Inferring the connectivity of neural circuits from incomplete observations is a fundamental challenge in neuroscience. We present a covariance-based method for estimating the weight matrix of a recurrent neural network from sparse, partial measurements across multiple recording sessions. By accumulating pairwise covariance estimates across sessions where different subsets of neurons are observed, we reconstruct the full connectivity matrix without requiring simultaneous recording of all neurons. A Granger-causality refinement step enforces biological constraints via projected gradient descent. Through systematic experiments on synthetic networks modeling small brain circuits, we characterize a fundamental control-estimation tradeoff: stimulation aids identifiability but disrupts intrinsic dynamics, with the optimal level depending on measurement density. We discover that the ``incorrect'' linear approximation acts as implicit regularization -- outperforming the oracle estimator with known nonlinearity at all operating regimes -- and provide an exact characterization via the Stein--Price identity.

翻译：从不完整观测中推断神经回路的连接性是神经科学中的一个基本挑战。我们提出了一种基于协方差的方法，用于从多个记录会话中的稀疏、部分测量中估计循环神经网络的权重矩阵。通过累积不同记录会话中观察到不同神经元子集的成对协方差估计，我们在无需同时记录所有神经元的情况下重建完整的连接矩阵。Granger因果精化步骤通过投影梯度下降施加了生物学约束。通过对模拟小脑回路的合成网络进行系统实验，我们刻画了一种基本的控制-估计权衡：刺激有助于可辨识性但会破坏内在动力学，其最优水平取决于测量密度。我们发现，“不正确”的线性近似起到了隐式正则化的作用——在所有操作条件下均优于已知非线性性的Oracle估计器——并通过Stein-Price恒等式提供了精确刻画。