The static synaptic connectivity of neuronal circuits stands in direct
contrast to the dynamics of their function. As in changing community
interactions, different neurons can participate actively in various
combinations to effect behaviors at different times. We introduce an
unsupervised approach to learn the dynamic affinities between neurons in live,
behaving animals, and to reveal which communities form among neurons at
different times. The inference occurs in two major steps. First, pairwise
non-linear affinities between neuronal traces from brain-wide calcium activity
are organized by non-negative tensor factorization (NTF). Each factor specifies
which groups of neurons are most likely interacting for an inferred interval in
time, and for which animals. Finally, a generative model that allows for
weighted community detection is applied to the functional motifs produced by
NTF to reveal a dynamic functional connectome. Since time codes the different
experimental variables (e.g., application of chemical stimuli), this provides
an atlas of neural motifs active during separate stages of an experiment (e.g.,
stimulus application or spontaneous behaviors). Results from our analysis are
experimentally validated, confirming that our method is able to robustly
predict causal interactions between neurons to generate behavior. Code is
available at this https URL

使用无监督方法从脑内活体神经元跟踪中学习动态亲和力，揭示神经元在不同时间形成的群体互动，进而构建动态功能连接图。

学习神经生物网络中功能连接组的动态表示

Learning dynamic representations of the functional connectome in  neurobiological networks

Learning relies on coordinated synaptic changes in recurrently connected
populations of neurons. Therefore, understanding the collective evolution of
synaptic connectivity over learning is a key challenge in neuroscience and
machine learning. In particular, recent work has shown that the weight matrices
of task-trained RNNs are typically low rank, but how this low rank structure
unfolds over learning is unknown. To address this, we investigate the rank of
the 3-tensor formed by the weight matrices throughout learning. By fitting RNNs
of varying rank to large-scale neural recordings during a motor learning task,
we find that the inferred weights are low-tensor-rank and therefore evolve over
a fixed low-dimensional subspace throughout the entire course of learning. We
next validate the observation of low-tensor-rank learning on an RNN trained to
solve the same task by performing a low-tensor-rank decomposition directly on
the ground truth weights, and by showing that the method we applied to the data
faithfully recovers this low rank structure. Finally, we present a set of
mathematical results bounding the matrix and tensor ranks of gradient descent
learning dynamics which show that low-tensor-rank weights emerge naturally in
RNNs trained to solve low-dimensional tasks. Taken together, our findings
provide novel constraints on the evolution of population connectivity over
learning in both biological and artificial neural networks, and enable reverse
engineering of learning-induced changes in recurrent network dynamics from
large-scale neural recordings.

通过大规模神经记录，我们研究了学习过程中权重矩阵形成的 3-Tensor 的秩，并发现推断得到的权重具有较低的张量秩，并且通过数学结果证明了较低的张量秩权重在训练低维任务的 RNN 中自然地产生。