Deep Residual Learning via Large Sample Mean-Field Stochastic Optimization

We study a class of stochastic optimization problems of the mean-field type arising in the optimal training of a deep residual neural network. We consider the sampling problem arising from a continuous layer idealization, and establish the existence of optimal relaxed controls when the training set has finite size. The core of our paper is to prove the Gamma-convergence of the sequence of sampled objective functionals, i.e., show that as the size of the training set grows large, the minimizer of the sampled relaxed problem converges to that of the limiting optimization problem. We connect the limit of the large sampled objective functional to the unique solution, in the trajectory sense, of a nonlinear Fokker-Planck-Kolmogorov (FPK) equation in a random environment. We construct an example to show that, under mild assumptions, the optimal network weights can be numerically computed by solving a second-order differential equation with Neumann boundary conditions in the sense of distributions

Circuitry of nuclear factor κB signaling

Over the past few years, the transcription factor nuclear factor (NF)-κB and the proteins that regulate it have emerged as a signaling system of pre-eminent importance in human physiology and in an increasing number of pathologies. While NF-κB is present in all differentiated cell types, its discovery and early characterization were rooted in understanding B-cell biology. Significant research efforts over two decades have yielded a large body of literature devoted to understanding NF-κB's functioning in the immune system. NF-κB has been found to play roles in many different compartments of the immune system during differentiation of immune cells and development of lymphoid organs and during immune activation. NF-κB is the nuclear effector of signaling pathways emanating from many receptors, including those of the inflammatory tumor necrosis factor and Toll-like receptor superfamilies. With this review, we hope to provide historical context and summarize the diverse physiological functions of NF-κB in the immune system before focusing on recent advances in elucidating the molecular mechanisms that mediate cell type-specific and stimulus-specific functions of this pleiotropic signaling system. Understanding the genetic regulatory circuitry of NF-κB functionalities involves system-wide measurements, biophysical studies, and computational modeling

Bootstrapping bilinear models of robotic sensorimotor cascades

We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior information, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of bilinear dynamics sensors, in which the derivative of the observations are a bilinear form of the control commands and the observations themselves. This class of models is simple yet general enough to represent the main phenomena of three representative robotics sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on hebbian learning, and that leads to a simple and bioplausible control strategy. The convergence properties of learning and control are demonstrated with extensive simulations and by analytical arguments

Integrated chaos generators

This paper surveys the different design issues, from mathematical model to silicon, involved on the design of integrated circuits for the generation of chaotic behavior.Comisión Interministerial de Ciencia y Tecnología 1FD97-1611(TIC)European Commission ESPRIT 3110

Yet Another Tutorial of Disturbance Observer: Robust Stabilization and Recovery of Nominal Performance

This paper presents a tutorial-style review on the recent results about the disturbance observer (DOB) in view of robust stabilization and recovery of the nominal performance. The analysis is based on the case when the bandwidth of Q-filter is large, and it is explained in a pedagogical manner that, even in the presence of plant uncertainties and disturbances, the behavior of real uncertain plant can be made almost similar to that of disturbance-free nominal system both in the transient and in the steady-state. The conventional DOB is interpreted in a new perspective, and its restrictions and extensions are discussed