Weighted Mutual Learning with Diversity-Driven Model Compression
Anonymous Author(s)
AffiliationAddress email
Abstract
Online distillation attracts attention from the community as it simplifies the traditional two-stage knowledge distillation process into a single stage.
Online distillation collaboratively trains a group of peer models, which are treated as students,and all students gain extra knowledge from each other.
However, memory consumption and diversity among students are two key challenges to the scalabilityand quality of online distillation.
To address the two challenges, this paper presentsa framework called Weighted Mutual Learning with Diversity-Driven Model Compression ( WML ) for online distillation.
First, at the base of a hierarchical structurewhere students share different parts, we leverage the structured network pruning togenerate diversified students with different models sizes, thus also helping reducethe memory requirements.
Second, rather than taking the average of students, thispaper, for the first time, leverages a bi-level formulation to estimate the relativeimportance of students with a close-form, to further boost the effectiveness of thedistillation from each other.
Extensive experiments show the generalization of theproposed framework, which outperforms existing online distillation methods on avariety of deep neural networks.
More interesting, as a byproduct, WML producesa series of students with different model sizes in a single run, which also achievescompetitive results compared with existing channel pruning methods.
Introduction
Deep neural networks (DNNs) have achieved impressive success for a variety of application fields,including computer vision [23, 39], natural language processing [2], time-series analytics [44] andso on [6, 41, 45].
However, the performance of DNNs is heavily dependent on model parameters andcomputations, which hinders its application on intelligent edge systems [17].
To relieve this issue,various techniques have been proposed to design lightweight models, including network pruning[15], network quantization [7] and neural architecture search [36].
Knowledge distillation [22],as a complementary method to further improve the performance of the lightweight models, cantransfer the discriminative ability from a high-capacity yet cumbersome teacher model to a smalland compact student model by encouraging the student to mimic the behavior of the teacher.
Thevanilla knowledge distillation [22], as shown in Figure 1 (a), includes two stages: it first trains thecumbersome teacher model, whose soft logits that contain informative dark knowledge [22] are thentransferred to a compact student model.
As the teacher is fixed during the knowledge transferring, thestudent can only learn from the teacher once it is trained, and the vanilla knowledge distillation is alsocalled offline distillation [12].
To further simplify the distillation process and relieve the restrictionwhen the larger-capacity teacher model is not available, the online distillation framework has beenproposed [4, 54, 55], which simultaneously trains a group of student models (a.k.a. peers) with similarstructures.
As each student can gain extra knowledge from each other, it is also called deep mutuallearning [54], as shown in Figure 1 (b).
Although online distillation conducts the distillation witha one-phase training scheme without pretraining a teacher, it has high memory consumption when
ResBlock
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ResNet (a): Vanilla Knowledge Distillation (b): Online Distillation (
[Figure]
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jointly training several independent models.
In addition, it is supposed to yield more informativeknowledge when diversity presents among students, while the similar structures in online distillationmay hinder the students from learning more informative knowledge from peers [9, 13].
In order to simultaneously overcome the two aforementioned difficulties, memory consumption anddiversity among peers, this paper proposes a novel framework, called Weighted Mutual Learningwith Diversity-Driven Model Compression ( WML ) for online distillation, as present in Figure 1(c).
Besides using a hierarchical structure where peers share different parts to reduce computationalcomplexity, we leverage the structured network pruning to generate diversified peer models underdifferent pruning ratios, which also further reduce the memory consumption.
On the other hand,simply treating the peers with different capacities to be equally important might neglect the diversityof all peer models, and limit the effectiveness of online distillation when learning from a group ofpeers with different capacities [9, 13].
In this paper, we formulate the weighted mutual learningbased online distillation as a bilevel optimization problem, where the inner loop is to learn compactpeers with the online distillation and the outer loop is to find suitable weights to determine a betteroptimization direction for knowledge distillation from a group of peers.
The weights are optimizedby the mirror descent [3, 5], and the hypergradient is analyzed in a theoretical way with a close-form.
Our formulation can be seen as a dynamic weighting strategy for online distillation, which adaptivelydistills knowledge from the peer models to a student.
A summary of our main contributions follows.
