Dynamics of Supervised Learning with Restricted Training Sets

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the relevant performance measures, incorporating the old formalism in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves to single-layer networks and realizable tasks.Comment: 36 pages, latex2e, 12 eps figures (to be publ in: Proc Newton Inst Workshop on On-Line Learning '97

Do Campaign Contribution Limits Curb the Influence of Money in Politics?

Over 40% of countries around the world have adopted limits on campaign contributions to curb the influence of money in politics. Yet, we have limited knowledge on whether and how these limits achieve this goal. With a regression discontinuity design that uses institutional rules on contribution limits in Colombian municipalities, we show that looser limits increase the number and value of public contracts assigned to the winning candidate’s donors. The evidence suggests that this is explained by looser limits concentrating influence over the elected candidate among top donors and not by a reduction in electoral competition or changes in who runs for office. We further show that looser limits worsen the performance of donor-managed contracts: they are more likely to run over costs and require time extensions. Overall, this paper demonstrates a direct link between campaign contribution limits, donor kickbacks, and worse government contract performance

Superfluidity of Dense 4^4He in Vycor

We calculate properties of a model of $^4$He in Vycor using the Path Integral Monte Carlo method. We find that $^4$He forms a distinct layered structure with a highly localized first layer, a disordered second layer with some atoms delocalized and able to give rise to the observed superfluid response, and higher layers nearly perfect crystals. The addition of a single $^3$He atom was enough to bring down the total superfluidity by blocking the exchange in the second layer. Our results are consistent with the persistent liquid layer model to explain the observations. Such a model may be relevant to the experiments on bulk solid $^4$He, if there is a fine network of grain boundaries in those systems.Comment: 4 pages, 4 figure