Adam J. Eisen

Anesthetic-induced unconsciousness may arise partly from a change in how brain areas can manipulate each other’s activity. To quantify this change, we use control-theoretic tools that can precisely characterize how easily subsystems in complex networks can control each other. These tools rely on the Jacobian of the dynamics, an object that fully specifies how inputs to a function affect the outputs. We built on JacobianODE, a method for data-driven Jacobian learning, to enable its application to neural recordings. We developed a deep learning framework that recovers directional, nonlinear control from partially observed multi-area recordings by combining delay-coordinate embedding, a volume-preserving invertible encoder, and latent dynamics via JacobianODE. We validated our framework on the Lorenz system and a partially observed working-memory recurrent neural network. We then applied it to local field potential recordings from posterior parietal (PPC), superior temporal gyrus (STG), frontal eye fields (FEF), and ventrolateral prefrontal cortex (vlPFC) in two non-human primates, comparing wakefulness with propofol anesthesia. Anesthesia pervasively reduced the ability of areas to control each other, both in terms of driving towards novel states and stabilizing along existing trajectories. This change in ease of control was driven by a decrease in the magnitude of interareal coupling. Directional ease of driving control from PPC to vlPFC and FEF to vlPFC was increased under anesthesia, providing a potential mechanism for paradoxical excitation observed during propofol infusion. Together, these results recast anesthetic unconsciousness as a directional breakdown of cortical control.

Different classes of anesthetics induce unconsciousness despite acting through distinct molecular mechanisms, raising the possibility that their convergent effects arise at the level of the dynamics of neural population activity. To explore this, we analyze intracortical electrophysiological recordings during infusions of propofol, ketamine, and dexmedetomidine, applying a rigorous method to estimate the stability of population dynamics during anesthesia. We find that all three anesthetics, despite their molecular differences, similarly affect cortical states by reducing dynamic stability. The estimated destabilization is corroborated by the slower recovery from sensory perturbations and longer stimulus-induced autocorrelation times observed during the anesthetic infusions. Destabilization is most prevalent in the low-frequency band of the population dynamics, linking it to the well-known increase in low-frequency power during anesthesia. Together, these findings suggest that cortical destabilization may be a shared neural correlate of anesthetic-induced unconsciousness and provide a plausible link to the low-frequency oscillations observed during anesthesia.

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 dy- namics 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 ad- dress 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 JacobianODEs 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.

Every day, hundreds of thousands of people undergo general anesthesia. One hypothesis is that anesthesia disrupts dynamic stability-the ability of the brain to balance excitability with the need to be stable and controllable. To test this hypothesis, we developed a method for quantifying changes in population-level dynamic stability in complex systems: delayed linear analysis for stability estimation (DeLASE). Propofol was used to transition animals between the awake state and anesthetized unconsciousness. DeLASE was applied to macaque cortex local field potentials (LFPs). We found that neural dynamics were more unstable in unconsciousness compared with the awake state. Cortical trajectories mirrored predictions from destabilized linear systems. We mimicked the effect of propofol in simulated neural networks by increasing inhibitory tone. This in turn destabilized the networks, as observed in the neural data. Our results suggest that anesthesia disrupts dynamical stability that is required for consciousness.

How can we tell whether two neural networks utilize the same internal processes for a particular computation? This question is pertinent for multiple subfields of neuroscience and machine learning, including neuroAI, mechanistic interpretability, and brain-machine interfaces. Standard approaches for comparing neural networks focus on the spatial geometry of latent states. Yet in recurrent networks, computations are implemented at the level of dynamics, and two networks performing the same computation with equivalent dynamics need not exhibit the same geometry. To bridge this gap, we introduce a novel similarity metric that compares two systems at the level of their dynamics, called Dynamical Similarity Analysis (DSA). Our method incorporates two components: Using recent advances in data-driven dynamical systems theory, we learn a high-dimensional linear system that accurately captures core features of the original nonlinear dynamics. Next, we compare different systems passed through this embedding using a novel extension of Procrustes Analysis that accounts for how vector fields change under orthogonal transformation. In four case studies, we demonstrate that our method disentangles conjugate and non-conjugate recurrent neural networks (RNNs), while geometric methods fall short. We additionally show that our method can distinguish learning rules in an unsupervised manner. Our method opens the door to comparative analyses of the essential temporal structure of computation in neural circuits.

To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that unobserved variables can be recovered from the history of only a handful of observed variables. To test whether language models are effectively constructing delay embeddings, we measure the capacities of sequence models to reconstruct unobserved dynamics. We trained 1-layer transformer decoders and state-space sequence models on next-step prediction from noisy, partially-observed time series data. We found that each sequence layer can learn a viable embedding of the underlying system. However, state-space models have a stronger inductive bias than transformers-in particular, they more effectively reconstruct unobserved information at initialization, leading to more parameter-efficient models and lower error on dynamics tasks. Our work thus forges a novel connection between dynamical systems and deep learning sequence models via delay embedding theory.