IM-Loss: Information Maximization Loss for Spiking Neural Networks
Authors: Yufei Guo
Yuanpei Chen
Liwen Zhang
Xiaode Liu
Yinglei Wang
Xuhui Huang
Zhe Ma
Venue: NeurIPS 2022 Accept (2022)

Abstract: Spiking Neural Network (SNN), recognized as a type of biologically plausible architecture, has recently drawn much research attention. It transmits information by $0/1$ spikes. This bio-mimetic mechanism of SNN demonstrates extreme energy efficiency since it avoids any multiplications on neuromorphic hardware. However, the forward-passing $0/1$ spike quantization will cause information loss and accuracy degradation. To deal with this problem, the Information maximization loss (IM-Loss) that aims at maximizing the information flow in the SNN is proposed in the paper. The IM-Loss not only enhances the information expressiveness of an SNN directly but also plays a part of the role of normalization without introducing any additional operations (\textit{e.g.}, bias and scaling) in the inference phase. Additionally, we introduce a novel differentiable spike activity estimation, Evolutionary Surrogate Gradients (ESG) in SNNs. By appointing automatic evolvable surrogate gradients for spike activity function, ESG can ensure sufficient model updates at the beginning and accurate gradients at the end of the training, resulting in both easy convergence and high task performance. Experimental results on both popular non-spiking static and neuromorphic datasets show that the SNN models trained by our method outperform the current state-of-the-art algorithms.

IM-Loss: Information Maximization Loss for Spiking Neural Networks
Yufei Guo", Yuanpei Chen", Liwen Zhang, Xiaode Liu, Yinglei Wang, Xuhui Huang, Zhe Ma Intelligent Science & Technology Academy of CASIC Eiguo@pku.edu. cn, rop4770163 com, mazhe_ ttte_tthue6..comm
Abstract
Spiking Neural Network (SNN), recognized as a type of biologically plausible architecture, has recently drawn much research attention. It transmits information by 0/1 spikes. This bio-mimetic mechanism of SNN demonstrates extreme energy efficiency since it avoids any multiplications on neuromorphic hardware. However, the paward-passing 0/1 spike quantization will cause information loss and accu- racy degradation. To deal with this problem, the Information maximization loss (IM-Loss)) that aims at maximizing the information flow in the SNN is proposed the paper. The IM-Loss not only enhances the information expressiveness of an SNN directly but also plays part of the role of normalization without introducing any additional operations (e.g., bias and scaling) in the inference phase. Addition- ally, we introduce novel differentiable spike activity estimation, Evolutionary Surrogate Gradients (ESG) in SNNs. By appointing automatic evolvable surrogate gradients for spike activity function, ESG can ensure sufficient model updates the beginning and accurate gradients at the end of the training. resulting in both easy convergence and high task performance. Experimental results on both popular non-spiking static and neuromorphic datasets show that the SNN models trained by our method outperform the current state-of-the-art algorithms.
Introduction
Recent progress in Artificial Neural Networks (ANNs) has been successfully applied in many machine intelligence fields. Although ANNs imitate the structure of the brain certain extent, their signal processing mechanism using operations on real, dense valued tensors, still differs from how the brain works based on sparse spike events. Being another sub-category of brain-inspired learning models, the Spiking Neural Networks (SNNs) utilize 0/1 binary spike signals to transmit information
between units, and ppatio-temporal dynamics to mimic brain behaviors [2T [3] 14] Unlike the ANN, where all neurons in the same layer need to be evaluated before passing information to the next layer, the SNN processes information asynchronously and sparsely based on sparse spike events. Benefitting from such an information processing paradigm, the SNN can efficiently run on specialized neuromorphic hardware (e.g., Loihi and has achieved substantial progress in recent years (28)
Although the SNN is more energy-efficient compared with the ANN, it still has some limitations achieve satisfactory task performance. Due the usage of spikes for information receiving and transmitting, the SNN needs to quantize real analog values into 0/ 1fformed spikes in implementation. This quantization causes information loss in forward propagation. There are some remarkable existing works that alleviate the problem of information loss of SNNs by adjusting the spike rate by learning more parameters. In 26 and (39,, method that aims learn the correct membrane leak-and and--innn threshold for each layer of the SNN was proposed. Results showed that learning the correct threshold
"Equal Contributions. t "orresponning author.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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Pre-spike
Post-spike
1100
Leaky Inlegrale-Fire
1001
2011
Weight Matrix
Evolutionary Surrogate Gradients
1001
Closifientio loss
0101
Epoch
Epoch
Epoch
Forward
Backward
Figure I: The overall workflow of the proposed algorithm, By minimizing the proposed IM-Loss, the information expressiveness of the SNN can be maximized directly. Meanwhile, the proposed ESG in the backward propagation will automatically evolve in each epoch to behave more like the accurate gradient of the spike activity.
can help increase the information capacity the SNN. wise choice of the firing threshold must be small enough that sufficient spikes are fired while also being large enough that avoids all neurons fired at the same time. Similarly, by incorporating the learnable membrane time parameter into the SNN, the parametric neuron 8 34] can not only increase the diversity of neurons but also the information expressiveness of the network. However, all these methods require more parameters and attempt to increase the information expressiveness of the SNN in an indirect manner. Meanwhile, the non-differentiable spike activities also prevent the SNN from producing accurate gradients in backward propagation, which increase the difficulty of the model optimization.
