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Converging evidence in human and animal models suggests that exogenous stimulation of the motor cortex (M1) elicits responses in the hand with similar modular structure to that found during voluntary grasping movements. The aim of this study was to establish the extent to which modularity in muscle responses to transcranial magnetic stimulation (TMS) to M1 resembles modularity in muscle activation during voluntary hand movements involving finger fractionation. EMG was recorded from eight hand-forearm muscles in nine healthy individuals. Modularity was defined using non-negative matrix factorization to identify low rank approximations (spatial muscle synergies) of the complex activation patterns of EMG data recorded during high density TMS mapping of M1 and voluntary formation of gestures in the American Sign Language alphabet. Analysis of synergies as a set, and individually, revealed greater than chance similarity between those derived from TMS and those derived from voluntary movement. Both datasets included synergies dominated by single intrinsic hand muscles presumably to meet the demand for highly fractionated finger movement. These results suggest a cortical role in combining corticospinal connectivity to individual intrinsic hand muscles with modular mulit-muscle activation via synergies. 

Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches generally assume a simple diagonal Gaussian prior and as a result are not able to reliably disentangle discrete factors of variation. We propose a two-level hierarchical objective to control relative degree of statistical independence between blocks of variables and individual variables within blocks. We derive this objective as a generalization of the evidence lower bound, which allows us to explicitly represent the trade-offs between mutual information between data and representation, KL divergence between representation and prior, and coverage of the support of the empirical data distribution. Experiments on a variety of datasets demonstrate that our objective can not only disentangle discrete variables, but that doing so also improves disentanglement of other variables and, importantly, generalization even to unseen combinations of factors