Seminars

We build upon and expand the efficient coding and predictive information models of neurons, presenting a novel perspective that neurons not only predict but also actively influence their future inputs through their outputs. We introduce the concept of neurons as feedback controllers of their environments, a role traditionally considered computationally demanding, particularly when the dynamical system characterizing the environment is unknown. By harnessing a novel data-driven control framework, we illustrate the feasibility of biological neurons functioning as effective feedback controllers. This innovative approach enables us to coherently explain various experimental findings that previously seemed unrelated. Our research has profound implications, potentially revolutionizing the modeling of neuronal circuits and paving the way for the creation of alternative, biologically inspired artificial neural networks.

The basal ganglia are a collection of brain areas that are connected by a variety of synaptic pathways and are a site of significant reward-related dopamine release. These properties suggest a possible role for the basal ganglia in action selection, guided by reinforcement learning. In this talk, I will discuss a framework for how this function might be performed and computational results using an upward mapping to identify putative low-dimensional control ensembles that may be involved in tuning decision policy. I will also present some recent experimental results and theory – related to effects of extracellular ion dynamics -- that run counter to the classical view of basal ganglia pathways and suggest a new interpretation of certain aspects of this framework. For those not so interested in the basal ganglia, I hope that the upward mapping approach and impact of extracellular ion dynamics will nonetheless be of interest!

Neural circuits exhibit complex activity patterns, both spontaneously and in response to external stimuli. Information encoding and learning in neural circuits depend on the ability of time-varying stimuli to control spontaneous network activity. In particular, variability arising from the sensitivity to initial conditions of recurrent cortical circuits can limit the information conveyed about the sensory input. Spiking and firing rate network models can exhibit such sensitivity to initial conditions that are reflected in their dynamic entropy rate and attractor dimensionality computed from their full Lyapunov spectrum. I will show how chaos in both spiking and rate networks depends on biophysical properties of neurons and the statistics of time-varying stimuli. In spiking networks, increasing the input rate or coupling strength aids in controlling the driven target circuit, which is reflected in both a reduced trial-to-trial variability and a decreased dynamic entropy rate. With sufficiently strong input, a transition towards complete network state control occurs. Surprisingly, this transition does not coincide with the transition from chaos to stability but occurs at even larger values of external input strength. Controllability of spiking activity is facilitated when neurons in the target circuit have a sharp spike onset, thus a high speed by which neurons launch into the action potential. I will also discuss chaos and controllability in firing-rate networks in the balanced state. For these, external control of recurrent dynamics strongly depends on correlations in the input. This phenomenon was studied with a non-stationary dynamic mean-field theory that determines how the activity statistics and the largest Lyapunov exponent depend on frequency and amplitude of the input, recurrent coupling strength, and network size. This shows that uncorrelated inputs facilitate learning in balanced networks. The results highlight the potential of Lyapunov spectrum analysis as a diagnostic for machine learning applications of recurrent networks. They are also relevant in light of recent advances in optogenetics that allow for time-dependent stimulation of a select population of neurons.

The richness of active matter's spatiotemporal patterns continues to capture our imagination. Shaping these emergent dynamics into pre-determined forms of our choosing is a grand challenge in the field. To complicate matters, multiple dynamical attractors can coexist in such systems, leading to initial condition-dependent dynamics. Consequently, non-trivial spatiotemporal inputs are generally needed to access these states. Optimal control theory provides a general framework for identifying such inputs and represents a promising computational tool for guiding experiments and interacting with various systems in soft active matter and biology. As an exemplar, I first consider an extensile active nematic fluid confined to a disk. In the absence of control, the system produces two topological defects that perpetually circulate. Optimal control identifies a time-varying active stress field that restructures the director field, flipping the system to its other attractor that rotates in the opposite direction. As a second, analogous case, I examine a small network of coupled Belousov-Zhabotinsky chemical oscillators that possesses two dominant attractors, two wave states of opposing chirality. Optimal control similarly achieves the task of attractor switching. I conclude with a few forward-looking remarks on how the same model-based control approach might come to bear on problems in biology.

It is common for animals to use self-generated movements to actively sense the surrounding environment. For instance, rodents rhythmically move their whiskers to explore the space close to their body. The mouse whisker system has become a standard model to study active sensing and sensorimotor integration through feedback loops. In this work, we developed a bioinspired spiking neural network model of the sensorimotor peripheral whisker system, modelling trigeminal ganglion, trigeminal nuclei, facial nuclei, and central pattern generator neuronal populations. This network was embedded in a virtual mouse robot, exploiting the Neurorobotics Platform, a simulation platform offering a virtual environment to develop and test robots driven by brain-inspired controllers. Eventually, the peripheral whisker system was properly connected to an adaptive cerebellar network controller. The whole system was able to drive active whisking with learning capability, matching neural correlates of behaviour experimentally recorded in mice.

