Neuronal Competition Groups with Supervised STDP for Spike-Based Classification
Authors: Gaspard Goupy
Pierre Tirilly
Ioan Marius Bilasco
Venue: NeurIPS 2024 poster (2024)
Keywords: Spiking Neural Networks
STDP
Winner-Takes-All Competition
Local Learning
First-Spike-Based Classification
Primary area: other

Abstract: Spike Timing-Dependent Plasticity (STDP) is a promising substitute to backpropagation for local training of Spiking Neural Networks (SNNs) on neuromorphic hardware. STDP allows SNNs to address classification tasks by combining unsupervised STDP for feature extraction and supervised STDP for classification. Unsupervised STDP is usually employed with Winner-Takes-All (WTA) competition to learn distinct patterns. However, WTA for supervised STDP classification faces unbalanced competition challenges. In this paper, we propose a method to effectively implement WTA competition in a spiking classification layer employing first-spike coding and supervised STDP training. We introduce the Neuronal Competition Group (NCG), an architecture that improves classification capabilities by promoting the learning of various patterns per class. An NCG is a group of neurons mapped to a specific class, implementing intra-class WTA and a novel competition regulation mechanism based on two-compartment thresholds. We incorporate our proposed architecture into spiking classification layers trained with state-of-the-art supervised STDP rules. On top of two different unsupervised feature extractors, we obtain significant accuracy improvements on image recognition datasets such as CIFAR-10 and CIFAR-100. We show that our competition regulation mechanism is crucial for ensuring balanced competition and improved class separation.

Neuronal Competition Groups with Supervised STDP for Spike-Based Classification
Gaspard Goupy', Pierre Tirilly', and loan Marius Bilasco
Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France "Corresponding author: marius. wilasso @univ-lilee.fr
Abstract
Plasticity (STDP) is promising substitute to backprop- agation for local training of Spiking Neural Networks (SNNs) on neuromorphic hardware. STDP allows SNNs to address classification tasks by combining un- supervised STDP for feature extraction and supervised STDP for classification. Unsupervised STDP is usually employed with Winner-Takes-All (WTA) competi- tion to learn distinct patterns. However, WTA for supervised STDP classification faces unbalanced competition challenges. In this paper, propose method effectively implement WTA competition in spiking classification layer employing first-spike coding and supervised STDP training. We introduce the Neuronal Com- petition Group (NCG), an architecture that improves classification capabilities by promoting the learning of various patterns per class. An NCG is a group of neurons mapped to a specific class, implementing intra-class WTA and novel competition regulation mechanism based on wwo-compartment thresholds. We incorporate our proposed architecture into spiking classification layers trained with state-of oftte-of-theaar the-art supervised STDP rules. On top two different unsupervised feature extractors, we obtain significant accuracy improvements on image recognition datasets such as CIFAR-10 and CIFAR-100 We show that our competition regulation mechanism is crucial for ensuring balanced competition and improved class separation.
Spike
Introduction
Neuromorphic computing [ with Spiking Neural Networks (SNNs) [2] is a promising solution address the high energy consumption of Artificial Neural Networks (ANNs) on von Neumann architectures (3. However, direct training of SNNs on neuromorphic hardware faces a major constraint: implementing network-level communication is difficult and requires significant circuitry overhead 44. As result, the learning mechanisms should be local, i.e., with weight updates based only on the activity of the two neurons that the synapse connects.
Training SNNs to achieve state-of-the-art (SOTA) performance is typically accomplished with adaptations of backpropagation (BP) [5] () However, these methods are challenging implement on neuromorphic hardware since they employ non-local learning 4 J. In addition, they only rely on supervised learning, making them highly dependent on labeled data. We believe that machine learning algorithms should minimize this dependence on supervision by leveraging unsupervised feature learning [8]. Hence, an appealing classification system may comprise both unsupervised and supervised components, for feature extraction and classification, respectively.
Hebbian learning 9 is an unsupervised and local alternative to BP, inspired by the principal form of plasticity observed in biological synapses. Specifically, Spike -eienn-Depnndnt Plasticity (STDP) [0] form of Hebbian learning where the time difference between the input and output neuron spikes defines synaptic plasticity. STDP could solve all the aforementioned limitations of BP,
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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making it more suitable for on-chip training on neuromorphic hardware [2] STDP is particularly effective with first-spike coding 14, where neurons can fire at most once per sample. Using one spike per neuron presents several advantages, including energy efficiency [15 16], fast information transfer [77. and high information capacity [8]. While primarily used for unsupervised feature learning 19 20 21], STDP can be extented to supervised learning [22] 23 24] As a result, SNNs can perform classification tasks by combining unsupervised STDP for feature extraction and supervised STDP for classification [25] 26 27 28 29] Employing the same type of local learning rule for both feature extraction and classification ensures consistency and may facilitate hardware implementation.
Unsupervised STDP is commonly paired with Winner- Takes-All (WTA) competitive learning to promote the discovery of distinct patterns [30] [9 31 20]. In WTA framework with first-spike coding, lateral inhibition is implemented to ensure that only the first neuron to fire receives a weight update, addition, homeostatic mechanisms, such as threshold adaptation, must be employed to regulate the competition among neurons [32 20
33 34 For supervised STDP, WTT competition also appealing as it may improve the learning capabilities of a classification layer with multiple neurons per class [22]. Specifically, intra-class WTA can promote the learning of various class- specific patterns. However, supervised STDP classification with WTA competition has been poorly studied in the literature (22k5) and presents unbalanced competition challenges. Indeed, there is a lack of competition regulation methods, and regular threshold adaptation rules can lead to unfair decision maiiinnn since output neurons may use different thresholds for inference.
In this paper, we address WTA-based competitive learning in supervised STDP, We aim to implement effective WTA competition in spiking classification layer employing first-spike coding and SOTA supervised STDP rules. Our main contributions can be summarized as follows:
1. We introduce the Neuronal Competition Group (NCG), an architecture that improves classification capabilities by promoting the learning of various patterns per class. In the classification layer, each class is mapped an NCG: group of neurons using intra-class WTT and competition regulation.
2. To ensure both balanced intra-class competition and fair decision-making, we design competition regulation mechanism based on (wo-compartment thresholds. Neurons are equipped with fixed threshold for Decision-makinge along with adaptive threshold used to regulate the frequency at which they update their weights on samples of their class.
To validate our architecture with input features of varying quality, we incorporate NCGs into spiking classification layers placed on top of two Hebbian-based feature extractors. Using NCGs with SOTA supervised STDP rules, we obtain significant accuracy gains on image recognition datasets: MNIST, regulation mechanism is crucial for ensuring balanced competition and improved class separation.
CIFAR- 10, and CIFAR- 100. We show that our competition
The source code is publicly available https://gitlab. wnii univ wille.lllll..... www.ille.fffff...e wtwp///oo//nnnnneeeeeeeeee
2 Related Work
Supervised Training with STDP Supervised training of SNNs with STDP introduces error signal (36) that is used to guide the STDP updates. Several supervised adaptations of STDP are
23 40). Yet, the aforementioned rules are designed to train SNNs with multiple spikes per neuron, which is not as efficient as first-spike coding. The literature exploring supervised STDP training of SNNs with one spike per neuron is limited (2 24 29). Reward-Modulated STDP (R-STDP) [22] involves supervised training by adjusting the sign of STDP, The employed error fairly simple (+1 or -1), resulting in inaccurate weight updates. SSTDP 224 and S2-STDP (29 are more recent methods that compute temporal errors to adjust both the sign and the intensity of weight updates, making them more accurate. However, unlike R-STDP, these methods cannot be used with various neurons per class in a classification layer.
reported in the literature 337 25 38
39
34
Competitive Learning for Classification Employing groups of neurons is an effective approach To maximize knowledge
for improving the learning capabilities of a classification layer 41 42
43
within the layer and learn distinct patterns, WTA-bbased competitive learning can be employed [31].
31 20 its application to supervised learning is limited. Prior work [32 44 45 implemented WTA competition at the
While WTA competition is widely adopted in unsupervised learning (30
19
classification layer but only with one neuron per class, making it impossible to learn various class-

