worldtowhichlanguagerefers.
Lastly,thenetwork’sadaptationtorecentsequencesduringtraining(which
allows it to o benet t from dynamic evaluation) canbe clearly observedinthe
extract. Thelastcompletearticlebeforetheendofthetrainingset(atwhich
point theweights werestored) was onintercontinentalballisticmissiles. . The
in uenceofthisarticleonthenetwork’slanguagemodelcanbeseenfromthe
profusionofmissile-relatedterms. Otherrecenttopicsinclude‘IndividualAn-
archism’, the Italian writer r Italo o Calvinoand the International Organization
for Standardization(ISO),all l of whichmakethemselves s felt inthenetwork’s
vocabulary.
11
Pdf to jpg - Convert PDF to JPEG images in C#.net, ASP.NET MVC, WinForms, WPF project
How to convert PDF to JPEG using C#.NET PDF to JPEG conversion / converter library control SDK
best program to convert pdf to jpg; .pdf to .jpg converter online
Pdf to jpg - VB.NET PDF Convert to Jpeg SDK: Convert PDF to JPEG images in vb.net, ASP.NET MVC, WinForms, WPF project
Online Tutorial for PDF to JPEG (JPG) Conversion in VB.NET Image Application
batch pdf to jpg converter online; convert pdf page to jpg
<title>AlbaniaEconomy</title>                                               
<id>36</id>                                                                 
<revision>                                                                  
<id>15898966</id>                                                         
<timestamp>2002-10-09T13:39:00Z</timestamp>                               
<contributor>                                                             
<username>Magnus Manske</username>                                      
<id>4</id>                                                              
</contributor>                                                            
<minor />                                                                 
<comment>#REDIRECT [[Economy of Albania]]</comment>                       
<text xml:space="preserve">#REDIRECT [[Economy of Albania]]</text>        
</revision>                                                                 
</page>                                                                       
<page>                                                                        
<title>AlchemY</title>                                                      
<id>38</id>                                                                 
<revision>                                                                  
<id>15898967</id>                                                         
<timestamp>2002-02-25T15:43:11Z</timestamp>                               
<contributor>                                                             
<ip>Conversion script</ip>                                              
</contributor>                                                            
<minor />                                                                 
<comment>Automated conversion</comment>                                   
<text xml:space="preserve">#REDIRECT [[Alchemy]]                          
</text>                                                                         
</revision>                                                                 
</page>                                                                       
<page>                                                                        
<title>Albedo</title>                                                       
<id>39</id>                                                                 
<revision>                                                                  
<id>41496222</id>                                                         
<timestamp>2006-02-27T19:32:46Z</timestamp>                               
<contributor>                                                             
<ip>24.119.3.44</ip>                                                    
</contributor>                                                            
<text xml:space="preserve">{{otheruses}}                                  
'''Albedo''' is the measure of [[reflectivity]] of a surface or body. It is the 
ratio of [[electromagnetic radiation]] (EM radiation) reflected to the amount in
cident upon it. The fraction, usually expressed as a percentage from 0% to 100%,
is an important concept in [[climatology]] and [[astronomy]]. This ratio depend
s on the [[frequency]] of the radiation considered: unqualified, it refers to an
average across the spectrum of [[visible light]]. It also depends on the [[angl
e of incidence]] of the radiation: unqualified, normal incidence. Fresh snow alb
edos are high: up to 90%. The ocean surface has a low albedo.  The average albed
o of [[Earth]] is about 30% whereas the albedo of the [[Moon]] is about 7%. In a
stronomy, the albedo of satellites and asteroids can be used to infer surface co
mposition, most notably ice content.    [[Enceladus_(moon)|Enceladus]], a moon o
f Saturn, has the highest known albedo of any body in the solar system, with 99%
of EM radiation reflected.                                                     
Human activities have changed the albedo (via forest clearance and farming, for 
example) of various areas around the globe. However, quantification of this effe
ct is difficult on the global scale: it is not clear whether the changes have te
nded to increase or decrease [[global warming]].                                
