Latent dynamics models have emerged as powerful tools for modeling and
interpreting neural population activity. Recently, there has been a focus on
incorporating simultaneously measured behaviour into these models to further
disentangle sources of neural variability in their latent space. These
approaches, however, are limited in their ability to capture the underlying
neural dynamics (e.g. linear) and in their ability to relate the learned
dynamics back to the observed behaviour (e.g. no time lag). To this end, we
introduce Targeted Neural Dynamical Modeling (TNDM), a nonlinear state-space
model that jointly models the neural activity and external behavioural
variables. TNDM decomposes neural dynamics into behaviourally relevant and
behaviourally irrelevant dynamics; the relevant dynamics are used to
reconstruct the behaviour through a flexible linear decoder and both sets of
dynamics are used to reconstruct the neural activity through a linear decoder
with no time lag. We implement TNDM as a sequential variational autoencoder and
validate it on simulated recordings and recordings taken from the premotor and
motor cortex of a monkey performing a center-out reaching task. We show that
TNDM is able to learn low-dimensional latent dynamics that are highly
predictive of behaviour without sacrificing its fit to the neural data