Feedback control in the nervous system: from cells and circuits to behaviour
The nervous system is fundamentally a closed loop control device: the output of actions continually influences the internal state and subsequent actions. This is true at the single cell and even the molecular level, where “actions” take the form of signals that are fed back to achieve a variety of functions, including homeostasis, excitability and various kinds of multistability that allow switching and storage of memory. It is also true at the behavioural level, where an animal’s motor actions directly influence sensory input on short timescales, and higher level information about goals and intended actions are continually updated on the basis of current and past actions. Studying the brain in a closed loop setting requires a multidisciplinary approach, leveraging engineering and theory as well as advances in measuring and manipulating the nervous system. I will describe our recent attempts to achieve this fusion of approaches at multiple levels in the nervous system, from synaptic signalling to closed loop brain machine interfaces.
Deep kernel methods
Deep neural networks (DNNs) with the flexibility to learn good top-layer representations have eclipsed shallow kernel methods without that flexibility. Here, we take inspiration from deep neural networks to develop a new family of deep kernel method. In a deep kernel method, there is a kernel at every layer, and the kernels are jointly optimized to improve performance (with strong regularisation). We establish the representational power of deep kernel methods, by showing that they perform exact inference in an infinitely wide Bayesian neural network or deep Gaussian process. Next, we conjecture that the deep kernel machine objective is unimodal, and give a proof of unimodality for linear kernels. Finally, we exploit the simplicity of the deep kernel machine loss to develop a new family of optimizers, based on a matrix equation from control theory, that converges in around 10 steps.
Firing Homeostasis in Neural Circuits: From Basic Principles to Malfunctions
Neural circuit functions are stabilized by homeostatic mechanisms at long timescales in response to changes in experience and learning. However, we still do not know which specific physiological variables are being stabilized, nor which cellular or neural-network components comprise the homeostatic machinery. At this point, most evidence suggests that the distribution of firing rates amongst neurons in a brain circuit is the key variable that is maintained around a circuit-specific set-point value in a process called firing rate homeostasis. Here, I will discuss our recent findings that implicate mitochondria as a central player in mediating firing rate homeostasis and its impairments. While mitochondria are known to regulate neuronal variables such as synaptic vesicle release or intracellular calcium concentration, we searched for the mitochondrial signaling pathways that are essential for homeostatic regulation of firing rates. We utilize basic concepts of control theory to build a framework for classifying possible components of the homeostatic machinery in neural networks. This framework may facilitate the identification of new homeostatic pathways whose malfunctions drive instability of neural circuits in distinct brain disorders.
Information and Decision-Making
In recent years it has become increasingly clear that (Shannon) information is a central resource for organisms, akin in importance to energy. Any decision that an organism or a subsystem of an organism takes involves the acquisition, selection, and processing of information and ultimately its concentration and enaction. It is the consequences of this balance that will occupy us in this talk. This perception-action loop picture of an agent's life cycle is well established and expounded especially in the context of Fuster's sensorimotor hierarchies. Nevertheless, the information-theoretic perspective drastically expands the potential and predictive power of the perception-action loop perspective. On the one hand information can be treated - to a significant extent - as a resource that is being sought and utilized by an organism. On the other hand, unlike energy, information is not additive. The intrinsic structure and dynamics of information can be exceedingly complex and subtle; in the last two decades one has discovered that Shannon information possesses a rich and nontrivial intrinsic structure that must be taken into account when informational contributions, information flow or causal interactions of processes are investigated, whether in the brain or in other complex processes. In addition, strong parallels between information and control theory have emerged. This parallelism between the theories allows one to obtain unexpected insights into the nature and properties of the perception-action loop. Through the lens of information theory, one can not only come up with novel hypotheses about necessary conditions for the organization of information processing in a brain, but also with constructive conjectures and predictions about what behaviours, brain structure and dynamics and even evolutionary pressures one can expect to operate on biological organisms, induced purely by informational considerations.