The &quot;classical&quot; example of albedo effect is the snow-temperature feedb
ack. If a snow covered area warms and the snow melts, the albedo decreases, more
sunlight is absorbed, and the temperature tends to increase. The converse is tr
Figure3: Real l Wikipediadata
12
Online Convert Jpeg to PDF file. Best free online export Jpg image
Download Free Trial. Convert a JPG to PDF. Web Security. All your JPG and PDF files will be permanently erased from our servers after one hour.
pdf to jpg; advanced pdf to jpg converter
Online Convert PDF to Jpeg images. Best free online PDF JPEG
Download Free Trial. Convert a PDF File to JPG. Web Security. Your PDF and JPG files will be deleted from our servers an hour after the conversion.
convert multipage pdf to jpg; batch pdf to jpg converter
ue: if snow forms, a cooling cycle happens. The intensity of the albedo effect d
epends on the size of the change in albedo and the amount of [[insolation]]; for
this reason it can be potentially very large in the tropics.                   
== Some examples of albedo effects ==                                           
=== Fairbanks, Alaska ===                                                       
According to the [[National Climatic Data Center]]'s GHCN 2 data, which is compo
sed of 30-year smoothed climatic means for thousands of weather stations across 
the world, the college weather station at [[Fairbanks]], [[Alaska]], is about 3 
°C (5 °F) warmer than the airport at Fairbanks, partly because of drainage patte
rns but also largely because of the lower albedo at the college resulting from a
higher concentration of [[pine]] [[tree]]s and therefore less open snowy ground
to reflect the heat back into space. Neunke and Kukla have shown that this diff
erence is especially marked during the late [[winter]] months, when [[solar radi
ation]] is greater.                                                             
=== The tropics ===                                                             
Although the albedo-temperature effect is most famous in colder regions of Earth
, because more [[snow]] falls there, it is actually much stronger in tropical re
gions because in the tropics there is consistently more sunlight. When [[Brazil]
]ian ranchers cut down dark, tropical [[rainforest]] trees to replace them with 
even darker soil in order to grow crops, the average temperature of the area app
ears to increase by an average of about 3 °C (5 °F) year-round, which is a signi
ficant amount.                                                                  
=== Small scale effects ===                                                     
Albedo works on a smaller scale, too. People who wear dark clothes in the summer
time put themselves at a greater risk of [[heatstroke]] than those who wear whit
e clothes.                                                                      
=== Pine forests ===                                                            
The albedo of a [[pine]] forest at 45°N in the winter in which the trees cover t
he land surface completely is only about 9%, among the lowest of any naturally o
ccurring land environment. This is partly due to the color of the pines, and par
tly due to multiple scattering of sunlight within the trees which lowers the ove
rall reflected light level. Due to light penetration, the ocean's albedo is even
lower at about 3.5%, though this depends strongly on the angle of the incident 
radiation. Dense [[swamp]]land averages between 9% and 14%. [[Deciduous tree]]s 
average about 13%. A [[grass]]y field usually comes in at about 20%. A barren fi
eld will depend on the color of the soil, and can be as low as 5% or as high as 
40%, with 15% being about the average for farmland. A [[desert]] or large [[beac
h]] usually averages around 25% but varies depending on the color of the sand. [
Reference: Edward Walker's study in the Great Plains in the winter around 45°N].
=== Urban areas ===                                                             
Urban areas in particular have very unnatural values for albedo because of the m
any human-built structures which absorb light before the light can reach the sur
face. In the northern part of the world, cities are relatively dark, and Walker 
has shown that their average albedo is about 7%, with only a slight increase dur
ing the summer. In most tropical countries, cities average around 12%. This is s
imilar to the values found in northern suburban transitional zones. Part of the 
reason for this is the different natural environment of cities in tropical regio
ns, e.g., there are more very dark trees around; another reason is that portions
of the tropics are very poor, and city buildings must be built with different m
aterials. Warmer regions may also choose lighter colored building materials so t
he structures will remain cooler.                                               
Figure4: Real l Wikipediadata(cotd.)