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specific patterns. Conversely, reward-basse based approaches [22 35 such as R-STDP, are the only methods that implement WTA with multiple neurons per class. Through lateral inhibition, neurons compete for weight updates, both within the same class (intra-class WTA) and across different classes (inter-class WTA). Intra-class WTA enables neurons to learn patterns from distinct samples. However, inter-class WTT prevents accurate control over the time difference between the spikes of target and non-target neurons (i.e. neurons mapped or not to the class), as only one neuron is updated per sample. In [29]. solely intra-class WTA and two neurons per class were employed to promote specialization toward target and non-target samples. Nonetheless, to the best of our knowledge, no prior work solely employed intra-class WTA to promote the learning of various class- patterns.
Competition Regulation In WTA-based competitive learning, it is crucial to implement regulation (also called homeostatic) mechanisms to ensure balanced competition among neurons 31
20
33
simple solution to use dropout [46] on the output neurons, as done with R-STDP 22 where
some neurons of each class are randomly deactivated during training to encourage weight updates on distinct samples. Yet, this solution is not optimal due to its stochastic nature. Other regulation mechanisms involve threshold adaptation [32 20 34, by increasing or reducing thresholds to promote or discourage firing. While threshold adaptation is an effective solution to ensure balanced competition, using different thresholds across neurons may prevent fair decision-male -making since their firing time is tied to their thresholds. Prior work employed multiple thresholds per neuron [27 47 but the authors did not incorporate threshold adaptation mechanisms. In this work, we draw inspiration and threshold adaptation to design competition regulation mechanism based on two-compartment thresholds, ensuring both balanced competition and fair decision-making
from
3 Preliminaries
3.1 Neuron Model
To align with first-spike coding, we use the Single-Spike Integrate-and-Prr (SSIF) model 48 where neurons can fire most once per sample. Since each neuron emits a single spike, the intensity of its activation is encoded via firing timestamp: the most activated neuron fires first. The membrane potential V, of a neuron ny is expressed as:
0V, (1) Ot
= Σ Wiy (t)
[1 iL
S, (t)
o.w.
where is the timestamp, S; (t) indicates the presence or absence of a spike from input neuron n, at timestamp and Way is the weight of the synapse from n, to nz-- When the membrane potential of neuron reaches its firing threshold 6, the neuron emits a spike, resets its membrane potential to zero, and remains deactivated until the next sample is shown. In our simulations, firing timestamps represented by floating-point values to align with event-driven neuromorphic hardware.
3.2 Spiking Classification Layer
The spiking classification layer is a fully-connected architecture comprising, for a C-class problem, N C x M neurons (N....., ,, where M is the number of neurons per class. Each neuron n, mapped to class cj- Aligned with the SSIF model, we employ first-spike- -basseee-beedd decision-making: the first output neuron to fire predicts the class. This method removes the need to propagate the entire input for inference, which can reduce computation time and the number of generated spikes. Formally, the prediction ý of the SNN is defined as:
Cj* jr argmin (ty), JE(I,N]
where l; denotes the firing timestamp of neuron ny. multiple neurons fire at the same timestamp, the one with the highest membrane potential is selected. In practice, the method employed to select neuron in the event of tie has little effect on performance. In this work, the classification layer placed on top of an unsupervised feature extraction network.
3

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3.3 Supervised STDP Training
Neurons of the classification layer are trained with supervised STDP rule. At the end of sample presentation, weights of non- non-inhibited neurons are updated with an error-modulatdd additive STDP:
Ej Cj A
A+
if 24
AW,
(3)
O.W.
where AW the weight change (such Wij We + AW;). Ej is the error of neuron nij. A+ > and A < 0 are the learning rates. These two learning rates control learning speed and determine the relative importance of long-term potentiation (A*) versus long-term depression (A in the learning process. Weights are manually clipped in [Wmin Wmax] after each update to ensure that they remain within a controlled range.
22 is rule combined with WTA competition. For each sample, only the first neuron fire receives weight update. The error is ej +1 if ny is mapped to the class of the sample, Ej = -1 otherwise. In practice, a classification layer trained with R-STDP requires multiple neurons per class to achieve reasonable performance. R-STDP is usually employed in conjunction with adaptive learning rates to reduce overfitting, and dropout to facilitate the learning of various patterns per class [22]
R-STDP Reward-Modulater STDP (R- STDP)
SSTDP Supervised STDP (SSTDP) (24 is a rule with SOTA performance. It is employed with one neuron per class and without WTA. This rule provides high adaptability input data by dynamically computing temporal errors for each sample, based on the average firing time T in the layer:
e, = e - fmin
min { T (
1--1-1 g}
e e =
(4)
max {4, T + [
o サ
where y is the class of the sample, and is a hyperparameter that controls the desired distance from T. The optimal value of partly depends on the input spike distribution: a narrower distribution requires smaller g. For each sample, due to the min and max functions, only the target neuron firing after T C_1 g and the non-target neurons firing before T + d update their weights.
S2-STDP Stabilized Supervised STDP (S2-STDP) 29 addresses two limitations of SSTDP: the limited number of updates per epoch and the saturation of firing timestamps toward the maximum firing time. In this rule, neurons are trained to fire desired timestamps instead of time ranges:
T وان - T
if if if サv
ej =
T c9
(5)
This enables more accurate control over the output firing times and reduces the saturation effect. Also, weight normalization used keep a similar weight average across neurons during learning (2)
Methods
4.1 Neuronal Competition Group
Training a classification layer involves teaching neurons to recognize a pattern specific to their class from the input samples. Different samples from given class can contain distinct, mutually exclusive patterns or combinations of patterns. Learning all these patterns concurrently with one neuron can be challenging and impose strong generalization constraints using a single supervised layer. Employing multiple neurons per class to learn various class-specific patterns may reduce these constraints and enable the emergence of more specialized patterns that better represent the training set distribution. Building on this concept, we introduce the Neuronal Competition Group (NCG), architecture promoting the learning of various class-specifie patterns through intra-class WTA and competition regulation.
its weights, especially when
The NCG architecture, illustrated in Figure | augments classification layer by mapping each class to an NCG instead of independent neurons. An NCG is group of M neurons that aim to learn different patterns from samples of their mapped class. Neurons of an NCG are interconnected with

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Input neurons
NCG of class
Sample of class y
T Best
n1
NCG,
D2
112
DM
NCG,
Sample of class y
DM
n1
Lateral inhibition
12
Competition vegal.
NCGG
Error
DM
Späke
Competition
Inhibited spike
C classes
Regulation
Figure 1: Spiking classification layer with Neuronal Competition Groups (NCGs). In this layer, each class is mapped to NCG and the prediction is based on the first spike. An NCG is group of M neurons connected with lateral inhibition to enable intra-class WTA competition: the first neuron to fire inhibits the other ones and undergoes weight update based on the learning rule considered). The sign and amplitude of the error pushes neurons to fire earlier (positive sign) or later (negative sign). Competition regulation occurs only within the NCG mapped to the class of the input sample to ensure balanced competition among neurons on samples of their class. NCGs improve the classification capabilities of layer by promoting the learning of various patterns per class.
temporal error (which depends
lateral inhibition, such as, for given sample, the first neuron to fire within group emits an inhibitory signal that prevents the other ones from firing. Lateral inhibition induces competitive learning through intra-class WTA: only the first neuron to fire undergoes the weight update. There is no lateral inhibition between NCGs (i.e. inter-class WTA). Hence, each sample triggers exactly one weight update per NCG. Removing inter-class WTT enables more accurate control over the time difference between the spikes of target and non-tare non-target neurons, which can improve class separation [29]. Each time sample is presented during training, competition regulation is triggered in the NCG mapped to the class of the sample. This mechanism ensures balanced competition within the NCGs, which facilitate the learning of various class-specific patterns.
4.2 Competition Regulation
Preliminary experiments highlighted that intra-class WTA competition provided by lateral inhibition not enough to ensure balanced competition. In practice, for each NCG, one neuron tends to dominate the others, receiving the majority of the weight updates from samples of its class. Although threshold adaptation can be employed to regulate competition 32 20 decision-makinn context, different thresholds between neurons may lead to unfair decisions because predictions are based on the first spike. To ensure both balanced intra-class competition and fair decision decision-making, we introduce competition regulation mechanism based on two-compartment thresholds.
In the classification layer, all the neurons are equipped with identical and fixed threshold, denoted as the test threshold B. This threshold remains fixed to ensure fair decision- making during inference, as the class is predicted by the neuron that fires first. On top of that, neurons are equipped with an additional varying threshold, denoted as the training threshold 6'_ Neurons switch to their #' only when they are exposed to samples of their class during training. Otherwise, they always employ 0, both for inference and for samples of other classes during training. 0' is the key component to balance intra-class competition: can be increased or decreased encourage or reduce neuron firing samples of its class. Each time neuron receives weight update from sample of its class,
5

