.
Revised: [Equation] The ’Hey Snips’ dataset Coucke et al. (2018) for wake phrase spotting distinguishes between two classes.

Original: The positive class153 contains 11‘000 utterances from over 2‘000 speakers of the wake phrase ’Hey Snips’ while the negative (ordistractor) class contains over 86‘000 negative examples from more than 6‘000 speakers.
Revised: The positive class contains 11‘000 utterances from over 2‘000 speakers of the wake phrase ’Hey Snips’ while the negative (or distractor) class contains over 86‘000 negative examples from more than 6‘000 speakers.

Original: We split the data into155 a training-, validation- and test-set as provided by the authors of the dataset.
Revised: We split the data into a training-, validation- and test-set as provided by the authors of the dataset.

Original: We standardized the sample lengthof each utterance in the training and validation set to ﬁve seconds.
Revised: We standardized the sample length of each utterance in the training and validation set to ﬁve seconds.

Original: As the dataset is already very large, we did 157 not augment the data with noise.
Revised: As the dataset is already very large, no noise augmentation was needed.

Original: 2.3.3 Speech Commands Dataset
Revised: 2.3. S PEECH C OMMANDS D ATASET

Original: The Speech Commands [24] describe a dataset containing 35 keywords uttered in total 105‘000 times from over160 2‘600 speakers.
Revised: The Speech Commands Warden (2018) describe a dataset containing 35 keywords uttered in total 105‘000 times from over 2‘600 speakers.

Original: The keywords contain the numbers 0 - 10 , commands such as "stop", "go", "left" and "right" aswell as other words like "Marvin", "Sheila", etc.
Revised: The keywords contain the numbers 0 - 10 , commands such as "stop", "go", "left" and "right" as well as other words like "Marvin", "Sheila", etc.

Original: This dataset was initially designed for keyword spotting in a162 limited vocabulary and the intended experiment is to detect 10 commands (plus silence) out of all 35 keywords( 12 classes in total).
Revised: This dataset was initially designed for keyword spotting in a limited vocabulary and the intended experiment is to detect 10 commands (plus silence) out of all 35 keywords ( 12 classes in total).

Original: Nevertheless, there are studies training models and showing results on all 35 classes [5].
Revised: Nevertheless, there are studies training models and showing results on all 35 classes Cramer et al.

Original: 164 We augment the training set with noise data from the MUSAN dataset using a SNR of 5 dB just as we do for the
Revised: We augment the training set with noise data from the MUSAN dataset using an SNR of 5 dB just as we do for the

Original: Aloha dataset.2.
Revised: Aloha dataset

Original: 4 Pre-processing
Revised: . 2. P RE - PROCESSING

Original: All datasets we use in this work contain many wave audio ﬁles of a few seconds length.

Original: The  data is pre-processed168 in several stages:
Revised: The raw audio data is pre-processed in several stages:

Original: • Noise augmentation The training data is augmented with noise from the MUSAN noise dataset usinga SNR of 5dB (except for the HeySnips data).• Length standardization and pre-ampliﬁcation The noise augmented waveform is cut into a standardlength (dependent on the dataset) and the amplitude is normalized.
Revised: • Noise augmentation The training data is augmented with noise from the MUSAN noise dataset using a SNR of 5dB (except for the HeySnips data). • Length standardization and pre-ampliﬁcation The noise augmented waveform is cut into a standard length (dependent on the dataset) and the amplitude is normalized.

Original: • Band-pass ﬁlters
Revised: • Band-pass ﬁlters

Original: The audio is then passed through 64 Butterworth bandpass ﬁlters  2 nd order.The
Revised: The audio is then passed through 64 Butterworth bandpass ﬁlters of 2 nd order.

Original: [Figure] bandpass ﬁlters are distributed in Mel-scale between 100Hz and 8 k Hz .[Figure]
Revised: The bandpass ﬁlters are distributed in Mel-scale between 100Hz and 8 k Hz .

Original: • Rectiﬁcation
Revised: • Rectiﬁcation

Original: The response of the 64 bandpass ﬁlters is rectiﬁed using a full-wave rectiﬁer.
Revised: The response of the 64 bandpass ﬁlters is rectiﬁed using a full-wave rectiﬁer.

