# Methodology for Evaluating the Generalization of ResNet
## 1 Introduction  
Convolutional neural networks (CNNs) are renowned for their exceptional data representation and fitting capabilities, typically exhibiting robust generalization performance with unseen data. In real-world applications such as autonomous driving and the medical field, it is crucial to evaluate the model's generalization ability based on the trained model and its training data. The generalization ability of a model is defined as the accuracy of the model using unseen data under independent identically distributed (i.i.d.) conditions [1]. However, the generalization of over-parameterized CNN models is not well understood theoretically, and there is a lack of precise methods to accurately evaluate this ability. This leaves the assessment of CNN model generalization as a complex and unresolved issue, particularly due to the risk of overfitting, where the number of parameters of deep CNN models often surpass the size of the training dataset [2]. The generalization ability of neural networks is vital for their practical application, thus necessitating a rigorous evaluation framework [3, 4]. If \(\mathbb{P}\) is the data distribution, the training data \(\mathcal{D}_{train}=\{(\mathbf{x}_{i},y_{i})\}_{i=1}^{N}\) is a set of input-output pairs sampled i.i.d. from \(\mathbb{P}\), where \(\mathbf{x}_{i}\) represents a sample of data, \(\mathbf{y}_{i}\) represents the label of the sample, and N represents the number of training samples. The model is trained on a known training dataset. However, the test data \(\mathcal{D}_{test}\) are unknown, which is also obtained by independently sampling from \(\mathbb{P}\). Evaluating the model's performance on unseen data, which is its generalization ability, requires consideration of both the known training data and the trained model itself. Generalization evaluation can be formally defined as \(\mu(f,D_{train})\to Acc_{D_{test}}(f)\), where \(\mu\) is the evaluation method and \(f\) represents the trained model. A good assessment method should have a strong correlation with the generalization gap [3; 5], a pivotal concept introduced in [1]. The generalization gap represents the model's generalization capability, and is the difference in accuracy between a model's training and test set performances upon convergence. A narrower generalization gap value indicates a better generalization ability of the model, while a wider gap suggests poorer generalization. This paper delves into the generalization evaluation of CNN models, with a focus on ResNet for image classification, aiming to fill the existing gaps in knowledge. The methods for assessing the generalization of CNN models can be categorized into two main groups: theoretical analysis and empirical research. The former relies primarily on traditional statistical learning theory [6], encompassing concepts such as VC dimension [7] and margin theory in support vector machines. These theoretical approaches aim to establish an upper bound for the generalization error of deep neural network models [8; 9]. However, these methods often lack experimental validation on extensive model sets and may not accurately provide the upper bounds for generalization errors [10]. The latter approach involves predictive modeling, where the generalization capability is forecasted based on the characteristics of network model weights [11] or intermediate layer outputs [1]. However, these methods are typically investigated on small-scale or simplified model sets [3], which limits their applicability and creates a gap between their findings and real-world tasks. To overcome these limitations, we used IoU, a well-established metric in the field of object detection [12; 13; 14; 15], as a method for evaluating the generalizability of CNN models, and constructed a model set to validate its effectiveness. The contributions of this paper can be summarized as follows:  
* We provide a new perspective for evaluating the generalizability of CNN models by application of IoU.