Reconstructing computational system dynamics from neural data with recurrent neural networks

Learning Fixed Points of Recurrent Neural Networks by Reparameterizing the Network Model

In computational neuroscience, recurrent neural networks are widely used to model neural activity and learning. In many studies, fixed points of recurrent neural networks are used to model neural responses to static or slowly changing stimuli, such as visual cortical responses to static visual stimuli. These applications raise the question of how to train the weights in a recurrent neural network to minimize a loss function evaluated on fixed points. In parallel, training fixed points is a central topic in the study of deep equilibrium models in machine learning. A natural approach is to use gradient descent on the Euclidean space of weights. We show that this approach can lead to poor learning performance due in part to singularities that arise in the loss surface. We use a reparameterization of the recurrent network model to derive two alternative learning rules that produce more robust learning dynamics. We demonstrate that these learning rules avoid singularities and learn more effectively than standard gradient descent. The new learning rules can be interpreted as steepest descent and gradient descent, respectively, under a non-Euclidean metric on the space of recurrent weights. Our results question the common, implicit assumption that learning in the brain should be expected to follow the negative Euclidean gradient of synaptic weights.

Intrinsic Dynamics and Neural Implementation of a Hypothalamic Line Attractor Encoding an Internal Behavioral State

Line attractors are emergent population dynamics hypothesized to encode continuous variables such as head direction and internal states. In mammals, direct evidence of neural implementation of a line attractor has been hindered by the challenge of targeting perturbations to specific neurons within contributing ensembles. Estrogen receptor type 1 (Esr1)-expressing neurons in the ventrolateral subdivision of the ventromedial hypothalamus (VMHvl) show line attractor dynamics in male mice during fighting. We hypothesized that these dynamics may encode continuous variation in the intensity of an internal aggressive state. Here, we report that these neurons also show line attractor dynamics in head-fixed mice observing aggression. We exploit this finding to identify and perturb line attractor-contributing neurons using 2-photon calcium imaging and holographic optogenetic perturbations. On-manifold perturbations demonstrate that integration and persistent activity are intrinsic properties of these neurons which drive the system along the line attractor, while transient off-manifold perturbations reveal rapid relaxation back into the attractor. Furthermore, stimulation and imaging reveal selective functional connectivity among attractor-contributing neurons. Intriguingly, individual differences among mice in line attractor stability were correlated with the degree of functional connectivity among contributing neurons. Mechanistic modelling indicates that dense subnetwork connectivity and slow neurotransmission are required to explain our empirical findings. Our work bridges circuit and manifold paradigms, shedding light on the intrinsic and operational dynamics of a behaviorally relevant mammalian line attractor.

Efficient Near-Infrared Spectrum Detection in Nondestructive Wood Testing via Transfer Network Redesign

This study systematically developed a deep transfer network for near-infrared spectrum detection using convolutional neural network modules as key components. Through meticulous evaluation, specific modules and structures suitable for constructing the near-infrared spectrum detection model were identified, ensuring its effectiveness. This study extensively analyzed the basic network components and explored three unsupervised domain adaptation structures, highlighting their applications in the nondestructive testing of wood. Additionally, five transfer networks were strategically redesigned to substantially enhance their performance. The experimental results showed that the Conditional Domain Adversarial Network and Globalized Loss Optimization Transfer network outperformed the Direct Standardization, Piecewise Direct Standardization, and Spectral Space Transformation models. The coefficients of determination for the Conditional Domain Adversarial Network and Globalized Loss Optimization Transfer network are 82.11% and 83.59%, respectively, with root mean square error prediction values of 12.237 and 11.582, respectively. These achievements represent considerable advancements toward the practical implementation of an efficient and reliable near-infrared spectrum detection system using a deep transfer network.

Trained recurrent neural networks develop phase-locked limit cycles in a working memory task

Neural oscillations are ubiquitously observed in many brain areas. One proposed functional role of these oscillations is that they serve as an internal clock, or 'frame of reference'. Information can be encoded by the timing of neural activity relative to the phase of such oscillations. In line with this hypothesis, there have been multiple empirical observations of such phase codes in the brain. Here we ask: What kind of neural dynamics support phase coding of information with neural oscillations? We tackled this question by analyzing recurrent neural networks (RNNs) that were trained on a working memory task. The networks were given access to an external reference oscillation and tasked to produce an oscillation, such that the phase difference between the reference and output oscillation maintains the identity of transient stimuli. We found that networks converged to stable oscillatory dynamics. Reverse engineering these networks revealed that each phase-coded memory corresponds to a separate limit cycle attractor. We characterized how the stability of the attractor dynamics depends on both reference oscillation amplitude and frequency, properties that can be experimentally observed. To understand the connectivity structures that underlie these dynamics, we showed that trained networks can be described as two phase-coupled oscillators. Using this insight, we condensed our trained networks to a reduced model consisting of two functional modules: One that generates an oscillation and one that implements a coupling function between the internal oscillation and external reference. In summary, by reverse engineering the dynamics and connectivity of trained RNNs, we propose a mechanism by which neural networks can harness reference oscillations for working memory. Specifically, we propose that a phase-coding network generates autonomous oscillations which it couples to an external reference oscillation in a multi-stable fashion.