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competition regulation is triggered across neurons of its NCG. Their 6' are updated as follows:
A0 t/t Ar-1 7hh
if
min ( ,t,)
M
o.w.
(6)
0/ = max {0z. 03
where f and 8 are the training and test thresholds of neuron ny, M is the number of neurons in the NCG, 7hh is the threshold learning rate, and 1 is the firing timestamp of neuron ny. several neurons fire at the same timestamp, the one with the highest membrane potential is selected (this has no impact on performance). O' is reset to 9 between epochs and its minimum achievable value These two components ensure that neurons learn patterns consistent with 0, which is the threshold that they use for inference. Tth defines the strength competition regulation: higher values favor more balanced competition but may deteriorate pattern learning since (' tend to increase within an epoch. It should be chosen together with the initial threshold (a higher threshold may require higher Ma.) To achieve better convergence and robustness, annealing factor Suh be added to reduce 7hh after each epoch, such as 7)hh : 7hh Pth. 9th affects the number of epochs during which competition regulation occurs and should be adjusted according to Maa higher 7/h requires lower 3th-
4.3 Neuron Labeling
29 WTA competition enhances a classification layer with two neurons per class and S2-STDP training by naturally promoting, for each class, neuron specialization toward target non-target samples. This behavior can also be implemented with NCGs, but it requires explicit neuron labeling to ensure that all neurons but specialize toward samples of their class. In such cases, neuron within each NCG can be labeled as non-target, whereas the others can be labeled as target. All the neurons connected with lateral inhibition but only target neurons regulation. Hence, if the non-targe neuron fires first for a sample of the class, it prevents target neurons from updating their weights and applying competition regulation. Regardless of the class of the sample, a non-target neuron n2 winning the competition always updates its weights as if c * y in Equation STDP training remains unchanged for target neurons. However, in Equation M must be updated as it refers to the number of target neurons. In Supplementary Material (Section 1), we provide the overall algorithm for training spiking classification layer with our proposed methods.
connected with competition
5
Experiments
5.1
Experimental Setup
5.1.1
Datasets
We select four image recognition datasets of growing complexity: MNIST 49,, Fashion-MNIST 50
CIFAR- 10 (51), and CIFAR-100 [5I]. MNIST and Fashion-MNIST comprise 28 x 28 grayscale images, 60, 000 samples for training and 10, 000 for testing, categorized into 10 classes. CIFAR-10
and CIFAR-100 comprise 32 x 32 RGB images, 50, 000 for training and 10, 000 for testing. They consist of, respectively, 10 and 100 classes
5.1.2 Classification Pipeline
Our classification system consist of a feature extractor trained with unsupervised Hebbian-basee learning, followed by a spiking classification layer trained with supervised STDP. Training layer- wise: the feature extractor is trained entirely before the training of the classification layer starts. The complete pipeline our classification system is illustrated in Supplementary Material (Section 2.1).
5.1.3 Unsupervised Feature Extractors
To improve image representation before classification without labeled data, consider two Hebbian- based unsupervised feature extractors built on Convolutional Neural Networks (CNNs):
1. STDP-CSNN 20
single-layer spiking CNN trained with STDP:
2. SoftHebb-CNT
52 three-layer non-spiking CNN trained with SoftHebb.

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Employing various feature extractors allows us to validate our methods with imput features of varying quality. These two feature extractors are SOTA in their category (spiking/non-spikinng share local learning properties, and offer different baseline performances. In particular, SoftHebb-CNN, while not spike-based, is a relevant alternative for exploring classification using features provided by effective multi-layer local learning. The extracted feature maps are flattened to match the fully-connected architecture of the classification layer. Since SoftHebb- is not spike-based, its output features are encoded into spike timestamps with form of first-spike coding [53]. STDP-CSNN outputs 4, 608 features for SANIST/FashionMMNISS features for MNIIT/FFshhon-MMN -NNIS,, and 24, 576 for CIFAR- CIFAR-10/100, Aligned with first-spike coding, each feature is a single floating point spike timestamp in [0, 1]. Additional details are reported in Supplementary Material (Section 2.2).
and 6, 272 for CIFAR- 10/100. SoftHebb-CNN outputs 13, 824
5.1.4 Spiking Classification Layers
We train fully-connected spiking classification layers with three existing supervised STDP rules designed for one spike per neuron: R-STDP [22]. SSTDP (24), and S2-STDP [29]. We incorpo- rate the NCG architecture into classification layers trained with SSTDP and S2-STDP, denoted as SSTDP+NCG and S2-STDP+NCG, respectively. R-STDP is incompatible with NCGs since requires inter-class WTA for weight convergence. Unless otherwise specified, we set M = 5 neurons per class for NCG-based methods, which is the smallest value providing, on average, near-optimal performance the evaluated datasets (see Section 3.2 of Supplementary Material). We evaluated R-STDP with both M = 5 and M 20, the value providing near optimal performance for this rule. With S2-STDP+NCG, one neuron of each NCG is labeled non-target, detailed in Section
5.1.5 Protocol
We divide our experimental protocol into two phases: hyperparameter optimization and evaluation. In both phases, we employ an early stopping mechanism (with a patience p) during training to prevent overfitting. For hyperparameter optimization, we construct validation set from the training set by randomly selecting, for each class, a percentage v of its samples. Then, we use the gridsearch algorithm to optimize the hyperparameters of the spiking classification layer (for each rule, dataset, and feature extractor). No gridsearch is performed on CIFAR-100: we employ the optimized hyperparameters from CIFAR- 10, given the similarities between the two datasets. Additional details regarding hyperparameters are provided in Supplementary Material (Section 2.3). For evaluation, we employ the K-fold cross- cross-validttion strategy. We divide the training set into K subsets and train K models, each using a different subset for validation while the remaining K- - subsets are used for training. Each model is trained with different seed. Then, we evaluate the trained models the test set and we compute the mean test accuracy and standard deviation (1-sigma). We use 10, K 10 and v K (i.e. we allocate 10% of the training sets for validation).
5.2 Accuracy Comparison
We compare, in Table I the performance of the different STDP-based methods for training spiking classification layer (see Section (5114) placed on top of each unsupervised feature extractor (see Section 5.1.3. Our proposed NCG architecture consistently improves the performance of SSTDP and S2-STDP across all datasets and feature extractors. The accuracy improvement tends to scale with the complexity of the dataset. With S2-STDP and the STDP-CSNN feature extractor, we measure an increase of 1.18 pp on MNIST, 2.83 pp on Fashion-MNIST. 5.33 pp on CIFAR-10 10, and 6.51 pp on 100. S2-STDP always outperforms SSTDP and enables higher accuracy improvement when paired with NCG as it leverages neuron labeling. While S2-STDP surpasses R-STDP when the input features are well-captured, it falls behind in scenarios involving lower-quality features (CIFAR-10 with STDP STDP+NCG effectively bridges this gap. outperforming R-STDP on both simpler and harder tasks while requiring four times fewer neurons per class. When R-STDP is used with the same number of neurons S2-STDP+NCG, the accuracy gap is even larger. These results highlight that WTA-based competitive learning in a supervised context can be achieved without inter-class WTA. Employing solely intra-class WTA and accurate STDP updates enables more effective training.
CIFAR-100) as R-STDP can learn various patterns per class. S2-
Regarding the literature on SNNs with fully-supervised local-based learning, SOTA performance is achieved by BTP (one spike per neuron) [54] MNIST (99.20% with 3-layer SNN) as well
7

