Tosatisfythenear -optimalityconstraintof(1), weusean estimateofthefunction (h), see(2), todefine , , (h):=1[ (h)< / ]forparameters , 0, 1. Thefunction , , (h)representswhetheran , / -optimumhasbeenfound. Wedefine r , , (h, a)=

You would be forgiven for thinking the rain this year has been relentless - because in some parts of the UK, it actually has been. Here at BBC Weather we have been watching computer models closely for signs of when that pattern will change. These computer-generated forecasts go out about two weeks into the future - and models have often been hinting at a change to colder and drier weather on that timescale. However, they have then reverted to the familiar wet pattern as we have got closer to the time. Now though, there are stronger signals of a change for some of us - albeit perhaps only a temporary one.

Paraphrases are sentences or phrases that convey the same meaning using different wording, and is fundamental to the understanding of languages [7]. Paraphrase Identification is a well-studied task of identifying if a given pair of sentences has the same meaning [51, 47, 56, 57, 31], and has many important downstream applications such as machine translation [61, 44, 40, 27], and question-answering[11,35].

Conv-PCA is a naive method proposed in Section 4.1.