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

The great turn-of-the-century housing boom

This article explains the recent high levels of residential investment and rates of homeownership.Home ownership ; Housing - Finance ; Housing - Prices

Price and tax policy for semi-subsistence agriculture in Ethiopia

In the case of semi-subsistence agriculture where wage employment is not available, the role played by prices and taxes in determining production and consumption decisions is not clearly established by economic theories of household choice. This study demonstrates that where choices in production, consumption, and leisure can be made independently, farmers will decide what to grow on the basis of their preferences for marketed goods. The paper also points out that the choice will be affected by the level and type of taxation imposed. The paper shows the impact of four taxes -- agricultural revenue, land, production and marketed goods consumption -- on crop production and tax revenues. This paper also reports on a model of production in Ethiopia. The results of this study give strong evidence of the role of producer and consumer prices in semi-subsistence agriculture. In addition, the results show the importance of production capacity, household and climatic factors in agricultural development.Environmental Economics&Policies,Economic Theory&Research,Crops&Crop Management Systems,Agricultural Knowledge&Information Systems,Consumption

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

Optimisation of on-line principal component analysis

Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very efficient in speeding up the learning process. They are investigated further for gaining insight into the learning rates' time-dependence, which is then employed for devising simple practical methods to improve training performance. Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure

Dynamics of Learning with Restricted Training Sets I: General Theory

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 and the learning dynamics is of a spin-glass nature, with the composition of the training set playing the role of quenched disorder. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the two relevant performance measures (training error and generalization error), incorporating the old formalism developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves in this paper to single-layer networks and realizable tasks.Comment: 39 pages, LaTe

The Case for Early Arabia and Arabic Language: A Reply to the New Arabia Theory by Ahmad al-Jallad

A reply to an article published on May 23rd, 2018, in The New Yorker magazine by Elias Muhanna, titled A New History of Arabia, Written in Stone, introducing a new theory by Ahmad al-Jallad, a Harvard trained scholar of ancient Near East languages and scripts, asserting that the Arabic language (and presumably the Arabs) was originated in the south Levant desert and migrated southward. This theory would reverse the established conclusions set forth by the esteemed work of numerous Islamic Arab linguists and historians, over more than a thousand years, who believed the Arabs and the Arabic language originated in the southern Arabian Peninsula region. This reply also addresses several claims raised by al-Jallad, Sofia Chair of Arabic at Ohio State University, to support his new theory, during his recent lecture in Kuwait on December 16th, 2019, titled The Rise of Arabic: From an Epic Past to an Evidence-Based History