Inferring computational dynamics from neural measurements using deep recurrent neural networks

在理论神经科学中，大脑中的计算过程通常被认为是根据潜在的随机神经系统动力学来实现的。认知过程，如工作记忆、决策、间隔时间或思维序列，已经被描述为吸引子状态、这些状态之间的概率转换、慢瞬态或鞍节点链。因此，从这个角度来看，为了理解认知的神经基础，人们应该解开行为表现和神经活动背后的神经系统动力学。然而，神经动力学不能直接观察到，而必须从有限的、嘈杂的生理测量中推断出来，这些测量通常只探测到系统的几个自由度。因此，如果一个人有方法论工具，可以（自动）从这种“稀疏”的生理测量中恢复潜在的神经动力学，这将是非常有价值的。本提案的中心目标是开发和验证基于深度递归神经网络（RNN）的这种方法，并在神经生理学数据上对其进行探测。我们以前使用延迟嵌入和非线性基展开的组合，从多个单单元（MSU）记录中提取基本的动态特性和流的各个方面，如收敛到假定的半吸引状态。最近，我们开发了一个基于实验数据的RNN模型统计估计框架。rnn在计算和动态上是通用的，因为它们可以模拟和近似任何动态系统，因此，理论上，它足够强大，可以表示任何神经动力学和计算过程，这些过程是观察到的神经活动和行为的基础。基于之前和初步的工作，这里我们将解决一些重要的开放问题：1)现有的（深度）RNN模型的统计推断方法不能很好地随系统大小缩放，但这对于实现对动力学的良好近似和处理更大的生理数据集非常重要。在这里，我们提出了几条方法改进路线。2)更重要的是，在不同生物物理复杂性的地面真值系统上，仍然缺乏对各种模型架构和训练/推理算法的系统验证和比较，特别是对于来自高维系统的相对稀疏的数据的实验现实场景，这些数据只被部分观察到，并且系统固有噪声和测量噪声都很高。3)作为这些方法有用性的案例研究，我们将重新分析在两个不同的工作记忆任务中获得的大鼠前额叶皮层和海马的MSU记录，以解决这些区域（耦合）动态的具体问题，超出了以前的分析工具的范围。

In theoretical neuroscience, computational processes in the brain are often thought to be implemented in terms of the underlying stochastic neural system dynamics. Cognitive processes like working memory, decision making, interval timing, or thought sequences, have been described in terms of attractor states, probabilistic transitions between these, slow transients, or chains of saddle nodes, for instance. Consequently, from this point of view, for understanding the neural basis of cognition one should unravel the neural system dynamics that underlies behavioral performance and neural activity. However, neural dynamics are not directly observable but have to be inferred from a limited and noisy set of physiological measurements that usually probe only a few of the system’s degrees of freedom. It would therefore be of great value if one had methodological tools for (automatically) recovering the underlying neural dynamics from such ‘sparse’ physiological measurements. The central goal of the present proposal is to develop and validate such methods based on deep recurrent neural networks (RNN), and probe them on neurophysiological data.We have previously used a combination of delay embeddings and nonlinear basis expansions to extract from multiple single-unit (MSU) recordings essential dynamical properties and aspects of the flow, like convergence to putative semi-attracting states. More recently, we have developed a framework for statistical estimation of RNN models from experimental data. RNNs are computationally and dynamically universal in the sense that they can emulate and approximate any dynamical system, thus, in theory, are powerful enough to represent whatever neural dynamics and computational processes underlie the observed neural activity and behavior.Based on this previous and preliminary work, here we will tackle a number of important open issues: 1) Existing methods for statistical inference of (deep) RNN models do not scale very well with system size, yet this is very important for achieving good approximations to the dynamics and dealing with larger physiological data sets. Here we suggest several lines of methodological improvement. 2) More importantly, a systematic validation and comparison of various model architectures and training/inference algorithms on ground truth systems of differing biophysical complexity is still lacking, especially for experimentally realistic scenarios with comparatively sparse data from high-dimensional systems, which were only partially observed, and with high levels of both system-intrinsic and measurement noise. 3) As a case study for the usefulness of such methods, we will re-analyze MSU recordings from rat prefrontal cortex and hippocampus obtained during two different working memory tasks, to address specific issues about the (coupled) dynamics of these areas that were beyond the realm of previous analysis tools.