The mouse is one of the most studied animal models in the field of systems neuroscience. Understanding the generalized patterns and decoding the neural representations that are evoked by the diverse range of natural scene stimuli in the mouse visual cortex is one of the key quests in computational vision. In recent years, significant parallels have been drawn between the primate visual cortex and hierarchical deep neural networks. However, their generalized efficacy in understanding mouse vision has been limited. In this study, we investigate the functional alignment between the mouse visual cortex and deep learning models for object classification tasks. We first introduce a generalized representational learning strategy that uncovers a striking resemblance between the functional mapping of the mouse visual cortex and high-performing deep learning models on both top-down (population-level) and bottom-up (single cell-level) scenarios. Next, this representational similarity across the two systems is further enhanced by the addition of Neural Response Normalization (NeuRN) layer, inspired by the activation profile of excitatory and inhibitory neurons in the visual cortex. To test the performance effect of NeuRN on real-world tasks, we integrate it into deep learning models and observe significant improvements in their robustness against data shifts in domain generalization tasks. Our work proposes a novel framework for comparing the functional architecture of the mouse visual cortex with deep learning models. Our findings carry broad implications for the development of advanced AI models that draw inspiration from the mouse visual cortex, suggesting that these models serve as valuable tools for studying the neural representations of the mouse visual cortex and, as a result, enhancing their performance on real-world tasks.