The Unreasonable Effectiveness of Fully-Connected Layers for Low-Data Regimes
Anonymous Author(s)
AffiliationAddress email
Abstract
Convolutional neural networks were the standard for solving many computer visiontasks until recently, when Transformers of MLP-based architectures have started toshow competitive performance.
These architectures typically have a vast numberof weights and need to be trained on massive datasets; hence, they are not suitablefor their use in low-data regimes.
In this work, we propose a simple yet effectiveframework to improve generalization from small amounts of data.
We augmentmodern CNNs with fully-connected (FC) layers and show the massive impact thisarchitectural change has in low-data regimes.
We further present an online jointknowledge-distillation method to utilize the extra FC layers at train time but avoidthem during test time.
This allows us to improve the generalization of a CNN-basedmodel without any increase in the number of weights at test time.
We performclassification experiments for a large range of network backbones and severalstandard datasets on supervised learning and active learning.
Our experimentssignificantly outperform the networks without fully-connected layers, reaching arelative improvement of up to 16% validation accuracy in the supervised settingwithout adding any extra parameters during inference.
Introduction
Convolutional neural networks (CNNs) [1, 2] have been the dominant architecture in the field ofcomputer vision.
Traditionally, CNNs consisted of convolutional (often called cross-correlation) andpooling layers, followed by several fully-connected layers [3–5].
The need for fully-connected layerswas challenged in an influential paper [6] and recent modern CNN architectures [7–11] discardedthem without a noticeable loss of performance and a drastic decrease in the number of trainableparameters.
Recently, the "reign" of all-convolutional networks has been challenged in several papers [12–16],where CNNs were either replaced (or augmented) by vision transformers or replaced by multi-layerperceptrons (MLPs).
These methods remove the inductive biases of CNNs, leaving more learningfreedom to the network.
While showing competitive performance and often outperforming CNNs,these methods come with some major disadvantages.
Because of their typically large number ofweights and the removed inductive biases, they need to be trained on massive datasets to reachtop performance.
As a consequence, this leads to long training times and the need for massivecomputational resources.
For example, MLPMixer [14] requires a thousand TPU days to be trainedon the ImageNet dataset [17].
Feature Refiner
[Figure]
𝑑 𝑓𝑟𝑓
F C + S o f t m a x
Predictions 𝑑 𝑓𝑟𝑓 F C
L a y e r
N o r m
F C
R e L U
F C
L a y e r
N o r m 𝑑
𝑓𝑟𝑓 𝑑 𝑓𝑟𝑓 𝑑 𝑓𝑟𝑓 𝑑 𝑓𝑟𝑓
[Figure]
𝑛 𝑐
In this paper, instead of entirely replacing convolutional layers, we go back to the basics, and augmentmodern CNNs with fully-connected neural networks, combining the best of both worlds.
Contraryto new alternative architectures [14, 15] that usually require huge training sets, we focus our studyon the opposite scenario: the low-data regime, where the number of labeled samples is very-lowto moderately low.
Remarkably, adding fully-connected layers yields a significant improvementin several standard vision datasets.
In addition, our experiments show that this is agnostic to theunderlying network architecture and find that fully-connected layers are required to achieve the bestresults.
Furthermore, we extend our study with two other settings that typically deal with a low-dataregime: active and semi-supervised learning.
We find that the same pattern holds in both cases.
An obvious explanation for the performance increase would be that adding fully-connected layerslargely increases the number of learnable parameters, which explains the increase in performance.
To disprove this theory, we use knowledge distillation based on a gradient gating mechanism thatreduces the number of used weights during inference to be equal to the number of weights of theoriginal networks, e.g., ResNet18.
We show in our experiments that this reduced network achievesthe same test accuracy as the larger (teacher) network and thus significantly outperforms equivalentarchitecture that does not use our method.
In summary, our contributions are the following:
• We show that adding fully-connected layers is beneficial for the generalization of convolutional networks in the tasks working in the low-data regime.•
We present a novel online joint knowledge distillation method (OJKD), which allows us to
utilize additional final fully-connected layers during training but drop them during inferencewithout a noticeable loss in performance.
Doing so, we keep the same number of weights
during test time.
• We show state-of-the-art results in supervised learning and active learning, outperformingall convolutional networks by up to 16% in the low data regime.
Methodology
We propose a simple yet effective framework for improving the generalization from a small amountof data.
In our work, we bring back fully-connected layers at the end of CNN-based architectures.
We show that by adding as little as 0 .
37% extra parameters during training, we can significantlyimprove the generalization in the low-data regime.