In this work, we propose information maximization (IM) loss deal with the information loss in SNNs. More specifically, we first analyze the information expressiveness ability of the SNN from the view of information entropy of the spikes. Then spike distribution loss is introduced for calculating the information loss, i.e., IM-Loss, of the SNN, thus the information expressiveness of the SNN can be maximized directly by minimizing this information loss, which benefits the accuracy improvement of the SNN. To overcome the non-differentiable spike activities during the model optimization in SNNs, we also introduce Evolutionary Surrogate Gradients (ESG) in the paper. The ESG can evolve automatically during training and provides pathway to bridge the gap between the pseudo derivative and appropriate derivative. With evolving, it not only ensures sufficient updating at the beginning but also accurate gradients calculation at the end of the training, resulting in networks with better performance. The overall workflow our algorithm can be seen in Fig I
Our contributions can be summarized as follows:
We propose the IM-Loss to preserve the information SNNs. It presents a new perspective to understand the ability of the SNN to express information. With the IM-Loss, a more accurate and deeper SNN.
train
We also introduce the ESG to effectively approximate the gradients of the spike activity function. The ESG can ensure both sufficient updating of weights at the beginning and accurate gradients at the end of the training in an evolutionary way so that the SNN would be more accurate and easier to converge.
Our method is evaluated on both static and dynamic datasets. Extensive experimental results show that our algorithm performs remarkably well across various network structures. To our best knowledge, this is the first work that can directly train deep SNNs from scratch without normalization or start techniques.
2
Related Work
In this section, we first briefly review the learning methods of SNNs to provide readers an overall understanding. Then we introduce the information theory used DNNs which gives us insight to design our method for handling information loss in SNNs.

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2.1 Learning Methods of Spiking Neural Networks
The learning algorithms for SNNs can be divided into three categories: (i) converting ANN to SNN (ANN2SNN) [9); (ii) unsupervised learning [6]; and (iii) supervised learning (24 26 3R 20 10 11. ANN2SNN converts special trained ANN to an SNN that yields the same input-output mapping for a given task. Since the research of the ANN has been very successful, ANN2SNN can gain competitive accuracy. Some recent conversion methods have achieved nearly loss-less accuracy with VGG and ResNet original ANN models [19]. However, this kind of method is restricted to rate- coding and can only handle static datasets. Moreover, ANN2SNN requires long timesteps (usually needs hundreds of timesteps) to converge and cannot exploit the spatio-temporal features during training for solving temporal tasks. Unsupervised learning is based on biological plausible local learning rules and is usually considered more biologically plausible than other categories. However, unsupervised learning can only train shallow SNNs and is hard to achieve desirable performance. Supervised learning uses the derivable approximation to overcome the non-differentiabiiity of the spike activities. Hence, the SNN can be optimized with gradient descent algorithms as the ANN and achieves high performance. Moreover, Supervised learning can greatly reduce the number of timesteps and handle dynamic datasets. Thus, supervised learning has increasingly aroused researchers' great interest in recent years. We focus on providing some insights to improve the performance of the supervised learning-based SNNs.
2.2 Information Theory in Deep Neural Networks
Information theory is widely used in DNNs, ranging from theoretical investigations (e.g., the gener- alization bound induced by mutual information (31) to practical applications (e.g., the variational information bottleneck in representation learning [2). It provides a useful way to understand the underlying behavior of random variables and this is key factor in developing and analyzing deep models. There are many popular information theorrei principles that have demonstrated great potential in DNNs 33). In [35, deep mergy-based models are trained with the f-divergence (a generalization of KL divergence) minimization. In reinforcement learning, the maximum entropy regularization is adopted to encourage exploration and avoid getting stuck in a local optima (1]. Mutual information maximization is used in [25] to improve the expressiveness of a model by shift- ing the distribution of weights zero-mean in every training iteration. In 3 training DNNs for classification is investigated via minimizing the information bottleneck functional. Despite the great success of information theory in DNNs, we find no related works in supervised learning of SNNs. In the paper, we propose the IM-Loss, which is based on the information maximization principle, to improve SNNs. Our implementation and idea of the information maximization are very different from these existing works, which may also provide a new idea to further improve these methods.
3 Preliminary
For better expression, we will first introduce the iterative Leaky Integrate-and-Finn (LIF) model and surrogate gradients of SNNs in detail, which also adopted in our method.
