Dual-Perspective Activation: Efficient Channel Denoising via Joint Forward-Backward Criterion for Artificial Neural Networks
Authors: Tian Qiu
Chenchao Gao
Zunlei Feng
Jie Lei
Bingde Hu
Xingen Wang
Yi Gao
Mingli Song
Venue: NeurIPS 2024 poster (2024)
Keywords: artificial neural network
activation
joint forward-backward criterion
channel denoising
neural response
neural representation
deep learning
Primary area: optimization_for_deep_networks

Abstract: The design of Artificial Neural Network (ANN) is inspired by the working patterns of the human brain. Connections in biological neural networks are sparse, as they only exist between few neurons. Meanwhile, the sparse representation in ANNs has been shown to possess significant advantages. Activation responses of ANNs are typically expected to promote sparse representations, where key signals get activated while irrelevant/redundant signals are suppressed. It can be observed that samples of each category are only correlated with sparse and specific channels in ANNs. However, existing activation mechanisms often struggle to suppress signals from other irrelevant channels entirely, and these signals have been verified to be detrimental to the network's final decision. To address the issue of channel noise interference in ANNs, a novel end-to-end trainable Dual-Perspective Activation (DPA) mechanism is proposed. DPA efficiently identifies irrelevant channels and applies channel denoising under the guidance of a joint criterion established online from both forward and backward propagation perspectives while preserving activation responses from relevant channels. Extensive experiments demonstrate that DPA successfully denoises channels and facilitates sparser neural representations. Moreover, DPA is parameter-free, fast, applicable to many mainstream ANN architectures, and achieves remarkable performance compared to other existing activation counterparts across multiple tasks and domains. Code is available at https://github.com/horrible-dong/DPA.

Dual-Perspective Activation: Efficient Channel Denoising via Joint forward-Backward Criterion for Artificial Neural Networks
Tian Qiu Chenchao Gao
Zunlei Feng 1.2*
Jie Lei
Bingde Hu 1,5
Xingen Wang 1.5 Yi Gao Mingli Song 1.2
1 State Key Laboratory of Blockehain and Data Security, Zhejiang University
2 Hangzhou High-Tech Zone (Binjiang) Institute Blockchain and Data Security
3 Dalian University of Technology Zhejiang University of Technology Bangsheng Technology Co., Ltd.
(tqiu, zunlei tonyhu, newroot, gaoyi, songml } @zju. @ezju.edu.co edu.cn gccgyl 1oggyllyle wtl.pmalllllll.eeeee.....o.... dlu..edu. jasonlei @zjut.edu.cct ed
Abstract
The design of Artificial Neural Network (ANN) is inspired by the working patterns of the human brain. Connections in biological neural networks sparse, they only exist between few neurons. Meanwhile, the sparse representation in ANNs has been shown possess significant advantages. Activation responses of ANNs are typically expected to promote sparse representations, where key signals get activated while inrelevantreduundant signals suppressed. It can be observed that samples of each category are only correlated with sparse and specific channels ANNs. However, existing activation mechanisms often struggle suppress signals from other irrelevant channels entirely, and these signals have been verified to be detrimental to the network's 's final decision. To address the issue of channel noise interference in ANNs, novel end-to-end trainable Dual-Perspective Activation (DPA) mechanism proposed. DPA efficiently identifies irrelevant channels and applies channel denoising under the guidance of a joint criterion established on- line from both forward and backward propagation perspectives while preserving activation responses from relevant channels. Extensive experiments demonstrate that DPA successfully denoises channels and facilitates sparser neural representa- tions. Moreover, DPA is parameter-fres fast, applicable to many mainstream ANN architectures, and achieves remarkable performance compared to other existing activation counterparts across multiple tasks and domains. Code is available at https:/ ///g thub. wow/horriie e- dong/DPP
Introduction
In recent years, Artificial Neural Networks (ANNs) [1] have achieved notable advancements in wide range of computer vision tasks [2] well various other tasks and domains [3-6].
The ANN design is inspired by the working patterns of the human brain [7]. Multi-Layer Perceptron (MLP) [8], classical artificial neural network that utilizes neurons its basic unit, closely resembles biological neural networks. Another significant development in the field is the Convolutional Neural
*Coreeponding author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

---

Networks (CNNs) [9], which were designed to mimic the local perception mechanisms in the visual cortex. With the availability of more com- putational power, Vision Transformers (ViTs) [10] have emerged as a prominent advancement, combining attention mechanisms and MLPs to achieve highly effective image recognition.
Dual-Perspective Activation (DPA)
Pre-Activation Forward Memory
Forward Criterion
Threshold Activation
Online
Joint
Connections within biological neural networks are sparse, as they only exist between small number of neurons [1 1. 12]. Even in a strongly driven visual cortex, only 1.6% to 4% of neu- rons are activated simultaneously at any moment [12]. Meanwhile, the sparse representation in ANNs has demonstrated notable benefits to net- work interpretability and generalization [13, 14]. Activation responses [15] of ANNs are typically intended to encourage sparse representations, where important signals are expected to get acti- vated while trelevant/redundat signals be sup- pressed during transmission. Rectified Linear Unit (ReLU) [14] is a commonly used activation mechanism in the deep learning field, with a re- sponse threshold of zero, allowing only inputs greater than zero to pass through while suppress- ing all other inputs zero. ReLU simple and robust, which enables a network to acquire a certain sparse representation and offers advantages such as information disentanglement, linear separability, and potential generalization ability [14]. As result, ReLU has gained widespread applications across diverse ANN architectures.
Channel Denoising
Criterion
Post-Activation Backward Momory
Backward Criterion
Farward Propagation
Backward Propugattoo
Figure I: The proposed Dual-Perspeecte Activation (DPA) consists of three components: Pre-Activation For- ward Mcmory (PreA-FM), Threshold Activation Unit (TAU), and Post-Activation Backward Memory (PostA- BM). DPA aims to efficiently identify irrelevant chan- nels and apply channel demoising under the guidance of a joint criterion established online from both forward and backward propagation perspectives while preserving activation responses from relevant channels.
However, although the existing activation mechanisms can achieve sparsity to some extent, they remain inadequate in climinating irrelevan//redundatt features. Firstly, as depicted in Figure 2, both forward and backward propagation reveal that samples from each category are only correlated with sparse and specific channels, while a considerable number of channels are redundant, and there are significant differences in the average activation response stimuli from different categories (also known as category specificity [16]). Additionally, as shown in Figure 3(a), the activation response distributions for each category reveal that the relevant channels mainly maintain positive responses, and ideally, the responses of irrelevant channels should be suppressed entirely; however, it can be observed in Figure 3(a) that a considerable number of responses still exist in potential irrelevant channels (indicated by red arrows). Furthermore. Figure 3(b) verifies the negative impact of the noise from these potential irrelevant channels on the network. When irrelevant channels are manually removed by forcing them to zero during training, the training accuracy significantly improves.
To address the observed deficiencies in the previous activation mechanisms regarding their limited ability to suppress noise from irrelevant channels, we propose a novel end-to-end trainable mechanism called Dual-Perspective Activation (DPA). This mechanism combines criteria established online from both forward and backward propagation perspectives to identify irrelevant channels. From the forward perspective, historical value statisties of pre-activation responses for each category are tracked online and in real time, establishing a forward criterion for channel relevance based on the threshold activation principle. From the backward perspective, historical gradient statisties of post-activation responses for each category are also tracked online and in real time, establishing a backward criterion for channel relevance based on the gradient attribution principle. The ultimate criterion is the intersection of the forward and backward criteria. Guided by this joint criterion, channel-wist denoising is conducted to suppress activation responses from irrelevant channels while preserving activation responses from relevant channels.
The contributions are summarized follows:
The observations on existing activation mechanisms in ANNs concerning their limited ability to suppress irrelevant features for pure sparsity, and the verification of the negative impact of noise from irrelevant channels on the network's 's final decision.
2

---

The proposal of a novel end-to-end trainable mechanism, called Dual- Persppeereee Activation (DPA), which efficiently identifies irrelevant channels and applies channel denoising by incor- porating criteria established and updated online from both forward and backward propagation perspectives while preserving activation responses from relevant channels.
Extensive experiments have been conducted assess the effectiveness and generalization of the proposed DPA mechanism. DPA is parameter-free and fast and achieves remarkable performance compared existing activation counterparts across various mainstream ANN architectures and datasets, as well as multiple tasks and domains.
Category
(a)
Average Activation Value Each Channel
Activation Value Each Chamell (100 samples calegoory 2)
Caegory
.10
(b)
Averuge Activation Grodient un Each Channel
Activation Gradient Each Chamel (100 sumples vallegory 2)
Figure 2: Category channel activation values (a) channel activation gradients (b) are computed on the block of Vin-Tiny. The activation layer used ReLU. Each vector (left) is obtained by taking the average of 100 samples (right) randomly selected from its respective category. The results for five categories in CIFAR-100 100 are presented, with the values and gradients of the first 100 channels displayed. The horizontal axis represents the channel index, and the vertical axis represents the category index (left) sample index (right). The brightmess reflects magnitude of value gradient. Here, we only focus on the sign the gradient as the magnitude of the gradient is unstable. Therefore, the gradient of each sample binarized to +1 and -1.
100
my M Mom
Accunicy
Valoe
baseline manually removing irrelevant channels
(4)
Channel
(b)
Category
Figure 3: (a) Distributions channel activation values in ViT-Tiny's 's last block are recorded by feeding samples from a given category in CIFAR-100. The activation layer used is ReLU, The horizontal axis represents the channel index, the vertical axis represents the channel activation value, and the area represents the value density. The distributions of the first 50 channels shown. The red arrows point potential irrelevant channels. (b) confirmatory experiment conducted CIFAR 100 compare the training accuracy between the original ViT-Tiny (baseline) and the ViT-Tiny with irrelevant channels manually removed for cach category.
2
Observations
This section presents the observed phenomena in the activation response of ANNs and explores how these phenomena affect the network's 's final decision. These explorations offer valuable insights for addressing imperfections in the activation mechanism of ANNs.
Observation 1: Each category is only correlated with sparse and specific channels in ANNs, while a considerable number of channels are redundant, and both the activation value and activation gradient show channel-wise differences between categories.
With threshold activation, relevant features activated while irrelevant features are suppressed, and the channel's 's average activation value is positively correlated with the importance of that channel. Regarding gradient attribution, the channel's average gradient positively correlated with the importance of that channel to the prediction. The channel's activation value and activation gradient of ANN for given category samples are illustrated in Figure The brighter the channel, the higher the channel relevance. Whether from the perspective of forward or backward propagation, intra-class consistency and inter-class differences can be observed. Each category is only highly correlated with sparse and specific channels, indicating that significant proportion of channels are redundant and
3