Our network architecture consists of two mainparts: a convolutional backbone network and our proposed Feature Refiner (FR) based on multi-layerperceptrons.
Our method is task and model-agnostic and can be applied to many convolutionalnetworks.
In our method, we extract features with the convolutional backbone network.
Then, we apply our
FR followed by a task-specific head.
More precisely, we first reduce the feature dimension d bbf tod frf with a single linear layer to reduce the number of extra parameters.
Then we apply a symmetric
Backbone
FeatureRefiner
F C + S o f t m a x
Gradient Gate
F C + S o f t m a x
Loss
[Figure]
CE
L FR
L Original CE two-layer multi-layer perceptron wrapped around by normalization layers.
We present the precisearchitecture of our Feature Refiner in Figure 1.
2.1 Online Joint Knowledge Distillation
One could argue that using more parameters can improve the performance just because of theincreased expressivity of the network.
To disprove this argument, we develop an online jointknowledge distillation (OJKD) method.
Our OJKD enables us to use the exact same architecture asour baseline networks during inference and utilizes our FR solely during training.
We base our training pipeline on the baseline network’s architecture.
We split the baseline networkinto two parts, the convolutional backbone for feature extraction and the final fully-connectedclassification head.
We append an additional head with our Feature Refiner.
We devise the finalloss as the sum of the two head’s losses, making sure both heads are trained in parallel (online) andenforcing that they share the same network backbone (joint).
During inference, we drop the additionalhead and use only the original one, resulting in the exact same test time architecture as our baseline.
In other words, our FR head is the teacher network that shares the backbone with the student originalhead, and we distill the knowledge of the teacher head into the student head.
However, the key ingredient of our OJKD is the gradient-gating mechanism; we call it Gradient
Gate (GG).
This gating mechanism blocks the gradient of the original head during training, makingthe backbone only depend on our FR head.
We implement this functionality with a single layer.
During the forward pass, GG works as identity and just forwards the input without any modification.
However, during the backward pass, it sets the gradient to zero.
This way, the original head’s gradientsare backpropagated only until the GG.
While the original head gets optimized, it does not influencethe training of the backbone but only adapts to it.
Consequently, the backbone is trained only withthe gradients of our FR head.
Furthermore, the original head can still fit to the backbone and reach asimilar performance as the FR head.
We find that we can still improve upon the baseline without ourgating mechanism but reach lower accuracy than when we use it.
We show the pipeline of our OJKDin Figure 2.
Experiments
In this section, we demonstrate the substantial effectiveness of our simple approach improving theperformance of neural networks in low-data regimes.
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V a li d a ti
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V a li d a ti
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[Figure] [Figure]
Datasets and the number of labels.
For all experiments, we report accuracy as the primary metricand use four public datasets: CIFAR10 [18], CIFAR100 [18], Caltech101 [19], and Caltech256 [19].
We use the predefined train/test split for the CIFAR datasets, while we split the Caltech datasets into70% training and 30% testing, maintaining the class distribution.
In the simpler datasets, CIFAR10and Caltech101, we start with an initial labeled pool of 1000 images, while in the more complicated,
CIFAR100 and Caltech256, we start with 5000 labeled images.
In both cases, we incrementally add1000 samples to the labeled pool in each cycle and evaluate the performance with the larger andlarger training datasets.
We use the active learning terminology for a’ cycle’, where a cycle is definedas a complete training loop.
CNN backbones.
For most experiments, we use ResNet18 [8] as our backbone ( d bbf = 512 ),and reduced feature size d frf = 64 .
We compare the results of our method with those of pure
ResNet18 on both the supervised and active learning setups.
Note that the supervised case (Figure 3)is equivalent to a random labeling strategy in an active learning setup.
We compare our method withvarious active learning strategies.
We also compare to a non-convolutional network, the MLPMixer[14].
Finally, to show the generability of our method, we also experiment with other backbonenetworks: ResNet34, EfficientNet, and DenseNet.
We run each experiment 5 times and report themean and standard deviation.
We train each network in a single GPU.
We summarize the results inplots and refer to our supplementary material for exact numbers and complete implementation details.
Training details.
For the CIFAR experiments, we follow the training procedure of [20].
More precisely, we train our networks for 200 epochs using SGD optimizer with learning rate 0 .
1 , momentum0 . 9 , weight decay 5 e − 4 , and divide the learning rate by 10 after 80% epochs.
We used cross-entropyloss as supervision.
For the more complex Caltech datasets, we start with an Imagenet-pre-trainedbackbone and reduce the dimensionality in our FR only to 256 .
We use the same training setup for afull fine-tuning, except that we reduce the initial learning rate to 1 e − 3 and train for only 100 epochs.