3.1 Explicitly Iterative LIF Model
The LIF neuron is a commonly used mathematical model to describe the behavior of neural activities, which includes spike firing and update of membrane potential. Formally, a LIF neuron in layer of an SNN with index can be given by
aul Ōt
T
- 1/, uf < Ven
(1)
fire a spike & ut Uyests ut 2 Ven
(2)
where uf is the membrane potential, Urest is the membrane resting potential, T is the membrane time constant to describe the membrane potential decaying, T! is the pre-synaptic input, and VT, is a given firing threshold. From Eq. we can see that uf actually acts as a leaky integrator of the pre-synaptic input T.. And Eq. 2 shows that when a neuron membrane potential reaches the firing threshold VnA. emits a spike to transfer its information to other neurons and reset its membrane potential to Ureat-
3

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The above differential expressions described in the continuous domain are difficult to be implemented on mainstream machine learning frameworks (e.g., Pytorch, Tensorflow), where the embedded automatic differentiation mechanism executes discretely. Alternatively, the iterative LIF model [33 used the Fuler method to solve the first-order differential equation of the LIF model. The iterative expression of the LIF model can be governed by
(1(
Tdecay u - 1) (t),
(1(() < Vin
fire spike & (1( Wyest (1(()) Vna
where Tdeeny is constant describe membrane potential decaying, (t( is the membrane potential in timestep i, and (t) is the pre-synaptic input. Since (t) is the accumulation of spikes from the neurons of layer 1 - connected to the current neuron, it can be described as (t() Σ, Way0;(t) (t). Where waj is the weight of j-th pre-synaptic of the current neuron, 0y(() is the output of the neuron from the previous layer, which interacts on the current neuron's s j-th pre-synaptic the moment of If set Ureset = 0, the whole iterative LIF model in both spatial and temporal domain can be determined by
(1()) Edonny u 1)(1 o - 1)) Σ Wazos(()
(5)
d(1)= = { 1, if v1(()) 2 Vih.
0, otherwise.
The iterative LIF model is friendly to be implemented on general machine learning programming frameworks.
3.2 Surrogate Gradients of SNNs
The spike activity function shown as Eq can be viewed as a variant of the sign function. Its derivative is O everywhere except for the infinity value Ven. Since the non-differentiabiiiyy of spike activity function, the back-propagatio challenge, we show the expression compute gradients of weights obtained by the spatial-temporal back-propagation (STBP) as follows,
cannot be applied directly for training SNN. To demonstrate this
JC
OL Dy' Ou Oy' ou oW
AW=
aw
where y denotes the target output vector, W is the matrix weights of the SNN, L is the loss function, and Øy is the gradient of the spike activity function. The weight update is computed as duz
= W nWW
(8)
Or' is either 0 almost everywhere or infinity at Vnn. where 7) is the learning rate. Considering that, Ou? AW is either everywhere or a very large value in a rare case, hence weights would likely not be changed updated to large value some times.
Most prior works adopted surrogate gradients (SG) overcome the non-differentiabiliy chal- 30). However, the SGs in existing methods are fixed during training, such strategy would limit the learning capacity of the network. We notice that the SG methods are also adopted in Quantization Neural Networks (QNNs) which also suffer from con-differnntiabiliyy. Some changeable surrogate gradient methods that can achieve better performance by changing SG in the training are proposed in QNNs [25 99. Combining characteristics of SNNs, evolutionary SG that can maintain strong updating ability in the early training phase and approach the accurate gradients gradually at the end of the training is introduced in the paper.
lenge 38 17
32
23
4 Methodology
In this paper, we argue that the challenge of training highly accurate spiking neural networks is mainly limited by the severe information loss caused by the spike activity function. To mitigate the problem, the IM-Loss is proposed. Furthermore, we also introduce the ESG to obtain the appropriate surrogate gradient for the non-differentiaalle spike activity in backward propagation.

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4.1 Information Maximization Loss
In the forward propagation, the membrane potential 0/1 spikes quantization of the spike activity function will cause information loss unquestionably. This is one of the main reasons why an SNN model cannot achieve as satisfactory performance as its ANN counterpart. Ideally, the spike tensor O should reflect the information of the membrane potential tensor U as much as possible. In the view of the information flow, to maximize the information flow from the full-precision tensor to the binary tensor O, the mutual information T(U:)) O) of the random variables U and O should be maximized as follows,
arg max / (U; - - U,0
where (O) is the entropy of O and HOU is the conditional entropy of O given U. It can be proved that, maximizing the mutual information [UU; O) is equivalent to maximize the information entropy (O) for SNNs (see Appendix A.l for detailed proofs) as follows,
arg max T(U: = H()).