Original: [Figure]

Original: • Spike conversion and binning The output of the rectiﬁer is applied as direct input to the membrane[Figure] of 64 simpliﬁed LIF neurons resulting in a rate code.
Revised: • Spike conversion and binning The output of the rectiﬁer is applied as direct input to the membrane of 64 simpliﬁed LIF neurons resulting in a rate code.

Original: The spike trains are binned into 10ms timesteps[Figure] allowing multiple spikes per timestep.
Revised: The spike trains are binned into 10ms timesteps allowing multiple spikes per timestep.

Original: [Figure]
Revised: [Figure]

Original: 2.5 Training Method
Revised: RAINING M ETHOD

Original: In order to train the parameters of  SNN (See Sec. 2.2) we use BPTT.
Revised: In order to train the parameters of the SNN (See Sec. 2.2) we use BPTT.

Original: In particular we aim to be able to deploy181 the network in streaming mode ie. the model receives the data stream directly generated from a sensor withoutany frame based (sliding window) buffering.
Revised: In particular we aim to be able to deploy the network in streaming mode i.e. the model receives the data stream directly generated from a sensor without any frame-based (sliding window) buffering.

Original: This requires us to employ an appropriate loss function.
Revised: This requires us to employ an appropriate loss function.

Original: Often in a classiﬁcation task, the output class can be determined by computing cross-entropy loss on the sum of184 the outputs over the sample length for each output neuron.
Revised: Often in a classiﬁcation task, the output class can be determined by computing cross-entropy loss on the sum of the outputs over the sample length for each output neuron.

Original: While this would yield a good classiﬁcation accuracy,the magnitude of the output trace at ‘a given point in time’ is not indicative of the network prediction.
Revised: While this would yield a good classiﬁcation accuracy, the magnitude of the output trace at ‘a given point in time’ is not indicative of the network prediction.

Original: This is not186 ideal for models being run in streaming mode.
Revised: This is not ideal for models being run in streaming mode.

Original: 2.5.1 Peak Loss
Revised: 2.5. P EAK L OSS

Original: [Figure] Typically for streaming models, a signal is predicted as belonging to a certain class when the corresponding189 output trace exceeds a ‘detection threshold’.
Revised: Typically for streaming models, a signal is predicted as belonging to a certain class when the corresponding output trace exceeds a ‘detection threshold’.

Original: This approach is also ideal for always-on neuromorphic systems.
Revised: This approach is also ideal for always-on neuromorphic systems.

Original: We therefore design our loss function to reﬂect this detection mechanism and train our neural networks.
Revised: We therefore design our loss function to reﬂect this detection mechanism and train our neural networks.

Original: We191 determine the peaks of the output traces and use only the activation values at the peaks to compute the crossentropy loss (see Figure 5) similar to max-over-time loss [5].
Revised: We determine the peaks of the output traces and use only the activation values at the peaks to compute the cross entropy loss (see Figure 4) similar to max-over-time loss Cramer et al.

Original: Consequently the loss is computed as follows:
Revised: Consequently the loss is computed as follows:

Original: [Equation]
Revised: [Equation]

Original: 9) where λ c yields 1 if class label c corresponds to the current input and 0 otherwise.
Revised: where λ c yields 1 if class label c corresponds to the current input and 0 otherwise.

Original: p c is the prediction probability195 by the neural network that the current input belongs to class c .
Revised: p c is the prediction probability by the neural network that the current input belongs to class c .

Original: It is calculated by a softmax operation as shownbelow.
Revised: It is calculated by a softmax operation as shown below.

Original: [Equation]
Revised: [Equation]

Original: where ˆy are the ’logits’ produced by the neural network.
Revised: where ˆy are the ’logits’ produced by the neural network.

Original: For temporal tasks, the input x = x T
Revised: For temporal tasks, the input x = x T

Original: = x 1 ...T and the output (logits)
Revised: = x 1 ...T and the output (logits)

Original: ˆ y of the neural network are time-seriesover time T .
Revised: ˆ y of the neural network are time-series over time T .

