Animals continuously merge information across their senses, and use these combined signals to guide their behaviour. In the brain, these multisensory computations are performed by circuits rich with complex connections like skips [1] - bypassing certain layers, and feedback pathways which allow information to flow from later (multisensory) to earlier (‘unisensory’) parts of the network [2]. However, pure-feedforward models have been shown to be optimal for many multisensory tasks [3,4], commonly used to test experimental subjects or computational models; raising the question, what role do non-feedforward connections play in multisensory computations? To explore this, we designed a series of increasingly complex tasks in which spatially-embedded agents must navigate, forage or hunt in multisensory environments (Fig.A). In these tasks agents mapped their local-sensations to actions using two types of policies. Some agents implemented feedforward, rule-based algorithms - which have previously been shown to be optimal for a wide class of multisensory tasks [4,5]. Others, used neural networks - with arbitrary architectures evolved using the NEAT (NeuroEvolution of Augmenting Topologies) algorithm [6], which begins with a population of networks (with various weights and architectures) then discovers solutions by iteratively: evaluating each network’s fitness, then creating new populations by varying the weights and architectures of the top networks (Fig.B). Using this approach we found notable differences in performance between the feedforward algorithms, though the evolved non-feedforward architectures performed significantly better. Beyond performance, studying the population of evolved networks allowed us to make clear links between structure, function, energetic cost, and robustness to noise. For example, to solve one of our navigation tasks networks evolved two main architectures, which performed equivalently in low noise settings (in which they were evolved) but diverged when tested with increasing sensor noise (Fig.C). Overall, our work demonstrates the utility of non-feedforward architectures in multisensory computations and, more broadly, provides a general framework for linking network structure to behavioural function.