(10)
0,0
Obviously, when the distribution of O satisfies p(0) p(1) = 0.5 the entropy H(O) is maximized, where the p is the marginal probability mass functions of the discrete variables Ô This means that to maximize the information flow from the full full-precision tensor U to the spike tensor O, the spike values should be evenly distributed, i.e., En<Vin p(u) = Σuzv, p(u) = 0.5. We set U(4) to denotes the q-quantile of U's elements in ascend order where 0 S q S 1. To maximize the (O)), we should have U/0.5 < VeL and U(0.51) 2 Veh- Since the U follows Gaussian distribution T0), U(.5)) is almost equal the mean value U. Then (Ü Vvh)²² can be regarded
metric of the information-lee caused by the quantization from the full-precision tensor U to the spike tensor O. Hereby, we define the proposed IM-Loss as:
LIM Σ (Ū
(11)
where Ug is the average membrane potential at all timesteps of 1-th layer, and is the total number of layers. Then the overall loss can be calculated as follows,
LTotal LCE + XLIM
(12)
where Leg is the cross-entropy loss, and À is a coefficient to balance the classification loss and the information loss. We set as this paper.
4.2 The Effect of IM-Loss
SNNs utilize 0/1 spikes to communicate between neurons. Benefitting from this information processing paradigm, SNNs run efficiently. However, since the spike rate of the network with random weights decreases sharply through layers, an SNN is difficult to train. In other words, the spike rate will usually soon become after several layers when training models from scratch, resulting in information flow disappearing and difficulty for training large and deep SNNs.
For better understanding, the layer-wise average spike rates of spiking CIFARNet and ResNet-19 initialized with random weights on the CIFAR10 test set are visualized in Fig. 2 Both networks were trained with a timestep of 4 and without normalization. When epoch is 0, i.e., the untrained networks, spike rates are becoming O in the deeper layers, resulting in untrainable networks. This means deep SNNs are not easy to train without any special techniques. Some works attempted to alleviate this phenomenon by using normalization techniques. However, normalization requires other additional operations. For instance, the bias operation consumes extra computations in the inference phase when implementing models on some specialized neuromorphic hardware. While for the case of epoch=l, where the proposed IM-Loss was applied, the spike rate in each layer can be restricted to an appropriate range (i.e,, about 50%), which enables the learning algorithm to train large and deep SNN. By maintaining an appropriate range for the spike rate, IM-Loss can effectively update the weights of the two deep SNNs even with random initialization. In this sense, IM-Loss also possesses the effect of normalization but without other additional operations or well-designed initialization strategies.
5

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61%
epoch=1000
epoch-1000 1000
epoch-1
epozh-1
opoch-o
opoch-0
679
63%
96
606
59%
22%
204
23%
Layers of CifarhNet
Layers Resne119
Figure 2: Layer-wise spike rate for CIFARNet (left) and ResNet-19 (right) during inference over entire CIFARIO test-set with epoch = O, and 1000.
5m5 5
k 5
0.8
0.2
-12 -0.7
-0.1
0.5
1.1
1.7
2.2
-1.2
-0.7
-0.1
0.5
1.1
1.7
2.2
Figure 3: The response curves of asymptotic function (left) and its corresponding gradient (right), under different values of the coefficient, k. The blue curves represent the spike activity function (left) and the true gradient of the spike activity (right).
To further demonstrate the information retention ability of IM-Loss, the of epoch=1000 in Fig. shows the spike rate the SNNs at the end of training. For ResNet-19, IM-Loss did not restrict the layers inside the residual blocks, since these layers tend to learn small perturbations which are incompatible with the restriction by IM-Loss. It can be seen that the spike rate of each layer restricted by IM-Loss is near 0.5, meaning the information flow be maximized by IM-Loss analyzed above.
4.3 Evolutionary Surrogate Gradients
The zero-derivative of spike activity function almost everywhere extremely prevents SNNs from training adequately. To our best knowledge, nearly all the prior works attempted to alleviate this problem by following the principle of replacing the gradient of the spike activity function with fixed SG in SNNs. As aforementioned, changeable surrogate gradient (CSG) methods in QNNs can achieve better performance. We guess that designing a suitable CSG can also increase accuracy in SNNs. To this end, we first introduce a differentiable asymptotic function to approximate the spike activity function follows,
((x) tanh(k(z Vox)) +
(13)
where the coefficient & determines the shape of the asymptotic function. The gradient of the asymptotic function, sp()) is used to replace the gradient the spike activity function.
For the sake of intuitive explanation, Fig. iillssrrates the influences of l on the asymptotic function (left) and corresponding gradient (right). can be seen that, when setting & with large value, more accurate gradient in backward can be obtained, as increase the difficulty of the training. Conversely, when becomes smaller, the gradient of the asymptotic function will tend be uniform and keep some relatively large value, thus the strong weight updating ability be obtained.

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ESG
ESG
10
10
10
10*
Figure 4: The accuracy curves of CIFARNet (left) and ResNet-19 (right) with k 10 k 10 and ESG. The ESG method maintains the updating ability at the early stage and progressively reduces the emor to achieve high accuracy.
