The relation between neural activity and behaviorally relevant variables is at the heart of neuroscience research. When strong, this relation is termed a neural representation. There is increasing evidence, however, for partial dissociations between activity in an area and relevant external variables. While many explanations have been proposed, a theoretical framework for the relationship between external and internal variables is lacking. Here, we utilize recurrent neural networks (RNNs) to explore the question of when and how neural dynamics and the network’s output are related from a geometrical point of view. We find that training RNNs can lead to two dynamical regimes: dynamics can either be aligned with the directions that generate output variables, or oblique to them. We show that the choice of readout weight magnitude before training can serve as a control knob between the regimes, similar to recent findings in feedforward networks. These regimes are functionally distinct. Oblique networks are more heterogeneous and suppress noise in their output directions. They are furthermore more robust to perturbations along the output directions. Crucially, the oblique regime is specific to recurrent (but not feedforward) networks, arising from dynamical stability considerations. Finally, we show that tendencies toward the aligned or the oblique regime can be dissociated in neural recordings. Altogether, our results open a new perspective for interpreting neural activity by relating network dynamics and their output.

Each sensory modality has its own primary and secondary thalamic nuclei. While the primary thalamic nuclei are well understood to relay sensory information from the periphery to the cortex, the role of secondary sensory nuclei is elusive. We trained head-fixed mice to attend to one sensory modality while ignoring a second modality, namely to attend to touch and ignore vision, or vice versa. Arrays were used to record simultaneously from the secondary somatosensory thalamus (POm) and secondary visual thalamus (LP). In mice trained to respond to tactile stimuli and ignore visual stimuli, POm was robustly activated by touch and largely unresponsive to visual stimuli. A different pattern was observed when mice were trained to respond to visual stimuli and ignore touch, with POm now more robustly activated during visual trials. This POm activity was not explained by differences in movements (i.e. whisking, licking, pupil dilation) resulting from the two tasks. Post hoc histological reconstruction of array tracks through POm revealed that subregions varied in their degree of plasticity. LP exhibited similar phenomena. We conclude that behavioral training reshapes activity in secondary thalamic nuclei. Secondary nuclei respond to the same behaviorally relevant, reward-predicting stimuli regardless of stimulus modality.