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Table 1: Accuracy of spiking classification layers trained with STDP-based methods, on top of unsupervised feature extractors.
Neurons per class
Accuracy (Mean:iStd %) SoftHebb-CNN
Datasct
Method
STDP-CSNN
96.82 + 0.29
97.72 = 0.26
R-STDP
97.49 + 0.12
98.24 1 0.15
MNIST
SSTDP
96.44 + 0.09
98.52 = 0.16
SSTDP+NCG (ours)
5
97.30 + 0.09
98.96 + 0.06
S2-STDP
97.74 + 0.06
98.81 1 0.09
S2-STDP+NCG (ours)
5
98.92 + 0.07
99.17 + 0.07
78.40 + 0.89
87.32 = 0.76
R-STDP
82.17 0.38
88.06 1 0.29
Rishion-MNIST
SSTDP
85.26 + 0.17
89.36 + 0.24
SSTDP+NCG (ours)
5
87.59 + 0.11
91.06 = 0.10
S2-STDP
85.89 + 0.27
90.61 + 0.19
S2-STDP+NCG (ours)
88.72 1: 0.23
91.86 1 0.14
5
62.12 + 0.62
74.12 + 0.34
R-STDP
20
65.92 + 0.68
75.54 + 0.57
CIFAR-10
SSTDP
60.87 + 0.53
76.57 + 0.58
SSTDP+NCG (ours)
5
64.05 + 0.48
78.53 + 0.32
S2-STDP
61.08 0.17
76.90 = 0.27
S2-STDP+NCG (ours)
66.41 1: 0.17
79.55 1 0.23
32.07 + 0.38
48.27 + 0.36
R-STDP
20
34.77 + 0.44
49.25 = 0.48
CIFAR-100
SSTDP
28. 28.49 + 0.49
48.73 = 0.39
SSTDP+NCG (ours)
5
31.19 + 0.27
49.81 + 0.23
S2-STDP
29.39 + 0.19
49.17 + 0.29
S2-STDP+NCG (ours)
35.90 + 0.42
53.49 = 0.18
as Mishion-MNIST (92.80% with 4-yer SNN), and by EMSTDP (multiple spikes per neuron) on CIFAR- 10 (64.40% with a 4-layer SNN). We did not find any work reporting results on CIFAR- 100. For approaches combining unsupervised and supervised local learning, SOTA performance is achieved by R- R-STPP 26 on MNIST (97. 20% with a 3-layer SNN) and by Sym-STDP (34] on Fashion-MNiST (85.31% % with a 2-layer SNN). We did not find any work reporting results on CIFAR- 10/100. Our best models, comprising 4-layer networks with only one supervised layer, achieve 99.17% on MNIST, 91.86% on MaSHion-MNIST, and 79.55% on CIFAR-10. Our results closely match surpass sulev-sue SOTA work and outperform semi-supervised SOTA work. Yet. it is important to acknowledge the role the feature extractor the final performance. There remains a huge gap between local-based and global-based approaches in terms of accuracy. In Supplementary Material (Section 4), we compare our methods with global- based approaches to highlight that, despite the accuracy gap. local-bre based methods show greater computational efficiency, lower memory usage, reduced energy consumption, and casier hardware implementation, justifying further exploration.
5.3 Ablation Study
We conduct, in Table 2 an ablation study on S2-STDP+NCG to evaluate each component of our methods. M-/ and M-5 represent S2-STDP+NCG with M = (one neuron per class, which is similar to S2-STDP) and M = 5, without competition regulation and neuron labeling. CR-/ denotes our competition regulation mechanism with single threshold per neuron (i.c. 0 = 0 in Equation 6).

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Table 2: Ablation study on S2-STDP4NCG, the number of neurons per class, CR competition regulation with or thresholds, L is neuron labeling, and Drop is dropout.
(a) Fashion-MNIST
(b) CIFAR-10
Accuracy SMean %)
Accuracy (Mean-Std %) SoftHebb-CNN
Method
Method
STDP-CSNN
SoftHebb-CNN
STDP-CSNN
M-I
85.89 + 0.27
90.61 + 0.19
M-/
61.08 + 0.17
76.90 + 0.27
M-5
86.74 1 0.25
91.25 1 0.20
M-5
62.61 1 0.27
78.29 0.27
M-5+CR-1
86.77 0.22
85.16 5.34
M-5+CR-1
64.73 0.41
77.35
M-5+CR-2
87.76 + 0.16
91.33 1 0.22
M-5+CR-2
65.51 1 0.26
78.78 1 0.15
M-5+CR-I+L
89.24 + 0.89
M-5+CR-I+L
65.46 = 0.40
78.67 + 0.19
M-5+CR-2+L
88.72 = 0.23
91.86 + 0.14
M-5+CR-2+L
66.41 0.17
79.55 + 0.23
M-5+Drop+L
87.33 + 0.20
91.34 + 0.08
M-5+Drop+L.
63.15 + 0.11
77.98 + 0.21
Thresholds are not clipped nor reset between epochs, and the learned values used for inference. CR-2 denotes competition regulation with two-compartment thresholds. L is neuron labeling. Drop is dropout on the output neurons, an alternative competition regulation mechanism employed with R-STDP [22). For each method, optimized hyperparameters with gridsearch (see Section 5.1.5). Results on both Fashion-MNIST and CIFAR-10 show that each component of our methods (cf. M-5, CR-2, L) brings an individual and significant accuracy gain. Competition regulation tends to be crucial for benefiting from improved class separation, especially with STDP-CSNN The accuracy gain gets lower with SoftHebb-CNI as the extracted features exhibit higher class separability. Neuron labeling enhances the performance of our models through neuron specialization. Our competition regulation mechanism based on two- compartment thresholds (cf. CR-2) outperforms the existing threshold adaptation with one threshold (cf. CR-/), as well as dropout (ef. Drop). first-spike- based decision-making context, we find that learning thresholds (cf. CR-1) is not mandatory for successfully learning various patterns. Instead, more important to ensure fair decision decision-making with fixed thresholds and use threshold adaptation as competition regulation mechanism only. In Supplementary Material, we provide ablation study on SSTDP+NCG with similar results (Section 3.4), as well as additional studies on the impact of neuron labeling (Section 3.1) and hyperparameters (Section 3.3).
as commonly used WTA-based SNNs
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5.4 Impact of Competition Regulation
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compatition rogul.
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(a) Number of target updates
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Figure 2: Number of weight updates per epoch received by the neurons of class 0 trained with S2-STDP+NCG, with and without competition regulation, on CIFAR-10. n, to n4 are labeled as target neurons and is labeled as non-target. The features are extracted with STDP-CSNN.
In this section, we show that competition regulation is crucial for ensuring balanced competition and improved class separation. Figure 2 iillustrates the number of updates per epoch received by the neurons of class trained with S2-STDP+NE
with and without competition regulation, on CIFAR-10. Target (resp. non-target) updates are triggered by samples of the class (resp. another class). Without competition regulation, no competition takes place between target neurons. Target