Then we design the evolutionary asymptotic function (EvAF) as follows,
(xx) 2
tanh(K(i)(x= Vix)) +
(14)
where p(x) is the backward approximation substitute for the spike activity function and ( the coefficient that changes dynamically with the training epoch as follows,
( (10+ 10%) max + (10² - 10 ( Kmin
(15)
where Kmin and Kmar denotes the lower bound and the upper bound of the value range of K respectively, and is the index of epoch starting from 0 to N 1. In practice, we set Kmin = 100 and Kmaz 10º. Without using any additional hyper-parameter, K (i) will increase with the accumulation of training epochs. Driven by (f), EvAF can gradually evolve to the spike activity function, and more accurate gradient will be obtained, correspondingly. Such dynamically changing gradient will be used as the SG in our method, namely Evolutionary Surrogate Gradient (ESG). By introducing the modified asymptotic function, EvAF into the SNNs, both weight updating ability in the early stage of training and more accurate backward gradient at the end of training can be fulfilled by the proposed ESG.
4.4 The Effect of ESG
To demonstrate the effect of ESG, we compared the accuracy curves of spiking CIFARNet and ResNet-19 (with timestep 4) on CIFARIO using the gradient of the asymptotic function with = 10 k = 10a and ESG derived from EvAF with E [10", 10a] in backward. From the visualized comparison results shown in Fig. 4 can that the SNNs with a small-valued & have stronger updating ability and are easier to converge compared to the SNNs with a large k. The SGs of SNNs with a large are very close to the gradients the spike activities. in such case, most weights of these SNNs cannot be updated sufficiently. Hence these SNNs will suffer slow convergence and face severe performance degradation. Our ESG starts with Kmin the early stage of training, that the strong updating ability can make the SNN converge easily; then it ends with K Kmaz at the end of training thus the backward gradient will be more accurate resulting in a better- netter-performed SNN. In general, by using dynamically changing coefficient, our ESG encourages the SNN with both easier convergence and higher accuracy.
Experiments
In this section, extensive experiments were conducted to demonstrate the effectiveness of the pro- posed methods. The algorithm of the training process of our method is presented in Appendix A.2. The experiments include widely-used network structures including spiking CIFARNet [33]. ResNet-19 38), modified VGG-16 (26). and ResNet-34 [12 for both popular non-spiking static and neuromorphic datasets: CIFAR 1 10/100, ImageNet (ILSVRC12) and CIFAR 10-DVS [8 For being friendly with neuromorphic hardware, the max-pooling layer was replaced with the average-pooling layer in the used network architectures.
7

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Table 1: Ablation experiments for IM-Loss and ESG.
Architecture
Methods
Accuracy
w/o normalization
89.83%
w/ tdBN (38)
90.69%
w/ IM-Loss
90,90%
CIFARNet
W/ ESG
91.17%
w/ IM-Loss ESG
91.75%
w/ IM-Loss, ESG & tdBN
92.20% %
w/o normalization
91.23%
w/ tdBN 38
92.92%
w/ IM-Loss
94.29%
ResNet-19
w/ ESG
94.44%
w/ IM-Loss & ESG
94.64%
w/ IM-Loss, ESG & tdBN
95.40%
5.1 Ablation Study
To understand how our method works in practice, the ablation experiments for IM-Loss and ESG with spiking CIFARNet and Re (timestep 4) first conducted CIFARIO. To make fair comparison with tdBN, the rectangular surrogate function was used for the model without ESG compute gradients, in tdBN. The performances of the networks with IM-Loss and ESG alone and their combinations are shown in Table 1. For the networks without normalization or IM-Loss, there certain probability that they might not be trainable from scratch with inappropriate random initialization as aforemmentoned. Therefore, in this series of experiments, the models trained by IM-Loss after several iterations (training was stopped when the spike rates of the last layer were not 0) as the initialization, which can also be regarded as warm-start for the networks. Results in table I show that both IM-Loss and ESG can improve the networks' performances alone. And by using the combination of these two methods, the performances can be further improved. Moreover, our method also compatible with other advanced technologies, such as tdBN (38) hence it can be applied in a plug-in manner to enhance the learning capacity of SNNs together with other techniques.
5.2 Comparisons with State-of-the-art Methods
As reported in the ablation study, our algorithm combined with tdBN can achieve better results, hence this training technique also adopted in our method. The results listed in table 2.
On CIFAR1O, 10, our models achieve better performances than the other state-of-the-art methods (92.20% top-1 accuracy with only 4 timesteps by CIFARNet, 93.85% top-1 accuracy with only 5 timesteps by VGG-16, and 95.49% top-1 accuracy with only timesteps by ResNet-19). Moreover, with only 2 timesteps, timesteps by 0.69% accuracy. And our CIFARNet- outperform the CIFARNet in (33 with 12 timesteps and the one in 37 with 5 timesteps by 1.67% and 0.79% accuracy, respectively. These comparison results clearly show the effective latency reducing the ability of our method. And the same situation also be seen from the results more complex dataset, CIFAR100.
method using ResNet-19 19 as backbone still outperforms the STBP-tdBN with
model with only timesteps can also
ResNet-34 and VGG-16 were used as backbones on ImageNet. Our ResNet-34 and VGG-16 achieve 67.43744499 .343%%%% and 70.03% top-1 accuracy with only and 5 timesteps, respectively. Compared to STBP-tdB and TET, our ResNet-34 obtains 3.7 1% and 2.64% accuracy improvement, respectively. Compared to Diet-SNN 26 our VGG-16 obtains 1.65% accuracy improvement. The Dspike is some better than our method. However, the Dspike is very time-consuming than our method since is computed by finite difference manner. Evaluating finite difference could be mone-consuming. where for each single weight, the model should run two times evaluate the difference of the loss, and a model can have more than ten million parameters.
