The curse of dimensionality in motor cortex
Understanding how motor cortex generates movement is a foundational challenge in neuroscience. Unsupervised dimensionality reduction techniques, such as principal component analysis (PCA), are widely used to transform high-dimensional neural recordings into a compact, low-dimensional space. The dimensionality of this space--that is, the number of principal components needed to explain a fixed fraction of variance--is broadly assumed to be an intrinsic property of the underlying neural dynamics, potentially modulated by task complexity. Here, by comparing con-strained reaching and unconstrained naturalistic behaviors recorded from the same animal on the same day, we show that this assumption breaks down in two distinct ways. First, across four non-human primates, the dominant axes of low-dimensional neural activity separate behavioral contexts rather than movement kinematics, with neural activity shifting rapidly between task-specific regions of state space at task transitions. Notably, traditional dimensionality metrics are insensitive to movement complexity across tasks. Instead, unsupervised dimensionality scales with the number of recorded neurons, exhibiting non-saturating growth up to 1000 simultaneously recorded electrodes, a pattern that holds across PCA, factor analysis, shared variance component analysis, and nonlinear autoencoders. This scaling has direct consequences for decoding: while decoders trained on unsupervised subspaces improve only modestly with electrode count, super-vised methods leverage additional electrodes to separate neural states from a vanishingly small fraction of total variance (<10% at 1000 electrodes). Together, these results challenge current views on cortical dimensionality, reveal a greater-than-appreciated role for behavioral context in shaping motor cortical activity, and motivate careful consideration of computational methods as experimental data volumes scale.