Original: [Equation]
Revised: [Equation]

Original: where f is the transformation of the neural network, Θ are the network parameters and s t is the internal state ofthe network at time t .
Revised: where f is the transformation of the neural network, Θ are the network parameters and s t is the internal state of the network at time t .

Original: In peak-loss we pass the peak of each output trace to the softmax function.
Revised: In peak-loss we pass the peak of each output trace to the softmax function.

Original: The peaks are202 calculated as follows:
Revised: The peaks are calculated as follows:

Original: [Equation]
Revised: [Equation]

Original: where t ∗ c = argmax( y Tc ) is the ’peak time’, the time of maximal activation of output trace c (see Figure 5).
Revised: where t ∗ c = argmax( y Tc ) is the ’peak time’, the time of maximal activation of output trace c (see Figure 4).

Original: 2.5.2 Spiking activity regularization
Revised: 2.5. S PIKING ACTIVITY REGULARIZATION

Original: The activity of LIF neurons can change dramatically during the learning process.
Revised: The activity of LIF neurons can change dramatically during the learning process.

Original: This is particularly true while 206 using the multi-spike neuron model as we do in this WaveSense implementation.

Original: This could potentially eliminatethe beneﬁt of using spiking neurons by spiking at a high ﬁring rate at every time step and consequently have no 208 sparsity. This could also lead to  high energy utilization of the network in a neuromorphic implementation.
Revised: It can either lead to the absence of spikes which stalls learning or in exploding activation which results in high energy utilization of the network in a neuromorphic implementation.

Original: In order to limit the activity of these neurons and maintain sparse activity, we include an activity regularizer term210 in our loss function [23].
Revised: In order to limit the activity of these neurons and maintain sparse activity, we include an activity regularizer term in our loss function Sorbaro et al.

Original: [Equation]
Revised: [Equation]

Original: (13) where the activation loss L act is dependent on the total excess number of spikes N † spk produced by the networkwith a population size N neurons in response to a input of length T time steps.
Revised: where the activation loss L act is dependent on the total excess number of spikes N † spk produced by the network with a population size N neurons in response to a input of length T time steps.

Original: N † spk is given as:
Revised: N † spk is given as:

Revised: [Table]

Original: [Equation]
Revised: [Equation]

Original: is the sum of spikes from all neurons N i exceeding 1 in each time bin t ( Θ is a heaviside function).
Revised: is the sum of spikes from all neurons N i exceeding 1 in each time bin t ( Θ is a heaviside function).

Original: Finally the loss function is given as:
Revised: Finally the loss function is given as:

Original: [Equation]
Revised: [Equation]

Original: where α was chosen to be 0 .
Revised: where α was chosen to be 0 .

Original:  Results
Revised:  R ESULTS

Original: In order to validate and verify that sufﬁcient information from the input is retained after pre-processing and218 conversion to spikes, we train a state-of-the-art WaveNet classiﬁer on the datasets considered in this work andcheck that we can obtain a high accuracy.
Revised: In order to validate and verify that sufﬁcient information from the input is retained after pre-processing and conversion to spikes, we train a state-of-the-art WaveNet classiﬁer on the datasets considered in this work and check that we can obtain a high accuracy.

Original: We implement a non-spiking dilated Convolutional Neural Network220 (CNN) to replicate the WaveNet architecture very similar to that described in Coucke et al.
Revised: We implement a non-spiking dilated Convolutional Neural Network (CNN) to replicate the WaveNet architecture very similar to that described in (Coucke et al., 2018; van den Oord et al., 2016)

Original: [4] and Oord et al.[16] (see Section 2.2 for details).
Revised: (see Section 2.2 for details).

Original: We train this ANN on the HeySnips, Aloha and Speechcommands datasets and compare our results to those223 reported in literature [4, 3, 5].
Revised: We train this ANN on the HeySnips, Aloha and SpeechCommands datasets and compare our results to those reported in literature Coucke et al. Blouw et al. ; Cramer et al.

Original: The results obtained from this network are then used as baseline to evaluate theperformance of the proposed SNN.[Table]
Revised: The results obtained from this network are then used as baseline to evaluate the performance of the proposed SNN.

