Efficient Representation of Natural Image Patches

In the complex domain of neural information processing, discerning fundamental principles from ancillary details remains a significant challenge. While there is extensive knowledge about the anatomy and physiology of the early visual system, a comprehensive computational theory remains elusive. Can we gain insights into the underlying principles of a biological system by abstracting away from its detailed implementation and focusing on the fundamental problems that the system is designed to solve? Utilizing an abstract model based on minimal yet realistic assumptions, we show how to achieve the early visual system's two ultimate objectives: efficient information transmission and sensor probability distribution modeling. We show that optimizing for information transmission does not yield optimal probability distribution modeling. We illustrate, using a two-pixel (2D) system and image patches, that an efficient representation can be realized via nonlinear population code driven by two types of biologically plausible loss functions that depend solely on output. After unsupervised learning, our abstract IPU model bears remarkable resemblances to biological systems, despite not mimicking many features of real neurons, such as spiking activity. A preliminary comparison with a contemporary deep learning model suggests that the IPU model offers a significant efficiency advantage. Our model provides novel insights into the computational theory of early visual systems as well as a potential new approach to enhance the efficiency of deep learning models.