The success of deep learning sparked interest in whether the brain learns by using similar techniques for assigning credit to each synaptic weight for its contribution to the network output. However, the majority of current attempts at biologically-plausible learning methods are either non-local in time, require highly specific connectivity motives, or have no clear link to any known mathematical optimization method. Here, we introduce Deep Feedback Control (DFC), a new learning method that uses a feedback controller to drive a deep neural network to match a desired output target and whose control signal can be used for credit assignment. The resulting learning rule is fully local in space and time and approximates Gauss-Newton optimization for a wide range of feedback connectivity patterns. To further underline its biological plausibility, we relate DFC to a multi-compartment model of cortical pyramidal neurons with a local voltage-dependent synaptic plasticity rule, consistent with recent theories of dendritic processing. By combining dynamical system theory with mathematical optimization theory, we provide a strong theoretical foundation for DFC that we corroborate with detailed results on toy experiments and standard computer-vision benchmarks.

The human brain is a complex organ characterized by heterogeneous patterns of interconnections. Non-invasive imaging techniques now allow for these patterns to be carefully and comprehensively mapped in individual humans, paving the way for a better understanding of how wiring supports cognitive processes. While a large body of work now focuses on descriptive statistics to characterize these wiring patterns, a critical open question lies in how the organization of these networks constrains the potential repertoire of brain dynamics. In this talk, I will describe an approach for understanding how perturbations to brain dynamics propagate through complex wiring patterns, driving the brain into new states of activity. Drawing on a range of disciplinary tools – from graph theory to network control theory and optimization – I will identify control points in brain networks and characterize trajectories of brain activity states following perturbation to those points. Finally, I will describe how these computational tools and approaches can be used to better understand the brain's intrinsic control mechanisms and their alterations in psychiatric conditions.

General anesthesia is a drug-induced, reversible condition comprised of five behavioral states: unconsciousness, amnesia (loss of memory), antinociception (loss of pain sensation), akinesia (immobility), and hemodynamic stability with control of the stress response. Our work shows that a primary mechanism through which anesthetics create these altered states of arousal is by initiating and maintaining highly structured oscillations. These oscillations impair communication among brain regions. We illustrate this effect by presenting findings from our human studies of general anesthesia using high-density EEG recordings and intracranial recordings. These studies have allowed us to give a detailed characterization of the neurophysiology of loss and recovery of consciousness due to propofol. We show how these dynamics change systematically with different anesthetic classes and with age. As a consequence, we have developed a principled, neuroscience-based paradigm for using the EEG to monitor the brain states of patients receiving general anesthesia. We demonstrate that the state of general anesthesia can be rapidly reversed by activating specific brain circuits. Finally, we demonstrate that the state of general anesthesia can be controlled using closed loop feedback control systems. The success of our research has depended critically on tight coupling of experiments, signal processing research and mathematical modeling.

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) for processing sequential data, and also in neuroscience, to understand the emergent properties of networks of real neurons. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions. However, real neurons can have gating i.e. multiplicative interactions, and gating is also a central feature of the best performing RNNs in machine learning. Here, we develop a dynamical mean-field theory (DMFT) to study the consequences of gating in RNNs. We use random matrix theory to show how gating robustly produces marginal stability and line attractors – important mechanisms for biologically-relevant computations requiring long memory. The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation-time of the dynamics. Gating is also shown to give rise to a novel, discontinuous transition to chaos, where the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity), contrary to a seminal result for additive RNNs. Critical surfaces and regions of marginal stability in the parameter space are indicated in phase diagrams, thus providing a map for principled parameter choices for ML practitioners. Finally, we develop a field-theory for gradients that arise in training, by incorporating the adjoint sensitivity framework from control theory in the DMFT. This paves the way for the use of powerful field-theoretic techniques to study training/gradients in large RNNs.

Synaptic scaling is a homeostatic normalization mechanism that preserves relative synaptic strengths by adjusting them with a common factor. This multiplicative change is believed to be critical, since synaptic strengths are involved in learning and memory retention. Further, this homeostatic process is thought to be crucial for neuronal stability, playing a stabilizing role in otherwise runaway Hebbian plasticity [1-3]. Synaptic scaling requires a mechanism to sense total neuron activity and globally adjust synapses to achieve some activity set-point [4]. This process is relatively slow, which places limits on its ability to stabilize network activity [5]. Here we show that this slow response is inevitable in realistic neuronal morphologies. Furthermore, we reveal that global scaling can in fact be a source of instability unless responsiveness or scaling accuracy are sacrificed." "A neuron with tens of thousands of synapses must regulate its own excitability to compensate for changes in input. The time requirement for global feedback can introduce critical phase lags in a neuron’s response to perturbation. The severity of phase lag increases with neuron size. Further, a more expansive morphology worsens cell responsiveness and scaling accuracy, especially in distal regions of the neuron. Local pools of reserve receptors improve efficiency, potentiation, and scaling, but this comes at a cost. Trafficking large quantities of receptors requires time, exacerbating the phase lag and instability. Local homeostatic feedback mitigates instability, but this too comes at the cost of reducing scaling accuracy." "Realization of the phase lag instability requires a unified model of synaptic scaling, regulation, and transport. We present such a model with global and local feedback in realistic neuron morphologies (Fig. 1). This combined model shows that neurons face a tradeoff between stability, accuracy, and efficiency. Global feedback is required for synaptic scaling but favors either system stability or efficiency. Large receptor pools improve scaling accuracy in large morphologies but worsen both stability and efficiency. Local feedback improves the stability-efficiency tradeoff at the cost of scaling accuracy. This project introduces unexplored constraints on neuron size, morphology, and synaptic scaling that are weakened by an interplay between global and local feedback.