Original: 3.1 Aloha dataset
Revised: 3. A LOHA DATASET

Original: In order to compare our model to other SNN implementations in the keyword spotting domain, we trained our227 WavseSense on the Aloha dataset [3].
Revised: In order to compare our model to other SNN implementations in the keyword spotting domain, we trained our WavseSense on the Aloha dataset Blouw et al.

Original: Table 1 shows thenetwork and memory resources  the proposed modelutilizes in comparison to the work demonstrated in Blouw et al.
Revised: Table 1 shows the memory resources of the proposed model in comparison to the work demonstrated in (Blouw et al., 2018).

Original: With an average accuracy of 98 . 0% with a229 standard deviation of 1.1% the model presented in this work performs signiﬁcantly better while at the same timerequiring a signiﬁcantly smaller number of parameters.
Revised: With an average accuracy of 98 . 0% with a standard deviation of 1.1%, the model presented in this work performs signiﬁcantly better while at the same time requiring a signiﬁcantly fewer parameters.

Original: The best runs of the WaveSense model yielded 99.5%231 accuracy which is equal to the performance of the ANN model.
Revised: The best runs of the WaveSense model yielded 99.5% accuracy which is equal to the performance of the ANN model.

Original: It is important to note that the key focus of thework by Blouw et al. [3] is to benchmark energy and power consumption and not model performance.
Revised: It is important to note that the key focus of the work by (Blouw et al., 2018) is to benchmark energy and power consumption and not model performance.

Original: 3.2 HeySnips dataset
Revised: 3. H EY S NIPS DATASET

Original: On the HeySnips dataset, our implementation of the WaveNet reaches an accuracy of 99 . 8% on the clean dataset.[-
-]
Revised: On the HeySnips dataset, our implementation of the WaveNet reaches an accuracy of 99 . 8% on the clean dataset.[-
-]

Original: In Coucke et al. [4], the authors do not report any accuracy number but rather report the false rejection rate (FRR)of 0 .
Revised: In (Coucke et al., 2018), the authors do not report any accuracy number but rather report the false rejection rate (FRR) of 0 .

Original: 12% for a ﬁxed false alarm per hours (FAPH) of 0 .
Revised: 12% for a ﬁxed false alarm per hours (FAPH) of 0 .

Original: In order to compare our results more accurately, we237 implement the same metrics; our WaveNet implementation reaches 0 .
Revised: In order to compare our results more accurately, we implement the same metrics; our WaveNet implementation reaches 0 .

Original: 95 FAPH and a 0 .
Revised: 95 FAPH and a 0 .

Original: 8% FRR on the test set.
Revised: 8% FRR on the test set.

Original: These results are slightly worse than the results reported by Coucke et al. [4] but that is expected as we do not239 apply the same speciﬁc methods to improve performance such as "End-Of-Keyword labeling" and "masking".
Revised: These results are slightly worse than the results reported by (Coucke et al., 2018) but that is expected as we do not apply the same speciﬁc methods to improve performance such as "End-Of-Keyword labeling" and "masking".

Original: Without those methods and without gating, the FRR reported by Coucke et al. [4] drops to 0 .
Revised: Without those methods and without gating, the FRR reported by (Coucke et al., 2018) drops to 0 .

Original: On the other241 hand, our WaveNet implementation reaches similar or even better results than the CNN and LSTM reported by Coucke et al.
Revised: On the other hand, our WaveNet implementation reaches similar or even better results than the CNN and LSTM reported by (Coucke et al., 2018).

Original: This fact shows that our pre-processing method indeed extracts sufﬁcient information from the243 input such that a neural network can reach very high accuracy.
Revised: This fact shows that our pre-processing method indeed extracts sufﬁcient information from the input such that a neural network can reach very high accuracy.

Original: Hence, we train a spiking version of the WaveNetarchitecture (WaveSense), as described in 2.2, on the same data.
Revised: Hence, we train a spiking version of the WaveNet architecture (WaveSense), as described in 2.2, on the same data.