---

ideally should not generate any responses. Additionally, the judgments from these two perspectives in opposite directions share an overlap that points some common channels.
Observation 2: Current activation mechanisms cannol entirely eliminate responses from irrelevant channels, which have negative impact on the network's 's final decision.
As shown in Figure 3(a), potential irrelevant channels are indicated by the red arrows, and it is evident that the current activation mechanism, such as ReLU, does not entirely suppress irrelevant channels, as a considerable number responses still persist in these channels. A confirmatory experiment is also conducted to investigate the potential impact of responses from irrelevant channels. Figure 3(b) illustrates the change in training accuracy when we retain only relevant channels for each category and manually set irrelevant ones to zero. After manually removing the irrelevant channels for each category, there is a substantial improvement in the training accuracy. This finding suggests that the responses from irreevvnt channels are perceived as noise interference by the network, which adversely affects the network's final decision.
3 Duss-peesee Activation
As shown in Figure 1, the proposed Dual-Perspective Activation (DPA) neuron consists of Pre- Activation Forward Memory (PreA-FM), a Threshold Activation Unit (TAU), and a Post-Activation Backward Memory (PostA-BM). TAU processes the input signals of the network. Meanwhile, PreA-FM and PostA-BM track the historical response value and gradient before and after TAU, respectively, for each category in real time. By utilizing the memories from both PreA-FM and PostA-BM, a joint forward-back backward criterion established and updated online to measure the relevance of channels. Under the guidance of this real-time updated criterion, channel denoising performed to suppress responses from irrelevant channels during training. The proposed DPA is end-to-end trainable, parameter-free and fast that does not affect the inference speed.
3.1 Threshold Activation Unit
Threshold Activation Unit (TAU) is a basic part of the proposed DPA, simulating the activation behavior of pulse neurons [17]. Given non-negative threshold r and an input value æ, if the input value exceeds the threshold it gets activated and propagated the subsequent layer, otherwise, it suppressed to zero. The TAU's operation on input x can be expressed as
I, if x2 {
(AU(#)
0, if
<<T
Generally, given pre-activation feature map F E IR #XWCC with C' channels, A E "xxW"xx refers the post-activation feature map obtained by passing F through the threshold activation unit TAU:
A (F).
TAU can achieve modest level of sparsity, but its ability to further climinate irrelevant noises is limited. Subsequently, will enhance this basic component by introducing a denoising mechanism.
3.2 Joint Backward Criterion
This section introduces the construction of the criterion for channel relevance from both forward and backward propagation perspectives, based on the Observation $2.
From the forward propagation perspective, we introduce a Pre-Activation Forward Memory (PreA- FM) to store and update historical global feature value statistics.
Define the pre-activation global feature value f IRC to be the globally average pooled output of F:
1 HW
Σ
H h= ΣW
FA,N-
Let K denote the number of categories of given dataset. PreA-FM contains K forward memories ) =k= respectively for the K categories, where μ² E R stores the historical mean value before the activation TAU. For input data of each category k. the pre-activation global feature value f*
{u*

---

within the network is computed and updated in the historical mean μ² separately and in real time. To avoid an increase in space complexity, μ is updated by using moving mean technique:
kif (1 (1-m) - m fh
(4)
where plet represents the pre-activation global feature value of a sample of category l at time t. uk--1 and n represent the historical mean value of category k at times / 1 and 4, respectively. The hyperparameter m the momentum for updating the moving mean. Therefore, only memory need be maintained throughout the entire process, whose space complexity is negligible. The statistical analysis of historical input values allows for the examination of long-term trends and patterns, providing more reliable evidence for identifying irrelevant channels.
vectors {n²
===1 {
Based on the principle of threshold activation, signals from irrelevant channels learn to be below the threshold before the activation, resulting in their being suppressed after the activation. The forward channel relevance criterion of each category denotes (RR 1R=11 " where denotes the term "Forward" and &R.. e RC can be established as
{ 0, if 1 27
RIF.F
(5)
1, is H
<T
where the indicator "1" signifies potential irrelevant channels.
From the backward propagation perspective, introduce Post-Activation Backward Memory (PostA-BM) to store and update historical global feature gradient statistics.
Define the post-activation global feature gradient g E RC to be the globally average pooled output of the gradient of the prediction score ý w.r.t. the activated feature map A:
W ag
(6)
Here, we only focus on the sign of gradient the magnitude of gradient is unstable. So, the gradient is binarized as follows:
1, if g- 20
ge - 1. if g. <
PostA-BM contains K backward memories { respectively for the K categories, where 4h E ICC stores the historical mean gradient after the activation TAU. For input data of each category k, the post-activation global feature gradient g within the network is computed through back-propagation, then binarized to g and updated in the historical mean vb" separately and in real time. To minimize space complexity, the update of th is also conducted in moving mean manner, similar to how PreA-FM updates =
sb hit = (1- m)) h.t-1 + m k.t.
(8)
Based on the principle of gradient attribution, positive average gradient of an activated channel indicates that this channel contributes positively to the prediction, whereas a negative average gradient indicates the opposite. The backward channel relevance criterion of each category denotes kB I k== where denotes the term "Backward" and Rr. RCC can be established as
0, if 1 20
R.
(9)
1, if 1 <0'
where the indicator "1" signifies potential irrelevant channels.
Combining both the forward and backward propagation perspectives, the final criterion {R* } Tk=1 for each category's is channel relevance is the intersection (i.c., logical "and") of the forward criterion and the backward criterion:
{R* K T = kR n k 1k=1
(10)
Using dual- ders-peeeee standard potentially more accurate than making judgments solely from single perspective.
5

---

3.3 Channel Denoising
The ultimate step, channel denoising, conducted online on the activated feature map A under the guidance of the joint forward-backe backward criterion { K for channel relevance.
k=1
Define the post- post-activation global feature value a E IR to be the globally average pooled output of A:
a
HW h= Σ w=
Ak,w-
(11)
Given input data of category k. compute its activated feature value a², then filter out irrelevant channels by :
R
(12)
where @ denotes the Hadamard Product. Finally, impose denoising the filtered irrelevant channels by constructing a new loss item Cch as follows:
Cch E
|
(13)
>c= R
In this way, only the activation responses from channels with low correlation will be gradually suppressed, while the ones from other channels with high correlation are getting preserved.
3.4 Neural Network Learning
The proposed Dual-Perspective Activation (DPA) can replace the network's original ones. The channel denoising applies to the network's activated global feature. Networks that extract feature maps/sequences compute the global feature by taking the global average of the feature maps/sequences along the channels. Regarding some Transformer models that incorporate class token, it is also possible to simply peel off the class token separately as the global feature vector while applying the corresponding denoising. Additionally, for Transformer models, the DPA is applied to each block, as Transformers excel in capturing global context throughout, while for CNN models, the proposed DPA is applied to the last block since high-level semantics only exist in deep representations [18]. The final loss C expressed as
= + A
N En=1 C.
(14)
where Lrask is the primary loss for the specific task; for example, in the context of standard classification task, Lresk represents the cross-entropy loss. N is the number of layers in the network that have channel denoising applied, and is the balanced parameter.
4 Experimental Study
Datasets. We adopt six datasets, including four vision datasets: CIFAR-IO [19], CIFAR-100 [19], ImageNet-100 [20], and ImageNet-1K 1K [20], and two non-vision datasets: DGraph [21] and 20News [22], to verify the effectiveness of the proposed DPA.
Compared methods. The proposed DPA compared with different types of mainstream activation mechanisms mentioned in Related Work (85.1), including Softplus [23), ELU [24], SELU [25], SiLU [26), ReLU [14], GELU [27], and GDN [28].
Experimental settings. The image size of CIFAR-(10,100) remains 32x32, while the images in ImageNet- IK0 are uniformly scaled 224x224. To ensure the generality of the network, the activation threshold 7 is uniformly set to 0. The momentum m is empirically set to 0.9, and the balanced parameter À varies depending on networks and datasets. More detailed discussions on T, m, and À can be found in Appendix $. All experiments use the same data augmentations provided by timm [29], AdamW optimizer with weight decay of 0.05, drop-path rate of 0. gradient clipping norm of 1.0, and cosine annealing learning rate scheduler with linear warm-up. All experiments are trained for 300 epochs from scratch. The automatic mixed precision training strategy is adopted to speed up the training. All other training settings, including batch size, learning rate, warm-up epochs, and so on, are kept identical throughout each set of comparative experiments. Note that the numerical results are the average under three different random seeds, and no pre-training is used.