To further verify the effectiveness of our methods, the neuromorphic dataset, CIFARIO-DVS. was also used to evaluate the proposed method. With ResNet-19 as the backbone, achieves the best performance with 72.60% accuracy in 10 timesteps, which is 4.80% higher than STBP-tdBN.

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Table 2: Performance comparisons of method and other state-of-the-ar networks.
Dataset
Method
Type
Architecture
Timestep
Accuracy
SpikeNorm 29
ANN2SNN
VGG-16
2500
91.55%
Hybrid-Train 227
Hybrid
VGG-16
200
92.02%
Spike-basedBP 16
SNN training
ResNet-11
100
90.95%
STBP 33
SNN training
CIFARNet
12
90.53%
TSSL-BP 37
SNN training
CIFARNet
91.41%
Diet-SNN 26
SNN training
VGG-16
92.70% 5
PLIF g
SNN training
PLIFNet
93.50%
Dspike 20
SNN training
ResNet-18
94.25% 6
93.16% 6
CIFARIO
STBP-tdB 38
SNN training
ResNet-19
92.92% 4
92.34% 2
94.50% 4
TET
SNN training
ResNet-19
94.44%
2
94.16%
6
95.49 % =0.05
ResNet-19
95.40 10.08
Our method
SNN training
2
93.85%
VGG-16
93.85 % +0.11
CIFARNet
4
92.20 % +
BinarySNN 22
ANN2SNN
VGG-15
62
63.20%
CIFAR100
Diet-SNN (26
SNN training
VGG-16
5
69.67%
Our method
SNN training
VGG-16
70.18% #0.09
SpikeNorm 29
ANN2SNN
ResNet-34
2500
65.47%
SEW ResNet
SNN training
ResNet-34
4
67.04%
STBP-tdBN 38
SNN training
ResNet-34
63.72% 6
Diet-SNN 226
SNN training
VGG-16
69.00% 5
ImageNet
TET
SNN training
ResNet-34
64.79%
ResNet-34
68.19% 6
Dspike 20
SNN training
VGG-16
71.24%
ResNet-34
6
67.43%.1..J
Our method
SNN training
VGG-16
70.65%+1..0
Rollout 15
Streaming
DenseNet
10
66.80%
CIFARIO-DVS
STBP-tdBN
38
SNN training
ResNet-19
10
67.80%
Our method
SNN training
ResNet-19
10
72.60 % 0.08
6
Conclusion
This work aims at addressing two main problems for training accurate and deep SNNs: (i) the information flow loss caused by the 0/1 spike quantization; (ii) the training obstacle caused by the non-differentiable spike activity function. Inspired by the correlation between membrane potentials and binary spike signals from the view information entropy, we design a novel loss, IM-Loss, which can directly maximize the information expressiveness of SNN, that well-performed SNN can be obtained. It also plays part of the normalization's 's role but does not require additional operations or well-designed initialization strategies. Then, by incorporating dynamically changing coefficient into a differentiable asymptotic function, we introduce the ESG method for training SNN more appropriate way. ESG encourages the SNN to enjoy both easy convergence and high accuracy by adjusting the weight updating ability and the accuracy of the gradients. Combining these two methods, our method outperforms the ofate-of-the-ar methods.
Acknowledgment
This work is supported by grants from the National Natural Science Foundation of China under contracts No. 12202412 and 12204413..

