神经流形上的模型预测控制
Model Predictive Control on the Neural Manifold
AI总结：
本文研究了神经流形上的潜在动力学控制，对比了PID和MPC两种方法，发现MPC在部分可观测和噪声环境下控制更准确且调参更少，为探索流形动力学与外部刺激的因果关系提供了框架。
摘要：
神经流形是刻画神经群体复杂行为的一种极具吸引力的理论框架。然而，许多用于识别这些低维子空间的工具仅具有相关性，对底层动力学的洞察力有限。精确控制回路的潜在活动能力将使研究人员能够研究神经流形的结构与功能。我们使用闭环、动态生成的感官输入，模拟了对神经群体潜在动力学的控制。使用脉冲神经网络（SNN）作为神经回路模型，我们找到了网络活动（神经流形）和一组显著视觉刺激的低维表示。经典和最优控制领域提供了多种方法来控制神经流形上的动力学，这些方法在性能、计算成本和实现难易程度上各不相同。在此，我们关注两种常用的控制方法：比例-积分-微分（PID）控制和模型预测控制（MPC）。PID 是一种计算量轻、易于实现的控制器。相比之下，MPC 是一种基于模型的预测性控制器，其计算成本和工程开销要高得多。我们在潜在空间的轨迹跟踪任务中评估了这两种方法，设定条件为部分可观测且存在未知噪声。虽然两种控制器在某些情况下都能成功控制神经流形上的潜在动力学，但 MPC 始终产生更准确的控制，且需要更少的超参数调整。这些结果展示了如何使用数据驱动的动力学模型在神经流形上应用 MPC，并提供了一个框架来实验测试流形动力学与外部刺激之间的因果关系。
英文摘要：
Neural manifolds are an attractive theoretical framework for characterizing the complex behaviors of neural populations. However, many of the tools for identifying these low-dimensional subspaces are correlational and provide limited insight into the underlying dynamics. The ability to precisely control the latent activity of a circuit would allow researchers to investigate the structure and function of neural manifolds. We simulate controlling the latent dynamics of a neural population using closed-loop, dynamically generated sensory inputs. Using a spiking neural network (SNN) as a model of a neural circuit, we find low-dimensional representations of both the network activity (the neural manifold) and a set of salient visual stimuli. The fields of classical and optimal control offer a range of methods to choose from for controlling dynamics on the neural manifold, which differ in performance, computational cost, and ease of implementation. Here, we focus on two commonly used control methods: proportional-integral-derivative (PID) control and model predictive control (MPC). PID is a computationally lightweight controller that is simple to implement. In contrast, MPC is a model-based, anticipatory controller with a much higher computational cost and engineering overhead. We evaluate both methods on trajectory-following tasks in latent space, under partial observability and in the presence of unknown noise. While both controllers in some cases were able to successfully control the latent dynamics on the neural manifold, MPC consistently produced more accurate control and required less hyperparameter tuning. These results demonstrate how MPC can be applied on the neural manifold using data-driven dynamics models, and provide a framework to experimentally test for causal relationships between manifold dynamics and external stimuli.
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