Low-rank recurrent neural networks (lrRNNs) are a class of models that uncover low-dimensional latent dynamics underlying neural population activity. Although their functional connectivity is low-rank, it lacks independence interpretations, making it difficult to assign distinct computational roles to different latent dimensions. To address this, we propose the Factored Recurrent Neural Network (FacRNN), a generative lrRNN framework that assumes group-wise independence among latent dynamics while allowing flexible within-group entanglement. These independent latent groups allow latent dynamics to evolve separately, but are internally rich for complex computation. We reformulate the lrRNN under a variational autoencoder (VAE) framework, enabling us to introduce a partial correlation penalty that encourages independence between groups of latent dimensions. Experiments on synthetic, monkey M1, and mouse voltage imaging data show that FacRNN consistently improves the disentanglement and interpretability of learned neural latent trajectories in low-dimensional space and low-rank connectivity over baseline lrRNNs that do not encourage group-wise independence.

翻译：低秩循环神经网络（lrRNNs）是一类揭示神经群体活动背后低维潜在动态的模型。尽管其功能连接具有低秩特性，但缺乏独立可解释性，导致难以将不同的计算角色分配给不同潜在维度。为解决此问题，我们提出分解循环神经网络（FacRNN），这是一种生成式lrRNN框架，假设潜在动态在组间保持独立，同时允许组内灵活耦合。这些独立潜在组使动态能分别演化，但其内部结构丰富以支持复杂计算。我们在变分自编码器（VAE）框架下重新构建lrRNN，从而引入部分相关性惩罚项，以促进潜在维度组间的独立性。在合成数据、猴M1区及小鼠电压成像数据上的实验表明，与不鼓励组间独立性的基线lrRNN相比，FacRNN能显著提升低维空间中学到的神经潜在轨迹及低秩连接的可解耦性与可解释性。