Biological function arises through the dynamical interactions of multiple subsystems, including those between brain areas, within gene regulatory networks, and more. A common approach to understanding these systems is to model the dynamics of each subsystem and characterize communication between them. An alternative approach is through the lens of control theory: how the subsystems control one another. This approach involves inferring the directionality, strength, and contextual modulation of control between subsystems. However, methods for understanding subsystem control are typically linear and cannot adequately describe the rich contextual effects enabled by nonlinear complex systems. To bridge this gap, we devise a data-driven nonlinear control-theoretic framework to characterize subsystem interactions via the Jacobian of the dynamics. We address the challenge of learning Jacobians from time-series data by proposing the JacobianODE, a deep learning method that leverages properties of the Jacobian to directly estimate it for arbitrary dynamical systems from data alone. We show that JacobianODE models outperform existing Jacobian estimation methods on challenging systems, including high-dimensional chaos. Applying our approach to a multi-area recurrent neural network (RNN) trained on a working memory selection task, we show that the “sensory” area gains greater control over the “cognitive” area over learning. Furthermore, we leverage the JacobianODE to directly control the trained RNN, enabling precise manipulation of its behavior. Our work lays the foundation for a theoretically grounded and data-driven understanding of interactions among biological subsystems.

Grid cells in the medial entorhinal cortex create remarkable periodic maps of explored space during navigation. Recent studies show that they form similar maps of abstract cognitive spaces. Examples of such abstract environments include auditory tone sequences in which the pitch is continuously varied or images in which abstract features are continuously deformed (e.g., a cartoon bird whose legs stretch and shrink). Here, we hypothesize that the brain generalizes how it maps spatial domains to mapping abstract spaces. To sidestep the computational cost of learning representations for each high-dimensional sensory input, the brain extracts self-consistent, low-dimensional descriptions of displacements across abstract spaces, leveraging the spatial velocity integration of grid cells to efficiently build maps of different domains. Our neural network model for abstract velocity extraction factorizes the content of these abstract domains from displacements within the domains to generate content-independent and self-consistent, low-dimensional velocity estimates. Crucially, it uses a self-supervised geometric consistency constraint that requires displacements along closed loop trajectories to sum to zero, an integration that is itself performed by the downstream grid cell circuit over learning. This process results in high fidelity estimates of velocities and allowed transitions in abstract domains, a crucial prerequisite for efficient map generation in these high-dimensional environments. We also show how our method outperforms traditional dimensionality reduction and deep-learning based motion extraction networks on the same set of tasks. This is the first neural network model to explain how grid cells can flexibly represent different abstract spaces and makes the novel prediction that they should do so while maintaining their population correlation and manifold structure across domains. Fundamentally, our model sheds light on the mechanistic origins of cognitive flexibility and transfer of representations across vastly different domains in brains, providing a potential self-supervised learning (SSL) framework for leveraging similar ideas in transfer learning and data-efficient generalization in machine learning and robotics.

Recurrent neural networks (RNNs) are often used to model circuits in the brain and can solve a variety of difficult computational problems requiring memory, error correction, or selection (Hopfield, 1982; Maass et al., 2002; Maass, 2011). However, fully connected RNNs contrast structurally with their biological counterparts, which are extremely sparse (about 0.1%). Motivated by the neocortex, where neural connectivity is constrained by physical distance along cortical sheets and other synaptic wiring costs, we introduce locality masked RNNs (LM-RNNs) that use task-agnostic predetermined graphs with sparsity as low as 4%. We study LM-RNNs in a multitask learning setting relevant to cognitive systems neuroscience with a commonly used set of tasks, 20-Cog-tasks (Yang et al., 2019). We show through reductio ad absurdum that 20-Cog-tasks can be solved by a small pool of separated autapses that we can mechanistically analyze and understand. Thus, these tasks fall short of the goal of inducing complex recurrent dynamics and modular structure in RNNs. We next contribute a new cognitive multitask battery, Mod-Cog, consisting of up to 132 tasks that expands by about seven-fold the number of tasks and task complexity of 20-Cog-tasks. Importantly, while autapses can solve the simple 20-Cog-tasks, the expanded task set requires richer neural architectures and continuous attractor dynamics. On these tasks, we show that LM-RNNs with an optimal sparsity result in faster training and better data efficiency than fully connected networks.

Content-addressable memory (CAM) networks, so-called because stored items can be recalled by partial or corrupted versions of the items, exhibit near-perfect recall of a small number of information-dense patterns below capacity and a ’memory cliff’ beyond, such that inserting a single additional pattern results in catastrophic loss of all stored patterns. We propose a novel CAM architecture, Memory Scaffold with Heteroassociation (MESH), that factorizes the problems of internal attractor dynamics and association with external content to generate a CAM continuum without a memory cliff: Small numbers of patterns are stored with complete information recovery matching standard CAMs, while inserting more patterns still results in partial recall of every pattern, with a graceful trade-off between pattern number and pattern richness. Motivated by the architecture of the Entorhinal-Hippocampal memory circuit in the brain, MESH is a tripartite architecture with pairwise interactions that uses a predetermined set of internally stabilized states together with heteroassociation between the internal states and arbitrary external patterns. We show analytically and experimentally that for any number of stored patterns, MESH nearly saturates the total information bound (given by the number of synapses) for CAM networks, outperforming all existing CAM models.