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neuron n2 receives the majority of the target updates, while the other target neurons 71, R3, R4 assume the role of non-target neurons (i.e. receive mainly non-target updates), as they are inhibited by n2 on samples of the class. With competition regulation, the target neurons (n1 to m4) effectively specialize toward samples of their class, while the non-target neuron (n5) specializes toward samples of other classes. Regarding target neurons, we observe a balanced competition in their target updates, illustrating the effectiveness of our competition regulation mechanism. In Supplementary Material (Section 3.5), we show similar results for other classes and datasets, as well as for SSTDP+NCG.
In another experiment, we analyze the weights trained using S2-STDP4NCG, with and without competition regulation. Figure t-SNE [56] visualizations of the learned weights on CIFAR-10. 10. Without competition regulation, there single cluster at the center, comprising the weights of the neurons that receive few target updates during train- ing. With competition regulation, the weights of the target neurons tend to form, for each class, dis- tinct clusters. The spread of their clusters suggests that they have learned various class -pasi-s patterns. The weights of the non-target neurons form single cluster at the center since their weights are very sim- ilar. This similarity arises because non-target neu- rons, regardless of their class, are trained to fire at the same desired timestamp. In Supplementary Ma- terial (Section 3.5), we further show that competition regulation increases the intra-class distinctiveness among weights, which improves class separation.
w/o competition regul.
w/ competition rogul.
Hit
Figure 3: t-SNE plots of the weights learned with S2-STDP+NCG on CIFAR-10, with and without competition regulation. Crosses and circles respectively represent the weights of target and non-target neurons, and colors indi- cate classes. The features are extracted with STDP-CSNN.
6 Discussion
The NCG architecture implements effective intra-class WTA in a spiking classification layer em- ploying first-spike coding and supervised STDP training. Our competition regulation mechanism based on two-compartment thresholds ensures both balanced competition and fair decision-making We showed that this mechanism improves class separation and achieves better performance than existing regulation methods. As result, NCGs significantly increased the accuracy of SOTA su- pervised STDP rules. This work highlights that more effective supervised competitive learning can be achieved without inter-class WTA. Also, the success in learning various patterns per class via threshold adaptation does not depend on learning various thresholds.
In this work, supervised STDP rules are employed in the classification layer to ensure consistency with the training of the feature extraction network. However, our contributions focus on the architecture of the classification layer, which is independent of the learning rule used to train it. Thus, NCGs may theoretically be used with any other rule designed for training SNNs with one spike per neuron. We performed preliminary experiments with S4NN 57 a gradient- based rule, and observed that the addition of NCGs led to accuracy improvements consistent with our previous results (see Section 3.6 of Supplementary Material). Yet, further research is required to validate the effectiveness of NCGs with gradient- based rules.
While NCGs successfully improve the performance of a classification layer, they also come with several limitations. First, they increase the costs in terms of parameters, computation, and hardware. The computational overhead of NCGs scales linearly with the number of neurons. In hardware design, they introduce another overhead due to the additional connections, both to the previous layer and within the layer. Second, increasing the number of neurons strengthens specialization on the training set, especially when faced with higher number of input features (cf. SoftHebb-CNN). This behavior limits the generalization capabilities of our models and requires additional research fully exploit their potential in these scenarios. Third, the NCG architecture applies only to the output layer of a network. Nevertheless, this work is the first to introduce WTA and competition regulation mechanisms specifically designed for classification. It establishes the relevance of such mechanisms in this context, laying the foundations for future research on WTA-based supervised competitive learning in multi-laye layer networks.
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Acknowledgements
This work is funded by Chaire Luxant-ANVI (Métropole de Lille) and supported by IRCICA (CNRS UAR 3380). Experiments presented in this paper were carried out using the Grid 5000 testbed, supported by scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see http:: //www wwwgg00i....... fr)
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Reviews:
[{"review_id": "d607CkJ6Dl", "reviewer": "Reviewer_ygD7", "summary": "The paper proposes Neuronal Competition Group (NCG), an architecture that maps each class in the task to a group of neurons using intra-class Winner-Takes-All (WTA) and competition regulation. The authors aim to implement effective WTA competition mechanisms in spiking neural networks (SNNs) employing first-spike coding and Spike Timing-Dependent Plasticity (STDP) learning rules.", "questions": "- Could the authors present a comparison of the method using STDP versus a simple delta rule over the group of neurons in the classification layer?\n- Could the authors present some results for sequential tasks where using SNNs could be more compelling than using other recurrent models?\n- Could the authors elaborate on why using STDP in the classification layer is important? Local learning methods are useful for learning in deep layers since using backpropagation on custom hardware is expensive, but the last layer does not suffer from this problem.\n- Could the authors discuss any computational benefits of using the proposed methods over others?\n- Could the authors discuss the relationship between accuracy performance and the number of neurons per NCG beyond the five units used in the experiments?", "limitations": "The main limitation of the work is that the proposed method targets only the last layer of a neural network, so it is unclear why it would be a preferable alternative to other simpler methods.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper is well-written, and many preliminary concepts are discussed, making it easy for readers to follow the discussion. The mechanisms discussed, such as WTA, lateral inhibition, STDP, and modulated STDP, have a solid foundation in neuroscience. Moreover, the experiments have been tested on fairly complex tasks, such as CIFAR-100, demonstrating the proposed method's effectiveness. The ablation studies provide compelling support for the design choices made for the method.", "weaknesses": "The main limitation of the proposed method and experiments is that essentially all the ideas used in the method have been previously explored, so the contributions might be limited to combining them and making them work together. Additionally, a major weakness is that the method only works for a model with one layer of spiking neurons, and this layer is the last layer in the model. It is not clear why using STDP would be a better alternative than simply using a delta rule, where weight updates are just the product of the classification error and the inputs. The proposed method also requires a significant increase in the number of parameters in the last layer (by a factor of 5 in the experiments). Furthermore, all the experiments focus exclusively on static image classification tasks where no temporal information is available, which are not the most suitable tasks for SNNs. It is well known that artificial neural networks (ANNs) perform significantly better in such tasks.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their constructive remarks, which have helped us improve the value of our work. \n\n> The main limitation of the proposed method and experiments is that essentially all the ideas used in the method have been previously explored, so the contributions might be limited to combining them and making them work together.\n\nWe agree with the reviewer that the main concepts behind our contributions (WTA competition and threshold adaptation) are not new and have a solid foundation in neuroscience. However, we argue that these concepts are broad and have mostly been explored in unsupervised learning contexts. The literature exploring WTA for classification is very limited (to R-STDP) and faces unbalanced competition issues. To the best of our knowledge, our work is the first to focus on these issues and adapt the aforementioned concepts for supervised competitive learning, which extends beyond combining them and making them work together. We introduced, for the first time, a competition regulation mechanism (through threshold adaptation) that accounts for the input class information. Also, while intra-class WTA was introduced in a recent paper (see ref. 29 in the manuscript), it was limited to learning target and non-target patterns. In this work, we introduce a similar concept but with a different aim: learning various class-specific patterns. We believe our work is important for the future development of WTA competition in supervised learning. \n\n**Q1:**\n\nIn the revised paper, we added a section discussing the benefits of STDP compared to other rules. The content is as follows:\n\nTo train the spiking classification layer, we employ an error-modulated additive STDP in which the weight change is the product of the error and the learning rate (see Eq. 3 in the main paper). The learning rate is positive for long-term potentiation (i.e. when the input neuron fires before the output neuron) and negative for long-term depression (i.e. when the input neuron fires after the output neuron). Given the simplicity of this STDP model, the weight updates without long-term depression resemble a gradient-based rule or a delta rule $^1$. To better understand the relevance of STDP with respect to this type of rule, we examine the accuracy of S2-STDP+NCG with and without long-term depression in Table 1 (the table is in the PDF attached with the **Author Rebuttal** answer). Results indicate that incorporating long-term depression generally leads to a slight improvement in accuracy. This improvement may be due to STDP considering all input spikes for weight updates. In addition, long-term depression enables faster training convergence by increasing the number of weight updates per sample. The number of epochs with long-term depression is reduced by an average of 15% for STDP-CSNN and 4% for SoftHebb-CNN.\n\n$^1$ *that uses the same error as the STDP rule and a Heaviside function to convert input spikes into a continuous signal.*\n\n**Q2:**\n\nOur work would indeed benefit from results on datasets with a temporal dimension. Nonetheless, the feature extraction networks employed in this work are not designed for such datasets, which means that we need to find another Hebbian-based feature extractor capable of extracting temporal/spatiotemporal features. We will not be able to get results before the end of the rebuttal.\n\nFrom a theoretical perspective, we believe that NCGs would still improve class separation in sequential tasks. Our architecture improves performance by promoting the learning of various patterns per class. If a classification layer with one neuron per class can classify temporal/spatiotemporal features, it should, when augmented with NCGs, also be capable of doing so with multiple neurons per class.