Neural Networks for Modeling Neural Spiking in S1 Cortex

Abstract

Somatosensation is composed of two distinct modalities: touch, arising from sensors in the skin, and proprioception, resulting primarily from sensors in the muscles, combined with these same cutaneous sensors. In contrast to the wealth of information about touch, we know quite less about the nature of the signals giving rise to proprioception at the cortical level. Likewise, while there is considerable interest in developing encoding models of touch-related neurons for application to brain machine interfaces, much less emphasis has been placed on an analogous proprioceptive interface. Here we investigate the use of Artificial Neural Networks (ANNs) to model the relationship between the firing rates of single neurons in area 2, a largely proprioceptive region of somatosensory cortex (S1) and several types of kinematic variables related to arm movement. To gain a better understanding of how these kinematic variables interact to create the proprioceptive responses recorded in our datasets, we train ANNs under different conditions, each involving a different set of input and output variables. We explore the kinematic variables that provide the best network performance, and find that the addition of information about joint angles and/or muscle lengths significantly improves the prediction of neural firing rates. Our results thus provide new insight regarding the complex representations of the limb motion in S1: that the firing rates of neurons in area 2 may be more closely related to the activity of peripheral sensors than it is to extrinsic hand position. In addition, we conduct numerical experiments to determine the sensitivity of ANN models to various choices of training design and hyper-parameters. Our results provide a baseline and new tools for future research that utilizes machine learning to better describe and understand the activity of neurons in S1.

Keywords: artificial neural networks; limb-state encoding; monkey; reaching; single neurons; somatosensory cortex.

FIGURE 1

Performance of the ANNs trained on different classes of inputs. The first three bars correspond to networks trained to predict S1 neural activity using different types of kinematic signals as inputs: extrinsic hand coordinates (red), joint angles (blue), and muscle lengths (green). The next three bars correspond to networks trained using the first derivative of these signals. The last three bars indicate encoding performance with all kinematic signals, their derivatives, and the full combination of signals and derivatives, respectively. Each ANN model was trained on the simultaneous prediction of the activity of all recorded neurons.

FIGURE 2

Boxplots illustrate the prediction performance across all neurons for all three datasets: H, L, and C. These results correspond to networks trained with the full combination of signals X (hand position, joint angles, and muscle lengths) and their derivatives $\dot{X}$ as inputs.

FIGURE 3

Effect of the firing rate on measures of encoding performance. (A) Relation between the firing rate of each neuron and the mean ability to predict its activity as measured by pseudo-R² (pR²). (B) Effect of the firing rate of each neuron on the variability (standard error of the mean; SEM) of prediction performance (pR²) for that neuron. Here SEM refers to fluctuations across the 10-folds used for cross validation.

FIGURE 4

Histogram of $\Delta {\mathit{pR}}_n^2$, the difference in pseudo-R² for each neuron in dataset H when subtracting the value obtained from a model that predicts only this specific neuron from the value obtained by the model that predicts all neurons together. A positive value implies an increase in performance in favor of the model trained to predict the activity of all neurons simultaneously.

FIGURE 5

Performance comparison between a recurrent ANN and a feedforward ANN using the same input variables. Here X refers to using hand position, joint angles, and muscle lengths as inputs; $\dot{X}$ refers to using the first time derivatives of these signals as inputs; and X + $\dot{X}$ refers to using both the signals and their temporal derivatives as inputs.

FIGURE 6

Dependence of the predictive performance of an ANN on the amount of training data. Randomly selected increasingly large contiguous subsets of the datasets H, L, and C were used to train a succession of ANNs.

FIGURE 7

Effects of early stopping, L1, and L2 regularization on the performance of ANN models for the three datasets: H, C, and L. No early stopping was used when either L1 or L2 weight decay regularization was added to the loss function.