2,234 research outputs found
Convergence Results for Neural Networks via Electrodynamics
We study whether a depth two neural network can learn another
depth two network using gradient descent. Assuming a linear output node, we show that the question of whether gradient descent converges to the target function is equivalent to the following question in electrodynamics: Given k fixed protons in R^d, and k electrons, each moving due to the attractive force from the protons and repulsive force from the remaining electrons, whether at equilibrium all the electrons will be matched up with the protons, up to a permutation. Under the standard electrical force, this follows from the classic Earnshaw\u27s theorem. In our setting,
the force is determined by the activation function and the
input distribution. Building on this equivalence, we prove the
existence of an activation function such that gradient descent learns at least one of the hidden nodes in the target network.
Iterating, we show that gradient descent can be used to learn the entire network one node at a time
Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument
We consider a new model for shunting inhibitory cellular neural networks,
retarded functional differential equations with piecewise constant argument.
The existence and exponential stability of almost periodic solutions are
investigated. An illustrative example is provided.Comment: 24 pages, 1 figur
QFlow lite dataset: A machine-learning approach to the charge states in quantum dot experiments
Over the past decade, machine learning techniques have revolutionized how
research is done, from designing new materials and predicting their properties
to assisting drug discovery to advancing cybersecurity. Recently, we added to
this list by showing how a machine learning algorithm (a so-called learner)
combined with an optimization routine can assist experimental efforts in the
realm of tuning semiconductor quantum dot (QD) devices. Among other
applications, semiconductor QDs are a candidate system for building quantum
computers. The present-day tuning techniques for bringing the QD devices into a
desirable configuration suitable for quantum computing that rely on heuristics
do not scale with the increasing size of the quantum dot arrays required for
even near-term quantum computing demonstrations. Establishing a reliable
protocol for tuning that does not rely on the gross-scale heuristics developed
by experimentalists is thus of great importance. To implement the machine
learning-based approach, we constructed a dataset of simulated QD device
characteristics, such as the conductance and the charge sensor response versus
the applied electrostatic gate voltages. Here, we describe the methodology for
generating the dataset, as well as its validation in training convolutional
neural networks. We show that the learner's accuracy in recognizing the state
of a device is ~96.5 % in both current- and charge-sensor-based training. We
also introduce a tool that enables other researchers to use this approach for
further research: QFlow lite - a Python-based mini-software suite that uses the
dataset to train neural networks to recognize the state of a device and
differentiate between states in experimental data. This work gives the
definitive reference for the new dataset that will help enable researchers to
use it in their experiments or to develop new machine learning approaches and
concepts.Comment: 18 pages, 6 figures, 3 table
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