We also hypothesize that multiple image inputs will increase the model's accuracy. This has been shown in previous work , in which the authors use the "early fusion" method where feature maps from 3 different images are concatenated on the channel axis in the early stage of the network. However, this method requires modification of the backbone network, and the number of images used in this method is fixed. Instead, our method passes individual images through the entire network and averages the softmax distribution of tokens, as shown in Equation where I is the input image set, M is the model, P (y t,j ) is the probability of token j at time t, and σ is the softmax function. This is similar to the multi-crop technique used since the early days of applying deep networks in computer vision, like in AlexNet and ResNet . We train our model on the synthetic dataset with AdamW and an exponential learning rate scheduler. With the fixed validation set, we did a hyperparameter search on the finetuning dataset using Weights and Biases to select models with the highest validation token-level accuracy. All accuracy reported is the last validation accuracy regardless of oscillating.