• First, this paper proposes a Weighted Mutual Learning with Diversity-Driven Model Com-
pression ( WML ) for online distillation, where the peer models share different parts in a
hierarchical structure and the structured network pruning is leveraged to further generate
diversified peers and reduce the memory consumption.
• Second, we formulate the weighted mutual learning based online distillation as a bilevel
optimization problem, and the hypergradient of optimizing the weights is derived with aclose-form.
The dynamic weighting strategy enables the online distillation to adaptivelydetermine the importance of each peer in distilling knowledge from a group of peers.
• Third, extensive experiments on several neural networks and three datasets verify the
effectiveness of the proposed framework, which significantly outperforms existing online
distillation and self-distillation methods.
More interesting, as a byproduct, WML can get
a series of pruned student models with different model sizes in a single run, which also
achieves competitive results when compared with existing channel pruning methods.
Related work2.1 Knowledge Distillation
Knowledge Distillation (KD) is the concept [22] that distills knowledge from a larger teacher modelto help the training of a smaller student model, by steering the student’s logits towards teacher’slogits, as shown in Figure 1 (a).
FitNet [37] further extends the feature maps as the learning targetinstead of logits, as shown in Figure 4 (a).
Rather than only learning from a single teacher, manyrecent studies [9, 13] investigate learning from a group of teachers, where the outputs of teachers areusually averaged to guide the student training, while how to effectively integrate different types ofknowledge from multiple teachers is less investigated [9, 13].
The traditional knowledge distillation isalso called offline distillation since the teacher models are first trained before distillation.
Differently,online distillation simultaneously trains a group of student models that can gain extra knowledgefrom each other without a pretrained teacher model, so it is also called the teacher-absent knowledgedistillation.
Deep mutual learning (DML) [54], in Figure 1 (b), is the first proposed online setting forknowledge distillation, which trains multiple peer models in a collaborative way that each model canbe seen as a teacher during others’ training process.
KDCL [13] further ensembles the output of allstudents as the teacher knowledge in the online distillation setting since the ensemble is supposed toyield better generalization ability than a single model [1].
To further reduce the training requirements,several recent works [55] enforce all students to share the same early blocks while equipped withindividual auxiliary head branches, shown in Figure 4 (b).
Although this paradigm can relieve theheavy memory consumption in online distillation, it suffers from the drawback of diversity as allpeers share the same backbone and with a similar structure.
Differently, Song and Chai [40] proposeda hierarchical structure so that the peers can share different parts in the early blocks, as show in4 (b).
Self-distillation is another recently-proposed distillation paradigm, which can be regardedas a special case of online distillation [12, 46, 50], shown in 4 (c).
Specifically, [50] leverages theknowledge from the deeper layers to guide the training for the shallow sections in the backbone.
Inthis paper, we consider a hierarchical structure [40] that each peer shares different parts and gainsweighted knowledge from other peers instead of the average ensemble.
Different from self-distillationthat reduces the “depth” to get peers, this paper leverage the channel pruning to “slim” models toget diversified peers.
More descriptions of the difference between the proposed framework and theexisting distillation frameworks are also described in Appendix B.
2.2 Network Pruning
Network pruning is an effective way to compress overparameterized neural networks by removingparameters with minimal performance degradation [47].
Based on the granularity, network pruningcan be divided into two types: unstructured and structured pruning, where the former individuallyremoves parameters in a network while the latter removes entire filters, channels, or even layers [34].
Although the unstructured pruning can mask most parameters in a network without performancedrop [11], it requires specific hardware or software to accelerate the sparse network’s inferencetime [10, 16].
Differently, structured pruning preserves the structural regularity and can acceleratenetwork on commodity hardware platforms [19, 28].
In this paper, we consider structured pruning forgeneric applications.
Next, the network pruning can happen after training vs. before training (a.k.a.at initialization) [42].
Most conventional pruning methods identify the redundant weights that areremoved with least degrading the performance of the trained model.
In contrast, recent works showthat the randomly initialized neural network can be pruned without incurring any training [26], where
SNIP [25], GraSP [43], and SynFlow [42] are three well-known metrics for the unstructured pruningat initialization.
[34] further extends these metrics for structured pruning through summing scores ofall parameters θ in a filter to determine its importance.