---

Table Top-I accuracy (%) across the CIFAR-IO, CIFAR-100, ImageNet-100, and ImageNet-IK datasets using the proposed DPA on Vision Transformer (ViT) and variants.
Top-1 1 Acc/ %
Softplus
ELU
SELU
SiLU
ReLU
GELU
GDN
DPA
ViT-Tiny
84.3
82.0
79.4
85.5
89.9
89.2
81.8
91.3
DeiT-Tiny
84.7
81.4
79.9
86.6
89.6
89.2
83.0
91.5
CIFAR-I0
CaiT-XXS
82.5
78.4
86.6
89.4
88.7
80.0
91.4
PVT-Timy
90.6
89.3
85.4
92.5
93.0
92.8
82.8
93.8
TNT-Small
88.3
85.4
83.7
90.5
90.8
91.1
85.1
92.4
ViT-Tiny
62.4
60.0
57.5
65.5
65.7
65.4
59.4
70.5
DeiT-Tiny
63.4
60.0
58.3
67.1
67.0
67.0
59.8
70.6
CIFAR-100
CaiT-XXS
60.4
59.3
55.8
63.9
65.8
65.5
56.2
68.5
PVT-Timy
69.5
69.3
65.7
70.2
70.9
70.6
64.4
75.3
TNT-Small
65.2
63.8
60.9
65.1
65.4
64.4
62.5
72.0
ViT-Tiny
74.1
68.9
66.4
74.1
75,4
76.4
67.9
80.4
DeiT-Tiny
75.3
69.4
67.0
75.1
75.6
74.6
66.3
81.0
ImageNet-100
CaiT-XXS
70.9
69.1
65.9
76.1
76.0
76.7
69.5
80.4
PVT--Tiy
79.5
77.1
76.1
79.5
81.9
81.4
75.8
85.2
TNT-Small
78.9
79.3
76.4
77.6
79.9
77.2
76.9
85.6
ViT-Tiny
70.0
64.2
63.1
66.9
70.9
70.4
65.2
72.2
DeiT-Tiny
71.9
67.9
66.2
72.0
73.2
73.0
66.4
73.4
ImageNet-IK
CaiT-XXS
70.3
68.1
66.7
73.2
74.0
73.6
66.1
75.0
PVT--Tiy
71.5
69.2
68.5
72.8
73.7
73.5
66.5
75.2
TNT-Small
72.0
70.7
70.3
71.5
73.4
73.3
68.2
77.8
Table Top-I accuracy (%) across the CIFAR-10, CIFAR-100, ImageNet-100, ImageNet- 1K datasets using the proposed DPA on various CNN architectures.
Top-1 Acc %
Softplus
ELU
SELU
SiLU
ReLU
GELU
GDN
DPA
AlexNet
85.6
86.1
85.7
86.0
86.0
85.8
85.4
86.4
VGG-11
91.3
92.0
91.5
91.9
92.2
91.9
92.2
CIFAR-10
MobileNel
87.4
87.7
87.2
87.8
87.4
87.4
87.0
87.8
ShuffleNet
89.2
89.0
88.9
89.3
89.4
89.3
88.5
89.8
R
94.6
94.7
94.6
95.1
95.0
94.9
94.0
95.1
AlexNet
57.6
58.4
58.1
58.1
57.2
57.4
56.8
58.5
VGG-11
69.6
69.9
69.7
69.9
70.2
70.0
70.1
70.3
CIFAR- 100
MobileNet
65.4
65.5
65.6
65.2
66.0
65.4
64.8
67.2
ShuffleNet
66.2
66.1
65.9
66.3
66.3
65.6
66.8
ResNet-18
75.5
75.7
75.6
76.1
75.7
75.6
74.3
76.8
AlexNct
75.7
76.0
75.7
76.6
76.3
76.3
75.5
76.9
VGG-11
87.0
87.3
87.6
87.8
87.7
87.5
86.7
88.4
ImageNet-100
MobileNet
80.6
79.3
80.1
80.6
80.5
78.7
81.7
ShuffleNet
80.9
80.9
80.4
81.7
81.6
81.6
80.0
81.9
ResNet-18
84.6
84.4
84.1
84.9
84.9
84.7
83.5
85.7
AlexNet
56.1
56.3
56.1
56.4
56.5
56.4
55.6
57.5
VGG-11
68.4
68.2
67.8
69.0
69.0
68.1
69.7
ImageNet-IK
MobileNet
67.2
66.7
67.1
67.4
68.1
68.2
66.3
68.9
ShuffleNet
68.5
68.3
68.4
69.1
69.0
68.9
68.0
69.5
R
69.3
69.4
68.9
69.7
69.7
69.4
68.3
70.3
4.1 DPA ViTs
The proposed DPA mechanism can be incorporated into popular Vision Transformer (ViT) and its variants. Table shows the top-1 accuracy (%) across CIFAR- 1,0000 and ImageNet- (100, using the proposed DPA on five different ViT architectures: ViT [30], DeiT [31], CaiT [32] PVT [33], and TNT [34]. The proposed DPA can replace the existing activations each block. The results consistently illustrate that the proposed DPA mechanism outperforms the baselines.

---

Table 3: Ablation study of the proposed DPA CIFAR-100. D DPAs, DPAFus and D denote DPA with the channel relevance criterion the forward only, backward only, forward-backward union, and borward-backwee
intersection, respectively. DP denotes denoising all chamnels indiscriminately.
Top-1 1 Acc /%
ReLU
GELU
DP
DPAF
DPAg
DPAFuB
DPAFrB
ViT-Tiny
65.7
65.4
65.8
68.9
67.9
67.6
70.5
ResNet-18
75.7
75.6
75.7
76.5
76.2
76.0
76.8
Table Computational costs during training and inference regarding "GPU Memory (GiB)" and "Latency (s)" for networks that utilize the proposed DPA, in comparison to networks utilizing other activation counterparts. The networks were fed 224x224-pixcl images with batch size of 1024 on an NVIDIA A40 GPU. "Lateney"
refers to the average time it takes for network to process batch of data.
ViT-Tiny
ResNet-18
Computational Costs
ReLU
GELU
DPA
ReLU
GELU
DPA
Training GPU Memory / GiB
33.09
37.14
33.11
27.06
30.38
27.08
Inference GPU Memory GiB
6.26
6.26
6.26
11.85
11.86
11.85
Training Latency /s Inference Latency s
0.71 0.39
0.83
0.89
0.57
0.65
0.62
0.42
0.39
0.39
0.39
0.39
Table 5: The generalization performance of DPA node classification and text classification tasks.
Node Classification
Text Classification
AUC/% %
GCN
GraphSAGE
Top-1 Acc / %
TexIGNN
BERT
ReLU GELU
72.5
75.1
ReLU GELU
86.2
86.7
71.9
74.4
86.1
86.9
DPA
73.7
76.6
DPA
86.9
87.8
4.2
DPA on CNNS
The proposed DPA is also evaluated various mainstream CNNs, including AlexNet [35], VGG [36], MobileNet [37]. ShuffleNe((22) [38], and ResNet [39]. The proposed DPA replaces the original activations in the last block since previous works have shown that high-level semantics in CNNs only exist deep representations [18]. The results in Table 2 highlight the versatility and robustness of the proposed DPA in handling diverse CNN architectures and datasets.
4.3 Ablation Study
The ablation study mainly focuses different combinations of the forward and backward criteria. Ta- ble presents the results, showing that the performance with the dual-perspective criterion (DPApme) better than using single-perspective criterion (DPA F DPA a). Furthermore, the intersection of the dual perspectives (DPAFnR) yields better results than the union of both (DPA as the
intersection of multiple perspectives can reduce misjudgments. Additionally, if denoise all channels indiscriminately (DPA,t), there will be no performance improvement.
4.4 Computational Costs
The proposed DPA introduces no extra parameters in any of its components. The two memory units (PreA-FM and PostA-BNt only work during the training phase, and in the inference phase, only TAU needs to be involved. The numerical computational costs during training and inference regarding "GPU Memory (GiB)" and "Latency (s)" (the average time it takes for a network to process batch of data) are shown in Table 4. Notably, the activation counterparts used in original networks should be implemented manually as our DPA does. Utilizing the counterparts directly from pre-made libraries (like torch.nn) can result in unfair comparisons due to their high optimization at the low level. Table 4 indicates that the GPU overhead required by DPA during training negligible, and the speed of DPA is on par with other counterparts during the inference stage.

---

ReLU
DPA (ours)
Value
denoisc
Channel
Channel
ReLU
DPA (ours)
Value
denoise
Channel
Channel
ReLU
(oursu
Value
denoise
Channel
Channel
RcLU
DPA (ours)
Value
denoise
Channel
Channel
Figure 4: Distributions channel activation values ViT-Tiny's last block are recorded by feeding samples from a given category in CIFAR-I00. The proposed DPA is compared with ReLU. The horizontal axis represents the channel index. the vertical axis represents the channel activation value, and the area represents the value density. In the figure, each row displays the changes in response distributions for specific category when transitioning from ReL.U to the proposed DPA. The distributions of the first 50 channels shown.
4.5 Generalization to Other Tasks
The proposed DPA also perform various other tasks domains, including non-vision tasks like node and text classification. For node classification, the DGraph dataset [21] is employed, and GCN [40] and GraphSAGE [41] chosen models. For text classification, the 20News dataset [22] is employed, and BERT [42] and TexIGNN [43] are chosen models. The results are shown in Table 5.
4.6 Activation Response Visualization
Figure 4 displays the change in channel-wise activation distributions of specific category in the last block of ViT-Tiny after using ReLU and the proposed DPA. With the typical ReLUU activation, the presented responses active almost every channel. Some irrelevant channels that should not be activated are mistakenly activated. After using the proposed DPA, the activation responses become sparser, implying that most irrelevant channels are suppressed. Moreover, the suppression of irrelevant channels leads to enhanced focus in the responses from other channels. These phenomena imply that the DPA facilitates the extraction of key features from input data with higher precision, which reduces the network's ' learning difficulty and improves its interpretability.
5 Related Work
5.1 Forward Activation Mechanism
The activation mechanism [15] plays a pivotal role in artificial neural networks as it defines how neurons respond to input signals, convert them into output signals, and transmit them to the subsequent layer. Each activation mechanism varies in mathematical properties and nonlinear forms, allowing neurons to simulate different neural phenomena, including excitation, inhibition, and modulation. Mathematically. activation mechanisms categorized into different types, including logistic Sigmoid

---

and Tanh variants [9], Rectified Linear Unit variants [14], Exponential Linear Unit variants [24],
Softplus variants [23]. probabilistic variants [27]. and others [26, 28].
In the widely used form of activation [9, 14, 23, 24, 27]. irrelevant features are suppressed, and relevant features gain amplified influence according the response rule of the neuron. Furthermore, some activation mechanisms [9. 14, 23] can effectively achieve data sparsity, diminish redundant information, and enable better feature distinction. Additionally, the activation mechanisms, such as ELU [24] and SiLU [26] mentioned above, and others [44, 45], contain learnable parameters. Parameters [44] can adapt to various data distributions, avoiding gradient vanishing and explosion. thereby enhancing the convergence speed and precision of ANNs. However, these extra parameters can only uniformly influence the response strength for all inputs. Parameters in [45] allow the original activation to adjust its response condition according to different external inputs. The inclusion of these extra parameters offer potential for the activation to eliminate irrelevant noise. Nevertheless, it is important to note that this is not a targeted design, since these extra parameters are completely adaptively learned without supervision signals, rather than specifically identifying irrelevant channels and selectively applying channel denoising.
5.2 Backward Gradient Attribution
The gradient attribution [46] includes a set of methods utilized explain the predictions made by ANNs. It is generally believed that the gradient of the neural network output w.r.t. the input can indicate the importance or relevance of the input.
Baehrens et al. [47] were pioneers in using the first-order derivative of the predicted class w.r.t. the input to elucidate the local decisions made by nonlinear classification algorithms. Simonyan et al. [48] employed the gradient to compute class saliency map that is specific to a given image and class. Bach et al. [49] further developed the Layer-wise Relevance Propagation (LRP), which attributes by propagating gradients layer by layer. Shrikumar et al. [50] proposed DeepLIFT, which uses backpropagation to identify each neuron's 's contribution
neural network toward the output prediction. Sundararajan et al. [51] introduced the Integrated Gradients algorithm to counter gradient saturation, which calculates gradient computation the path integral of the first-order derivative of the output w.r.t. the input features along straight path from baseline to the input.
Additionally, the gradient- based Class Activation Mapping (CAM) family [52-544 (4] has become widely popular for its computational efficiency, requiring no structural changes or re- re-training. The most classical one is Grad-CAM [52], which can be used explain activations in any layer of deep network by computing the importance (relevance score) for each channel of the activated feature map and performing weighted sum. The relevance score of channel is derived by taking the average gradient of the predicted class score w.r.t. the activated feature map in that channel, which motivates us utilize similar principles when designing criteria for channel relevance in our study.
Conclusion
It is observed in Artificial Neural Networks (ANNs) that each category is only associated with sparse and specific channels, however, current activation mechanisms often struggle to suppress the signals from other irrelevant channels, which negatively impacts the network's final decision. To alleviate such noise interference, a novel end-to-end trainable Dual- Perppeeeseettve Activation (DPA) mechanism is proposed. DPA is guided by joint criterion established online from both forward and backward propagation perspectives, aiming to efficiently identify irrelevant channels and apply channel denois- ing while preserving activation responses from relevant channels. Extensive experiments showcase that DPA is compatible with various mainstream ANN architectures, can achieve sparser neural representations and outperform other activation counterparts, demonstrating its effectiveness and versatility. Additionally, DPA is parameter-free and offers fast inference speed on par with other activation counterparts, indicating its potential for practical application in real-world scenarios.
Acknowledgments
This work is supported by the Zhejiang Province "JianBingLing Yan+X" Research and Development Plan (2024C01114),
10

