Recurrent Neural Networks (RNN) are commonly used models to study neural computation. However, a comprehensive understanding of how dynamics in RNN emerge from the underlying connectivity is largely lacking. Previous work derived such an understanding for RNN fulfilling very specific constraints on their connectivity, but it is unclear whether the resulting insights apply more generally. Here we study how network dynamics are related to network connectivity in RNN trained without any specific constraints on several tasks previously employed in neuroscience. Despite the apparent high-dimensional connectivity of these RNN, we show that a low-dimensional, functionally relevant subspace of the weight matrix can be found through the identification of \textit{operative} dimensions, which we define as components of the connectivity whose removal has a large influence on local RNN dynamics. We find that a weight matrix built from only a few operative dimensions is sufficient for the RNN to operate with the original performance, implying that much of the high-dimensional structure of the trained connectivity is functionally irrelevant. The existence of a low-dimensional, operative subspace in the weight matrix simplifies the challenge of linking connectivity to network dynamics and suggests that independent network functions may be placed in specific, separate subspaces of the weight matrix to avoid catastrophic forgetting in continual learning.

Recurrent Neural Networks (RNN) are commonly used models to study neural computation. However, a comprehensive understanding of how dynamics in RNN emerge from the underlying connectivity is largely lacking. Previous work derived such an understanding for RNN fulfilling very specific constraints on their connectivity, but it is unclear whether the resulting insights apply more generally. Here we study how network dynamics are related to network connectivity in RNN trained without any specific constraints on several tasks previously employed in neuroscience. Despite the apparent high-dimensional connectivity of these RNN, we show that a low-dimensional, functionally relevant subspace of the weight matrix can be found through the identification of \textit{operative} dimensions, which we define as components of the connectivity whose removal has a large influence on local RNN dynamics.

Today's most powerful machine learning approaches are typically designed to train stateless architectures with predefined layers and differentiable activation functions. While these approaches have led to unprecedented successes in areas such as natural language processing and image recognition, the trained models are also susceptible to making mistakes that a human would not. In this paper, we take the view that true intelligence may require the ability of a machine learning model to manage internal state, but that we have not yet discovered the most effective algorithms for training such models. We further postulate that such algorithms might not necessarily be based on gradient descent over a deep architecture, but rather, might work best with an architecture that has discrete activations and few initial topological constraints (such as multiple predefined layers). We present one attempt in our ongoing efforts to design such a training algorithm, applied to an architecture with binary activations and only a single matrix of weights, and show that it is able to form useful representations of natural language text, but is also limited in its ability to leverage large quantities of training data. We then provide ideas for improving the algorithm and for designing other training algorithms for similar architectures. Finally, we discuss potential benefits that could be gained if an effective training algorithm is found, and suggest experiments for evaluating whether these benefits exist in practice.