Neural activity in the brain is known to encode low-dimensional, time-evolving, behaviour-related variables. A long-standing goal of neural data analysis has been to identify these variables and their mapping to neural activity. A productive and canonical approach has been to simply visualise neural "tuning curves" as a function of behaviour. However, significant discrepancies between behaviour and the true latent variables -- such as an agent thinking of position Y whilst located at position X -- distort and blur the tuning curves, decreasing their interpretability. To address this, latent variable models propose to learn the latent variable from data; these are typically expensive, hard to tune, or scale poorly, complicating their adoption. Here we propose SIMPL (Scalable Iterative Maximization of Population-coded Latents), an EM-style algorithm which iteratively optimises latent variables and tuning curves. SIMPL is fast, scalable and exploits behaviour as an initial condition to further improve convergence and identifiability. It can accurately recover latent variables in spatial and non-spatial tasks. When applied to a large hippocampal dataset SIMPL converges on smaller, more numerous, and more uniformly sized place fields than those based on behaviour, suggesting the brain may encode space with greater resolution than previously thought.

Advances in generative models have recently revolutionised machine learning. Meanwhile, in neuroscience, generative models have long been thought fundamental to animal intelligence. Understanding the biological mechanisms that support these processes promises to shed light on the relationship between biological and artificial intelligence. In animals, the hippocampal formation is thought to learn and use a generative model to support its role in spatial and non-spatial memory. Here we introduce a biologically plausible model of the hippocampal formation tantamount to a Helmholtz machine that we apply to a temporal stream of inputs. A novel component of our model is that fast theta-band oscillations (5-10 Hz) gate the direction of information flow throughout the network, training it akin to a high-frequency wake-sleep algorithm. Our model accurately infers the latent state of high-dimensional sensory environments and generates realistic sensory predictions. Furthermore, it can learn to path integrate by developing a ring attractor connectivity structure matching previous theoretical proposals and flexibly transfer this structure between environments. Whereas many models trade-off biological plausibility with generality, our model captures a variety of hippocampal cognitive functions under one biologically plausible local learning rule.