---

References
[1] Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436-444 2015.
[2] Athanasios Voulodimos, Nikolaos Doulamis, Anastasios Doulamis, Eftychios Protopapadakis, et al. Deep learning for computer vision: A brief review. Computational intelligence and neuroscience, 2018, 2018.
[3] Zonghan Wu, Shirui Pan, Fengwen Chen, Guodong Long, Chengqi Zhang, and Yu Philip. A comprehensive survey graph neural networks, IEEE transactions on neural networks and learning systems, 32(1) (((1):4422) 3:4-44, 2020.
[4] Shervin Minaee, Nal Kalchbrenner. Erik Cambria, Narjes Nikzad, Meysam Chenaghlu, and Jianfeng Gao. Deep learning- based text classification: a comprehensive review, ACM computing surveys, 54(3):1444 1-00, 2021.
[5] Jingxuan He, Lechao Cheng, Chaowei Fang, Zunlei Feng, Tingting Mu, and Mingli Song. Progressive feature renforreifrr for weakly supervised semantic segmentation. In Pro- ceedings of the AAAI conference artificial intelligence, volume 38, pages 2085-2093, 2024.
[6] Yuzhu Wang, Lechao Cheng, Manni Duan, Yongheng Wang, Zunlei Feng, and Shu Kong. Improving knowledge distillation via regularizing feature norm and direction. arXiv preprint arXiv:2305.17007, 2023.
[7] Warren S McCulloch and Walter Pitts. A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5:115-133, 1943.
[8] James McClelland, David Rumelhart, PDP Research Group, al. Parallel Distributed Processing, Volume 2: Explorations in the Microstructure of Cognition: Psychological and Biological Models, volume 2. MIT press, 1987.
[9] Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86( 86(11):227--3224 1998.
[10] Kai Han, Yunhe Wang, Hanting Chen, Xinghao Chen, Jianyuan Guo, Zhenhua Liu, Yehui Tang, An Xiao, Chunjing Xu, Yixing Xu, et al. A survey on vision transformer. IEEE transactions on pattern analysis and machine intelligence, 45(1):87-110, 2022.
[11] David Attwell and Simon B Laughlin. An energy budget for signaling in the grey matter the brain. Journal of cerebral blood flow & metabolism, 133-1111 2001.
[12] Peter Lennie. The cost of cortical computation. Current biology, 13(6):493-43) 497, 2003.
[13] Bruno Olshausen and David Field. Emergence of simple-cell receptive field properties by learning sparse code for natural images. Nature, 38 (6588))6607-6694) 1996.
[14] Xavier Glorot, Antoine Bordes, and Yoshua Bengio. Deep sparse rectifier neural networks. In Proceedings of the fourteenth international conference on artificial intelligence and statistics, pages 115-323. JMLR workshop and conference proceedings, 2011.
[15] Shiv Ram Dubey, Satish Kumar Singh, and Bidyut Baran Chaudhuri. Activation functions in deep learning: A comprehensive survey and benchmark. Neurocomputing, 503:92-108, 2022.
[16] Zunlei Feng, Jiacong Hu, Sai Wu, Xiaotian Yu, Jie Song, and Mingli Song. Model doctor: A simple gradient aggregation strategy for diagnosing and treating enn classifiers. In Proceedings of the AAAI conference artificial intelligence, volume 36, pages 616-624, 2022.
[17] Alan I. Hodgkin and Andrew F Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology, 117ee, 117(4):500, 1952.
[18] Maithra Raghu, Thomas Unterthiner, Simon Kornblith, Chiyuan Zhang, and Alexey Dosovitskiy. Do vision transformers see like convolutional neural networks? Advances neural information processing systems, 34:12 14:121 16-12228, 2021.

---

[19] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009.
[20] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scall hierarchical image database. In IEEE conference on computer vision and pattern recognition, pages 255. IEEE, 2009.
[21] Xuanwen Huang. Yang Yang. Yang Wang. Chunping Wang. Zhisheng Zhang, Jiarong Xu, Lei Chen, and Michalis Vazirgiannis. Dgraph: A large-scale financial dataset for graph anomaly detection. Advances Neural Information Processing Systems, 11-22765-22777 2022.
[22] The 20 newsgroups dataset. http://qwone..cm http://ee....eoooooooooooooooooo 2021.
[23] Charles Dugas, Yoshua Bengio, François Bélisle, Claude Nadeau, and René Garcia. Incor- porating second-ore order functional knowledge for better option pricing. Advances in neural information processing systems, 13, 2000.
[24] Djork-Amé Clevert, Thomas Unterthiner, and Sepp Hochreiter, Fast and accurate deep network learning by exponential linear units (elus). arXiv preprint wxXv:/551.072889 2015.
[25] Günter Klambauer, Thomas Unterthiner, Andreas Mayr, and Sepp Hochreiter. Self-normalizin neural networks. Advances neural information processing systems, 30, 2017.
[26] Prajit Ramachandran, Barret Zoph, and Quoe V Le. Searching for activation functions. arXiv preprint arXiv: 2017.
[27] Dan Hendrycks and Kevin Gimpel. Gaussian error linear units (gelus). arXiv preprint 1606v 08415, 2016.
[28] Johannes Ballé, Valero Laparra, and Eero Simoncelli. Density modeling of images using a generalized normalization transformation. arXiv preprint arXiv:/5/1.0628// 2015.
[29] Ross Wightman. Pytorch image models. https//giihbb.oom///wggaaaaaaaar image-models, models, 2019.
[30] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.1 1929, 2020.
[31] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou. Training data-efficient image transformers & distillation through attention. In International conference machine learning, pages 10347-10357. PMLR, 2021.
[32] Hugo Touvron, Matthieu Cord, Alexandre Sablayrolles, Gabriel Synnaeve, and Hervé Jégou. Go- ing deeper with image transformers. In Proceedings of the IEEF/CVF international conference on computer vision, pages 32-42, 2021.
[33] Wenhai Wang, Enze Xie, Xiang Li, Deng-Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pyramid vision transformer: A versatile backbone for dense prediction without convolutions. In Proceedings of the IEEF/CVF international conference on computer vision, pages 568-578, 2021.
[34] Kai Han, An Xiao, Enhua Wu, Jianyuan Guo, Chunjing Xu, and Yunhe Wang. Transformer in 2021. [35] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Communications of the ACM, 60(6):84-90, 2017.
transformer. Advances in neural information processing systems,
[36] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv: 0111409..15..... 2014.
[37] Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXi::1004.04861 2017.
12

---

[38] Ningning Ma, Xiangyu Zhang, Hai-Tao Tao Zheng, and Jian Sun. Shufflenet v2: Practical guidelines for efficient enn architecture design. In Proceedings of the european conference on computer vision, pages 1 16-131, 2018.
[39] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016.
[40] Thomas Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. ArXiv,
2016.
[41] Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. Advances in neural information processing systems, 30, 2017.
[42] Jacob Devlin, Ming- King-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidirectional transformers for language understanding. arXiv preprint 2018.
[43] Liang Yao, Chengsheng Mao, and Yuan Luo. Graph convolutional networks for text classi- fication. In Proceedings of the AAAI conference on artificial intelligence, volume 33, pages 7370-7377, 2019.
[44] Aizhu Liu, Haigen HU, Tian Qiu, Qianwei Zhou, Qiu Guan, and Xiaoxin Li. Exploring optimal adaptive activation functions for various tasks. In IEEE international conference on bioinformatics and biomedicine (BIBM), pages 2290-2297. IEEE, 2020.
[45] Tian Qiu, Wenxiang Xu, Lin Chen, Linyun Zhou, Zunlei Feng, and Mingli Song, Dynamic neural response tuning. In The twelfth international conference on learning representations, 2024.
[46] Marco Ancona, Enea Ceolini, Cengiz Öztireli, and Markus Gross. Gradient-based attribution methods. Explainable Al: interpreting, explaining and visualizing deep learning, pages 199-191, 2019.
[47] David Bachrens, Timon Schroeter, Stefan Harmeling, Motoaki Kawanabe, Katja Hansen, and -lauer Müller. How to explain individual classification decisions. The journal of machine learning research, 11:1803-1833 2010.
[48] Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. Deep inside convolutional networks: Visualising image classification models and saliency maps. arXiv preprint arXiv:1312.6600 2013.
[49] Sebastian Bach, Alexander Binder, Grégoire Montavon, Frederick Klauschen, Klaus-Robert Müller, and Wojciech Samek. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PloS one, 301440, 2015.
[50] Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje. Learning important features through propagating activation differences. In International conference on muchine learning, pages 3145-3153, 2017.
[51] Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic attribution for deep networks. In International conference on machine learning, pages 2319-3328. PMLR, 2017.
[52] Ramprasaath R Selvaraju, Michael Cogswell, Abhishek Das, Ramakrishna Vedantam, Devi Parikh, and Dhruv Batra. Grad-cam: Visual explanations from deep networks via brased localization. In Proceedings of the IEEE international conference on computer vision, pages 618-626, 2017.
[53] Aditya Chattopadhay, Anirban Sarkar, Prantik Howlader, and Vinceth N Balasubramaniann Grad-cam++: Generalized maudient-based visual explanations for deep convolutional networks. In IEEE winter conference on applications of computer vision, pages 347. IEEE, 2018.
[54] Daniel Omeiza, Skyler Speakman, Celia Cintas, and Komminist Weldermariam. Smooth grad- cam++ An enhanced inference level visualization technique for deep convolutional neural network models. arXiv preprint 1908.019900002224 2019.
13