Original: In the WaveSense model we do not use any gating mechanism, a kernel size of 2 and only 8 layers; much246 less compared to the 24 layers and kernel size of 3 as used in our WaveNet implementationand the WaveNetimplementation by  Couckeet al.
Revised: In the WaveSense model we do not use any gating mechanism, a kernel size of 2 and only 8 layers; much less compared to the 24 layers and kernel size of 3 as used in the WaveNet implementation by Publication [Table] Coucke

Revised: [Table]

Revised: al

Original: The memory in our model is still long enough as the WaveSense implements 248 the dilations using synaptic dynamics with long time constants but the number of parameters drops from 47090 to13042 .
Revised: [Table] Coucke et al [Table] [Table]

Revised: Coucke et al., 2018)

Revised: [Table]

Revised: This work

Revised: [Table]

Revised: work

Revised: [Table]

Revised: al

Revised: [Table]

Revised: [Table]

Revised: Nieves

Revised: [Table]

Revised: This work

Revised: [Table]

Revised: This work

Revised: [Table]

Revised: Blouw et al

Revised: [Table]

Revised: [Table]

Revised: This work

Revised: [Table]

Revised: This work

Revised: [Table]

Revised: (Coucke et al., 2018).

Revised: The memory in our model is still long enough as WaveSense implements the dilations using synaptic dynamics with long time constants but the number of parameters drops from 47 (cid:48) 090 to 13 (cid:48) 042 .

Original: Despite the low number of parameters and quantization from spiking activations, the WaveSense model 250 acheives an average accuracy of 99 . 6% over 11 runs (only drops by 0 .
Revised: Despite the low number of parameters and quantization from spiking activations, the WaveSense model achieves an average accuracy of 99 . 6% over 11 runs (only drops by 0 .

Original: Our best run of the WaveSensemodel yielded the same accuracy (of 99 . 8% ) as our WaveNet implementation.
Revised: Our best run of the WaveSense model yielded the same accuracy (of 99 . 8% ) as our WaveNet implementation.

Original: With an FRR = 1 . 0% and FAPH252 = 1 . 34 the performance is indeed lower than the WaveNet, but it is comparable to that of LSTM and CNN asreported by Coucke et al.
Revised: With an FRR = 1 . 0% and FAPH = 1 . 34 the performance is indeed lower than the WaveNet, but it is comparable to that of LSTM and CNN as reported by (Coucke et al., 2018).

Original: 3.3 Speechcommands dataset
Revised: 3. S PEECH C OMMANDS DATASET

Original: We also trained WaveSense on the Speechcommands dataset.
Revised: We also trained WaveSense on the SpeechCommands dataset.

Original: We evaluated our model by training it to classify256 all 35 classes in the dataset.
Revised: We evaluated our model by training it to classify all 35 classes in the dataset.

Original: In a study by Perez-Nieves et al. [17] in which the authors investigate the impactof heterogenity of time constants on the performance, the best model reached ∼ 57 .
Revised: In a study by (Perez-Nieves et al., 2021), in which the authors investigate the impact of heterogenity of time constants on the performance, the best model reached ∼ 57 .

Original: 3% accuracy on the same258 dataset.
Revised: 3% accuracy on the same dataset.

Original: In Cramer et al. [5] the best performing SNN is a recurrent network which yields ∼ 50 .
Revised: In (Cramer et al., 2020) the best performing SNN is a recurrent network which yields ∼ 50 .

Original: 9% accuracy ofall 35 classes.
Revised: 9% accuracy of all 35 classes.

Original: In the same study, also an LSTM and CNN are trained on the same data resulting in an accuracy260 of ∼ 73% resp.
Revised: In the same study, also an LSTM and CNN are trained on the same data resulting in an accuracy of ∼ 73% resp.

Original: ∼ 77 .
Revised: ∼ 77 .

Original: The WaveSense model reaches an average accuracy of 79 .
Revised: The WaveSense model reaches an average accuracy of 79 .

Original: 6% over 11 runs (best80 . 0% ) which is signiﬁcantly higher than the best SNN described in previous studies.
Revised: 6% over 11 runs (best 80 . 0% ) which is signiﬁcantly higher than the best SNN described in previous studies.

Original: Notably, WaveSense262 performs better than the reported LSTM and CNN [5].
Revised: Notably, WaveSense performs better than the reported LSTM and CNN Cramer et al.