In this paper, we extend SNIP to determinethe pruning ratio for each layer at initialization as [34] demonstrates it is the most effective amongthe three to determine the filter importance for channel pruning at initialization.
Methodology
This section describes our Weighted Mutual Learning with Diversity-Driven Model Compression( WML ) framework for online distillation, which consists of three main parts: the overall structureand the optimization for learning a group of peer models, the pruning approach to get a series ofpeers with different model sizes, and a bi-level formulation based weighted mutual learning.
3.1 Overview Structure and Loss Function
Figure 1 (c) depicts the overall structure of the proposed WML framework, where we take ResNet-32,which is divided into three sections in terms of depth, as an example for easy understanding.
Differentfrom the most commonly-used auxiliary heads [55] that all peer models share the same part, weconsider a hierarchical structure [40] where each peer model shares different parts.
The framework issimilar to the binary tree, where the branches at the same levels are copies of each other, and eachpath is considered as a peer model.
In addition, we further prune each block in WML with differentratios to further enhance the diversity among peer models and also reduce the memory consumption.
Different from the vanilla knowledge distillation, which requires a much larger pretrained model asthe teacher, the online distillation directly learns from each other or the ensembles of students [1].
Inthis paper, we consider the linear combination of knowledge from all peer models, and the weight ofeach peer model is determined by a bi-level formulation which will be discussed in Sec.
This paper focuses on the multi-class classification problems, and X = { x n } Nn =1 is the trainingimages with N samples, Y = {
y n } Nn =1 is the corresponding labels.
The output logit for i-th peermodel is represented as z i , and its corresponding cross entropy loss is L CE which is computed withthe
z i and labels Y .
The overall loss to train the whole framework containing M peers is defined as:
[Equation]
where ω i indicates the importance of the i-th peer model and α is the hyperparameter to balance thesupervision from labels and teachers.
(cid:80)
Mj
=1 ω j KL
( z i , z j ) is the weighted knowledge from peers,which is one of the main differences between our WML and DML [54] in loss function, where DMLconsiders each peer equally important in distillation.
Another alternative distillation strategy is tocalculate the KL divergence between each student with the ensemble of all students [13], while [54]found it is not as competitive as directly learning from multiple teachers.
3.2 Diversifying Peer Models with Channel Pruning
Although the hierarchical structure can proportionally reduce the memory consumption as peersshare different blocks to reduce complexity, it still has higher computational cost than traditionalknowledge distillation.
To further reduce the memory requirements, we introduce the channelpruning, the most commonly-used paradigm in structured pruning, to our framework, which alsoencourage the diversity among homogenized peers.
The training-free network pruning has shownits superiority in finding competitive subnetwork with extreme efficiency [25, 42, 43], and [34]has demonstrates SNIP [25] is informative to determine the filter importance for channel pruning.
To be more specific, the relative importance of each filter f based on SNIP can be calculated as:
I f
[Equation]
L (
[Equation]
i )
∂θ i ⊙ θ i (cid:12)(cid:12)(cid:12) , where (cid:12)(cid:12)(cid:12) ∂
L ( θ i )
∂θ i ⊙ θ i (cid:12)(cid:12)(cid:12) is the SNIP score of parameter θ i .
This value gives an expectation of the impact on loss when the filter is pruned, and filters with smaller
SNIP scores tend to produce weak impact to the loss as compared to the other filters in that layer[34].
In this paper, we further propose a relative importance I l to determine the importance of eachlayer at initialization, which is defined as:
[Equation]
where N l is the number of parameters in layer l .
Given a pruning ratio P of a model, the number ofpruned parameters of each layer is then obtained by p l = P × N × ˜ I
l , where ˜ I l is a normalizationof 1 I l and N is the total number of parameters in the model, and the number of preserved filter iscalculated accordingly which aims to preserve more filters in a more important layer.
In the practicalimplementation, we set a upper bound of the pruned ratio for each layer to avoid layer collapse [43].
In this way, given different P to peers, we can get a series of peer models with different structures.
3.3 Weighted Distillation with Bi-level Formulation
The proposed framework contains M peer models whose outputs can be also combined to generatea powerful ensemble.
