The brain's computations are constrained by factors such as metabolic expenses for neural activity and signal noise. In this thesis, we investigate how the brain performs complex tasks under such constraints. We focus on two specific tasks to explore these computational costs.

First, we analyze the brain's process of making inferences from ambiguous sensory information. This task involves optimizing inference performance while considering the energy cost of transmitting reliable information between different cortical regions. We found that for sensory inputs that are sufficiently predictable, it is advantageous to send predictions from higher to lower cortical areas to conserve energy. However, when signals are harder to predict, it becomes best to send the raw sensory input directly from lower to higher cortical regions. We demonstrate how the required predictability for sending predictions changes according to different computational constraints.

Second, we explore a task where attentiveness is required to earn rewards but incurs a cost. We aim to understand how the brain balances reducing attention costs against obtaining rewards. To do this, we propose a reinforcement learning-based normative model to determine how to strategically deploy attention, and how it varies with task utility and signal statistics. Our model suggests that efficient attention involves alternating blocks of high and low attention. In extreme cases, where sensory input is quite weak during low attention states, we see that high attention is used rhythmically.