\n\n**Q3:**\n\nWe refer the reviewer to the **Author Rebuttal** answer (Section 2), which explains the importance of STDP in the classification layer. \n\n**Q4:**\n\nWe refer the reviewer to the **Author Rebuttal** answer (Section 3), which compares our methods to global-based approaches.\n\n**Q5:**\n\nIn Supplementary Material (Section 3.2), we studied the impact of varying the number of neurons per class ($M$). We found that smaller values ($M=5$) are optimal for simple datasets (MNIST, Fashion-MNIST). However, larger values ($M=10$) can further increase the performance of NCGs for harder datasets (CIFAR-10). On CIFAR-10 with STDP-CSNN, S2-STDP+NCG obtained an accuracy of 66.41 with $M=5$ and 67.17 with $M=10$. SSTDP+NCG obtained an accuracy of 64.05 with $M=5$ and 64.77 with $M=10$.\n\nWe are aware that NCGs improve performance with an additional parameter cost. In the revised paper, we highlighted that our methods remain effective even with a minimal number of additional parameters (3 neurons per class). We refer the reviewer to our response to **Weakness 4** from reviewer **EvbR** for additional details.\n\n> The main limitation of the work is that the proposed method targets only the last layer of a neural network, so it is unclear why it would be a preferable alternative to other simpler methods.\n\nIt is unclear which simpler methods the reviewer is referring to but we believe they refer to training methods capable of multi-layer learning. We would like to emphasize that the contributions of this work focus on the architecture of the classification layer (NCG), rather than on the specific learning rule used to train it (supervised STDP). NCGs can theoretically be integrated into the classification layer of a multi-layer network with one spike per neuron and trained with a (non-)STDP-based method. We find it more interesting to study the gain that NCGs can bring to an existing method rather than comparing our models (e.g. S2-STDP+NCG) to other methods. However, we agree that the NCG architecture is currently limited to the classification layer and refer the reviewer to the **Author Rebuttal** answer (Section 1), which discusses this limitation.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sWZD6HTQBF", "reviewer": "Reviewer_EvbR", "summary": "The authors proposed the Neuronal Competition Group (NCG) and a novel competition regulation mechanism based on two-compartment thresholds, to effectively implement intra-class WTA competition in a spiking classification layer employing first-spike coding and supervised STDP training, which improves classification capabilities by promoting the learning of various patterns per class. The results on several image recognition datasets such as CIFAR-10 and CIFAR-100, demonstrate the effectiveness of the proposed methods.", "questions": "1. It may benefit better understanding to include some important parts and brief pipeline of the training algorithm in the main text, such as the definition of the average firing time.\n\n2. The definition and role of important hyperparameters should be described in the main text.\n\n3. The right part of Figure1 is not clearly explained, especially the “Error” indication. Besides, inhibited spikes should not exist in the “y≠1” condition?\n\n4. See the weaknesses listed above.", "limitations": "An additional limitation maybe the effectiveness of the proposed methods on large-scale datasets like ImageNet.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The authors proposed the Neuronal Competition Group (NCG) for effective intra-class WTA competition in a spiking classification layer employing first-spike coding and supervised STDP training.\n\n2. The authors proposed a novel competition regulation mechanism based on two-compartment thresholds to promote balanced competition and fair decision-making.\n\n3. The proposed methods significantly increased the accuracy of SOTA supervised STDP rules on several common datasets.", "weaknesses": "1. It lacks clear explanation why do we need to promote the learning of various patterns per class (intra-class competition), because the final aim is to separate samples from different classes.\n\n2. The authors talk about the advantage of proposed methods for neuromorphic hardware, which needs more analyses or discussion. Besides, its unfavorable impacts should also be considered, such as using high-precision floating-point values to represent firing timestamps.\n\n3. The classification accuracies lag behind BP-based models (e.g., see “Spike-driven Transformer” by Yao et al., NeurIPS 2024), which are usually trained on GPUs. And the trained model can be deployed on neuromorphic hardware for inference, which is also highly energy-efficient.\n\n4. The proposed methods improve the performance with more cost, so it’s better to add analyses or discussion about this tradeoff.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their feedback and value their enthusiasm for our work.\n\n**W1:**\n\nWe clarified this aspect in Section 4.1: \"Different samples from a given class can contain distinct, mutually exclusive patterns or combinations of patterns. Learning all these patterns concurrently with one neuron may be challenging and impose strong generalization constraints (especially when using a single layer). Learning various patterns per class reduces these constraints and enables the emergence of more specialized patterns that better represent the training distribution. Since the prediction is based on the neuron that fires first, having multiple neurons per class increases the likelihood of a target neuron firing first for a sample of the class, thereby improving class separation.\".\n\n**W2 & W3:**\n\nIn the revised manuscript, we compared our methods with global-based approaches across several aspects, including hardware implementation. We refer the reviewer to the **Author Rebuttal** answer (Section 3), which includes the content of this section.\n\nNote that training models on neuromorphic hardware offer several advantages, such as energy-efficient alternatives to GPU-based training and support for continuous learning. Also, representing firing timestamps by floats is not a limitation because, as mentioned in the paper, we are aiming for event-driven neuromorphic hardware, where spike times are not constrained by a hardware clock.\n\n**W4:**\n\nWe discussed the limitation in Section 6 of the revised paper: \"First, while NCGs successfully improve the performance of a classification layer, they also increase the costs in terms of parameters, computation, and hardware. The computational overhead of NCGs scales linearly with the number of neurons. In hardware design, they introduce another overhead due to the additional connections, both to the previous layer and within the layer.\".\n\nWe analyzed this tradeoff in more detail in Supplementary Material (Section 3.2 - Impact of the Number of Neurons): \"[...] Figures 1 and 2 show that significant accuracy gains can usually be achieved with only three neurons per class. This reveals that our method remains effective even with a minimal number of additional parameters. When selecting the value of $M$, the tradeoff between optimizing accuracy and minimizing parameter cost must be considered.\".\n\n**Q1:**\n\nWe included the definition of the average firing time and weight normalization. Unfortunately, we do not have enough space to add a brief pipeline of the training algorithm in the main text. We direct readers to the complete algorithm in Supplementary Material.\n\n**Q2:**\n\nIn the revised paper, we described the role of important hyperparameters:\n- The firing threshold $\\theta$ influences the number of integrated input spikes needed to classify a sample. It should be chosen in conjunction with the initial weight distribution.\n- The time gap $g$ controls the distance between the desired timestamps and the average firing time. Its optimal value depends on the nature of the input data and the maximum firing time.\n- The positive and negative learning rates ($A^+$ and $A^-$) control learning speed and determine the relative importance of long-term potentiation ($A^+$) versus long-term depression ($A^-$) in the learning process. The optimal ratio $A^+/A^-$ depends on the number of integrated input spikes at spike time.\n- Increasing the number of neurons per class $M$ enables the learning of more diverse class-specific patterns but incurs additional costs in terms of parameters and computation.\n- The threshold learning rate $\\eta_{\\mathrm{th}}$ defines the strength of competition regulation: higher values favor more balanced competition but may deteriorate pattern learning as training thresholds ($\\theta'$) tend to increase progressively within an epoch. It should be chosen in conjunction with the firing threshold.\n- The threshold annealing $\\beta_{\\mathrm{th}}$ influences the number of epochs during which competition regulation occurs. It should also be adjusted according to the threshold learning rate: higher threshold learning rates necessitate lower threshold annealing.\n\n**Q3:**\n\nThe error arrow corresponds to any temporal error used to control the sign and intensity of the STDP update. Its value depends on the supervised STDP rule employed, which means that we cannot be more specific about it. In the figure, only the direction of the error is relevant. Also, inhibited spikes are shown for clarity, even though they do not \"exist\" because the associated neurons are inhibited. Due to lateral inhibition, each NCG produces only one spike per sample, whether it is a target or a non-target sample. We refer the reviewer to the attached PDF file with the **Author Rebuttal** answer for the figure with the revised caption.\n\n**Limitation:**\n\nWe agree with the reviewer that our work would benefit from evaluation on more complex tasks. However, dealing with datasets like ImageNet remains a significant challenge for local-based approaches, particularly for networks combining unsupervised and supervised learning. As mentioned in the paper, we found no SNN work based on local learning rules, whether fully-supervised or semi-supervised, reporting results on CIFAR-100 or more complex datasets. Regarding ANNs, SoftHebb-CNN (Journé et al., Hebbian Deep Learning Without Feedback, CVPR 2023) reports SOTA performance on ImageNet (for local-based semi-supervised methods), with an accuracy of only 27.3% (they used a 5-layer CNN trained using Softhebb followed by a classification layer trained using GD). We believe that additional supervised layers (together with unsupervised feature learning) are required to address this type of task. Hence, in the future, we will extend our NCG architecture to hidden layers while preserving the local properties needed for on-chip training. We discuss the extension of NCGs to hidden layers in more detail in the **Author Rebuttal** answer (Section 1).", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "EW0oKloi17", "reviewer": "Reviewer_AF7r", "summary": "This paper introduces Neuronal Competition Groups (NCGs) with a two-compartment threshold mechanism to optimize Winner-Takes-All competition in spiking classification layers using supervised STDP. NCG integration with supervised STDP rules significantly boosts image recognition accuracy on CIFAR-10 and CIFAR-100 datasets, showcasing balanced competition and improved class separation.", "questions": "Can the author's method be extended to the previous feature extraction layer.\nThe authors' experiments seem to have only a few comparisons of methods.\nThe experiments of the authors do not seem to have more analysis about the more detailed features of the method proposed by the authors. Experiments are now limited to the results of classification, and very little analysis of method properties.\nstdp itself is an unsupervised local algorithm, so what is the point of extending it to supervised algorithm? If it no longer meets the local property and unsupervised property, then why not use other supervised algorithm which is better.