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Technical report: supervised training of convolu-
11


Reviews:
[{"review_id": "u72L0FBrqi3", "reviewer": "Reviewer_jVTP", "summary": "The paper focuses on improving spiking neural networks' performance, and presents two major contributions:\n\n### 1. IM-loss\n\nThe information maximization loss (IM-loss) is evaluated by the $l_2$ distance between membrane potential and the neuron threshold. This form is based on three assumptions:\n\n- Maximizing the information flow between membrane potential and output spike train can benefit SNNs' accuracy performance.\n\n- The information flow is maximized when the spike trains' probability of 0 and 1 are equal.\n\n- The membrane potential follows the Gaussian distribution, which implies the distribution's mean value is roughly equal to the distribution's half probability point (cumulative distribution function = 0.5).\n\n### 2. ESG\n\nThe evolutionary surrogate gradient (ESG) adjusts the shape of the surrogate gradient function along the training process. The strategy is based on two assumptions:\n\n- The wider shape of the surrogated gradient of the activation function, the stronger weight updating ability.\n\n- The more accurate (sharp) of the gradient, the better training accuracy can be reached.\n\n", "questions": "1. Can you prove that the proposed regularizer can achieve a better trade-off between spiking sparsity and accuracy?\n\n2. If one includes the temporal dependency into consideration, will the results of information flow maximization change?\n\n3. What does the membrane potential distribution looks like in your experiment? Does it approximately follow the Gaussian distribution with a free-to-change mean value?\n\n4. How do you evaluate the difference between ESG and  [2] mentioned above?\n", "limitations": "Yes.", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Strengths\n\nThe paper is well-drafted and presents the ideas clearly. The ideas are well evaluated experimentally.\n\n### Weaknesses\n\n1. Novelty. \n\n- Adding homeostatic mechanisms to regularize spiking neuron's firing activity is not a new trick. Previously, [1] adds a regularizer to drive SNNs' firing activity more sparse to save energy. However in this work, the author proposed regularizer drives membrane potential near threshold, which potentially increases the firing activity and leads to poorer energy efficiency. \n\n- Updating the shape of the surrogated function is also not new. [2] proposed to automatically adjust the temperature of the surrogated activation function in order to achieve the best training performance. Comparing to this work, [2] is more flexible.\n\n2. Soundness\n\n- The theoretical reasons (see summary above) the authors proposed that lead to the IM-loss are questionable. First, information loss is necessary for classification tasks (The whole image is compressed through a neural network and leaves its classes information only in the output layer). Therefore we do not know whether maximizing informaton flow benefits the performance. Second, the measurement of information flow neglects the important temporal dependency of LIF neurons, so the result that p(0)=p(1)=0.5 maximizes the information flow based on elementary information theory is oversimplified. Third, the membrane potential actually does not follow the Gaussian dist with free to change mean value. The paper cites [3] here to back up their claim, yet [3] only mentioned that the membrane potential distribution approximately follows a *zero mean* Gaussian distribution.\n\n- The heuristic description of the ESG is also questionable. How do the authors evaluate the \"weight updating ability\"? I understand that too sharp a surrogated gradient function cannot sustain training, but the function is also not \"the wider the stronger\". Too wide the function is also harmful for training. Besides, it is also dubious to claim adjusting the function more and more accurate benefits the training of SNNs. Please refer to discussions in [2] [4] [5].\n\n\n[1] Zenke F, Ganguli S. Superspike: Supervised learning in multilayer spiking neural networks[J]. Neural computation, 2018, 30(6): 1514-1541.\n\n[2] Li Y, Guo Y, Zhang S, et al. Differentiable spike: Rethinking gradient-descent for training spiking neural networks[J]. Advances in Neural Information Processing Systems, 2021, 34: 23426-23439.\n\n[3] Zheng H, Wu Y, Deng L, et al. Going deeper with directly-trained larger spiking neural networks[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2021, 35(12): 11062-11070.\n\n[4] Zenke F, Vogels T P. The remarkable robustness of surrogate gradient learning for instilling complex function in spiking neural networks[J]. Neural computation, 2021, 33(4): 899-925.\n\n[5] Yang Y, Zhang W, Li P. Backpropagated neighborhood aggregation for accurate training of spiking neural networks[C]//International Conference on Machine Learning. PMLR, 2021: 11852-11862.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "nIKOaMSCJX8", "reviewer": "Reviewer_4Mt9", "summary": "The paper proposed the information maximization (IM) loss for training deep SNN which maximizes information flow of the network and indirectly provides normalization during training. The IM loss is constructed to strengthen the mutual information between the membrane potential and the following spiking activity. In addition, the ESG method is propossed to improve network training. Experiments on benchmark image classification tasks show that the method improves the accuracy of SNN, and on CIFAR10 it surpass current SOTA SNN.   ", "questions": "The ESG method seems quite intuitive and empirical, is there any theoretical justification that can help to support it?\n", "limitations": "It would be helpful if the potential negative impact of moving membrane potential towards the spiking threshold can be discussed.\nAll SOTA SNN works should be listed on table to avoid misleading.