The basis of transfer learning methods is the ability of deep neural networks to use knowledge from one domain to learn in another domain. However, another important task is the analysis and explanation of the internal representations of deep neural networks models in the process of transfer learning. Some deep models are known to be better at transferring knowledge than others. In this re-search, we apply the Centered Kernel Alignment (CKA) method to analyze the in-ternal representations of deep neural networks and propose a method to evaluate the ability of a neural network architecture to transfer knowledge based on the quantitative change in representations during the learning process. We introduce the Transfer Ability Score (TAs) measure to assess the ability of an architecture to effectively transfer learning. We test our approach using Vision Transformer (ViT-B/16) and CNN (ResNet, DenseNet) architectures in computer vision tasks in several datasets, including medical images. Our work is a contribution to the field of explainable AI and an attempt to explain the learning transfer process.
Various methods are used to evaluate the similarity of neural representations: Linear-Reg [
The deep neural network
( ) = is mapping from the example space to the class labels
space. DNN=fL○…○f1. where functions fi, 1 ≤ ≤ , are called layer functions, θ is a set of
parameters. The design paradigms of modern DNN
model architectures are divided into
architectures based on the convolution (CNN) [
∈ × denote the 2 sets of neural activations of layer i and
j of the DNN model with d = d1 and d2 neurons respectively in response to a batch of n examples.
The measure CKA ∈ [
1 ( , ) = ( −1)2 ( ) = | ( )|2, where tr is the trace matrix, cov is the covariance matrix, F is the Frobenius norm, n – the number of examples in a batch. Linear CKA can be calculated as follows: ( , ) = √ ( , ) ( , ) ( , ) ,
We propose a Transferability score (TAs) – a measure of the ability of a DNN to transfer knowledge to a new domain. Consider the problem of transferring knowledge by the model with architecture from source domain to target domain . The adaptation to the can be interpreted via evolving of the feature space on different layers. A slight change in feature representations on different layers during finetuning on domain indicates that the DNN has a high ability to transfer knowledge to a new domain. In contrast significantly change shows that the information extracted from is not enough to generalize knowledge to a new domain , or the domains are very different and a substantial change in the learned features representation is required. A low TAs value is an indication of less parameter change during DNN training. =1 = { 1, 2. . } is a set of representations for model DNNX with n1 layers trained =1 = { 1, 2. . } is a set of representations for model DNNY with n2 layers finetuned on Dt. Let’s define CKA matrix M1, where 1 is the value of the ( , ) between the representations on layers i and j. And CKA matrix M2, where 2 is the value of the between the and representations on layers i and j, respectively. Let’s denote ′ = 1 − 2 ′ shows how much the representations on different layers have changed after fine-tuned on the target domain. ′
– i,j-th element of matrix ′. We estimate the ability of a model with architecture to transfer knowledge (Transferability score – TAs) from the domain to the domain via a quantitative change in the feature space after fine-tuning and define it as = ∑ , =1 | ′ | / 2. The ′ values show the absolute change in the similarities of representations. The lower the Transferability score, the greater the DNN model's ability to transfer knowledge. In addition, the ′ matrix provides a visual understanding of how much the similarity of representations on different layers of the DNN has changed after fine tuning on data in the . (1) (2)
We test ResNet-50 [24], ResNet-101, DenseNet-121[25] and ViT-B/16 architecture models pretrained on ImageNet-1k [26]. We analyze the ability of various DNN models to transfer knowledge to a new target domain on several datasets: Eurosat (ESAT) [27], PatchCamelyon (PCAM) [28], The Cars dataset [29], DTD [30], CIFAR-10 [31]. For DNN training we used Adam [32] stochastic optimizer, lr = 5∙10-5, batch size = 32.
The success of transfer learning depends on the similarity between the and : the more
similar the data, the more effective the transfer of knowledge [
The dynamics of TAs during fine-tuning to a new dataset shows that when the accuracy of the test stabilizes, the values of the TA score also stabilize (Figure 2). In ViT, we observe a slight change in representations, because when trained on , the ViT model extracts more complete information from a large dataset and generalizes better, and when adapted to , the adaptation of the feature space is not so significant [34], which is consistent with the lower value of TAs.
In this paper, we touch upon the issue of interpreting the change in the similarity of internal
features representations in the transfer learning process. We have proposed a method to evaluate
the ability of a DNN architecture to transfer knowledge from the source domain to target domain
based on similarity of feature representations. Experiments were performed for several
architectures on different datasets. Based on TAs we can conclude the ViT architecture has a
better ability to transfer knowledge than CNN models, which is consistent with previous research
[
Improving our approach may be useful for choosing the optimal architecture. For future research, we propose to pay attention to the transfer of knowledge not only within the modality of images, but also cross-modality, for example, the use of features extracted from an image for an audio or text classification task.
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