Less-forgetful Learning for Domain Expansion in Deep Neural Networks

Abstract

Expanding the domain that deep neural network has already learned without accessing old domain data is a challenging task because deep neural networks forget previously learned information when learning new data from a new domain.

本文提出一种less-forgetful learning方法在domain expansion scenario。这个方法不需要知道输入是从old domain或new domain来的，就能在old domain和new domain上工作得很好。

Introduction

Domain adaptation: the same tasks but in different domains. The domain adaptation problem concerns how well a DNN works in a new domain that has not been learned. These domain adaptation techniques focus on adapting only to new domains.
但是实际情况中，应用经常需要记住old domain而没有再次看old domain data。本文提出这个问题，并称为DNN domain expansion problem.
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DNN domain expansion problem非常重要的三个主要原因：
1. 它使DNNs能够不断地从连续不断的输入数据中学习。(学习方式的优势)
2. 在实践中，用户可以只使用从新环境收集的新数据来微调他们的DNN，而不访问来自old domain的数据。（学习的数据只来自new domain）
3. 建立一个在多个领域执行的统一网络是可能的。（学习结果是一个能在多个domain工作）
Two challenging issues：
1. network在old domain的performance不能下降，即不能发生catastrophic forgetting problem
2. DNN需要在没有关于输入数据从哪个domain来的prior knowledge。

Domain Expansion Problem

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Figure 2 (a),(b)需要关于数据domain的prior knowledge，Figure 2 (c)是本文提出的方法，不需要关于数据domain的prior knowledge

domain expansion problem是continual learning problem的一部分。continual learning通常考虑multiple task learning或者sequence learning (more than two domains), 但是domain expansion problem只考虑两个domains，old 和 new domain。

Related work

dropout method + maxout activation function 能够帮助减少遗忘学习到的信息。
large DNN + dropout method可以解决catastrophic forgetting problem
learning without forgetting (LwF)Figure 2 (a) 利用knowledge distillation loss method保持performance
progressive learning (PL) (Figure 2 (b))在学习新task时通过侧面连接使用之前学习的features
Elastic weight consolidation (EWC)使用Fisher information matrix computed from the old domain training data，将diagonal elements作为l2 regularization的coefficients，在学习new domain data时达到old and new network之间的weight parameter相似。
generative adversarial networks被用来学习生成old domain data
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Type $A^{'}$ 通过ad-hoc training process去提取useful information from old domain data；
Type $B^{'}$ 通过通常的方法使用old domain data训练network，该方法可以直接应用到pre-trained models上。

Naive Approach

Fine-tuning only the softmax classifier layer

freeze lower layers，fine-tune the final softmax classifier layer
the feature extractor is shared between the old and new domains
这个方法是希望old domain和new domain共享的weight parameter不要改变

Weight constraint approach

使用l2 regularization去达到old domain和new domain之间相似的weight parameters

$\mathcal{L}_w(x;\theta^{(o)},\theta^{(n)})=\lambda_c \mathcal{L}_c(x;\theta^{(n)})+\lambda_w\|\theta^{(o)}-\theta^{(n)}\|_2 \\ \mathcal{L}_c(x;\theta^{(n)})=-\sum^C_{i=1}t_i\log(o_i(x;\theta^{(n)}))$

这个方法是期望weight parameter不要改变太大来保留学习到的信息。

Comment:以上两个方法都是希望尽量使new network和old network之间的差异或变化小，Fine-tuning only the softmax classifier layer使old domain和new domain共享的weight parameter差异为0，Weight constraint approach使old domain和new domain之间的weight parameters相似，差异不要太大。两种方法本质一样，只是程度不同。

Less-forgetful learning

softmax classifier的weight代表分类feature的decision boundary，从top hidden layer提取feature是线性可分的，因为top layer classifier有线性的性质。
Property 1. The decision boundaries should be unchanged.
Property 2. The features extracted by the new net- work from the data of the old domain should be present in a position close to the features extracted by the old network from the data ofthe old domain.

实现Property 1可以设置boundary的learning rate为0.
实现Property 2，由于不能访问old domain data，所以可以使用training data of the new domain。

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本文提出的方法和传统的fine-tune method一样，将old network copy到new netwrok。然后，为了保持boundary不变，将softmax classifier layer的weight freeze。Loss function如下：

$\mathcal{L}_t(x;\theta^{(o)},\theta^{(n)})=\lambda_c\mathcal{L}_c(x;\theta^{(n)})+\lambda_e\mathcal{L}_e(x;\theta^{(o)},\theta^{(n)})$
$\mathcal{L}_c$ cross entropy loss, $\mathcal{L}_e$ Euclidean loss, $\lambda_c=1$ , $\lambda_e$ 通常比 $\lambda_e$ 通常比 $\lambda_c$ 小。

$\mathcal{L}_e(x;\theta^{(o)},\theta^{(n)})=\frac{1}{2}\|\mathbf{f}_{L-1}(x;\theta^{(o)})-\mathbf{f}_{L-1}(x;\theta^{(n)})\|_2^2$
$\mathbf{f}_{L-1}$ 使softmax classifier layer之前的feature，new network学习提取与old network 提取的feature相似的feature。

$\hat{\theta}^{(n)}=\arg\min_{\theta^{(n)}}\mathcal{L}_t(x;\theta^{(o)},\theta^{(n)})+\mathcal{R}(\theta^{(n)})$
$\mathcal{R}(\cdot)$ 是general regularization term，such as weight decay。这里与Weight constraint approach一样。

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Comment: Less-forgetful learning的方法将Fine-tuning only the softmax classifier layer和Weight constraint approach结合起来。（1）同时提出decision boundary应该不变，所以freeze softmax的weight。（2）还提出 $\mathcal{L}_e$ ,与distillation loss类似。

Experimental results

task：image classification
dataset：CIFAR-10，MNIST，SVHN，ImageNet

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comparison methods：（1）bashline：fine-tuning+weight constraint+ReLU/Maxout/LWTA；（2）LwF;(3)EWC
result

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ablation study
1. Relationship between the classification rates for the old and new domains with different values of $\lambda_e$ .
2. Average classification rates with respect to $\lambda_e$ .
3. Classification rates according to the size of the old-domain data using the CIFAR-10 dataset.
4. Further Analysis of Scratch learning, Fine-tunig and LF learning
5. Feasibility for Continual Learning

Less-forgetful Learning for Domain Expansion in Deep Neural Networks

Less-forgetful Learning for Domain Expansion in Deep Neural Networks

Abstract

Introduction

Domain Expansion Problem

Related work

Naive Approach

Fine-tuning only the softmax classifier layer

Weight constraint approach

Less-forgetful learning

Experimental results

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