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The work proposed the IM loss to reduce information loss from membrane potential to spike, which moves the mean membrane potential towards the spiking threshold during training. The idea is new for the training of SNN and the soundness of the approach is sufficient, based on the derived equal relation between the mutual information (MI) of the membrane potential and the spike and the entropy of spiking distribution. However, driving the mean membrane potential near the threshold becomes an inductive bias, which could be suboptimal for the network performance under certain situation. Another outcome of the approach is that it increases the activation of the resulting network, which impairs the sparse computation advantage of SNN.\nThe ESG function is similar to the Dspike function (NeurIPS 2021, Yuhang Li, et. al), which should be cited.\nIn the experiment, except CIFAR10, the approach is outperformed by current SOTA SNN (e.g. Dspike (2021 NeurIPS), TET (2022 ICLR) have higher accuracies on CIFAR100, ImageNet and CIFAR10-DVS, though not listed on the table), leaving the general usage of the method questionable.\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "gaC8d6L9np2", "reviewer": "Reviewer_t7Yt", "summary": "The paper proposes an IM loss based training method for SNNs that shows high accuracy at low latency.", "questions": "Please see my above comments on weakness and clarify teh technical novelty of the work.", "limitations": "Please see weakness section comments.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "+The paper's experiments shows that the IM loss trains SNNs with SOTA results compared to works cited by the author.\n-The paper presents a direct training method using BP for SNNs. This work is very derivative and incremental. There is a lot of work from Priya Panda's group at Yale, Emre Neftci's group, and many others with regard to SNN training. The authors have failed to acknowledge most recent works and the method they are proposing is very incremental in the context of those works. Further, many recent works on SNNs have targeted larger datatsets including video segmenattion with direct training. \n-Recent works like [5] show SNN training at very low latency with novel architectures. [10] uses a BN rule to train temproal SNNs. Is there a relationship between the implicit IM loss normalizationa nd the expicit normalization employed in [10]?\n\nBelow is a list of publications (not exhaustive) that the author should check:\n\n[1] Towards spike-based machine intelligence with neuromorphic computing K Roy, A Jaiswal, P Panda Nature 575 (7784), 607-617\n\n[2] Enabling spike-based backpropagation for training deep neural network architectures C Lee, SS Sarwar, P Panda, G Srinivasan, K Roy Frontiers in neuroscience, 119\n\n[3] Rate Coding Or Direct Coding: Which One Is Better For Accurate, Robust, And Energy-Efficient Spiking Neural Networks? Y Kim, H Park, A Moitra, A Bhattacharjee, Y Venkatesha, P Panda ICASSP 2022-2022\n\n[4] Neuromorphic Data Augmentation for Training Spiking Neural Networks Y Li, Y Kim, H Park, T Geller, P Panda arXiv preprint arXiv:2203.06145\n\n[5] Neural architecture search for spiking neural networks Y Kim, Y Li, H Park, Y Venkatesha, P Panda arXiv preprint arXiv:2201.10355\n\n[6] Optimizing deeper spiking neural networks for dynamic vision sensing Y Kim, P Panda Neural Networks 144, 686-698\n\n[7] Federated Learning with Spiking Neural Networks Y Venkatesha, Y Kim, L Tassiulas, P Pand IEEE Transactions on Signal Processing 2021\n\n[8] Beyond classification: directly training spiking neural networks for semantic segmentation Y Kim, J Chough, P Panda arXiv preprint arXiv:2110.07742\n\n[9] Visual explanations from spiking neural networks using interspike intervals Y Kim, P Panda Scientific Reports 11, Article number: 19037 (2021)\n\n[10] Revisiting batch normalization for training low-latency deep spiking neural networks from scratch Y Kim, P Panda Frontiers in neuroscience, 1638", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "gD3KBnidxGt", "reviewer": "Reviewer_DHw2", "summary": "The manuscript tackles the problem of supervised learning in spiking neural nets (SNNs). The authors claim that SNNs loose information in feed-forward pass because of the binary nature of their responses and propose an information-maximizing loss function to reduce such loss. \nFor gradient back-propagation they propose to extend the popular surrogate gradient approach with a surrogate gradient who's spike activity function changes during the training. In multiple experiments the authors demonstrate advantages of their approach. ", "questions": "Section 4.2 is confusing. If the spikes can not reach the output as shown in figure 2, how the SNNs can be trained at all?\n\nThe dependence of results on the integration time of outputs is stated only for selected numbers (lines 283-291). It would be helpful to instead plot them as in figure  4. Without these plots these results seem as cherry-picked.\n\n", "limitations": "The authors did not address limitations of their approach.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths. The authors propose two interesting extensions of existing surrogate backprop learning method for SNNs. The first one, infomax-inspired loss, maximizes the entropy of individual neuronal outputs under the assumption of independent neuronal responses. This is a valuable insight that SNN community may find of interest. The second one, using a schedule to adjust the activation function is quite innovative. The experiments with two SNN architectures and ablations provide compelling evidence that the proposed approach has advantages over previous work.\nWeaknesses. While the aforementioned ideas are somewhat innovative, the implementation is quite limited. For example, the infomax assumes that the network outputs are independent, thus optimizing only spiking rate. Moreover, the \"Evolutionary Surrogate Gradients\" is essentially a manually set schedule for adjusting a (hyper)parameter, gradient width, with training time. THe form of ESG change with time is hand-picked and no experiments are offered to shed light as to why this form is preferred and how it compares with alternative schedules.\nI also found the term \"evolutionary\" highly confusing as the approach has nothing to do with evolutionary optimization, and only referes to the aforementioned manually selected dependence of gradient width on time. A much better term would be \"adjustable, train time-dependent\" or alike.\n\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept