# Review — R-Drop: Regularized Dropout for Neural Networks

## KL-Divergence Minimization With the Use of Dropout

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R-Drop: Regularized Dropout for Neural Networks,R-Drops, by Soochow University, and Microsoft Research Asia,2021 NeurIPS, Over 140 Citations(Sik-Ho Tsang @ Medium)

NLP, LM, NMT, Image Classification Transformer, Vision Transformer, ViT, Dropout

Image Classification: 1989…2023[Vision Permutator (ViP)]Language Model: 1991 … 2022[GPT-NeoX-20B] [InstructGPT]Machine Translation: 2013 …2022[DeepNet]

==== My Other Paper Readings Are Also Over Here ====

- A simple
**consistency training strategy**to**regularize****Dropout**,**R-Drop**, is proposed, which**forces the output distributions of different sub models**generated by Dropout to be**consistent with each other.** **R-Drop minimizes the bidirectional KL-divergence**between the output distributions of two sub models sampled by Dropout.- R-Drop can be applied to
**language modeling**,**neural machine translation**and**image classification**.

# Outline

**Motivations****R-Drop****Results**

**1. Motivations**

- Given the
**training data**where*D*={(*xi*, yi)}*i*is from 1 to*n*, the main learning objective for a deep learning model is to**minimize the negative log-likelihood loss function**, which is as follow:

However, deep neural networks are prone to

over-fitting. Because there is ahuge inconsistency between training and inferencethat hinders the model performance.

**2. R-Drop**

## 2.1. Loss Functions

- Given the input data
*xi*at each training step,Therefore, we can obtain*xi*is fed to go through the forward pass of the network twice.**two distributions of the model predictions**, denoted asand*Pw*1(*yi*|*xi*).*Pw*2(*yi*|*xi*) - Since Dropout is used, the
**two forward passes are indeed based on two different sub models.**As the dropped units are different,**two distributions**and*Pw*1(*yi*|*xi*)*Pw*2(*yi*|*xi*) are also different.

R-Dropmethod tries to regularize on the model predictions byminimizing the bidirectional Kullback-Leibler (KL) divergencebetween these two output distributions for the same sample, which is:

- With the basic
**negative log-likelihood learning objective***LiNLL*of the**two forward passes**:

- The
**final training objective**is to**minimize***Li**xi*,*yi*):

- where
is the*α***coefficient weight**.

## 2.2. Training Algorithm

**Lines 3–4:**The input data*x*is repeated itself and**concatenated ([**in batch-size dimension, and perform*x*;*x*])**forward pass**to save the training cost.**Lines 5–6:**calculate the**negative log-likelihood**and the**KL-divergence**.**Line 7**: Finally, the model parameters are updated.

## 2.3. Theoretical Analysis

- (Please skip this part for quick read.)
- Let
denote the*hl*(*x*)**output of the**.*l*-th layer of input*x* is the*ξli***random vector**of each dimension of which is independently sampled from a**Bernoulli distribution**:*B*(*p*)

- Dropout can be interpreted as:

- where ⊙ denotes the element-wised product.
- The objective for R-Drop enhanced training can be
**formulated as**solving the following**constrained optimization problem**:

- Therefore, R-Drop optimizes the constrained optimization problem in a
**stochastic manner**, i.e., it**samples two random vectors**(corresponding to two Dropout instantiations) from Bernoulli distribution and one training instance (*ξ*(1) and*ξ*(2)*xi*,*yi*).

R-Drop enhanced training

reduces this inconsistencybyforcing the sub structures to be similar.

# 3. Results

## 3.1. Neural Machine Translation

- Transformer is used. R-Drop is denoted as RD.
*α*=5.

R-Drop achieves

more than 2.0 BLEU score improvementson 8 IWSLT translation tasks.

After applying RDon the basic Transformer network,the state-of-the-art (SOTA) BLEU score is achieved on WMT14 En→De (30.91) and En→Fr (43.95) translation tasks, which surpass current SOTA models, such as the BERT-fused NMT [80].

## 3.2. Language Understanding

- The BERT-base and strong RoBERTa-large pre-trained models are used as backbone.
dynamically adjusted as*α is***{0.1; 0.5; 1.0}**for each setting. - For the regression task STS-B, MSE is used instead of KL-divergence to regularize the outputs.

R-Drop achieves

1.21 points and 0.80 points (on average) improvement over the two baselinesBERT-base andRoBERTa-large, respectively, which clearly demonstrate the effectiveness of R-Drop.

- Specifically,
**RoBERTa****-large + RD**also**surpasses**the other two strong models:**XLNet****-large**and**ELECTRA****-large**, which are specially designed with different model architecture and pre-training task.

## 3.3. Summarization

- Pretrained BART is used.
*α*=0.7.

R-Drop based training

outperforms the fine-tunedBARTmodel by 0.3 points on RG-1 and RG-2 score and achieves the SOTA performance. Specifically, it also surpasses the PEGASUS method [74].

## 3.4. Language Modeling

- Two models: One is the basic Transformer decoder, another is the more advanced one: Adaptive Input Transformer [5].
*α*=1.0.

R-Drop based training

improves the perplexity on both two different model structures, e.g., 0.80 perplexity improvement on test set over Adaptive Input Transformer [5].

## 3.5. Image Classification

- Pre-trained models, ViT-B/16 and ViT-L/16, with 86M and 307M parameters respectively, are used.
*α*=0.6.

For

CIFAR-100, RD achieves about0.65 accuracy improvementover ViT-B/16 baseline, and0.41 pointsover ViT-L/16 model. Similarly, on the large-scaleImageNetdataset,consistent improvementsare also obtained.

## 3.6. Ablation Study

Left:Transformerquickly becomes over-fitting, and the gap between train and valid loss of Transformer is large, whileR-Drop has a lower valid loss.

Right:R-Drop can be performed everyksteps instead of each step (k=1).is thek=1best.Also, R-Drop can have more than

m=2 distributions. Butis found out to bem=2good enough.

Dropout rates with the same value

(0.3, 0.3)is thebestchoice (current setting). R-Drop canstably achieve strong resultswhen the two Dropout rates are in a reasonablerange (0.3-0.5)without a big performance difference.

The

bestbalanced choice is.α=5

Since R-Drop doubles the batch size,

doubling batch size without using R-drop (Green)is also tested and the results arenot good.Thus, R-Drop iseffective.

Authors mentioned that, due to the limitation of computational resources, for pre-training related tasks, authors only tested R-Drop on downstream task fine-tuning in this work. One of the future works is to test it on** pre-training**.

Authors also said that they only focused on Transformer based models. Another future work is to apply R-Drop to other network architectures such as **convolutional neural networks**.