Expressive dynamics models with nonlinear injective readouts enable reliable recovery of latent features from neural activity.

The advent of large-scale neural recordings has enabled new approaches that aim to discover the computational mechanisms of neural circuits by understanding the rules that govern how their state evolves over time. While these neural dynamics cannot be directly measured, they can typically be approximated by low-dimensional models in a latent space. How these models represent the mapping from latent space to neural space can affect the interpretability of the latent representation. We show that typical choices for this mapping (e.g., linear or MLP) often lack the property of injectivity, meaning that changes in latent state are not obligated to affect activity in the neural space. During training, non-injective readouts incentivize the invention of dynamics that misrepresent the underlying system and the computation it performs. Combining our injective Flow readout with prior work on interpretable latent dynamics models, we created the Ordinary Differential equations autoencoder with Injective Nonlinear readout (ODIN), which learns to capture latent dynamical systems that are nonlinearly embedded into observed neural activity via an approximately injective nonlinear mapping. We show that ODIN can recover nonlinearly embedded systems from simulated neural activity, even when the nature of the system and embedding are unknown. Additionally, we show that ODIN enables the unsupervised recovery of underlying dynamical features (e.g., fixed points) and embedding geometry. When applied to biological neural recordings, ODIN can reconstruct neural activity with comparable accuracy to previous state-of-the-art methods while using substantially fewer latent dimensions. Overall, ODIN's accuracy in recovering ground-truth latent features and ability to accurately reconstruct neural activity with low dimensionality make it a promising method for distilling interpretable dynamics that can help explain neural computation.

Expressive architectures enhance interpretability of dynamics-based neural population models.

Artificial neural networks that can recover latent dynamics from recorded neural activity may provide a powerful avenue for identifying and interpreting the dynamical motifs underlying biological computation. Given that neural variance alone does not uniquely determine a latent dynamical system, interpretable architectures should prioritize accurate and low-dimensional latent dynamics. In this work, we evaluated the performance of sequential autoencoders (SAEs) in recovering latent chaotic attractors from simulated neural datasets. We found that SAEs with widely-used recurrent neural network (RNN)-based dynamics were unable to infer accurate firing rates at the true latent state dimensionality, and that larger RNNs relied upon dynamical features not present in the data. On the other hand, SAEs with neural ordinary differential equation (NODE)-based dynamics inferred accurate rates at the true latent state dimensionality, while also recovering latent trajectories and fixed point structure. Ablations reveal that this is mainly because NODEs (1) allow use of higher-capacity multi-layer perceptrons (MLPs) to model the vector field and (2) predict the derivative rather than the next state. Decoupling the capacity of the dynamics model from its latent dimensionality enables NODEs to learn the requisite low-D dynamics where RNN cells fail. Additionally, the fact that the NODE predicts derivatives imposes a useful autoregressive prior on the latent states. The suboptimal interpretability of widely-used RNN-based dynamics may motivate substitution for alternative architectures, such as NODE, that enable learning of accurate dynamics in low-dimensional latent spaces.

Encoding of limb state by single neurons in the cuneate nucleus of awake monkeys.

The cuneate nucleus (CN) is among the first sites along the neuraxis where proprioceptive signals can be integrated, transformed, and modulated. The objective of the study was to characterize the proprioceptive representations in CN. To this end, we recorded from single CN neurons in three monkeys during active reaching and passive limb perturbation. We found that many neurons exhibited responses that were tuned approximately sinusoidally to limb movement direction, as has been found for other sensorimotor neurons. The distribution of their preferred directions (PDs) was highly nonuniform and resembled that of muscle spindles within individual muscles, suggesting that CN neurons typically receive inputs from only a single muscle. We also found that the responses of proprioceptive CN neurons tended to be modestly amplified during active reaching movements compared to passive limb perturbations, in contrast to cutaneous CN neurons whose responses were not systematically different in the active and passive conditions. Somatosensory signals thus seem to be subject to a "spotlighting" of relevant sensory information rather than uniform suppression as has been suggested previously.NEW & NOTEWORTHY The cuneate nucleus (CN) is the somatosensory gateway into the brain, and only recently has it been possible to record these signals from an awake animal. We recorded single CN neurons in monkeys. Proprioceptive CN neurons appear to receive input from very few muscles, and their sensitivity to movement changes reliably during reaching relative to passive arm perturbations. Sensitivity is generally increased, but not exclusively so, as though CN "spotlights" critical proprioceptive information during reaching.

Cuneate nucleus: The somatosensory gateway to the brain.

Much remains unknown about the transformation of proprioceptive afferent input from the periphery to the cortex. Until recently, the only recordings from neurons in the cuneate nucleus (CN) were from anesthetized animals. We are beginning to learn more about how the sense of proprioception is transformed as it propagates centrally. Recent recordings from microelectrode arrays chronically implanted in CN have revealed that CN neurons with muscle-like properties have a greater sensitivity to active reaching movements than to passive limb displacement, and we find that these neurons have receptive fields that resemble single muscles. In this review, we focus on the varied uses of proprioceptive input and the possible role of CN in processing this information.

Methodological considerations for a chronic neural interface with the cuneate nucleus of macaques.

While the response properties of neurons in the somatosensory nerves and anterior parietal cortex have been extensively studied, little is known about the encoding of tactile and proprioceptive information in the cuneate nucleus (CN) or external cuneate nucleus (ECN), the first recipients of upper limb somatosensory afferent signals. The major challenge in characterizing neural coding in CN/ECN has been to record from these tiny, difficult-to-access brain stem structures. Most previous investigations of CN response properties have been carried out in decerebrate or anesthetized animals, thereby eliminating the well-documented top-down signals from cortex, which likely exert a strong influence on CN responses. Seeking to fill this gap in our understanding of somatosensory processing, we describe an approach to chronically implanting arrays of electrodes in the upper limb representation in the brain stem in primates. First, we describe the topography of CN/ECN in rhesus macaques, including its somatotopic organization and the layout of its submodalities (touch and proprioception). Second, we describe the design of electrode arrays and the implantation strategy to obtain stable recordings. Third, we show sample responses of CN/ECN neurons in brain stem obtained from awake, behaving monkeys. With this method, we are in a position to characterize, for the first time, somatosensory representations in CN and ECN of primates.NEW & NOTEWORTHY In primates, the neural basis of touch and of our sense of limb posture and movements has been studied in the peripheral nerves and in somatosensory cortex, but coding in the cuneate and external cuneate nuclei, the first processing stage for these signals in the central nervous system, remains an enigma. We have developed a method to record from these nuclei, thereby paving the way to studying how sensory information from the limb is encoded there.