Learned multi-stability in mechanical networks

We contrast the distinct frameworks of materials design and physical learning in creating elastic networks with desired stable states. In design, the desired states are specified in advance and material parameters can be optimized on a computer with this knowledge. In learning, the material physically experiences the desired stable states in sequence, changing the material so as to stabilize each additional state. We show that while designed states are stable in networks of linear Hookean springs, sequential learning requires specific non-linear elasticity. We find that such non-linearity stabilizes states in which strain is zero in some springs and large in others, thus playing the role of Bayesian priors used in sparse statistical regression. Our model shows how specific material properties allow continuous learning of new functions through deployment of the material itself

Platonic model of mind as an approximation to neurodynamics

Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view

Optogenetic perturbations reveal the dynamics of an oculomotor integrator

Many neural systems can store short-term information in persistently firing neurons. Such persistent activity is believed to be maintained by recurrent feedback among neurons. This hypothesis has been fleshed out in detail for the oculomotor integrator (OI) for which the so-called “line attractor” network model can explain a large set of observations. Here we show that there is a plethora of such models, distinguished by the relative strength of recurrent excitation and inhibition. In each model, the firing rates of the neurons relax toward the persistent activity states. The dynamics of relaxation can be quite different, however, and depend on the levels of recurrent excitation and inhibition. To identify the correct model, we directly measure these relaxation dynamics by performing optogenetic perturbations in the OI of zebrafish expressing halorhodopsin or channelrhodopsin. We show that instantaneous, inhibitory stimulations of the OI lead to persistent, centripetal eye position changes ipsilateral to the stimulation. Excitatory stimulations similarly cause centripetal eye position changes, yet only contralateral to the stimulation. These results show that the dynamics of the OI are organized around a central attractor state—the null position of the eyes—which stabilizes the system against random perturbations. Our results pose new constraints on the circuit connectivity of the system and provide new insights into the mechanisms underlying persistent activity

Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients

Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients in response to stimulation. Even when using the same stimulation parameters in the same patient, wide variability in the duration of transient response has been reported. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well understood. To understand the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and excitable states, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell there before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. Based on the analysis, we propose an explanation of why stimulation induced epileptiform activity may vary between trials, and predict how the variability could be related to ongoing oscillatory background activity.Comment: http://journal.frontiersin.org/article/10.3389/fncom.2017.00025/ful

A survey of random processes with reinforcement

The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Controlling Chaotic Maps using Next-Generation Reservoir Computing

In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic H\'enon map, including controlling the system between unstable fixed-points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only 10 data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error.Comment: 9 pages, 8 figure

Enhancing associative memory recall and storage capacity using confocal cavity QED

Funding: Y.G. and B.M. acknowledgefunding from the Stanford Q-FARM Graduate Student Fellowship and the NSF Graduate Research Fellowship, respectively. J.K. acknowledges support from the Leverhulme Trust (IAF-2014-025), and S.G. acknowledges funding from the James S. McDonnell and Simons Foundations and an NSF Career Award.We introduce a near-term experimental platform for realizing an associative memory. It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity. The associative memory is realized by a confocal cavity QED neural network, with the modes serving as the synapses, connecting a network of superradiant atomic spin ensembles,which serve as the neurons. Memories are encoded in the connectivity matrix between the spins and can be accessed through the input and output of patterns of light. Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms. Our scheme has two conceptually novel elements. First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin glass regime as a physical parameter is tuned—the positions of ensembles within the cavity. Second, and more importantly, the spins relax via deterministic steepest-descent dynamics rather than Glauber dynamics. We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network’s ability to store and recall memories beyond that of the standard Hopfield model. Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase. Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible.Publisher PDFPeer reviewe