Kameron Decker Harris

Large-scale recordings of neural activity over broad anatomical areas with high spatial and temporal resolution are increasingly common in modern experimental neuroscience. Recently, recurrent switching dynamical systems have been used to tackle the scale and complexity of these data. However, an important challenge remains in providing insights into the existence and structure of recurrent linear dynamics in neural time series data. Here we test a scalable approach to time-varying autoregression with low-rank tensors to recover the recurrent dynamics in stochastic neural mass models with multiple stable attractors. We demonstrate that the parsimonious representation of time-varying system matrices in terms of temporal modes can recover the attractor structure of simple systems via clustering. We then consider simulations based on a human brain connectivity matrix in high and low global connection strength regimes, and reveal the hierarchical clustering structure of the dynamics. Finally, we explain the impact of the forecast time delay on the estimation of the underlying rank and temporal variability of the time series dynamics. This study illustrates that prediction error minimization is not sufficient to recover meaningful dynamic structure and that it is crucial to account for the three key timescales arising from dynamics, noise processes, and attractor switching.

Large-scale recordings of neural activity over broad anatomical areas with high spatial and temporal resolution are increasingly common in modern experimental neuroscience. Recently, recurrent switching dynamical systems have been used to tackle the scale and complexity of these data. However, an important challenge remains in providing insights into the existence and structure of recurrent linear dynamics in neural time series data. Here we test a scalable approach to time-varying autoregression with low-rank tensors to recover the recurrent dynamics in stochastic neural mass models with multiple stable attractors. We demonstrate that the sparse representation of time-varying system matrices in terms of temporal modes can recover the attractor structure of simple systems via clustering. We then consider simulations based on a human brain connectivity matrix in high and low global connection strength regimes, and reveal the hierarchical clustering structure of the dynamics. Finally, we explain the impact of the forecast time delay on the estimation of the underlying rank and temporal variability of the time series dynamics. This study illustrates that prediction error minimization is not sufficient to recover meaningful dynamic structure and that it is crucial to account for the three key timescales arising from dynamics, noise processes, and attractor switching.

The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.

The pre-Bötzinger complex (preBotC), located in the medulla, is the essential rhythm-generating neural network for breathing. The actions of opioids on this network impair its ability to generate robust, rhythmic output, contributing to life-threatening opioid-induced respiratory depression (OIRD). The occurrence of OIRD varies across individuals and internal and external states, increasing the risk of opioid use, yet the mechanisms of this variability are largely unknown. In this study, we utilize a computational model of the preBötC to perform several in silico experiments exploring how differences in network topology and the intrinsic properties of preBötC neurons influence the sensitivity of the network rhythm to opioids. We find that rhythms produced by preBötC networks in silico exhibit variable responses to simulated opioids, similar to the preBötC network in vitro . This variability is primarily due to random differences in network topology and can be manipulated by imposed changes in network connectivity and intrinsic neuronal properties. Our results identify features of the preBötC network that may regulate its susceptibility to opioids. Significance Statement: The neural network in the brainstem that generates the breathing rhythm is disrupted by opioid drugs. However, this response can be surprisingly unpredictable. By constructing computational models of this rhythm-generating network, we illustrate how random differences in the distribution of biophysical properties and connectivity patterns within individual networks can predict their response to opioids, and we show how modulation of these network features can make breathing more susceptible or resistant to the effects of opioids.

Brains must represent the outside world so that animals survive and thrive. In early sensory systems, neural populations have diverse receptive fields structured to detect important features in inputs, yet significant variability has been ignored in classical models of sensory neurons. We model neuronal receptive fields as random, variable samples from parameterized distributions and demonstrate this model in two sensory modalities using data from insect mechanosensors and mammalian primary visual cortex. Our approach leads to a significant theoretical connection between the foundational concepts of receptive fields and random features, a leading theory for understanding artificial neural networks. The modeled neurons perform a randomized wavelet transform on inputs, which removes high frequency noise and boosts the signal. Further, these random feature neurons enable learning from fewer training samples and with smaller networks in artificial tasks. This structured random model of receptive fields provides a unifying, mathematically tractable framework to understand sensory encodings across both spatial and temporal domains.

The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classic theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.

Brains must represent the outside world so that animals survive and thrive. In early sensory systems, neural populations have diverse receptive fields structured to detect important features in inputs, yet significant variability has been ignored in classical models of sensory neurons. We model neuronal receptive fields as random, variable samples from parameterized distributions and demonstrate this model in two sensory modalities using data from insect mechanosensors and mammalian primary visual cortex. Our approach leads to a significant theoretical connection between the foundational concepts of receptive fields and random features, a leading theory for understanding artificial neural networks. The modeled neurons perform a randomized wavelet transform on inputs, which removes high frequency noise and boosts the signal. Further, these random feature neurons enable learning from fewer training samples and with smaller networks in artificial tasks. This structured random model of receptive fields provides a unifying, mathematically tractable framework to understand sensory encodings across both spatial and temporal domains.

We prove an analogue of Alon’s spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara–Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A by-product of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

We prove an analogue of Alon's spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara-Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A byproduct of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full-rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.