Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of “kick neurons” initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures — fully connected, cyclic, and linear-chain — reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

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.

According to a widely held view, neurons in lateral geniculate nucleus (LGN) operate on visual stimuli in a linear fashion. There is ample evidence, however, that LGN responses are not entirely linear. To account for nonlinearities we propose a model that synthesizes more than 30 years of research in the field. Model neurons have a linear receptive field, and a nonlinear, divisive suppressive field. The suppressive field computes local root-mean- square contrast. To test this model we recorded responses from LGN of anesthetized paralyzed cats. We estimate model parameters from a basic set of measurements and show that the model can accurately predict responses to novel stimuli. The model might serve as the new standard model of LGN responses. It specifies how visual processing in LGN involves both linear filtering and divisive gain control.