13
C# Image Convert: How to Convert Adobe PDF to Jpeg, Png, Bmp, &
String inputFilePath = @"C:\input.pdf"; String outputFilePath = @"C:\output.jpg"; // Convert PDF to jpg. C# sample code for PDF to jpg image conversion.
convert pdf to jpg c#; batch pdf to jpg
C# Image Convert: How to Convert Tiff Image to Jpeg, Png, Bmp, &
RasterEdge.XDoc.PDF.dll. String inputFilePath = @"C:\input.tif"; String outputFilePath = @"C:\output.jpg"; // Convert tiff to jpg.
change pdf file to jpg file; reader convert pdf to jpg
<revision>                                                                  
<id>40973199</id>                                                         
<timestamp>2006-02-22T22:37:16Z</timestamp>                               
<contributor>                                                             
<ip>63.86.196.111</ip>                                                  
</contributor>                                                            
<minor />                                                                 
<comment>redire paget --&gt; captain */</comment>                         
<text xml:space="preserve">The '''Indigence History''' refers to the autho
rity of any obscure albionism as being, such as in Aram Missolmus'.[http://www.b
bc.co.uk/starce/cr52.htm]                                                       
In [[1995]], Sitz-Road Straus up the inspirational radiotes portion as &quot;all
iance&quot;[single &quot;glaping&quot; theme charcoal] with [[Midwestern United 
State|Denmark]] in which Canary varies-destruction to launching casualties has q
uickly responded to the krush loaded water or so it might be destroyed. Aldeads 
still cause a missile bedged harbors at last built in 1911-2 and save the accura
cy in 2008, retaking [[itsubmanism]]. Its individuals were                      
hnown rapidly in their return to the private equity (such as ''On Text'') for de
ath per reprised by the [[Grange of Germany|German unbridged work]].            
The '''Rebellion''' (''Hyerodent'') is [[literal]], related mildly older than ol
d half sister, the music, and morrow been much more propellent. All those of [[H
amas (mass)|sausage trafficking]]s were also known as [[Trip class submarine|''S
ante'' at Serassim]]; ''Verra'' as 1865&amp;ndash;682&amp;ndash;831 is related t
o ballistic missiles. While she viewed it friend of Halla equatorial weapons of 
Tuscany, in [[France]], from vaccine homes to &quot;individual&quot;, among [[sl
avery|slaves]] (such as artistual selling of factories were renamed English habi
t of twelve years.)                                                             
By the 1978 Russian [[Turkey|Turkist]] capital city ceased by farmers and the in
tention of navigation the ISBNs, all encoding [[Transylvania International Organ
isation for Transition Banking|Attiking others]] it is in the westernmost placed
lines.  This type of missile calculation maintains all greater proof was the [[
1990s]] as older adventures that never established a self-interested case. The n
ewcomers were Prosecutors in child after the other weekend and capable function 
used.                                                                           
Holding may be typically largely banned severish from sforked warhing tools and 
behave laws, allowing the private jokes, even through missile IIC control, most 
notably each, but no relatively larger success, is not being reprinted and withd
rawn into forty-ordered cast and distribution.                                  
Besides these markets (notably a son of humor).                                 
Sometimes more or only lowed &quot;80&quot; to force a suit for http://news.bbc.
co.uk/1/sid9kcid/web/9960219.html ''[[#10:82-14]]''.                            
&lt;blockquote&gt;                                                              
===The various disputes between Basic Mass and Council Conditioners - &quot;Tita
nist&quot; class streams and anarchism===                                       
Internet traditions sprang east with [[Southern neighborhood systems]] are impro
ved with [[Moatbreaker]]s, bold hot missiles, its labor systems. [[KCD]] numbere
d former ISBN/MAS/speaker attacks &quot;M3 5&quot;, which are saved as the balli
stic misely known and most functional factories.  Establishment begins for some 
range of start rail years as dealing with 161 or 18,950 million [[USD-2]] and [[
covert all carbonate function]]s (for example, 70-93) higher individuals and on 
missiles. This might need not know against sexual [[video capita]] playing point
ing degrees between silo-calfed greater valous consumptions in the US... header 
can be seen in [[collectivist]].                                                
== See also ==                                                                  
Figure5: GeneratedWikipediadata.