However, the generalization capacity of the peer model is different from the model size.
Intuitively, we would expect to raise the importance of model
i with the highest capacityin distillation, i.e., enlarging ω i when peer model i contains most parameters [4, 9].
In this paper, weconsider a dynamic weighting method to determine the importance of each peer, and the weightedmutual learning for online distillation can be formulated as a bilevel optimization problem:
[Equation]
where z ∗ i is obtained by training the whole framework θ with loss function in Eq.(1).
The innerloop is to optimize the whole network θ with the loss defined in Eq.(1), and the outer loop is toadjust the importance ω to make the weighted ensemble match the ground truth so that it reflects theimportance of each peer more precisely.
We define the loss function of inner loop optimization as
L 1 and outer loop as L 2 for simplicity.
Since z ∗ i is the local optimizer in the inner loop, Eq.(3) is acomplicated nested optimization problem [31, 35, 53].
In this paper, we consider a common one-stepunroll learning paradigm [31, 35] that θ ∗ =
θ − γ ∇ θ L 1 with learning rate γ , and the gradient for theouter loop (which is also called as hypergradient) can be formulated as:
[Equation]
However, it is still impractical to calculate the second-order information for a large neural network,e.g., ∂ 2 L 1 ∂ω∂θ .
The finite-difference approximation is usually leveraged to roughly approximate this term[31], while it only considers the first two terms with the Taylor expansion.
In the following theorem,we show that we can exactly calculate ∂ 2 L 1 ∂ω∂θ without approximation in our framework.
Theorem 1 With one-step unroll learning paradigm, the gradeint for ω i in Eq.
(3) is formulated as:
[Equation]
where L a = (1 − α )
L CE ( z i , Y ) + α (cid:80) Mj
=1 KL ( z j , z i ) .
Proof: Based on the definition of L 1 in Eq.(1), we have
[Equation]
Accordingly, Theorem 1 is proved.
□
Theorem 1 shows that the second-order term ∂ 2 L 1 ∂ω∂θ can be analyzed in a close-form without Taylorexpansion approximation.
Now that we can simply get the gradient to update model parameters θ
[Table] [Table]
and the weights for peers ω with autograd .
Since ω is a probability simplex that (cid:80) Mi =1 ω i = 1 , weuse the mirror descent to update ω [3, 5].
Algorithm 1 outlines our weighted mutual learning foronline distillation.
To be more specific, we first run several steps of SGD based on the loss functionin Eq.(1) to update model parameters θ with a fixed ω .
Then we calculate the gradient of ω i based on Eq.5, and run one step of mirror descent to update ω i that:
[Equation]
where η is the step size, and ω ki is the model importance for i-th peer in k-th step.
We repeat this loopuntil the stopping criterion meets.
Experiments
We perform a series of experiments to evaluate the effectiveness of our framework on seven convolutional neural networks with three image classification datasets.
We first compare our frameworkwith two self-distillation baselines, SD [50]and SCAN [51], and the deeply supervised net (DSN)[24], since they share similar structures as our WML.
Specifically, SD and SCAN add early-exitblocks to the shallow blocks to get peer models, where SCAN contains additional attention modules.
DSN shares a similar structure as SD while without knowledge distillation.
After that, we compared
WML with existing knowledge distillation and online distillation baselines.
More interesting, as abyproduct, we also compared the pruned models produced by our framework with channel pruningbaselines.
A series of ablation studies on dynamic weighting strategy and pruning are also discussed.
4.1 Comparison with Self-Distillation
For fair comparisons in this experiment, we consider 4 peer models in our WML, and also prune peermodels into similar model size as classifiers in self-distillation (SD) [50], where Model1-3 are underdifferent pruning ratios to match Classifier1-3 in self-distillation [50], and Model4 and Classifier4are the same as the baseline network.
More experiments with other pruning ratios for WML can befound in Sec.4.4 and Appendix D. We adapt our framework with several ResNets [18] and also the
MobileNetV2 [38], where results on CIFAR100 and ImageNet are present in Table 1 and Table 2,respectively.
There are two interesting pieces of evidence showing the advantage of the proposed WML on
CIFAR100.