Original:  Discussion and Conclusion
Revised:  D ISCUSSION AND C ONCLUSION

Original: While the results demonstrated here are obtained using a ﬁxed set of time constants, it is conceivable that265 according to the constraints of the neuromorphic hardware, an appropriate network could be trained to obtainqualitatively similar results.
Revised: While the results demonstrated here are obtained using a ﬁxed set of time constants, it is conceivable that according to the constraints of the neuromorphic hardware, an appropriate network could be trained to obtain qualitatively similar results.

Original: This holds true even for mixed-signal neuromorphic devices [10] with programmable267 weights and tune-able time constants.
Revised: This holds true even for mixed-signal neuromorphic devices Indiveri et al. (2011) with programmable weights and tune-able time constants.

Original: Because the algorithm provides a recipe for how to choose the timeconstants in the network, even if a neuromorphic substrate has a limited range of time constants, a number of269 layers with an appropriate combination (sum) of time constants can always be chosen to ﬁt the temporal task.
Revised: Because the algorithm provides a recipe for how to choose the time constants in the network, even if a neuromorphic substrate has a limited range of time constants, a number of layers with an appropriate combination (sum) of time constants can always be chosen to ﬁt the temporal task.

Original: This is in stark contrast to recurrent neural networks that often require a tight balance between excitation and271 inhibition and long time constants [1, 27]. [Table] [Table] [Table]
Revised: This is in stark contrast to recurrent neural networks that often require a tight balance between excitation and inhibition and long time constants Bellec et al.

Original: al [Table]
Revised: ; Yin et al.

Original: The choice of time constants and number of layers is informed by the total temporal memory required by the task.
Revised: The choice of time constants and number of layers is informed by the total temporal memory required by the task.

Original: We choose them in a similar fashion to that of WaveNet with time constants increasing with factors of 2 andsuch that the sum of all the time constants is proportional to τ task .
Revised: We choose them in a similar fashion to that of WaveNet with time constants increasing with factors of 2 and such that the sum of all the time constants is proportional to τ task .

Original: Typically we observe that a proportionality275 of 2 . 5 is suitable with a kernel size of 2 .
Revised: Typically we observe that a proportionality of 2 . 5 is suitable with a kernel size of 2 .

Original: The proportionality factor is the length of time after which the effect ofa PSP is negligible.
Revised: The proportionality factor is the length of time after which the effect of a Post Synaptic Potential (PSP) is negligible.

Original: This also translates to compact networks with fewer parameters for the same amount of277 temporal memory (at the same time resolution).
Revised: This also translates to compact networks with fewer parameters for the same amount of temporal memory (at the same time resolution).

Original: In other words, given a network, the temporal memory of agiven task can be computed as follows:
Revised: In other words, given a network, the temporal memory of a given task can be computed as follows:

Original: [Equation]
Revised: [Equation]

Original: where i is the list of all the layers in the WaveSense network.
Revised: where i is the list of all the layers in the WaveSense network.

Original: While the results reported here are signiﬁcantly high, we believe this can be further improved by improving the281 loss function.
Revised: While the results reported here are signiﬁcantly high, we believe this can be further improved by modifying the loss function.

Original: For instance the max-over-time loss computed only during the presence of a keyword as opposedto the entire sample [4] has been shown to improve performance of such models.
Revised: For instance the peak loss computed only during the presence of a keyword as opposed to the entire sample Coucke et al. (2018) has been shown to improve performance of such models.

Original: Furthermore, a thorough283 architecture search could potentially result in a better combination of time constants τ m and τ s , number ofchannels, kernel sizes etc.
Revised: Furthermore, a thorough architecture search could potentially result in a better combination of time constants τ m and τ s , number of channels, kernel sizes etc.

Original: A crucial factor in adopting a model is ease of training, deployment and power efﬁciency.
Revised: A crucial factor in adopting a model is ease of training, deployment and power efﬁciency.

Original: By utilizing simple286 LIF neurons, we take full advantage of their computational efﬁciency [27] in additional to sparse computationsafforded by SNNs.
Revised: By utilizing simple LIF neurons, we take full advantage of their computational efﬁciency Yin et al. (2020) in additional to sparse computations afforded by SNNs.