---

A Appendix
A.1 Hyperparameter Impact Analysis
Momentum for updating the moving mean μ. Theoretically, high value of m risks making the mean value unstable, and conversely, low value of m smoothens the mean value update, but may cause the mean value to lag behind. As illustrated in Figure 5, the network's s performance is not sensitive to the m between around 0.2 and 0.99, from which m=0.9 performs the best, and extremely small m values lead to negative effects. Therefore, for the rest of the experiments presented in the paper, we empirically set the m to 0.9 without too much consideration.
Balanced parameter À for the channel loss Leh- The optimal balanced parameter À for Les is specific to individual tasks. The relationship between and the accuracy on CIFAR-100 with the ViT-Tiny model is depicted in Figure 6. In this case, the optimal À is roughly 5, and too large À can result in negative side effects. For other trials, we found the optimal À to be when training DeiT-Tiny and TNT-Small CIFAR-10. Searching the optimal parameters for each task can be time-consuming, but one thing is for sure: smaller À values do not hurt accuracy. Therefore, for the majority of our experiments, set the default value of to 1.
CIFAR-100 and the optimal À to be I when training ViT-Tiny on
Activation threshold for the Threshold Activation Unit (TAU). To achieve preliminary sparsity, only input signals that exceed the threshold т are activated, while those below the threshold are suppressed to zero. Therefore, is non-negative value. Figure 7 demonstrates that as increases, the performance decreases. Possible reasons could be the influence weight initialization and feature normalization operations. Typically, weights initialized using distribution with mean of zero, and normalization techniques such as layer normalization and batch normalization are used to make the feature distribution centered around zero (by subtracting the feature mean) to eliminate shifts in data covariates. Under this circumstance, T = 0 becomes the optimal activation threshold. Additionally, it may be feasible to modify the strategy for weight initialization and feature normalization to achieve optimal effects when considering a positive T.
70
Accuracy (%))
70-
Accuracy
68
68
66
0.9
0.999
Figure 5: Top-1 accuracy (%) w.r.t the momentum m for updating the moving mean μ when training on CIFAR- 100 with ViT-Tiny.
Figure 6: Top-1 accuracy (%) w.r.t the balanced parameter for the channel loss Let when training on CIFAR-100 with ViT-Tiny.
70
65-
mnly)
Accuracy
60
55-
50
0.1
0.2
0.4
0.8
2
Figure 7: Top-1 accuracy (%) w.r.t. the activation threshold r for the Threshold Activation Unit (TAU) when training on CIFAR-100 100 with ViT-Tiny.
A.2 Overfitting Test
Deep neural networks are susceptible to overfitting when the available data is insufficient. Therefore, the network requires robust support from data augmentations as illustrated in this study. We assess the performance of ViT-Tiny with ReLU and the proposed DPA on the CIFAR-10 10 dataset when using weak data augmentations consisting solely of "random horizontal flipping" and "normalization" Figure 8 showcases the loss and accuracy curves. Specifically, the "val" loss curve provides further evidence that DPA effectively mitigates overfitting by reducing noise interference from irrelevant channels and promoting sparsity the representation level.
14

---

ReLU (Irim)
(val (val)
2.0
(train)
Accuracy (%)
80
1.5-
75
1.0-
70
0.0
65
DPA
100
200
250
200
300
Epoch
Epoch
Figure 8: The performance of ViT-Tiny with ReLU and the proposed DPA on the CIFAR-10 datasct using weak data augmentations comprising only "random horizontal flipping" and "normalization".
A.3 Differences between Channel Denoising and Channel Pruning
(a) Explanation of "channel denoising": : i) We regard the responses from potential irrelevant channels as channel noise (see Figure 3()). ii) Also, each channel tends to exhibit response distributions with high variance, which is also symbol of channel noise (see Figure 3(a)). Therefore, the proposed DPA aims to denoise these channels (i & ii), thus achieving sparser representations and remarkable accuracy improvements. Figure shows the denoising effect where the responses (not the weights) from irrelevant channels are suppressed (not forcibly set to zero), and the ones from relevant channels become more focused.
(b) The proposed channel denoising differs from the channel pruning as:
The target of channel pruning is the channel weights (W (W))=n1 while the target of channel denoising is the channel responses f' (x; (W WW)c==). Specificallyy for the e-th channel, given an input sample x and the channel weight W... it generates channel response fa:; W Channel pruning operates by setting the weights on pruned channels for samples of any category (This is why channel pruning typically leads to a decrease in model accuracy.). In contrast, channel denoising operates by suppressing the responses of certain channels zero, in which case, the channel weights not necessarily zero, and the suppressed channels can vary for samples of different categories.
certain channels to zero, resulting in no responses
Channel pruning needs post-processing to remove irrelevant channel weights and some need further fine-tuning, while channel denoising is conveniently trained end-to-end from scratch and does not require any post-processing or fine-tuning.
The objective of channel pruning is trying to reduce computation and storage requirements without sacrificing accuracy, while the objective of channel denoising is trying to improve accuracy without increasing computational overhead.
A.4 Limitation and Discussion
The proposed DPA still has a gap to achieve the ideal performance as Observation shows. This limitation can be attributed to several factors. Firstly, the confirmatory experiment in Observation 2 assumes the category label is always known, but in applications, the category label is unknown during the testing phase. Therefore, to address this challenge, we introduced channel denoising during training, allowing the network to learn how to reduce the response from irrelevant channels in the testing stage when the category label is unknown. Through this approach, we expect to approximate the way manually removing irrelevant channels in Observation as much as possible. However, the joint criterion devised for identifying irrelevant channels is not always precise, highly depending on the historical context of each training moment, and some categories that share similarities at the representation level could add to the difficulty of precise denoising while still preserving category discrimination. At present, we are actively researching these areas and are confident that it will achieve more promising results.
Performance.
Tasks. In certain scenarios, e.g., the box regression part of object detection, the proposed DPA may not be applicable. This is because DPA is associated with categories, whereas box regression is not. Despite this, the generalization ability of DPA is already commendable, as it can perform various other tasks or domains, including image classification and non-vision tasks like node classification and text classification, whose generalization has been verified in the presented experiments.
15

---

NeurIPS Paper Checklist
Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: $1 "Introduction"
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results be expected to generalize other settings.
is fine include aspirational goals as motivation as long is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: $A.4 "Limitation and Discussion" "
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification. asymptotic approximations only holding locally). The authors should reflect how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low images are taken in low lighting. Or speech-to-text system might be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach address problems of privacy and faimess.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question:
For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
16

---

Justification:
The paper does not include theoretical results.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibiliyy
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: $3 "Dual- Pers-Peeree Activation" & $4 "Experimental Study" The source code provided in the supplementary materials
Guidelines:
The answer NA means that the paper does include experiments. If the paper includes experiments, No answer this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome deseribe the particular way they provide for reproducibility, In the case of closed-source models, it may be that access to the model is limited in some way (e.g., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
17

---

Answer:
[Yes]
Justification:
The source code has been provided in the supplementary material.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https:/nnips.cc/ubbiicgg (deesCooeSuummisiooPollyy) for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run reproduce the results. See the NeurlPS code and data submission guidelines
for more details.
The authors should provide instructions on data access and preparation, including how access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code is permitted.
6. Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: $4 "Experimental Study Experimental settings" & $A.1 "Hyperparameter Selection"
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, supplemental material.
7. Experiment Statistical Significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer:
[NA]
Justification:
The numerical results are the average under three different random seeds.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi- dence intervals, or statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the enror bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
18

---

It should be clear whether the error bar is the standard deviation or the standard error of the mean.
is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out range (e.g. negative enror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments Compute Resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification: $4.4 "Compuutaaiii Costs"
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount compute required for each of the individual experimental runs well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary failed experiments that didn't make into the paper).
9. Code Of Ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurlPS Code of Ethics http:///wwppp..oo/oolllc/ttceens
Answer: [Yes]
Justification: The research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., there a special consid- eration due to laws or regulations in their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification:
No negative societal impacts.
Guidelines:
The answer NA means that there no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
19

---

The conference expects that many papers will be foundational research and not tied particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of MI..
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: The paper poses no such risks.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Lieenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper. properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: The source code & The citations in the paper.
Guidelines:
The answer NA means that the paper does not existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (c.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use the package should be provided. For popular datasets, paperswitheode, httpssiithcddcccomttttteee has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
20

---

If this information is not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification:
The source code provided in the supplementary material.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/moodl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification:
The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According the NeurIPS Code of Ethies, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification: The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
21


