Natural perception relies inherently on inferring causal structure in the environment. However, the neural mechanisms and functional circuits that are essential for representing and updating the hidden causal structure during multisensory processing are unknown. To address this, monkeys were trained to infer the probability of a potential common source from visual and proprioceptive signals on the basis of their spatial disparity in a virtual reality system. The proprioceptive drift reported by monkeys demonstrated that they combined historical information and current multisensory signals to estimate the hidden common source and subsequently updated both the causal structure and sensory representation. Single-unit recordings in premotor and parietal cortices revealed that neural activity in premotor cortex represents the core computation of causal inference, characterizing the estimation and update of the likelihood of integrating multiple sensory inputs at a trial-by-trial level. In response to signals from premotor cortex, neural activity in parietal cortex also represents the causal structure and further dynamically updates the sensory representation to maintain consistency with the causal inference structure. Thus, our results indicate how premotor cortex integrates historical information and sensory inputs to infer hidden variables and selectively updates sensory representations in parietal cortex to support behavior. This dynamic loop of frontal-parietal interactions in the causal inference framework may provide the neural mechanism to answer long-standing questions regarding how neural circuits represent hidden structures for body-awareness and agency.

We understand the brain in representational terms. E.g., we understand spatial navigation by appealing to the spatial properties that hippocampal cells represent, and the operations hippocampal circuits perform on those representations (Moser et al., 2008). Philosophers have been concerned with the nature of representation, and recently neuroscientists entered the debate, focusing specifically on neural representations. (Baker & Lansdell, n.d.; Egan, 2019; Piccinini & Shagrir, 2014; Poldrack, 2020; Shagrir, 2001). We want to know what representations are, how to discover them in the brain, and why they matter so much for our understanding of the brain. Those questions are framed in a traditional philosophical way: we start with explanations that use representational notions, and to more deeply understand those explanations we ask, what are representations — what is the definition of representation? What is it for some bit of neural activity to be a representation? I argue that there is an alternative, and much more fruitful, approach. Rather than asking what representations are, we should ask what the use of representational *notions* allows us to do in neuroscience — what thinking in representational terms helps scientists do or explain. I argue that this framing offers more fruitful ground for interdisciplinary collaboration by distinguishing the philosophical concerns that have a place in neuroscience from those that don’t (namely the definitional or metaphysical questions about representation). And I argue for a particular view of representational notions: they allow us to impose the structure of one domain onto another as a model of its causal structue. So, e.g., thinking about the hippocampus as representing spatial properties is a way of taking structures in those spatial properties, and projecting those structures (and algorithms that would implement them) them onto the brain as models of its causal structure.