1,449 research outputs found
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 of a Noetherian ring
. It is shown that an -module is cofinite with respect to ,
if and only if, \Ext^i_R(R/\frak a,M) is finitely generated for all , whenever . In addition, we show that
if is finitely generated and are weakly Laskerian for
all , then are -cofinite for all
and for any minimax submodule of , the
-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
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 -weakly cofinite modules over
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
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