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At least 73 records · Page 4

Cycle equivalence classes, orthogonal Weingarten calculus, and the mean field theory of memristive systems

Abstract It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators, the dynamics can be understood in terms of lower dimensional equations. This is the case, for instance, of memristive circuits. Memristive systems are important classes of devices with wide-ranging applications in electronic circuits, artificial neural networks, and memory storage. We show that such mean-field theories can emerge from averages over the group of orthogonal matrices, interpreted as cycle-preserving transformations applied to the projector operator describing Kirchhoff’s laws. Our results provide insights into the fundamental principles underlying the behavior of resistive and memristive circuits and highlight the importance of conservation laws for their mean-field theories. In addition, we argue that our results shed light on the nature of the critical avalanches observed in quasi-two-dimensional nanowires as boundary phenomena.

97 MATHEMATICS AND COMPUTING↗

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

Gonzalez, J. Jesus↗

Ferroelectric Memory Capacitors For Neural Networks

Thin-film ferroelectric capacitors proposed as nonvolatile analog memory devices. Intended primarily for use as synaptic connections in electronic neural networks. Connection strengths (synaptic weights) stored as nonlinear remanent polarizations of ferroelectric films. Ferroelectric memory and interrogation capacitors combined into memory devices in vertical or lateral configurations. Photoconductive layer modulated by light provides variable resistance to alter bias signal applied to memory capacitor. Features include nondestructive readout, simplicity, and resistance to ionizing radiation. Interrogated without destroying stored analog data. Also amenable to very-large-scale integration. Allows use of ac coupling, eliminating errors caused by dc offsets in amplifier circuits of neural networks.

Thakoor, Sarita↗

Analytic Theory for the Dynamics of Wide Quantum Neural Networks

Here, parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parametrized quantum circuits in the limit of a large number of qubits and variational parameters. Then, we find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. Finally, we validate our analytic results with numerical experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolution of connectivity architecture in the Drosophila mushroom body

Brain evolution has primarily been studied at the macroscopic level by comparing the relative size of homologous brain centers between species. How neuronal circuits change at the cellular level over evolutionary time remains largely unanswered. Here, using a phylogenetically informed framework, we compare the olfactory circuits of three closely related Drosophila species that differ in their chemical ecology: the generalists Drosophila melanogaster and Drosophila simulans and Drosophila sechellia that specializes on ripe noni fruit. We examine a central part of the olfactory circuit that, to our knowledge, has not been investigated in these species—the connections between projection neurons and the Kenyon cells of the mushroom body—and identify species-specific connectivity patterns. We found that neurons encoding food odors connect more frequently with Kenyon cells, giving rise to species-specific biases in connectivity. These species-specific connectivity differences reflect two distinct neuronal phenotypes: in the number of projection neurons or in the number of presynaptic boutons formed by individual projection neurons. Finally, behavioral analyses suggest that such increased connectivity enhances learning performance in an associative task. Our study shows how fine-grained aspects of connectivity architecture in an associative brain center can change during evolution to reflect the chemical ecology of a species.

59 BASIC BIOLOGICAL SCIENCES↗

Cell specific photoswitchable agonist for reversible control of endogenous dopamine receptors

Dopamine controls diverse behaviors and their dysregulation contributes to many disorders. Our ability to understand and manipulate the function of dopamine is limited by the heterogenous nature of dopaminergic projections, the diversity of neurons that are regulated by dopamine, the varying distribution of the five dopamine receptors (DARs), and the complex dynamics of dopamine release. In order to improve our ability to specifically modulate distinct DARs, here we develop a photo-pharmacological strategy using a Membrane anchored Photoswitchable orthogonal remotely tethered agonist for the Dopamine receptor (MP-D). Our design selectively targets D1R/D5R receptor subtypes, most potently D1R (MP-D1 ago ), as shown in HEK293T cells. In vivo, we targeted dorsal striatal medium spiny neurons where the photo-activation of MP-D1 ago increased movement initiation, although further work is required to assess the effects of MP-D1 ago on neuronal function. Our method combines ligand and cell type-specificity with temporally precise and reversible activation of D1R to control specific aspects of movement. Our results provide a template for analyzing dopamine receptors.

59 BASIC BIOLOGICAL SCIENCES↗

Porous-Floating-Gate Field-Effect Transistor

Porous-floating-gate, "vertical" field-effect transistor proposed as programmable analog memory device especially suitable for use in electronic neural networks. Analog value of electrical conductance of device represents synaptic weight (strength of synaptic connection) repeatedly modified by application of suitable writing or erasing voltage. Suited for hardware implementations of massively parallel neural-network architectures for two important reasons: vertical transistor structure requires only two external electrodes, and use of tailored amorphous semiconductors provides choice of very wide range of low conductivity values, dictated by overall power dissipation requirements in massively parallel neural-network circuits.

Thakoor, Anilkumar P.↗

Artificial Neural Network with Hardware Training and Hardware Refresh

A neural network circuit is provided having a plurality of circuits capable of charge storage. Also provided is a plurality of circuits each coupled to at least one of the plurality of charge storage circuits and constructed to generate an output in accordance with a neuron transfer function. Each of a plurality of circuits is coupled to one of the plurality of neuron transfer function circuits and constructed to generate a derivative of the output. A weight update circuit updates the charge storage circuits based upon output from the plurality of transfer function circuits and output from the plurality of derivative circuits. In preferred embodiments, separate training and validation networks share the same set of charge storage circuits and may operate concurrently. The validation network has a separate transfer function circuits each being coupled to the charge storage circuits so as to replicate the training network s coupling of the plurality of charge storage to the plurality of transfer function circuits. The plurality of transfer function circuits may be constructed each having a transconductance amplifier providing differential currents combined to provide an output in accordance with a transfer function. The derivative circuits may have a circuit constructed to generate a biased differential currents combined so as to provide the derivative of the transfer function.

Tuan A Duong↗

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

When in-memory computing meets spiking neural networks—A perspective on device-circuit-system-and-algorithm co-design

This review explores the intersection of bio-plausible artificial intelligence in the form of spiking neural networks (SNNs) with the analog in-memory computing (IMC) domain, highlighting their collective potential for low-power edge computing environments. Through detailed investigation at the device, circuit, and system levels, we highlight the pivotal synergies between SNNs and IMC architectures. Additionally, we emphasize the critical need for comprehensive system-level analyses, considering the inter-dependencies among algorithms, devices, circuit, and system parameters, crucial for optimal performance. An in-depth analysis leads to the identification of key system-level bottlenecks arising from device limitations, which can be addressed using SNN-specific algorithm–hardware co-design techniques. This review underscores the imperative for holistic device to system design-space co-exploration, highlighting the critical aspects of hardware and algorithm research endeavors for low-power neuromorphic solutions.

Physics↗