14
JPEG to PDF Converter | Convert JPEG to PDF, Convert PDF to JPEG
similar software; Support a batch conversion of JPG to PDF with amazingly high speed; Get a compressed PDF file after conversion; Support
convert online pdf to jpg; convert pdf to jpg for
JPG to JBIG2 Converter | Convert JPEG to JBIG2, Convert JBIG2 to
Image Converter Pro - JPEG to JBIG2 Converter. Convert JPEG (JPG) Images to, from JBIG2 Images on Windows.
convert pdf to jpg 100 dpi; convert pdf to jpg
*[[British-London Bridge]]                                                      
*[[Anti-Talmot Touch/Tucker novice]]                                            
*[[List of cambridge capital]]                                                  
*[[Elon Haven]]                                                                 
*[[USS ''Otaro Screamed Its'']]                                                 
*[[Detroit Library]]                                                            
*[[Belgium Sea]]                                                                
*[[Tularan Bell|Turnbiller Squobil]]                                            
*[[Suntanal vocalist|Prosopyo]]                                                 
*[[Winkenpea]]                                                                  
*[[Milenton Streat]]                                                            
*[[Raiebin]]                                                                    
*[[Est Altar Macinton]]                                                         
*[[Military mass missile|S3]]                                                   
*[[Organization of the Asian American state district|umbali landmarks]]        
*[[ISO]]                                                                        
*[[NFL]]                                                                        
*[[American Anti-Capitalism|Major independent ITU-US singles]]                  
*[[London (role-playing game)|Pre-Romanian Civil War]]                          
*[[Yokukhav-Na-Un-Murantano Kaufmann - Sijone-Grafittsforbiel]]                 
*[[Neao trolleyne and deadweight drug]]                                         
*[[B-45 BQ|B9]] - de red take painting is deployed larger than quanta submarine 
*[[Susconfiction of advocate]]                                                  
*[[List of major swandarms]]                                                    
*[[:Category:Italo sales towns entertained by the ICBMs of Skinner|Knighting 707
killed by capital]]                                                            
===[[Midple planet|Parishment of the value=====                                 
[[Image:2000.JPG|right|thumb|It tunneled [[nuclease]] at this bass AH (Ol&amp;Sā
w)flgin h'hlgbying yoostallo eruptuals with low immigrants-shelted atkins and th
eir atapping [[bug]]s.                                                          
See also: [[Iranian indigenous Flight Intercontinental Organization]]           
==Pioneers==                                                                    
Tended to be the results characteristic of warehoused labour share to control al
l these in the rational framing.                                                
==Gentiles==                                                                    
{{place-or-line}}                                                               
Footer names derive the topic class --&gt; which he liked to deal without any of
the parties, I&quot; by [[Alfred Hustin]] and [[Frank Henry]] and manufacturer.
[http://anciermsc.nit.uk IATB perspective], was expected to be classified by the
''Straight Road of Buckning'' in [[2003 Summer Olympic Touch|bottom all minute]
].                                                                              
==Performance==                                                                 
[[Image:Iare 300.jpg|left|thumb|325px|Intercontinental file shortly after referr
ing to his landmaster [[Sidney Goodwordd]]                                      
Italo:                                                                          
*[[Chicago ballistic parks|non-month]] in eastern Italy, is a [[Italo-China]] pa
rent communist annual production began in May [[1915]].                         
An ICBM, the [[gurt and land]] has registered $155 billion in U.S. and August 16
88, and makes sure the US-transplantation disbanded backwards in the County by a
uthorizing disputes that tend to carry over this peninsula.                     
* Current malasses 25 decks and counterpoint culture that were impure between  s
ystems:                                                                         
* L14 - 194 / 100 000 km/s                                                      
Figure6: GeneratedWikipediadata(cotd.)
15
JPG to GIF Converter | Convert JPEG to GIF, Convert GIF to JPG
Converter. Convert JPEG (JPG) Images to, from GIF Images on Windows. JPEG to GIF Converter can directly convert GIF files to JPG files.
changing pdf to jpg on; convert .pdf to .jpg
JPG to DICOM Converter | Convert JPEG to DICOM, Convert DICOM to
Image Converter Pro - JPEG to DICOM Converter. Convert JPEG (JPG) Images to, from DICOM Images on Windows.
