instruction:
In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
question:
This paper describes a new method for reducing the error in a classifier. It uses a weight adjustment update, but includes the very simple rule of either adding or subtracting the adjustment, based on whether the data point is currently larger or smaller than the desired value, and on a pointby-point basis. This gives added flexibility to the convergence procedure, where through a series of transpositions, values far away can continue towards the desired value, whereas values that are originally much closer can oscillate from one side to the other. Tests show that the method can successfully classify some known datasets. It can also work in a batch mode, with reduced training times and can be used as part of a neural network, or classifiers in general. There are also some updates on an earlier wave shape paper.
answer:
A New Oscillating-Error Technique for Classifiers


question:
Surely we want solid foundations. What kind of castle can we build on sand? What is the point of devoting effort to balconies and minarets, if the foundation may be so weak as to allow the structure to collapse of its own weight? We want our foundations set on bedrock, designed to last for generations. Who would want an architect who cannot certify the soundness of the foundations of his buildings?
answer:
Why Do We Need Foundations for Modelling Uncertainties?


question:
<lb>We show that any model trained by a stochastic gradient method with few iterations has<lb>vanishing generalization error. We prove this by showing the method is algorithmically stable<lb>in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex<lb>and continuous optimization. Our results apply to both convex and non-convex optimization<lb>under standard Lipschitz and smoothness assumptions.<lb>Applying our results to the convex case, we provide new explanations for why multiple<lb>epochs of stochastic gradient descent generalize well in practice. In the nonconvex case, we<lb>provide a new interpretation of common practices in neural networks, and provide a formal<lb>rationale for stability-promoting mechanisms in training large, deep models. Conceptually, our<lb>findings underscore the importance of reducing training time beyond its obvious benefit.
answer:

Stability of stochastic gradient descent