\chapter*{Abstract}
Predictive coding is one of the most influential theories and computational models of the brain in modern neuroscience. It posits that the brain constructs an internal generative model of the world, continuously predicting sensory input and updating itself by minimizing the mismatch between prediction and reality. Neural activity, in this framework, reflects the brain’s attempt to infer the hidden causes behind its sensory experiences. With strong theoretical roots in the Bayesian Brain hypothesis and a concrete implementation through artificial neural networks that resemble biological circuitry, predictive coding has significantly influenced theoretical neuroscience and has begun to inform methods in artificial intelligence.

This thesis aims to push the boundary of predictive coding towards three crucial  topics of the brain that are underexplored within the predictive coding framework: space, time and memory. These aspects are important as they support how the continuum of sensory experiences are represented in the brain. They are also intertwined, which requests a single, unified theoretical account. This thesis will start with modeling \textit{memories} of individual events, using an extension of predictive coding models that incorporates recurrent connections observed in the brain's memory system. We will establish a theoretical relationship between this recurrent predictive coding model with other influential memory models in neuroscience, suggesting a shared underlying principle that may reflect real brain mechanisms. We will then step into the realm of \textit{time}, proposing a temporal extension of predictive coding. Applying it to the visual system, we will show that the model develops similar dynamic representations to the visual cortex. We will also apply this model to memory, although this time sequential memories of dynamic events. We will show that it successfully performs sequential memory, and presents evidence for an internal map of the events. Inspired by the latter point, we will further apply predictive coding to \textit{space}. We show that the model gives rise to grid cell–like responses—spatial patterns characterized by striking hexagonal geometry, as seen in the brain’s navigation circuits. This discovery is the first to show that predictive coding can yield biologically plausible representations beyond the sensory cortex. 

Together, these contributions suggest that predictive coding may offer a unifying computational framework for understanding how the brain encodes memory, time, and space, providing fresh insights into the computational mechanisms underlying various neural functions and representations.