3.1 Supervised Learning
Comparisons with ResNet18 [8].
We compare the results of our method with those of ResNet18.
Asshown in Figure 3a, on the first training cycle ( 1000 labels), our method outperforms ResNet18 by7 .
6 percentage points ( pp ).
On the second cycle, we outperform ResNet18 by more than 10 pp .
Wekeep outperforming ResNet18 until the seventh cycle, where our improvement is half a percentagepoint.
For the remaining iterations, both methods reach the same accuracy.
On the CIFAR100 dataset (see Figure 3a), we start outperforming ResNet18 by 5 .
7 pp , and in thesecond cycle, we are better by almost 7 pp .
We continue outperforming ResNet18 in all ten cycles,in the last one being better by half a percentage point.
We see similar behavior in Caltech101 (see
Figure 3c) and Caltech256 (see Figure 3d).
A common tendency for all datasets is that with an increasing number of labeled samples, the gapbetween our method and the baseline shrinks.
Therefore, dropping the fully-connected layers in case
1k 2k 3k 4k 5k 6k 7k 8k 9k 10k Dataset size [samples]
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ResNet
FR-ResNet
MLPMixer
ViT-B (a) CIFAR10 test accuracy.
5k 6k 7k 8k 9k 10k 11k 12k 13k 14k
Dataset size [samples]
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ResNet
FR-ResNet
MLPMixer
ViT-B (b) CIFAR100 test accuracy.
of a large labeled dataset does not cause any disadvantage, as was found in [6].
However, that workdid not analyze this question in the low-data regime, where using FC layers after CNN architecturesis clearly beneficial.
Comparisons with MLPMixer [14] and ViT [12].
We also compare the results of our methodwith that of two non-convolutional networks, the MLPMixer and ViT. Similar to us, the power of
MLPMixer is on the strengths of the fully-connected layers.
On the other hand, ViT is a transformerbased architecture.
Each Transformer block contains an attention block and a block consistingof fully-connected layers.
Unlike these methods, our method uses both convolutional and fullyconnected layers to leverage the advantages of both the high-level convolutional features and theglobal interrelation from the fully-connected layers.
In Figure 4a, we compare to MLPMixer and ViTon the CIFAR10 dataset.
On the first cycle, we outperform MLPMixer by 4 . 4 pp and ViT by circa6 pp .
We keep outperforming both methods in all other cycles, including the last one where we dobetter than them by circa 13 pp .
As we can see, MLPMixer and ViT do not perform well even in thelatest training cycles and require to be trained on massive datasets.
We show a similar comparisonfor CIFAR100 in Figure 4b.
Comparisons with Knowledge Distillation baselines.
To show that our method’s main strengthcomes from our FR head, we compare to several knowledge distillation (KD) methods.
DML [21]trains two networks in an online KD setting.
KDCL [22] aims to improve the generalization ability of
DML by treating every network as students and training them to match the pooled logit distribution.
Finally, KD [23] is the original offline method, which trains a teacher network, then distills itsknowledge into a student.
In each experiment, the teacher network is ResNet50, the student is
ResNet18.
As can be seen in Figure 5, our method significantly outperforms the KD methods, by upto 8.5pp on CIFAR10 and 3.6pp on CIFAR100 in the second iteration.
In the later iterations, whenmore data is available and our approach converged to the baseline network’s performance, we start tosee the benefit of the other KD methods.
However, while our method comes with only 0 .
37 pp extraparameters during training, the other KD methods use 210 .
5 pp more parameters.
3.2 Active Learning
We put our method to the test under a typical low-data setting, active learning, where instead ofrandomly choosing samples to label, we choose them based on an acquisition score.
The results in
Section 3.1 can be considered a special case of active learning with a random acquisition score.
Weuse maximum entropy acquisition score with our network and compare it with plain ResNet18 withmaximum entropy and two state-of-the-art active learning methods, LLAL [20] and core-set [24].
In Figure 6, we summarize the results on all four datasets, showing our method’s superior performance.
On CIFAR10, we outperform all methods in early cycles by a large margin, up to 7 .
3 pp comparedto the core-set approach in the second cycle.
As more labels become available during training, allthe methods tend to converge to the same result.
A similar trend can be observed on the {+CIFAR
 [Figure] dataset.+}
Here, our approach achieves 5 .
2 pp better accuracy in the second cycle.
On the Caltech101dataset, we have a slight advantage ( < 0 .
5 pp )
compared with the vanilla ResNet18.
We have alarger advantage on the Caltech256 dataset, where we tend to outperform the second-best method by1 − 1 .
