Stability of neural manifolds at minimal dimensionality despite motor representational drift

Recent work has modeled the generation of movement as emerging from a latent dynamical system. While the relationship between recorded neural populations and latent variables is non-stationary, latent trajectories populate low-dimensional manifolds that appear stable over time. However, the dimensionality of these manifolds and their relationship to motor cortical circuitry remains unclear. We propose a simple framework for extracting labeled latent variables that maintain a fixed relationship to movement parameters in a two-dimensional reaching task. Despite only capturing 3-7% of total variance and spanning two dimensions, this supervised method outperforms other common methods at an offline decoding task, and explains the long-term stability of neural manifolds observed in previous literature. We demonstrate that changes in the encoding map (from neurons to latents) is the dominant source of drift in motor cortex, while the latent map (from latents to behavior) remains stable over years. Additionally, we find that, for a two-dimensional task, neural structure is constrained by task complexity, limiting the insights that neural manifolds offer onto underlying circuitry. Our results motivate future studies to uncover causal relationships between neural computation and behavior.