Firstly , we can observe that WML leads to significant accuracy boosts, where our peer
Model4 outperforms baseline networks with an increment of 2.29% to 3.56% on CIFAR100 for the
[Table]
three networks. In addition, our peer models beat the most classifiers in the three self-distillationbaselines under similar model sizes, verifying the superiority of the proposed framework over selfdistillation.
Although SCAN achieves better results in Model1 and Model2 for ResNet18, we shouldnotice that SCAN adds additional attention modules over SD, which has more parameters than
SD and our WML.
When the peer model is small, the additional attention module that containsrelatively numerous parameters plays a more important role to improve the performance, while whoseadvantage decreases with the peer models become larger.
Secondly , compared with self-distillationbaselines, which usually encounter significant performance drops in the shallower classifiers, ourpeer models can maintain similar performance with moderate network pruning, especially on thelarge networks.
Taking the Model2 on ResNet50 as an example, whose model size is only 50% asthe baseline, our WML obtains 79.69% accuracy, while SD only achieved 74.21% accuracy.
SCANadded additional attention modules to further improve self-distillation performance, achieving 78.34%accuracy while still worse than our WML.
The above results demonstrate that reducing the widthis a better way to get more competitive peers than the self-distillation paradigm using the shallowmodels.
The comparison results on ImageNet in Table 2 again verify the advantage of the proposedframework, where our WML also outperforms the self-distillation baseline under different modelsizes on the ImageNet dataset.
As shown in the last column of Table 1, which is the ensemble of thefour peer models, our WML outperforms the three baselines by large margins.
This superiority comesfrom two aspects.
One is that our weighted mutual learning can boost all peers’ performance, thusenhancing the ensemble.
The other is that our optimized weights can capture the peers’ importancemore precisely, where more ablation studies can be found in the Appendix C.
4.2 Comparison with Knowledge Distillation and Online Distillation
Table 3 compares the proposed WML with three traditional knowledge distillation methods, including
KD [22], FitNet [37], and AT [49], and three online distillation methods, including DML [54], ONE[55], self-distillation (SD) [50] on CIFAR10, CIFAR100, and ImageNet.
In the traditional knowledgedistillation, we leverage the ResNet152 as the teacher [52].
In these online distillation methods, weconsider four peer models as our WML for fair comparisons, and all reported results for baselines canalso be found in [52].
We can see that knowledge distillation and online distillation both outperformthe directly trained baseline model with a large margin, showing the effectiveness of knowledgedistillation.
More interesting, different from traditional knowledge distillation which requires apowerful and large teacher model, online distillation methods can learn more meaningful informationfrom peer models and gain performance improvements without a teacher.
These comparison resultsagain verified the effectiveness of the proposed framework, which outperforms existing knowledgedistillation and online distillation methods on different datasets and neural networks.
4.3 Comparison with Channel Pruning
In our WML, we leverage channel pruning to generate peer models with different pruning ratiosat initialization.
As a byproduct, we can get a series of pruned models with different FLOPs aspeer models.
In this subsection, we compared the performance of the pruned models generated byour WML with existing channel pruning methods.
For fair comparisons, we conduct experimentswith ResNet32 and ResNet56 on CIFAR10, and MobileNetV2 on ImageNet, which are the commonsetting to compare with existing works [52].
One clear advantage of WML over existing channelpruning methods is that we can get a series of pruned models with different FLOPs in a single run.
Table 4 and 5 compared our pruned peer models with existing baselines on CIFAR10 and ImageNet.
We make the peer models toward { 30% , 40% , 50% } pruning ratios on FLOPs for ResNet32 and
ResNet56 on CIFAR10, and { 30% , 50% , 70% } for MobileNetV2 on ImageNet.
[Table] [Table] As shown in Table 4, there are two interesting findings.
First , WML obtains higher accuracy thanall channel pruning competitors on CIFAR10 after pruning similar FLOPs.
For example, the modelwith 40% pruned FLOPs by WML only has a 0.40% accuracy drop for ResNet32 and even 0.20%performance increase for ResNet56, which both outperform the competitors on CIFAR10.
Second ,our pruned models with moderate pruning achieve better performance than the baseline model whilewith much fewer FLOPs.