5 pp .
Furthermore, note that core-set and LLAL approaches perform much worse on these morecomplex datasets.
The final gap between the maximum entropy acquisition and LLAL is 4 .
5 pp onthe Caltech256 and 1 .
pp on the Caltech101 dataset.
3.3 Semi-Supervised Learning
We now do an experiment where we present preliminary results in semi-supervised learning.
Wechoose to couple MixMatch [25] with our method and compare it with the original version of
MixMatch.
We use ResNet18 for the experiment and train the methods using only 250 labels.
MixMatch reaches 91 .
07 accuracy, while our method reaches 91 .
56 accuracy, improving by half apercentage point, and showing that our method can be used to improve semi-supervised learning.
3.4 Backbone Agnosticism
We check if our method can be used with other backbones than ResNet18.
We show the results for
ResNet34, DenseNet121, and EfficientNetB3 on CIFAR10 and CIFAR100 in Figure 7.
The goal ofthe experiment is to show that our method is backbone agnostic and generalizes both to differentversions of ResNet as well as to other types of convolutional neural networks.
As we can see, ourmethod significantly outperforms the baselines on both datasets and for all three types of backbones.
3.5 Ablation
Feature Refiner We conduct a detailed ablation of the architecture of our Feature Refiner, showingthe effect of the specific elements.
We start with the backbone ResNet18 and build our Feature
Refiner up step-by-step.
Figure 8a shows the results on the CIFAR10 dataset.
First, we apply only asingle linear layer without any activation function before the output layer (512x512 w/o Activation).
Interestingly, we can already see a great improvement of 4 .
9 pp in the first cycle, reaching 5 .
pp inthe second cycle.
Second, we change the previously applied linear layer to reduce the dimension,as we did in our Feature Refiner (512x64 w/o Activation).
This step further improves the results upto 2 .
3 pp in the third cycle.
Third, we add our fully-connected layers with the ReLU activation (FRw/o LayerNorm), which yields an improvement of 3 . 1 pp in the second cycle.
Finally, we use ourcomplete architecture by applying the normalization layers, reaching the best results in the earlierstages, giving an additional performance boost of 1 . 2 pp in the second stage.
Online joint knowledge distillation We now evaluate our proposed OJKD.
In these experiments,we highlight that during inference, we can drop the Feature Refiner head without any noticeable [Figure] performance loss.
We use the same training strategy as described in Section 2.1.
We train togetherwith the original and Feature Refiner heads.
However, during inference, we evaluate both heads.
In
Figure 8b
we show both heads’ performance on the CIFAR10 dataset.
As we can see, both headshave barely distinguishable performance, showing that the knowledge of our teacher FR head can beproperly distilled into the student original head.
Furthermore, we ablate the effect of our proposed
Gradient Gate.
Without our gating mechanism, we can still improve upon the baseline up to 4 .
5 pp ,but using it can give us a further 5 .
6 pp improvement in the second stage.
The effect of the number of layers.
We now study the number of layers with nonlinearities.
To doso, we add nonlinear layers in our Feature Refinement.
We show the results on the CIFAR10 datasetin Figure 8c.
As we can see, adding more nonlinear layers comes with a decrease in performance.
In fact, the more layers we add, the larger is the decrease in performance compared to our originalmodel.
This makes sense considering that by increasing the number of layers, we increase the numberof learnable parameters, and thus we might cause overfitting.
Related Work
All-convolutional networks.
Convolutional neural networks [1, 2] have made a breakthrough inmany computer vision tasks since the pioneering work of [4].
Other works [26, 5] improved overthose architectures, typically by increasing the number of convolutional layers but by keeping thesame architecture: many convolutional and pooling layers followed by a few fully-connected layers.
However, this design choice was questioned in the famous Striving for simplicity [6] paper, where itwas argued that there is no need for fully connected layers.
Fully convolutionized architectures suchas Google-Inception [7] or ResNets [8] followed, significantly outperforming the previous state-ofthe-art.
Some more recent works typically tended to improve the architecture of ResNet architectureseither by enlarging the number of convolutional filters [8] or densely connecting convolutional layers[10].
Probably the best solution was found in the EfficientNet [27], which simultaneously increasesthe image resolution, number of convolutional channels, and number of convolutional layers.
Aconstant of these approaches is that they completely get rid of the fully connected layers.
Contrary tothem, we find out that adding fully-connected layers comes with a massive benefit in performancewhen the number of labeled points is limited.
By doing so, we are able to improve the performanceof several backbones in different learning tasks.
Non-convolutional networks.