Reviews:
[{"review_id": "5lHekRlncq", "reviewer": "Reviewer_EUgL", "summary": "This paper addresses the question of how to suppress inputs from irrelevant channels in a deep neural network. The authors develop a novel end-to-end trainable mechanism called Dual-Perspective Activation (DPA) to suppress irrelevant information and increase sparsity. The method is parameter-free, and increases performance across tasks and domains relative to baselines without this mechanism. Networks with DPA activation layers uniformly outperform standard activation functions (ReLU, GELU, SELU, GDN, etc.) across a wide range of datasets (Cifar{10,100}, ImageNet{100,1K}), and architectures (VITs, CNNs). Ablation studies show that the forward and backward components contribute to the effectiveness of DPA, with minimal computational overhead.", "questions": "Minor: Have you compared DPA to other regularlization methods that lead to greater sparsity?", "limitations": "OK", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "The paper does an excellent job motivating the design of a novel activation function and demonstrating its prowess across a range of ANN architectures (VITs, CNNs, GNNs), and datasets. Across the board DPA shows improvements in top1 accuracy, though the assessments were limited to these particular (albeit ubiquitous) benchmark assessments, somewhat limiting the broader relevance/impact of the work.\n\nThe ability to outperform existing activation functions across the board suggests potential for high impact in the field of computer vision, and other areas of AI/ML (as briefly demonstrated), given that activation functions are a fundamental component in all ANN models.", "weaknesses": "The paper convincingly demonstrates the effectiveness of DPA for image classification (with limited presentation of generalization to node and text classification), but the work seems lacking in clear demonstration of relevance/impact beyond these benchmark assessments (i.e., less clear how this might impact AI/ML theory, or impact cogsci/neurioscience applications of these models). That said, the noted sparsification of representations suggest there’s a clear thread to follow up on for these more theory-focused areas.\n\nMinor: the paper does not distinguish between sparse connectivity and “activation sparsity”, and doesn’t distinguish between “population sparsity” (only a few neurons active at any given time) and “lifetime sparsity” (a given neuron fires rarely, only for a small percentage of input images). These are often confused (or not distinguished) in the ML and Neuro literatures, and might be worth being clear about which one you are referring to (it seems like category-level lifetime sparsity?).\n\nMinor: no mention of dropout, which directly impacts activation sparsity\n\nMinor: How did you identify and manually remove irrelevant channels? (Figure 3)? Are these just the low activations? Would a channel norm on this layer have the same effect/benefit?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> **W1:** ... but the work seems lacking in clear demonstration of relevance/impact beyond these benchmark assessments (i.e., less clear how this might impact AI/ML theory, or impact cogsci/neurioscience applications of these models). That said, the noted sparsification of representations suggest there’s a clear thread to follow up on for these more theory-focused areas.\n\nThank you for your thoughtful review and valuable feedback on our paper. Here is our discussion on how our work might impact AI/ML theory, or impact cogsci/neurioscience applications of ANN models:\n\n- **_Impact on AI/ML theory:_** DPA has demonstrated interpretable solutions at the AI/ML theoretical level in channel selection, which helps to reveal the \"black box\" characteristics of deep networks. Especially from the backward perspective, DPA aligns well with the principles of theory-based backward gradient attribution, identifying irrelevant channels based on gradient, uncovering the contributions of each channel to the model's final decision, and achieving more precise feature selection. This is different from the activation function that relies only on forward propagation. DPA can provide new insights into the design theory of activation mechanisms. Additionally, by effectively inhibiting irrelevant channels, DPA not only improves the model accuracy, but also promotes a more sparse neural representation, which is closely related to research in sparse coding and compressive sensing.\n\n- **_Impact on cogsci/neuroscience applications:_** The ANN design is strongly influenced by the working patterns of the human brain. The proposed DPA takes inspiration from the sparse activation pattern observed in biological neural networks. This indicates that by simulating the characteristics of biological neural networks, we could potentially make up for the imperfections of current ANNs. If possible, future research might investigate the utilization of neuroimaging and computational neuroscience methods to gain new insights into simulating the properties of biological neural networks.\n\n> **W2:** Minor: the paper does not distinguish between sparse connectivity and “activation sparsity”, and doesn’t distinguish between “population sparsity” (only a few neurons active at any given time) and “lifetime sparsity” (a given neuron fires rarely, only for a small percentage of input images). These are often confused (or not distinguished) in the ML and Neuro literatures, and might be worth being clear about which one you are referring to (it seems like category-level lifetime sparsity?).\n\nThank you for your constructive comment. We apologize for not clearly distinguishing between the terms \"sparse connectivity\" and \"activation sparsity\", and between \"population sparsity\" and \"lifetime sparsity\". As you said, the correct terms of sparsity that our paper aimed to achieve are \"activation sparsity\" and \"category-level lifetime sparsity\". We will correct it appropriately in the final revised version.\n\n> **W3:** Minor: no mention of dropout, which directly impacts activation sparsity.\n\nThank you for your constructive suggestion. Here, we present additional experiments comparing DPA with Dropout, which directly impacts activation sparsity:\n\n|Top-1 Acc / %|ViT-Tiny|ResNet-18|\n|-|-|-|\n|ReLU+Dropout (ratio=0.1)|67.0|76.2|\n|ReLU+Dropout (ratio=0.2)|67.6|76.1|\n|ReLU+Dropout (ratio=0.5)|65.9|76.2|\n|GELU+Dropout (ratio=0.1)|67.3|76.0|\n|GELU+Dropout (ratio=0.2)|67.2|76.1|\n|GELU+Dropout (ratio=0.5)|65.5|75.8|\n|DPA|**70.5**|**76.8**|\n\nThe results suggest that Dropout has a limited impact on improving performance. One possible reason is that randomly forcing activation responses to zero during training cannot effectively transfer knowledge to the testing phase.\n\n> **W4:** Minor: **(A)** How did you identify and manually remove irrelevant channels? (Fig. 3)? Are these just the low activations? **(B)** Would a channel norm on this layer have the same effect/benefit?\n\nWe are sincerely sorry for the confusion.\n\n**(A)** Channels whose mean response distribution before the activation is lower than the activation threshold are considered potentially irrelevant and are highlighted by red arrows in Fig. 3(a). The procedure utilized for manually removing the irrelevant channels in Fig. 3(b) is forcing the responses of irrelevant channels indicated by red arrows below the threshold. In the paper, the activation threshold is set at zero; thereby, we forcibly bring the responses of these irrelevant channels down to zero (not low activations) as well.\n\n**(B)** Fig. 3(b) is a confirmatory experiment on the training set. Forcibly setting responses from irrelevant channels to zero on the training set cannot generalize the knowledge to the testing set. Therefore, to address this challenge, we proposed channel denoising (channel norm) during training, allowing the network to learn how to reduce the response from irrelevant channels in the testing stage. Through this approach, we expect to approximate the way of manually removing irrelevant channels in Fig. 3(b) as much as possible.\n\n> **Q1:** Minor: Have you compared DPA to other regularlization methods that lead to greater sparsity?\n\nThank you for your constructive suggestion. Yes, our paper compares Softplus, SiLU, ReLU, and GELU, which can result in sparse activations. In addition, we also compare DPA to Dropout, which leads to greater sparsity. Our response to **W3** presents the results of this comparison, showing that DPA performs better than Dropout.", "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": "EPoaoGWDmo", "reviewer": "Reviewer_YhhA", "summary": "The authors argue that sparsity in the activations is a desirable property and should be enforced. They observe that there exist category-specific channels in the network's activations which have a high value only for specific categories while other channels remain low. These low activations are considered as noise that impairs performance and should be removed.\nTo this end, the DPA method is introduced which tracks for a given category the intensity of activations per channel (and gradient magnitudes) and supresses channels with low intensity. The resulting DPA activation is used as a replacement for activations of transformer-based models and in the last block of CNN-based models. Experiments show consistent improvements over other activation functions, especially in transformers.", "questions": "My main concern regards the fairness of the experiments, in particular the degree to which the good performance of DPA is due to the choice of the hyperparameters. How robust is DPA when other hyperparameters are chosen? The authors state that the $\\lambda$ parameter of the DPA loss was varied depending on network and dataset. Was this parameter selection conducted on the test set (Fig. 7 from the appendix suggests this, as the value for $\\lambda=1$ is the one reported in Tab. 1)? Were parameters of the other activation functions also varied? \nAs mentioned in weaknesses, in some cases (I only checked a subset) the reported scores of DPA are lower than the corresponding ReLU-based state-of-the art. Does DPA consistently improve scores here, too? One way to demonstrate this would be taking a somewhat start-of-the-art Imagenet model like the ResNet18 using the training from [1] and show that DPA improves performance here, too.", "limitations": "- Limited to settings where categories are present during training. Hence, self-supervised training is not supported. This could be made clearer in the text.", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- Substantial effect for transformers, potentially impactful.\n- Clear presentation for most parts.\n- Code is provided (although I could not find the experiment configurations).", "weaknesses": "- The key results reported in Tab. 1 and Tab.2 were conducted using the author's own evaluation. On ImageNet-1K the respective original papers report accuracies of 75.1 (vs. 75.2 DPA) for PVT-Tiny and 81.5 (vs. 77.8 DPA) for TNT-small. ResNet18 achieves a score of 71.5 (vs. 70.8 DPA) with an improved trainig procedure [1].\n- The effect sizes are small. For smaller datasets (CIFAR and ImageNet-100) standard deviations over multiple training runs should be reported for DPA.\n- Sometimes the paper writing is unclear: \n    - Sec. 4.1 \"can replace all existing activations in each block\": Does this mean that the softmax activation is replaced?\n- Given the substantial differences between biological neurons and ANNs, I don't think one can conclude from the observation of sparse activations in biological networks that this is necessarily also a desirable property for ANNs.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> **Q1: (A)** How robust is DPA when other hyperparameters are chosen? The authors state that the $λ$ parameter of the DPA loss was varied depending on network and dataset. **(B)** Was this parameter selection conducted on the test set? **(C)** Were parameters of the other activation functions also varied?\n\nWe appreciate your valuable feedback and apologize for any confusion.\n\n**(A)** The hyperparameters ($m$ and $λ$) are robust when their values are not extreme (Please refer to paper Sec. A.3 & Fig. 6-7). The DPA can consistently bring performance improvements when $λ$ is small, and too large $λ$ can result in negative side effects. In fact, for most experiments (CaiT & PVT on CIFAR-100, and all the models on CIFAR-10 & ImageNet-{100,1K}), since hyperparameter selection is quite time-consuming and also for fair comparison, **we did not select $λ$ but empirically used the default $λ$ as 1 (see Lines 484-485).** If we were to conduct hyperparameter search for each experiment, the performance of our method might be further improved.\n\n**(B)** We regret any confusion caused by the misleading title \"Hyperparameter Selection\" for Sec. A.3. It should have been correctly referred to as **\"Impact of Hyperparameters on Model Performance\"**. In fact, the original intention of Sec. A.3 was to analyze the impact of hyperparameters on model performance for few and specific models and datasets on the test set, rather than performing hyperparameter selection for each experiment. Most experiments have their hyperparameters set uniformly ($λ$=1) based on the aforementioned analysis (see Lines 484-485 & Fig. 6-8). Please also refer to **(A)** and **Global Response** above.\n\n**(C)** ReLU, GELU, and Softplus do not contain parameters, and the parameters in ELU, SELU, SiLU, and GDN are trainable.\n\n> **Q2:** ... in some cases the reported scores of DPA are lower than the corresponding ReLU-based state-of-the art. Does DPA consistently improve scores here, too? One way to demonstrate this would be taking a somewhat start-of-the-art Imagenet model like the ResNet18 using the training from [1] ...\n\nThanks for the constructive comment.\n\nFor training Transformers, the baseline models and the training settings on ImageNet-1K were taken from timm. We apologize for using a smaller batch size and fewer GPUs than previous literature during training due to the limited computing resources we had, which might result in the difference between the results we obtained and those reported in previous literature. However, to maintain fairness in comparison, we have ensured that each experiment in a set of comparative studies used the same public training settings.\n\nFor training CNNs, our baselines' performance has already reached the ones reported in the original literature. We have also maintained fairness in comparison by using the same public training settings in each set of comparative studies. Additionally, we used the improved training procedure in [1] and trained the ResNet-18 on our local devices. The results are as follows, which also showcases DPA's effectiveness.\n|Top-1 Acc / %|ResNet-18|\n|-|-|\n|ReLU|71.4|\n|GELU|71.2|\n|DPA|**71.8**|\n> **W1:** The key results reported in Tab.1 and Tab.2 were conducted using the author's own evaluation ...\n\nPlease refer to **Q2** above.\n> **W2:** ... For smaller datasets (CIFAR and ImageNet-100) standard deviations over multiple training runs should be reported for DPA.\n\nWe are sincerely sorry for the confusion. Actually, the numerical results in the paper are the average under 3 random seeds (42, 0, 100), and the results are stable. For example, here are the detailed results of training ViT-Tiny and ResNet-18 on CIFAR-100:\n|Top-1 Acc / %|ViT-Tiny|ResNet-18|\n|-|-|-|\n|ReLU|65.9, 65.4, 65.7|75.7, 75.8, 75.7|\n|GELU|65.4, 65.4, 65.5|75.5, 75.6, 75.6|\n|DPA|70.8, 70.2, 70.6|76.9, 76.6, 76.7|\n\nWe will include standard deviations in the revised version.\n> **W3:** Sec. 4.1 \"can replace all existing activations in each block\": Does this mean that the softmax activation is replaced?\n\nWe apologize for the confusion. The softmax is not replaced. We will revise it to \"can replace all existing activations (except for the softmax) in each block\".\n> **W4:** ... I don't think one can conclude from the observation of sparse activations in biological networks that this is necessarily also a desirable property for ANNs.\n\nThanks for the interesting comment. We would like to gently clarify that our \"conclusion\" (or rather **\"conjecture\"**) regarding \"sparse activation is a desirable property for ANNs\" was not solely derived from the observation of sparse activations in biological networks. Instead, we supported our **conjecture** through relevant literature and extensive experiments, demonstrating that sparse activations do provide advantages to ANNs:\n\n- Connections within biological networks are sparse (our paper Lines 3-4 & 31-33). ANNs were originally designed to mimic biological networks. The sparse representation in ANNs has also shown notable benefits to network interpretability and generalization [1-3] (our paper Lines 4-5 & 33-34). Notably, the original paper of ReLU [3] also used similar writing logic. Inspired by biological sparse activations, the paper [3] designed the ReLU and demonstrated the advantages of sparsity in ANNs.\n\n  [1] Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 1996.\n\n  [2] Sparse feature learning for deep belief networks. NIPS, 2007.\n\n  [3] Deep sparse rectifier neural networks. AISTATS, 2011.