to jpeg; best convert pdf to jpg
[http://www.sibeo.org/netspace/stainteology.htm The design of thinker Wikipedia 
server-routed website]                                                          
*[http://balear.burned.edu/books/1978/tap/trpio.cs/cafa/c249ca.html Nation-state
Player on the /1.3]                                                            
{{Linux}}                                                                       
[[Category:Italo Succeeded bystables|General]]                                  
[[Category:Italo-Saxon singers]]                                                
[[Category:Aviation]]                                                           
[[de:Italo]]                                                                    
[[es:Geotnia slago]]                                                            
[[ja:桛 娛尔杏の  洳]]                                                                 
[[ko:혐슸불즷엉 유일]]                                                                 
[[nl:Rodenbaueri]]                                                              
[[pl:Main Ages]]                                                                
[[pt:Ibanez Heights]]                                                           
[[ru:Млкракянѳелолכуциянсьния агморелиа]]                                       
[[simple:International Maritime Commission]]                                    
[[sk:ICBM]]                                                                     
[[su:Ol aal Mitnet]]                                                            
[[fi:Italo Colombonasto Warkō]]                                                 
[[sv:Opin den mail-climbere panczeur]]                                          
[[zh:  
]]</text>                                                           
</revision>                                                                 
</page>                                                                       
<page>                                                                        
<title>Italo-II article</title>                                             
<id>14848</id>                                                              
<revision>                                                                  
<id>15912447</id>                                                         
<timestamp>2004-11-19T19:47:39Z</timestamp>                               
<contributor>                                                             
<username>El andres</username>                                          
<id>509991</id>                                                         
</contributor>                                                            
<minor />                                                                 
<comment>disambiguation from [[List of ISBN]] newsletters, see [[ISO site]
]</comment>                                                                     
<text xml:space="preserve">#REDIRECT [[Quartic war]]                      
</text>                                                                         
</revision>                                                                 
</page>                                                                       
<page>                                                                        
<title>ICSM</title>                                                         
<id>14939</id>                                                              
<revision>                                                                  
<id>42109942</id>                                                         
<timestamp>2006-02-28T17:22:02Z</timestamp>                               
<contributor>                                                             
<username>Dtelclan</username>                                           
<id>26</id>                                                             
</contributor>                                                            
<minor />                                                                 
<comment>/* Possible catheterman */</comment>                             
<text xml:space="preserve">[[Image:Isaac.org/ice.html [[Independent nation
al stage development|Shatting and Catalogue standardering]] in the IRBMs.       
Up-2000 they called the SC 4220 system: he was swalloped early in Calvino, or si
nce each trial mentioned based on [[Balbov's new single-jarget|bit-oriann guess]
Figure7: GeneratedWikipediadata(cotd.)
16
] self-acharged versions ([[Mt. Costall Leyton]]) was the two largest calashia a
t destored universities, all fleeted with the customary calfed clipper.         
His way to take in this literature called ICBMs-AN a [[Softvalue speed]] ([[Astr
onomical Classification Railway]])                                              
LACN645 Snowshore val nominated - made [[missile submandration|continental missi
le]]s (steam musicians) not of each club having on the ball and procedure at the
last century.                                                                  
Another communistic stark &quot;I'  submarine&quot; is [[building|corruptable]],
a [[della missile]] missile than the [[Royal Society Society]] (12-258): &quot;
Glide sun wag [[lubrician]]. They stay numerous capitalists and gas masks more w
idely interested. This scheme has declarations before the certain emerging facto
ries compelled by labour allowed to produce.                                    
In the United States, there is no hard resort in computation significantly.     
In [[1868]] the [[Italo Capital Territories Unit started to the Continental Rail
way Centre]]  was called ''UC'' or two of his usage before being written by othe
r students against the [[elective-ballistic missile]]'s deployment. Steam is sti
ll &quot;20 to Nacht&quot; and [[Fia Citation Quantity Logo]]s (since 1967). The
y pass a [[Brigade management|Quarry]]-stated missile system resolution taunting
out of about 175 million ([[Lochroom River|Tri-]]).                            
Alien from 1985 to 1999, it was an English and -Network struggling basedal with 
the Lombardo capital in Silvio and Murray, and heavily built in sub-parties addr
ess to $11,188. Their forces gained prisoners to stalked a last missile mobili s
ite.                                                                            
Spanning civilization is quanting Software Society's ballistic missile.  The sam
e as [[anti-intellectual anthropology]] continued in [[Southern Italy]] in 1914,
and the [[French Confederation of Parliament's rapid favourable rise that began
settled in March 2004|1983]]&amp;nbsp;49.                                      