A parallel line of research has shown that convolutional neuralnetworks can be replaced either by vision transformers [12, 13] or multi-layer perceptrons [14–16].
The main idea behind these works is to leave the network as much freedom as possible duringthe learning procedure instead of injecting inductive bias into the network.
Indeed, in multi-layerperceptrons, every unit is connected to all the units in both the previous and the next layer, allowing
[Figure]
-B3 backbones. In all cases, our method significantly improves over the original network. it to use all the information of the proceeding layer as well as pass it into the next one.
Works like
MLPMixer [14] and others have shown promising results in several vision tasks.
Still, they come witha series of limitations, such as the need for pre-training on very large datasets and requiring a massiveamount of computational resources.
Our work is similar to MLPMixer [14] in the sense that we alsoleverage the power of multi-layer perceptrons to solve different vision tasks.
However, unlike them,we do not get rid of the convolutional layers, but we advocate for hybrid networks.
Our networks donot need pre-training and massive computational resources, while it manages to significantly improvestate-of-the-art results when trained with a limited number of labeled points.
Knowledge distillation.
With the advancements in computational power, larger neural networks arepossible to train.
However, effective neural networks are required during inference in many practicalapplications, especially mobile or embedded applications.
This requirement motivates the field of
Knowledge Distillation (KD).
The goal of KD is to reduce the computational demand of a trainednetwork’s inference by maintaining its performance.
This could be in the form of offline distillation,where one network is used as a teacher to distill its knowledge into another smaller network, thestudent [23].
However, online distillation has gained more attention lately, thanks to its simplerpipeline [28].
In such a setup, the student and teacher models are trained together end-to-end.
Formore details on this field, we refer to the work of Gou et al.
The published online distillationmethodologies are mainly specifically applied for ensemble distillation [29].
On the contrary, wepropose an effective yet general online distillation method.
We attach a separate head during thetraining (the Feature Refiner) while using a gating mechanism that blocks the gradients coming fromthe original softmax layer of the network.
On inference, we can simply drop the Feature Refiner headwithout noticeable performance drop, thus, using no extra parameters.
Stop-gradient.
SimSiam [30] and BYOL [31] train two branches jointly in a self-supervised settingwith different augmentations.
In BYOL, the target is provided by the averaged version of the mainnetwork, while in SimSiam the same network is used with the stop-gradient technique.
These methodsshare similarities with our OJKD; however, they cannot be directly applied to supervised learning,and they are trained on large datasets.
Instead, we focus on generalization from a low amount of datain a supervised setting.
[Figure]
OJKD
8b
Number of layers ablation 8c: We study the effect of the number of nonlinear fully-connected layers.
More layers do not lead to better performance.
Conclusion
In this paper, we question the long-believed idea that convolutional neural networks do not needfully-connected layers.
Perhaps surprisingly, we show that using hybrid networks that use bothconvolutional high features and interrelations coming from fully-connected layers improves thegeneralization performance in the low-data regime, without any drawback in the high-data regime.
Toshow a fair comparison, we also introduce a gating mechanism that allows distilling the knowledgefrom our extra head with the added FC layers to the baseline network.
We show that our approachis model agnostic by evaluating different backbone networks.
We show in our experiments that ourmethod yields a significant improvement over the state-of-the-art in supervised and active learning, ina wide range of standard classification datasets without an increase in the number of used parameters.
Broader Impact / Limitations
A shortcoming of our method is that we cannot improve the networks that already contain fullyconnected layers, such as the VGG Network [5].
In the supplementary material, we do an experimentshowing that our Feature Refiner cannot further improve VGG Network’s accuracy.
However, wewere able to decrease the number of learnable parameters by 67% .
Another deficiency of our paper is the lack of a theoretical explanation.
Although the empiricalresults underline our methodology, we could not find any mathematical proof for it.
Our speculativeexplanation is that if the network has only a single final layer, then the backbone’s feature space mustbe linearly separable.
Our intuition is that in the case of a low amount of data, the convolutionallayers do not get enough supervision to find the right local reasoning, which limits its flexibility.
Having additional final fully-connected layers gives global supervision and increases the flexibility ofthe network to reach better optima.
We note that the research in deep learning has been mostly headby empirical results.
We believe that theoretical explanations are desirable and ultimately needed.
At the same time papers without a clear (or a downright wrong) theoretical explanation have had amassive impact on deep learning, as is the case of the batch-normalization [32] paper.
We hope thatour work can open a new interesting line of research, and inspire other researchers to question the’common knowledge’ in deep learning.
Furthermore, it would be interesting to see if our results canbe generalized in domains where the number of labeled data is very scarce, such as medical imaging.
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