\n\n- The sparse activation is the focus of our study, offering numerous benefits to ANNs. Directly supported by the confirmatory experiment in Fig. 3(b), forcibly constructing sparse activations for each category enhances training accuracy. The proposed DPA denoises redundant/irrelevant channels, leading to sparse activations and performance gains. These findings collectively validate the beneficial role of sparse activations in ANNs.", "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": "zP1KxmFkI3", "reviewer": "Reviewer_A1s7", "summary": "Artificial neural networks apply the principles of the human brain and leverage sparse representations to their advantage. However, existing activation methods still struggle to suppress irrelevant signals, affecting the network's decision-making. To overcome this, a novel Dual-Perspective Activation (DPA) mechanism is proposed, which efficiently identifies and denoises channels with weak correlation through an online updating criterion from both forward and backward perspectives while not affecting the activation response of other channels with high correlation. Extensive experiments demonstrate that DPA facilitates sparser neural representations and outperforms existing activation methods, and it applies to various model architectures across multiple tasks and domains.", "questions": "1. Please explain why the channels pointed out by red arrows in Fig. 3(a) are potentially irrelevant channels, in order to enhance readers' understanding. Including examples or case studies where similar channels were found to be irrelevant in other contexts might also reinforce the explanation.\n\n2. Explain the exact procedure utilized for manually removing the irrelevant channels. Is it by forcing the irrelevant channels in Fig. 3(a) to zero, or by any other way?\n\n3. Does the ability of the forward-backward criterion to make judgments get impacted by the model's performance? Additionally, when the judgment is suboptimal, will it influence the model's learning trajectory?\n\n4. This paper achieves sparsity of features/representations, which is good. However, in some cases, sparse representation may not be the most suitable option. For example, if the data is not sparse, using sparse representation may lead to loss of information, impeding the model from learning complex patterns. Is sparse representation consistently beneficial for this study? Are there more factors that need to be taken into account?", "limitations": "The authors include a detailed section on the limitations of the work.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The proposed DPA method starts from a novel joint forward-backward perspective. By designing forward and backward memories to track each channel's historical response and gradient, a criterion is established to identify irrelevant channels and denoise them. The design of the forward-backward criterion is smooth and natural, adhering to the principles of activation response and gradient attribution.\n\n2. The idea is interesting and presented coherently. The method design is smooth and natural. The literature review on activation and gradient attribution is comprehensive. The method achieves desired sparse representations and performance gains. \n\n3. The paper is well-organized. The problem, motivation, methodology, and results descriptions are easy to understand.  \n\n4. This method improves the model's performance from an interpretable perspective and is versatile for various model architectures (CNN, Transformer, MLP, etc.) and different tasks and domains.", "weaknesses": "1. Some claims seem not so clear. For the channel activation distribution observed in Figure 3(a), providing more detailed descriptions for the potentially irrelevant channels pointed out by the red arrows could further improve the clarity of the paper.\n\n2. It is not clear for some figures: For Fig. 3(b), the legend \"manually removing irrelevant channels\" needs more explanation. The authors do not explain how exactly the irrelevant channels are manually removed.\n\n3. The benefits of sparse representation are not convincing enough. Considering that sparse representation may not always be beneficial, additional discussion on the pros and cons of sparsity for this work could help enhance the main claim of the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> **Q1:** Please explain why the channels pointed out by red arrows in Fig. 3(a) are potentially irrelevant channels, in order to enhance readers' understanding. Including examples or case studies where similar channels were found to be irrelevant in other contexts might also reinforce the explanation.\n\nThank you for your constructive suggestion. Commonly used activation functions such as ReLU generally perform by setting an activation threshold, mimicking the membrane potential in biological neurons to suppress irrelevant signals while allowing useful signals to pass. During network learning, relevant signals tend to be above the threshold, whereas irrelevant signals tend to be below it, which is consistent with the principle of threshold activation. Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs, and Fig. 3(a) shows that the activation distributions of certain channels, indicated by the red arrows, are truncated by the threshold and are concentrated in a small range above it. Therefore, we consider that these channels are potentially irrelevant and should not have any response. That is, the granularity of our claim of signal correlation is at the channel level. In order to support our point, we conducted a confirmatory experiment, as shown in Fig. 3(b), where the potential irrelevant channels indicated by the red arrows were manually removed by forcing their responses below the activation threshold. As expected, the training accuracy substantially improved, providing evidence that these channels are indeed potentially irrelevant. We will expand upon the discussion of this section in the final revised version.\n\n> **Q2:** Explain the exact procedure utilized for manually removing the irrelevant channels. Is it by forcing the irrelevant channels in Fig. 3(a) to zero, or by any other way?\n\nSorry for the confusion. Channels whose mean response distribution is lower than the response threshold are considered potentially irrelevant and are highlighted by red arrows in Fig. 3(a). The procedure utilized for manually removing the irrelevant channels is forcing the responses of irrelevant channels indicated by red arrows below the threshold. In the paper, the activation threshold is set at zero, thereby we forcibly bring the responses of these irrelevant channels down to zero as well. We will include this detail in the final revised version.\n\n> **Q3:** Does the ability of the forward-backward criterion to make judgments get impacted by the model's performance? Additionally, when the judgment is suboptimal, will it influence the model's learning trajectory?\n\nThanks for the insightful comment. The channel denoising loss $L_{ch}$ is maintained as a weak constraint throughout the training process. \n\nThe responses at the beginning of training indeed exhibit considerable noise and make suboptimal judgments. Setting channel denoising to a high intensity during the initial stages can indeed affect convergence. Hence, we adopt $L_{ch}$ as a weak regularization term, where we adjust the weight of $L_{ch}$ to maintain it an order of magnitude smaller than $L_{task}$. This strategic approach ensures that $L_{task}$ remains dominant, effectively dictating the range of feature distribution. As long as the $L_{task}$ learns much faster than $L_{ch}$, the model's performance will not be affected by early suboptimal judgments, and the judgments will become more accurate as the model's performance improves.\n\nWe also considered alternatives, such as activating $L_{ch}$ after a certain number of iterations or gradually increasing the weight of $L_{ch}$ from zero at the beginning of training. However, we observed that foregoing these steps did not yield negative effects during initial training. This observation aligns with our implementation of the warm-up learning rate scheduler, which also serves to alleviate this concern to a certain extent.\n\n> **Q4:** This paper achieves sparsity of features/representations, which is good. However, in some cases, sparse representation may not be the most suitable option. For example, if the data is not sparse, using sparse representation may lead to loss of information, impeding the model from learning complex patterns. Is sparse representation consistently beneficial for this study? Are there more factors that need to be taken into account?\n\nThanks for the interesting comment. Yes, sparse representation is the goal of this study, and it does bring a lot of benefits, which can be directly supported by the confirmatory experiment, as shown in Fig. 3(b). By manually removing the irrelevant channels for each category (which is equivalent to forcibly constructing sparse representation), there is a substantial improvement in the training accuracy. Moreover, the observation in Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs. The proposed DPA effectively denoises redundant channels while not affecting relevant channels, resulting in sparse representation and performance enhancements. All of these collectively validate that the role of sparse representation in this study is to eliminate redundant signals while preserving key signals, rather than causing the loss of information.", "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": "n5IpTiLtK7", "reviewer": "Reviewer_4FwJ", "summary": "This paper introduces a novel activation mechanism, namely Dual-Perspective Activation (DPA), to identify irrelevant channels and thus apply channel denoising for the ANN architecture. The proposed DPA incorporates criteria established and updated online from both forward and backward propagation perspectives while preserving activation responses from relevant channels, which can effectively eliminate the interference of irrelevant or redundant features, thereby improving the overall performance of the neural network. \n\nMoreover, the authors conduct extensive experiments across various mainstream ANN architectures and datasets, as well as multiple tasks and domains, where the results show (1) DPA is parameterless and fast, (2) DPA achieves remarkable performance compared to existing activation counterparts, and (3) DPA can be applied to other tasks and domains.", "questions": "- It would be helpful if the authors could explore and compare the performance of more complex channel selection techniques to determine the most appropriate method. \n\n- In Lines 105-107, the authors claim that each category shows a strong relation with its specific channels, and ideally, the other channels should not generate any responses. Please provide additional evidence in support of the second half of the claim.\n\n- In Lines 198-199, the authors apply the DPA to the last block in CNN. Are the high-level semantics the main reason for this choice? Why is this approach taken? Please provide a detailed explanation.\n\n- In Figure 6, the value sampling of momentum $m$ does not follow any particular pattern, and the prediction performance does not exhibit significant variations across different $m$ values. Please provide a detailed explanation.", "limitations": "The paper has discussed the potential limitations and future directions of the research. Moreover, there is no societal impact from the work performed.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This paper is meticulously crafted, with a well-structured and clarified presentation.\n\n- The motivation originates from detailed and clear explorations of ANN activation mechanisms by the authors, which are valuable and deserve to be investigated.\n\n- The idea of combining both forward and backward perspectives to track and evaluate the importance of each channel in real time sounds novel and valid.\n\n- The theoretical foundations and experimental validations are detailed and sufficient.\n\n- The proposed method can perform various other tasks or domains, including vision and non-vision tasks.", "weaknesses": "- The authors have not provided a clear justification for why the intersection operation is the only suitable channel selection approach.\n\n- While the authors claim in Lines 105-107 that each category shows a strong relation with its specific channels, more sufficient evidence would be advantageous to support the second part of their claim, which states that the other channels should not generate any responses.\n\n- The authors have not explored the impact of applying the DPA to different layers of the CNN and presented a more thorough analysis to justify their design choice.\n\n- In Figure 6, the authors may not have thoroughly investigated the impact of the momentum parameter $m$ on the model's performance, and their choice of $m$ values may not have been well-justified.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "> **Q1:** It would be helpful if the authors could explore and compare the performance of more complex channel selection techniques to determine the most appropriate method. (Corresponding to **W1:** The authors have not provided a clear justification for why the intersection operation is the only suitable channel selection approach.)\n\nThank you for your comment. Firstly, the proposed forward-backward criterion has been carefully designed, where the forward criterion follows the principle of threshold activation, and the backward criterion follows the principle of gradient attribution. Using an intersection of these two perspectives allows for more accurate judgments compared to relying solely on a single perspective. Moreover, we have compared the forward-backward intersection operation with forward only, backward only, and forward-backward union operations, respectively. The results in Sec. 4.3 & Tab. 3 indicate that the intersection operation performs the best. Therefore, the forward-backward intersection operation currently stands as the best and most reasonable channel selection technique.\n\n> **Q2:** In Lines 105-107, the authors claim that each category shows a strong relation with its specific channels, and ideally, the other channels should not generate any responses. Please provide additional evidence in support of the second half of the claim.\n\nThanks for the constructive suggestion. Commonly used activation functions such as ReLU generally perform by setting an activation threshold, mimicking the membrane potential in biological neurons to suppress irrelevant signals while allowing useful signals to pass. During network learning, relevant signals tend to be above the threshold, whereas irrelevant signals tend to be below it, which is consistent to the principle of threshold activation. Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs, and Fig. 3(a) shows that the activation distributions of certain channels, indicated by the red arrows, are truncated by the threshold and are concentrated in a small range above it. Therefore, we consider that these channels are potentially irrelevant which should not have any response. That is, the granularity of our claim of signal correlation is at the channel level. In order to support our point, we conducted a confirmatory experiment, as shown in Fig. 3(b), where the potential irrelevant channels indicated by the red arrows were manually removed by forcing their responses below the activation threshold. As expected, the training accuracy substantially improvements, providing evidence that these channels are indeed potentially irrelevant.\n\n> **Q3:** In Lines 198-199, the authors apply the DPA to the last block in CNN. Are the high-level semantics the main reason for this choice? Why is this approach taken? Please provide a detailed explanation.\n\nThanks for the comment. Yes, the high-level semantics are the main reason. Previous works have shown that high-level semantics in CNNs only exist in deep representations [1,2]. These features are crucial for the downstream tasks. Features in the shallow layers of CNNs are too concrete. Therefore, imposing the regularization to a channel (an element) cannot directly control the change in the corresponding space-level feature map. Moreover, we have explored the impact of applying the DPA to different layers of ResNet-18 as follows, where L4 is the last layer:\n\n|**Constrained Layer(s)**|Top-1 Acc / %|**Constrained Layer(s)**|Top-1 Acc / %|\n|-|-|-|-|\n|L1|76.2|L1-3|76.3|\n|L2|76.0|L3-4|76.7|\n|L3|76.0|L2-4|76.6|\n|L4|76.8|L1-4|76.8|\n\nThe results indicate that applying the constraint to shallow layers has little effect, and only constraining the last layer can achieve the optimal effect.\n\n[1] Raghu et al., Do vision transformers see like convolutional neural networks? NeurIPS 2021\n\n[2]  Selvaraju et al., Grad-CAM: Visual explanations from deep networks via gradient-based localization. ICCV 2017\n\n> **Q4:** In Figure 6, the value sampling of momentum $m$ does not follow any particular pattern, and the prediction performance does not exhibit significant variations across different $m$ values. Please provide a detailed explanation.\n\nWe appreciate your comment. Theoretically, a high value of $m$ risks making the mean value unstable, and conversely, a low value of $m$ smoothens the mean value update, but it may cause the mean value to lag behind. According to our analyses (see Appendix A.3) on the ViT-Tiny model trained on CIFAR-100, the network's performance is not sensitive to the $m$ between around 0.2 and 0.99, from which $m$=0.9 performs the best, and extremely small $m$ values lead to negative effects. Therefore, for the rest of the experiments presented in the paper, we empirically set the $m$ to 0.9 without too much consideration. For the prediction performance that does not exhibit significant variations across different $m$ values, we think this is a good thing, as the model performance with the proposed DPA is robust to changes in the hyperparameter $m$, which indicates that a fixed $m$ can be adaptive across different models, datasets, and tasks, thereby reducing the adjustment costs.", "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:
&nbsp;

