Training Input-Output Recurrent Neural Networks through Spectral Methods

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score functions. We guarantee consistent learning with polynomial sample and computational complexity under transparent conditions such as non-degeneracy of model parameters, polynomial activations for the neurons, and a Markovian evolution of the input sequence. We also extend our results to Bidirectional RNN which uses both previous and future information to output the label at each time point, and is employed in many NLP tasks such as POS tagging

Financial Instability and Optimal Monetary Policy Rule

This paper investigates the effect of financial instability on the design of monetary policy rule for a small open economy. We find evidence that optimal monetary policy rule reacts directly to financial imbalances and, as a result, to the real exchange rate movements. However, optimal rule would not react to the real exchange rate changes directly if central bank does not care about the financial instability. For a quantitative analysis, impulse responses of some macroeconomic variables and financial instability to the domestic productivity and foreign country output shocks, resulting from simulation, are also analysed in this paper.Financial instability, Optimal monetary policy rule, Real exchange rate, Open economy

Modules cofinite and weakly cofinite with respect to an ideal

The purpose of the present paper is to continue the study of modules cofinite and weakly cofinite with respect to an ideal $\frak a$ of a Noetherian ring $R$. It is shown that an $R$-module $M$ is cofinite with respect to $\frak a$, if and only if, \Ext^i_R(R/\frak a,M) is finitely generated for all $i\leq {\rm cd}(\frak a,M)+1$, whenever $\dim R/\frak a=1$. In addition, we show that if $M$ is finitely generated and $H^i_{\frak a}(M)$ are weakly Laskerian for all $i\leq t-1$, then $H^i_{\frak a}(M)$ are ${\frak a}$-cofinite for all $i\leq t-1$ and for any minimax submodule $K$ of $H^{t}_{\frak a}(M)$, the $R$-modules \Hom_R(R/{\frak a}, H^{t}_{\frak a}(M)/K) and \Ext^{1}_R(R/{\frak a}, H^{t}_{\frak a}(M)/K) are finitely generated, where $t$ is a non-negative integer. Finally, we explore a criterion for weakly cofiniteness of modules with respect to an ideal of dimension one. Namely for such ideals it suffices that the two first \Ext-modules in the definition for weakly cofiniteness are weakly Laskerian. As an application of this result we deduce that the category of all ${\frak a}$-weakly cofinite modules over $R$ forms a full Abelian subcategory of the category of modules.Comment: 15 pages, To appear in J. Algebra Appl. arXiv admin note: text overlap with arXiv:1308.604