Original: While training SNNs is relatively slow on CPUs and GPUs, utilizing the SRM in combination288 with the SLAYER algorithm [21], we are able to train at a relatively high speed.
Revised: While training SNNs is relatively slow on CPUs and GPUs, utilizing the Spike Response model (SRM) in combination with the SLAYER algorithm Shrestha & Orchard (2018), we are able to train at a relatively high speed.

Original: All experimental results reportedin this manuscript were performed on a single NVIDIA 

Revised: All experimental results reported in this manuscript were performed on a single NVIDIA

Original: Ti with a few hours of run time per experiment.
Revised: Ti with a few hours of run time per experiment.

Original: We290 further improve upon this efﬁciency with a custom fork of the SLAYER implementation 3 .
Revised: We further improve upon this efﬁciency with a custom fork of the SLAYER implementation 1 .

Original: The resulting modelswhile accurate within the SRM framework, are not identical to simulations based on LIF neurons, supported by292 most digital neuromorphic devices.
Revised: The resulting models, while accurate within the SRM framework, are not identical to simulations based on LIF neurons, supported by most digital neuromorphic devices.

Original: But we ﬁnd that they are a close approximation and a quick retraining canrecover the model’s performance using LIF neurons.
Revised: But we ﬁnd that they are a close approximation and a quick retraining can recover the model’s performance using LIF neurons.

Original: The WaveNet architecture requires storing activations of each of its layers depending on their kernel size and295 dilation value: N buf ∝ ( k − 1) · d + 1 .
Revised: The WaveNet architecture requires storing activations of each of its layers depending on their kernel size and dilation value: N buf ∝ ( k − 1) · d + 1 .

Original: In contrast, WaveSense does not buffer any spikes(activations) from thepast explicitly.
Revised: In contrast, WaveSense does not buffer any spikes(activations) from the past explicitly.

Original: Instead the information is retained in the neuron and synaptic states: N buf ∝ k + 1 .
Revised: Instead, the information is retained in the neuron and synaptic states: N buf ∝ k + 1 .

Original: This makes297 WaveSense extremely efﬁcient in terms of memory utilization in contrast to WaveNet.
Revised: This makes WaveSense extremely efﬁcient in terms of memory utilization in contrast to WaveNet.

Original: The results demonstrated here show that the WaveSense architecture is suitable for audio classiﬁcation tasks and299 show a promising performance improvement in comparison to prior state-of-the-art.
Revised: The results demonstrated here show that the WaveSense architecture is suitable for audio classiﬁcation tasks and show a promising performance improvement in comparison to prior state-of-the-art.

Original: Audio signals, after they arepre-processed are equivalent to a population of neurons producing spike patterns with complex spatio-temporal301 correlations.
Revised: Audio signals, after they are pre-processed are equivalent to a population of neurons producing spike patterns with complex spatio-temporal correlations.

Original: We argue therefore, that the results presented here can be extended to other modalities of sensorydata such as ECG, PPG, machine vibrations or DVS data.
Revised: We argue therefore, that the results presented here can be extended to other modalities of sensory data such as ECG, PPG, machine vibrations or DVS data.

Original: This work we believe could contribute towards a future with a ubiquitous abundance of always-on audio and304 other sensory devices responding to user commands.
Revised: This work we believe could contribute towards a future with a ubiquitous abundance of always-on audio and other sensory devices responding to user commands.

Original: This could lead to potential misuse of the technologyfor surveillance.
Revised: This could lead to potential misuse of the technology for surveillance.

Original: Thankfully, neuromorhic algorithms such as the one proposed here require specialized306 neuromorphic hardware to take full advantage.
Revised: Thankfully, neuromorphic algorithms such as the one proposed here require specialized neuromorphic hardware to take full advantage.

Original: If the availability of such hardware could be regulated, we hopethat the society can beneﬁt from this technology while protecting itself from misuse.
Revised: If the availability of such hardware could be regulated, we hope that society can beneﬁt from this technology while protecting itself from misuse.

Original: Checklist
Revised: A A PPENDIX A. N EURON M ODEL

Original: For all authors. (a) Do the main claims made in the abstract and introduction accurately reﬂect the paper’s contribu- tions and scope? [Yes]
Revised: In this work we used the Leaky Integrate and Fire (LIF) neuron model with synaptic time constant τ s and membrane time constant τ v .