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The authors proposed a supervised STDP method to achieve better results on this type of task.\nThe authors proposed a method for NCG that attempts to solve the problems encountered in STDP training.", "weaknesses": "The number of experiments was not sufficient; he compared only a few exist methods.\nstdp is an unsupervised algorithm, and it is hard to associate it with supervised methods. Although there are some supervised stdp methods before, it is hard to believe its rationality.\nThe features of the authors' method are extracted by other methods and do not seem to have been designed or trained by themselves. That is to say, the author's work is only limited to the classification layer.\nThe methods of stdp are not comprehensive, especially unsupervised, and should be investigated more widely.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their feedback and their time reviewing our work. We respond to their comments below.\n\n> stdp is an unsupervised algorithm, and it is hard to associate it with supervised methods. Although there are some supervised stdp methods before, it is hard to believe its rationality.\n\nAlthough it has not received as much attention as other learning methods, error-modulated STDP (or supervised STDP) has a solid foundation in neuroscience [1]. For example, in our brain, neuromodulators (such as dopamine) are known to influence synaptic plasticity. Our results, along with those of other papers (e.g. EMSTDP, GLSNN), show encouraging performance, which provides empirical evidence of its rationality. We believe this area of research deserves more exploration. Also, while we integrate our methods on top of supervised STDP rules, the contributions of this work are not focused on supervised STDP but rather on the training architecture (NCG) and the competition regulation mechanism (two-compartment threshold adaptation). In the revised paper, we showed that our STDP rule resembles a gradient-based or delta rule and that our methods can be used with other learning rules. We refer the reviewer to the **Author Rebuttal** answer (Section 2) and our response to the first question from reviewer **ygD7** for additional details.\n\n[1] Frémaux et al. Neuromodulated Spike-Timing-Dependent Plasticity, and Theory of Three-Factor Learning Rules. Front. Neural Circuits, 2015.\n\n> The features of the authors' method are extracted by other methods and do not seem to have been designed or trained by themselves. That is to say, the author's work is only limited to the classification layer.\n\nIndeed, our work focuses on the classification layer, as stated in the introduction. While features are extracted using existing methods, we implemented and trained the feature extractors by ourselves. We believe that using established methods for feature extraction, rather than custom approaches, is not a weakness. On the contrary, it demonstrates that our work is more likely to work with any kind of feature extractor and may motivate other researchers to use our classification layer on top of their own feature extractors.\n\nHowever, we agree with the reviewer that the proposed NCG architecture is currently limited to the classification layer. We refer them to the **Author Rebuttal** answer (Section 1), which discusses this limitation.\n\n> The methods of stdp are not comprehensive, especially unsupervised, and should be investigated more widely.\n\nGiven the limited number of pages, we have chosen not to study these components as they are not part of our contributions. We invite readers to read the papers on the supervised STDP rules (references 22,24,29 in the manuscript) and the unsupervised feature extractors (references 20,52) employed to get a better understanding of these methods.\n\n> Can the author's method be extended to the previous feature extraction layer.\n\nThe feature extraction layer is trained in an unsupervised fashion. Our methods are designed for supervised training: the NCGs require labeling each neuron to a class and the competition regulation mechanism must be aware of the input class. Hence, we cannot employ our methods for this layer. Also, it is important to recall that our work aims to address the unbalanced competition issues encountered in WTA-based supervised learning. In unsupervised learning, WTA competition has been widely studied in the literature (references 19,20,30,31 in the manuscript) and numerous solutions exist to solve the aforementioned issues.\n\n> The authors' experiments seem to have only a few comparisons of methods.\n\nFor the accuracy comparison, Table 1 includes three methods: R-STDP, SSTDP, and S2-STDP. As far as we know, these three methods are the only existing supervised STDP rules designed for training SNNs with one spike per neuron (as mentioned in the paper). Therefore, there was no other relevant method available for comparison that could have been implemented in our classification layer. However, in the second paragraph of Section 5.2, we compared our methods with SOTA local-based approaches (comprising BP-based approaches and SNNs with multiple spikes per neuron). We showed that our results closely match or surpass fully-supervised SOTA work and outperform semi-supervised SOTA work.\n\n> The experiments of the authors do not seem to have more analysis about the more detailed features of the method proposed by the authors. Experiments are now limited to the results of classification, and very little analysis of method properties. \n\nOur main contribution relies on promoting, in a supervised context, the learning of various patterns per class through competition regulation. We analyzed the qualitative impact of NCGs with our competition regulation mechanism in Section 5.4 of the main paper and Section 3.5 of the Supplementary Material. In particular, we covered the number of updates (target/non-target) received by neurons during training, neuron behavior with labeling, and the similarities and differences between learned weights. We believe we have discussed the main properties of our methods that support their effectiveness in learning various patterns per class.\n\n> stdp itself is an unsupervised local algorithm, so what is the point of extending it to supervised algorithm? If it no longer meets the local property and unsupervised property, then why not use other supervised algorithm which is better.\n\nWe refer the reviewer to the **Author Rebuttal** answer (Section 2), which explains why we use supervised STDP. Also, note that supervised STDP maintains its local property when used to train a classification layer since the error is computed on the output of the layer.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xt7fUsmDyL", "reviewer": "Reviewer_k4WN", "summary": "This paper aims to enhance the classification capabilities of SNNs using STDP learning rule. The authors introduce the Neuronal Competition Group architecture to address the limitations of existing WTA mechanisms in supervised STDP classification. This architecture promotes balanced intra-class competition and improves class separation by employing a two-compartment threshold system. The paper demonstrates the effectiveness of NCGs in achieving accuracy improvements on some relatively large datasets like CIFAR-100.", "questions": "What is the latency used in the paper?", "limitations": "The scalability of the proposed method to larger and more complex datasets beyond CIFAR-10 and CIFAR-100 is not thoroughly explored. Future work could address how well the NCG architecture scales with increasing data complexity and size.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The focus on local learning and the time-to-first-spike coding is highly encouraged. It improves energy efficiency in both training and inference parts, which is crucial for neuromorphic hardware applications.\n\n2. The extensive experiments show the effectiveness of the proposed framework. Compared with other local learning rules, the proposed one achieves better performance.", "weaknesses": "Global learning methods, such as surrogate gradient and ANN-to-SNN conversions, achieve significantly better performance. Consequently, in terms of accuracy, the proposed method is far from attractive. Could the authors provide a quantitative comparison between global learning methods and the proposed method across different aspects (energy, hardware implementability, etc.) to highlight the advantages of the proposed approach?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their feedback. We appreciate their encouragement regarding local learning and time-to-first-spike coding. We respond to their comments below.\n\n> Global learning methods, such as surrogate gradient and ANN-to-SNN conversions, achieve significantly better performance. Consequently, in terms of accuracy, the proposed method is far from attractive. Could the authors provide a quantitative comparison between global learning methods and the proposed method across different aspects (energy, hardware implementability, etc.) to highlight the advantages of the proposed approach?\n\nWe appreciate the reviewer's useful suggestion, which helps highlight the value of our methods. We have added a section in Supplementary Material to compare our methods to global-based approaches. We included the content of this section in the **Author Rebuttal** answer (Section 3). We emphasized that, although our methods lag behind global-based algorithms in terms of accuracy, they offer benefits in computational and memory costs, energy efficiency, and better compatibility with on-chip training on ultra-low-power neuromorphic hardware.\n\n> What is the latency used in the paper?\n\nAs stated in Section 3.1, firing timestamps are represented by floating-point values to align with event-driven neuromorphic hardware.  We converted each normalized input feature $x$ into a spike timestamp as follows: $T\\left(x\\right) = 1 - x$. Hence, we can not quantify the latency in terms of timesteps. Our spike encoding procedure is detailed in Supplementary Material (Section 2.1).\n\n> The scalability of the proposed method to larger and more complex datasets beyond CIFAR-10 and CIFAR-100 is not thoroughly explored. Future work could address how well the NCG architecture scales with increasing data complexity and size.\n\nWe agree with the reviewer that our work would benefit from evaluation on more complex tasks beyond CIFAR-100. However, dealing with datasets like ImageNet remains a significant challenge for local-based approaches, particularly for networks combining unsupervised and supervised learning. As mentioned in the paper, we found no SNN work based on local learning rules, whether fully-supervised or semi-supervised, reporting results on CIFAR-100 or more complex datasets. Regarding ANNs, SoftHebb-CNN (Journé et al., Hebbian Deep Learning Without Feedback, CVPR 2023) reports SOTA performance on ImageNet (for local-based semi-supervised methods), with an accuracy of only 27.3% (they used a 5-layer CNN trained using Softhebb followed by a classification layer trained using GD). We believe that additional supervised layers (together with unsupervised feature learning) are required to address this type of task. Hence, in the future, we will extend our NCG architecture to hidden layers while preserving the local properties needed for on-chip training. We discuss the extension of NCGs to hidden layers in more detail in the **Author Rebuttal** answer (Section 1).", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We sincerely appreciate the constructive feedback from the reviewers on our submission. We have made our best efforts to address all questions and concerns, which we believe have improved the quality of our work. We have attached a PDF file with a figure and two tables to support some of our responses. Below, we respond to the commonly raised concerns.