This benefit comes from the online distillation as we find the SNIP baselinein [34], which adopts the same pruning method as us while without knowledge distillation, obtainsworse results than those elaborately designed pruning methods.
However, combined with onlinedistillation, our pruned model can achieve better performance than elaborately pruned models.
Astraightforward direction for future work is to apply those competitive pruning methods into ourframework for further performance improvements.
Table 5 presents the comparison results of our pruned peer models on ImageNet, which also achievescompetitive results compared with other SOTA channel pruning methods under different FLOPsconstraints.
For example, when the FLOPs are reduced by about 30%, WML30 only has 0.08% Top1accuracy drop, which is better than MetaPruning’s 0.60%, AMC’s 1.00%, and DMCP’s 0.10% at thesimilar pruning ratio.
A similar advantage can also be found when pruning 50% and 70% FLOPs.
4.4 Ablation Study on Peer Pruning and Dynamic Weighting Strategy
In this section, we first conduct ablation studies to investigate whether the dynamic weighting strategyand peer pruning help improve the performance of online distillation.
Figure 2 only reports the resultson ResNet50, and more experiments on other networks can be found in Appendix D and C.
Then, weshow increasing the number of peers gradually enhance the performance of the proposed framework.
Figure 2 (a) presents how the performance of Model4 and ensemble change with different pruninglevels.
As shown, when slightly pruning peers (only prune less than 10% parameters for Model1-3),
WML can get better results than the unpruned framework in terms of both Model4 and ensemble
[Figure] [Figure]
performance.
An underline reason is that slightly pruning rarely decreases the performance ofpeer models, while the diversity it brings can further enhance the distillation.
However, when thepruning ratio is too high (the last data point in the Figure 2 (a) prunes more than 70% parametersfor Model1-3),we can see a clear performance drop since the pruning damages the performance of
Model1-3 seriously, which also further affects the distillation for Model4.
Figure 2 (b) presents howthe dynamic weighting strategy works in our WML, where the pruning ratio is set as Sec.4.1.
Asshown, the first data point in Figure 2 (b) indicates that we follow deep mutual learning [54] thatremove the ω in Eq.(1), and the remaining points are with different η to update ω .
We can see aclear performance boost from unweighted distillation to weighted distillation, which verifies theeffectiveness of our dynamic weighting strategy, which is also robust to the step size η .
In Figure 2(c), we prune Model 1-3 with 75%, 55%, and 20% parameters to match with Classifier 1-3 in [50],and the four lines in Figure 2 (c) track the change of weights ω for each peer model.
As shown, theweight of Model4 and Model4 consistently increase since they contains much more parameters andwith better generalization ability.
In contrast, the weights for the other two models both decrease, and
Model1 with the least parameters descents the fastest.
This phenomenon also verifies our weightingstrategy can adaptively adjust the importance of peers in distillation.
The main experiments show good results of the proposed framework with four peers.
We also verifythe superiority of WML with different number of peers in Figure 3.
For M = 2 , we leave one peerunpruned and the other is pruned with 50%, and for M = 4 , 8 , we leave one peer unpruned and theremained peer models are pruned gradually from 30% to 70%.
As show in Figure 3, WML scale wellwith more peers although gain decrease with the number of peers increase.
The phenomenon verifiesthat more knowledge from peers can further enhance the performance of the students.
Conclusion and Future Work
This paper proposes a new framework for online distillation, called Weighted Mutual Learning with
Diversity-Driven Model Compression ( WML ), which introduces the structured network pruningto obtain diversified peer models, and a bi-level formulation is further leveraged to estimate therelative importance of peers in forming a powerful teacher during the online distillation.
The WMLinnovatively combines network pruning and online distillation to enhance performance and compressmodels simultaneously.
Extensive experimental results have verified the proposed framework, whichleads to consistent accuracy improvements on various neural networks and datasets under differentmodel sizes.
This paper considers a simple and efficient training-free channel pruning method to getthe peer models while which is not as competitive as recent training-based channel pruning methods.
Combining more advanced channel pruning methods with online distillation for further performanceand efficiency boost and extending WML to feature distillation or other applications, e.g., objectdetection, natural language processing, and architecture search, are among directions for future work. Checklist For all authors...
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