# Exploring Deep Neural Networks in Simulating Human Vision through Five Optical Illusions
## 2 Materials and Methods
### Optical Illusions
#### 2.2.2 Brain-like Deep Neural Networks  
In this study, we aimed to bridge the gap between artificial intelligence and human cognitive science by focusing on the functional mapping relationship between deep neural networks (DNNs) and the human visual ventral pathway [23]. The high similarity between CNNs and the human early visual cortex in terms of regional mapping correlation reveals the similarity between the advanced layers of DNNs and the advanced regions of human brain visual processing in terms of visual recognition and understanding. This perspective provides a theoretical foundation for us to comprehensively evaluate the ability of DNNs in simulating the human visual system by considering both brain hierarchy (BH) scores [24] and brain score [22; 23] rankings. A basic DNN model can be represented as a series of layers, each being a nonlinear transformation of the previous layer. The specific expression of DNNs can be represented as follows:  
\[h_{1}=\sigma(W_{1}x+b_{1}) \tag{1}\]\[h_{2}=\sigma(W_{2}h_{1}+b_{2}) \tag{2}\] \[\vdots\] \[h_{n-1}=\sigma(W_{n-1}h_{n-2}+b_{n-1})\] (3) \[y=\sigma(W_{n}h_{n-1}+b_{n}) \tag{4}\]  
where:  
* \(x\) is the input vector.
* \(h_{i}\) is the output of the \(i\)th hidden layer.
* \(W_{i}\) and \(b_{i}\) are the weight and bias of the \(i\)th layer, respectively.
* \(\sigma\) is the activation function, such as ReLU or Sigmoid.
* \(y\) is the output vector.  
We selected models with a single-path sequential feedforward architecture and extensive spatial integration features proposed based on BH scores (Figure 3), such as the Inception series (Inception_v3 [15], Inception_v4 [15]), AlexNet [7], and VGG series [8] (VGG16, VGG19). At the same time, for a more comprehensive perspective in evaluation, we also considered the ResNet and DenseNet series with high brain score rankings (including ResNetv2_50 [29], ResNetv2_101 [29], ResNet152 [16], ResNext_v2 [30], DenseNet121 [31], DenseNet169 [31], DenseNet201 [31]). This selection method is aimed at balancing two important but sometimes contradictory scoring systems: BH scores focus on assessing the brain-like characteristics of the model in hierarchical processing, while brain score evaluates the model's similarity to the brain across multiple dimensions, including but not limited to image recognition capabilities. Brain score measures the overall 'brain-likeness' of a model by its alignment with neural and behavioral measurements, thereby providing a comprehensive assessment of the model's ability to simulate the human brain's processing of visual information.  
These models were deployed utilizing PyTorch's torchvision package (v0.11.2) and the timm package [32] (v0.6.11), facilitating standardization and accessibility while harnessing PyTorch's efficiency and adaptability. These pre-trained models were trained on large image datasets (such as ImageNet [33]), which not only saved substantial training resources but also performed excellently in simulating human visual processing tasks due to their optimization in processing a rich array of visual features.  
Table 2 shows the pre-trained weights and total model parameters of each model.  
Figure 3: Brain-like deep neural networks and mapping relationships.