## **Global Response**

We thank all the reviewers for their time and constructive feedback, providing us with valuable insights into the areas that require improvement. We have meticulously addressed each reviewer's concerns through our comprehensive responses. In this global response, we would like to reiterate the important and common issues raised by the reviewers.

### ***Fairness in comparison***

To maintain fairness in comparison, we have strictly ensured that each experiment in a set of comparative studies used the same public training settings. The numerical results on Transformers, CNNs, and other architectures can fairly demonstrate the effectiveness of our proposed DPA method. 

### ***Impact of hyperparameters***

For the proposed DPA method, the impact of hyperparameters $m$, $λ$, and $τ$ on CIFAR-100 with ViT-Tiny are presented in the original paper Sec. A.3 and Fig. 6-8. The $τ$ has been verified to be optimal at zero. The network's performance is not sensitive to $m$ and $λ$ when their values are not extreme.

The original intention of Sec. A.3 was to analyze the impact of hyperparameters on model performance. We apologize for the confusion caused by the misleading title of Sec. A.3. We would like to clarify that we did not select hyperparameters for each experiment, as this process is quite time-consuming. This also highlights the fairness in comparison. The consistent performance gains brought by our method also indicate the insensitivity/generalizability of the hyperparameter values. Here is our detailed explanation:

- For hyperparameter $m$, we have only analyzed it on CIFAR-100 with ViT-Tiny and found that $m$=0.9 performed the best. Consequently, for the rest of the experiments presented in the paper, we empirically set the $m$ to 0.9 without too much consideration.
- For hyperparameter $λ$, we have only analyzed it on CIFAR-100 with ViT-Tiny, DeiT-Tiny, and TNT-Small. As shown in Fig. 7 of the original paper, too large $λ$ can result in negative side effects, and one thing is for sure: smaller $λ$ values do not hurt accuracy. Therefore, for the majority of our experiments (CaiT & PVT on CIFAR-100, and all the models on CIFAR-10 & ImageNet-{100,1K}), we did not select $λ$ but empirically used the default $λ$ as 1 (see our paper Lines 484-485).
- For hyperparameter $τ$, it has been verified to be optimal at zero in the original paper. Therefore, we set the $τ$ to 0 across all the experiments.

Notably, the performance of the proposed DPA method might be further improved if we were to conduct hyperparameter search on $m$ and $λ$ for each experiment.

### ***Benefits of sparse activations***

In this paper, we first conducted experiments (see our paper Fig. 2) to validate that each category is only correlated with sparse and specific channels in ANNs. Combined with the patterns of the activation response distribution (Fig. 3(a)), we conjectured that constructing sparse activations based on the above observations might be beneficial for ANNs in eliminating irrelevant/redundant features. Subsequently, we supported our conjecture through a review of relevant literature and extensive experiments, demonstrating that sparse activations do provide advantages to ANNs.

The sparse activation is the goal of this study, which can be directly supported by the confirmatory experiment, as shown in Fig. 3(b). By manually removing the irrelevant channels for each category (which is equivalent to forcibly constructing sparse activations), there is a substantial improvement in the training accuracy. Moreover, the observation in Fig. 2 indicates that each category is only correlated with sparse and specific channels in ANNs. The proposed DPA effectively denoises redundant channels while not affecting relevant channels, resulting in sparse representation and performance enhancements. All of these collectively validate the beneficial role of sparse activations in ANNs.

&nbsp;

We are committed to upholding a higher standard in our revised manuscript.

Finally, we would like to express our sincere gratitude again to all the reviewers for their meticulous review and constructive feedback on our manuscript, which will undoubtedly enhance the quality of our work.

Meta-review: The reviewers find the paper well motivated and well written with a clearly novel contribution. The experimental results are clear and convincing. The effect sizes are small for convets, meaning the benefit is potentially specific to the architecture chosen (bigger improvements for Transformers). The impact is also limited somewhat by showing improvements only on relatively basic image classification tasks (CIFAR, ImageNet). Overall it is a very solid paper that makes a good poster presentation but doesn't quite provide enough expected impact to qualify as a spotlight.
Decision: Accept (poster)