### 1. Limitation to a single layer
In this work, we propose the NCG architecture to implement WTA-based supervised competitive learning in a spiking classification layer. It is important to recall that the literature on WTA competition for spike-based classification is very limited (to R-STDP), ineffective (due to inter-class WTA), and faces unbalanced competition issues. To the best of our knowledge, this work is the first implementation of WTA and competition regulation mechanisms specifically designed for classification. Before progressing to multi-layer networks, we intended to establish the relevance and effectiveness of such mechanisms in a single-layer supervised context. The concepts introduced in this work will benefit future research on implementing WTA-based supervised competitive learning in hidden layers:
- Hidden layers, like a classification layer augmented with NCGs, require more neurons than classes.
- Training hidden layers implies learning multiple patterns per class, which aligns with the objective of NCGs.
- Unbalanced competition issues may persist in hidden layers, making our competition regulation mechanism still relevant.

We discussed the limitation in Section 6 of the revised paper.

### 2. Importance of STDP in the classification layer
Our classification system comprises an unsupervised feature extractor and a supervised classifier. Unsupervised STDP is employed for training the feature extractor. For consistency and ease of implementation on neuromorphic hardware, the classifier should use the same type of learning rule as the feature extractor. Also, we target memristor-based neuromorphic hardware, where STDP is inherently implemented in memristor circuits (see reference 11 in the paper). Supervised STDP may therefore be realized by simply incorporating an error signal. We clarified these aspects in the introduction.

While we have justified the use of supervised STDP for this work, it is important to keep in mind that our contributions focus on the architecture, which is independent of the learning rule. Thus, NCGs may theoretically be used with any other rule designed for training SNNs with one spike per neuron. We performed preliminary experiments with S4NN [1], a gradient-based rule, and obtained similar accuracy improvements with NCGs (see Table 2 in the attached PDF). The lower accuracies on CIFAR-10 compared to S2-STDP are due to the approach used for defining the desired timestamps, not the update method (GD/STDP). We need more time to compute scores for other datasets and feature extractors but can provide them before the end of the reviewer-author discussion if requested. Since further research is needed to validate the effectiveness of NCGs with gradient-based rules, we will discuss this point in Section 6 of the revised paper and include S4NN results in Supplementary Material to support our discussion.

[1] Kheradpisheh et al. Temporal backpropagation for spiking neural networks, International Journal of Neural Systems, 2020.

### 3. Comparison with SOTA methods
In the revised paper, we included a section to compare our methods with global-based approaches regarding accuracy, computational efficiency, and hardware implementation. The content is as follows (we removed references due to space constraints):

SOTA methods for direct training of SNNs rely on backpropagation through time (BPTT) and surrogate gradient. These methods usually allow multiple spikes per neuron and support the training of very deep networks using global supervised learning. In this work, we allow one spike per neuron, train all layers with local learning (limiting our networks to shallow architectures), and use a semi-supervised training strategy, where only the last layer is trained with supervision. In terms of performance, our methods lag behind SOTA methods.
For instance, Li et al. (SEENN, NeurIPS 2023) report an accuracy of 96.44% on CIFAR-10 (our best model achieves 79.55%) and 81.65% on CIFAR-100 (our best model achieves 53.49%). This decrease in accuracy can partially be attributed to the number of layers employed (4 against 19) and the use of supervision limited to the last layer. In terms of computational and memory costs, BPTT is extremely inefficient since these costs scale with the latency (i.e. the number of time steps), whereas the costs of our methods are independent of the latency. Also, a backward pass with BPTT adjusts all synapses in the network, whereas our methods adjust only the synapses of neurons that have fired. In terms of energy efficiency, our single-spike strategy may limit the number of generated spikes significantly compared to multiple-spike methods, which reduces power consumption in both training and inference. In terms of hardware suitability, BPTT is challenging to implement on neuromorphic hardware because it relies on non-local learning. BPTT-based SNNs must be trained on GPUs, which is energy-intensive, and can be deployed on chip for inference only. To fully exploit the energy-efficient capabilities of SNNs, both training and inference should be performed on chip. We target memristive-based chips for hardware implementation of our methods. They are excellent candidates for ultra-low-power applications, potentially reducing energy consumption by several orders of magnitude compared to GPUs. Also, STDP is inherently implemented in memristor circuits, which facilitates on-chip training. There are still several challenges to address before our work can be implemented on this type of chip, such as the need for a digital module to calculate the error. This will be the focus of future work.

Meta-review: The manuscript presents an interesting study on supervised learning with local learning rules, in particular variants of supervised STDP. The authors propose to use neural competition groups for each class with intra-class competition. They further propose a novel competition regulation mechanism to enhance within-class variability within the competition group. The paper is well-written and the method is tested on a variety of data sets, also reasonably large ones (CIFAR-100). The method cannot be easily extended to supervised training in multiple layers, but it shows significant gains in performance for the given single-layer supervised setup (with unsupervised learning in lower layers). One weak point is that a theoretical underpinning is missing. Nevertheless, all reviewers believe the paper can be accepted, although their ratings are borderline. I read the paper and agree that the paper is not the strongest, but can be accepted.
Decision: Accept (poster)