Active learning of neural population dynamics using two-photon holographic optogenetics

TL;DR

This work tackles data-inefficient inference of neural population dynamics under causal perturbations by combining a low-rank autoregressive model with an active-learning strategy for photostimulation design. It develops a nuclear-norm regression framework under non-isotropic inputs and derives bounds that emphasize learning along the tangent space of the low-rank structure, enabling targeted stimuli to accelerate estimation of the causal connectivity matrix $H$ and the population dynamics. The authors demonstrate substantial data-efficiency gains (approximately 1.5–2× fewer samples) in both synthetic simulators and real mouse motor cortex data, showing that active design outperforms random or uniform stimulation baselines. The results offer a principled approach for efficient, causally interpretable interrogation of neural circuits and suggest avenues for online, closed-loop experimental implementations that leverage low-rank structure. Overall, the paper contributes a rigorous, actionable framework for active experimental design in neural population dynamics, with implications for faster discovery of circuit function and connectivity.

Abstract

Recent advances in techniques for monitoring and perturbing neural populations have greatly enhanced our ability to study circuits in the brain. In particular, two-photon holographic optogenetics now enables precise photostimulation of experimenter-specified groups of individual neurons, while simultaneous two-photon calcium imaging enables the measurement of ongoing and induced activity across the neural population. Despite the enormous space of potential photostimulation patterns and the time-consuming nature of photostimulation experiments, very little algorithmic work has been done to determine the most effective photostimulation patterns for identifying the neural population dynamics. Here, we develop methods to efficiently select which neurons to stimulate such that the resulting neural responses will best inform a dynamical model of the neural population activity. Using neural population responses to photostimulation in mouse motor cortex, we demonstrate the efficacy of a low-rank linear dynamical systems model, and develop an active learning procedure which takes advantage of low-rank structure to determine informative photostimulation patterns. We demonstrate our approach on both real and synthetic data, obtaining in some cases as much as a two-fold reduction in the amount of data required to reach a given predictive power. Our active stimulation design method is based on a novel active learning procedure for low-rank regression, which may be of independent interest.

Figures (10)

• Figure 1: (a) Two-photon imaging and holographic photostimulation platform (left) and a representative image frame (right). Purple circles indicate neurons photostimulated immediately before frame acquisition. Red and blue indicate increases and decreases of firing activity, respectively, relative to before photostimulation. (b) Example time series photostimulation inputs (top) and neural responses (bottom) from 100 randomly selected neurons (out of $d = 663$ recorded neurons identified in the FoV). (c) Neural responses $y_t$ occupy a low-dimensional subspace. Singular values from a representative dataset's demeaned neural activity data matrix (blue) indicate substantially more data variance residing in a few dozen dimensions (out of the full $d=663$ dimensional neural activity space) than is expected by chance (orange, singular values when removing low-dimensional structure by shuffling time indices independently for each neuron; note clipped horizontal axis).
• Figure 2: Example data and cross-validated model predictions. (a) Roll-out predictions of the activity of an example neuron $i$ using low-rank AR-$k$ models ($k=4$) and GRU networks for 22 example data segments (3.3s per segment; segments separated by brief horizontal spaces). Each model's predictions are seeded with the first $k=4$ timesteps (200ms) of activity from $d=663$ neurons and are then unrolled to predict the activity across all $d$ neurons over the next 66 timesteps, given the full 70-timestep sequence of photostimulation to all $d$ neurons. Most responses of neuron $i$ are tied to "direct" photostimulation of neuron $i$ (pink, first row of panels). Several "indirect responses" are tied to stimulation of other neurons $j \neq i$ that influence neuron $i$ through the population dynamics. To avoid showing all indirect stimuli (to $d-1$ neurons), only select indirect stimuli are shown (green, second row of panels). (b) Receiver operator characteristic (ROC) curve of true-positive rate and false-positive rate for response detection are calculated on indirect responses only (left) and all direct and indirect responses (right). (c) Area under ROC curve (AUROC) and (d) mean square error (MSE) for all predictions.
• Figure 3: Performance of active stimulation design on estimating learned dynamics model. For each mouse dataset, we fit a low-rank AR-$k$ model as described in \ref{['sec:model_fits']} (for ranks of 15 and 35, and $k = 4$). Treating this as a simulator of the true dynamics, we compare our active stimulation design procedure (Active, \ref{['alg:main_alg']}) to randomly choosing groups of neurons to excite (Random), and uniformly allocating stimulation across all neurons (Uniform), and plot how effectively each is able to estimate the connectivity of the simulator dynamics. For each figure and method we average over 20 trials, and plot the mean performance with error bars denoting 1 standard error (note that the error bars are barely visible as the standard deviation is very small).
• Figure 4: Performance of active learning estimating photostimulation response on held-out trials. Each mouse dataset is split into trials corresponding to a stimulus-response pair, and we consider how these trials might be ordered to obtain more effective estimates with fewer training data trials, simulating the active learning process. Our approach (Active) is motivated by the low-rank excitation criteria of \ref{['alg:main_alg']} (see \ref{['sec:detail_exp2']} for more details) and we compare with randomly choosing which trial to observe next (Random). We plot the accuracy of the learned model in predicting neural responses on held-out test trials. We consider 20 different train-test splits (with 20 trials per split), and include plots of average performance across these splits, as well as splits where Active has the largest and smallest improvement over Random. We plot error bars denoting 1 standard error (note again that the error bars are barely visible as the standard deviation is very small).
• Figure 5: Longer roll-out evaluations. Same format as in Figure \ref{['fig:low rank model']}.

Theorems & Definitions (10)

• Theorem 1
• Theorem 2: Corollary 1 of tang2011lower
• Lemma A.1
• proof
• Lemma A.2
• proof
• Lemma A.3
• proof
• Lemma A.4
• proof