Original: (b) Did you describe the limitations of your work?
Revised: The sub-threshold dynamics of this neuron are described below.

Original: [Yes]
Revised: [Equation]

Original: (c) Did you discuss any potential negative societal impacts of your work? [Yes] The potential impact of this work extends from a broader discussion on the potential impact of low-power
Revised: where v is the membrane potential, i s is the synaptic current, w the synaptic weight and s is the input spike train. In-order to optimize simulation time and computational efﬁciency, we make some alterations.

Original: keyword spotting technologies.
Revised: Unlike a traditional LIF which resets to a resting potential upon reaching threshold θ , we subtract a ﬁxed value θ from the membrane potential.

Original: (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?
Revised: Furthermore, if the membrane potential increases beyond Nθ , where N is an arbitrary positive integer, then this neuron produces N spikes, and proportionally Nθ is subtracted from the membrane potential.

Original: [Yes]
Revised: [Equation]

Original: If you are including theoretical results... (a) Did you state the full set of assumptions of all theoretical results?
Revised: The use of a mechanism for generating multiple spikes enables the computation to be more robust to the choice of simulation time steps. This enables us to choose a relatively large time step for our simulations.

Original: [N/A] (b) Did you include complete proofs of all theoretical results?
Revised: In practice we observe that some neurons occasionally do produce multiple spikes.

Original: [N/A] If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental
Revised: (Producing multiple spikes in a single simulation time-step is not necessary if one chooses a small enough time step.)

Original: results (either in the supplemental material or as a URL)?
Revised: For further simulation efﬁciency the LIF neurons were simulated using the SRM Gerstner (2001).

Original: [Yes]
Revised: [Equation]

Original: (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?

Original: [Yes]
Revised: [Equation]

Original: (c) Did you report error bars (e.g., with respect to the random seed after running experimentsmultiple times)?
Revised: where

Original: [Yes]
Revised: [Equation]

Original: (d) Did you include the total amount of compute and  the type of resources used (e.g., type of GPUs,internal cluster, or cloud provider)?
Revised: We use exponential kernels for synaptic (cid:15) s ( t ) and membrane dynamics (cid:15) v ( t ) and derive the PSP kernel (cid:15) ( t ) .

Original: [Yes] If you are using existing assets (e g., code, data, models) or curating/releasing new assets... (a) If your work uses existing assets, did you cite the creators?
Revised: The refractory kernel ν ( t ) is also a negative exponential kernel with the same time constant τ v as the membrane potential.

Original: [Yes] (b) Did you mention the license of the assets?
Revised: The symbol ∗ denotes a convolution operation.

Original: [Yes] (c) Did you include any new assets either in the supplemental material or as a URL? [Yes] (d) Did you discuss whether and how consent was obtained from people whose data you’re us-
Revised: As spike generation is non-differentiable, we use a surrogate gradient Neftci et al.

Original: ing/curating? [N/A] (e) Did you discuss whether the data you are using/curating contains personally identiﬁable
Revised: Several proﬁles for the surrogate gradients have been proposed in literature. We use a modiﬁed exponential kernel for the surrogate gradient function.

Original: informa-
Revised: In order to accommodate the multi-spike behavior of the neuron, we choose a periodic exponential function (Figure 5) as the surrogate gradient. This function peaks as the membrane potential approaches multiples of neuron spiking threshold θ . Intuitively, this gradient function maximizes the impact of a parameter when the neuron is close to spiking or has just spiked and is a variant of the exponential gradient function. An extreme simpliﬁcation of the periodic exponential would be a Heaviside function 2 .

Original: tion or offensive content?
Revised: The simulations were run with the library ‘sinabs’ Sheik & Sorbaro (2013) 3 using an adaptation of SLAYER Shrestha & Orchard (2018). A. S IMULATION PARAMETERS The various parameters used in the experiments described in this article are listed below.

Original: [N/A]
Revised: [Table]

Original: If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable?[N/A]
Revised: [Table] [Table]

Original: (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?
Revised: [Table]

Original: [N/A]
Revised: [Table]

Original: (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?
Revised: true

Original: [N/A]
Revised: [Table]