Mammography is one of the most important/reliable techniques/procedures for detecting early-stage cancers and associated abnormalities, enabled by the very high resolution of full-field digital mammography (FFDM). However, this poses extensive challenges for Artificial Intelligence (AI) models that perform image classification. The very high resolution requires computational resources usually not available to most clinicians while the identification of small and extremely varied abnormalities present in breast tissue necessitates the need for large and deep AI models. Convolutional neural networks (CNNs), as one of the main image processing models, have shown good performance in biomedical image classification tasks. In this work we develop image classification models based on two well performing CNN architectures, ResNeXt and EfficientNet. To ensure the needed model size, depth and sufficient contextual information present in the image while balancing computational requirements we utilize non-overlapping 512x512 pixel patches. The two models are trained and compared using a recently presented dataset with very high resolution FFDM images VinDr-Mammo..