In [[1904]], the Court began a British backed into a [[SR1]]) missile of [[trial
ship]] in the [[Municipal Eightime Calendar|Asiatic]] regime, including [[Benja
min Tudor Turner|Arthur Ravis]] and [[Abraham's Liberation|Canton Olombus]]. The
re was still land factory most turned up before lacking closers to the sitting s
hed backwards, in primary science.                                              
==Weights and resolutions==                                                     
[[Image:Spanish 300 Protectionald landballi110.svg|small capital surface compute
r]]                                                                             
[[Image:Claudius.jpg|345px|right|Olympiad concert of Calvino and Eastern Calvino
, ''Mughal Ralvaldens'' above, at the beginning strike the substrated roles of r
ich intellectual property, visualizing the entire system, but this missiles sugg
est that accounting differs between a giving [[train sleep|'''withdrawn''']] or 
the dinosaur in and aucting.                                                    
===Internationally===                                                           
{{main|Unmanned Justice Address}}                                               
The ICBM created a [[the significant]] [[land railway]] called &quot;[[M-Gallipo
tte]]&quot;, and it needed stopped benzafk/Macdonalical Sciences.               
Electros appeared to be the [[Soviet Union]]'s &quot;first&quot; vehicle from 25
00 selling officials DORLAN STM-331 - by missilence illustrations with &quot;Raj
.&quot; the Tunnel Hall of America, an entity upon IL pages so missiles must try
, with a trademark must develop the land allowing traffic mass to a very few min
utemen. The missiles market is slow, much easier is represented by GMMAz of BSM.
Software, the utility of scale-out scale pime racks are normally crumbled about
Figure8: GeneratedWikipediadata(cotd.)
17
4 HandwritingPrediction
Totestwhetherthepredictionnetworkcouldalsobeusedtogenerateconvincing
real-valued sequences,weappliedittoonlinehandwritingdata(online e inthis
contextmeansthat thewritingisrecordedas asequenceofpen-tiplocations,
asopposedtooine handwriting,whereonlythepageimagesareavailable).
Onlinehandwritingis anattractive choice for sequencegenerationdue toits
lowdimensionality(tworealnumbersperdatapoint)andeaseofvisualisation.
AllthedatausedforthispaperweretakenfromtheIAMonlinehandwriting
database(IAM-OnDB)[21].IAM-OnDBconsistsofhandwrittenlinescollected
from221dierentwritersusinga‘smartwhiteboard’. Thewriterswereaskedto
writeformsfromtheLancaster-Oslo-Bergentextcorpus[19],andtheposition
oftheir penwastrackedusinganinfra-reddeviceinthecorneroftheboard.
Samples fromthetrainingdataareshowninFig.9. . Theoriginalinputdata
consistsofthexandypenco-ordinatesandthepoints inthesequencewhen
the pen n is lifted o the e whiteboard. . Recording g errors in the x;y data a was
correctedby interpolating toll in n for r missingreadings, , andremovingsteps
whoselengthexceededacertainthreshold. Beyondthat,nopreprocessingwas
usedandthenetworkwastrainedtopredictthex;yco-ordinatesandtheend-
of-strokemarkersonepointatatime. Thiscontrastswithmostapproachesto
handwritingrecognitionandsynthesis,whichrelyonsophisticatedpreprocessing
andfeature-extractiontechniques. Weeschewedsuchtechniquesbecausethey
tendtoreducethevariationinthedata(e.g.bynormalisingthecharactersize,
slant,skewandso-on)whichwewantedthenetworktomodel. Predictingthe
pentracesonepointatatimegivesthenetworkmaximum exibilitytoinvent
novelhandwriting,butalsorequires alotofmemory,withthe averageletter
occupyingmorethan25timestepsandtheaveragelineoccupyingaround700.
Predictingdelayedstrokes(suchasdotsfor‘i’sorcrossesfor‘t’sthatareadded
aftertherestofthewordhasbeenwritten)isespeciallydemanding.
IAM-OnDB is s divided d intoa training set, , twovalidation n sets s and d a test
set,containingrespectively5364,1438,1518and3859handwrittenlinestaken
from775,192,216and544forms. Forourexperiments,eachlinewastreated
asaseparatesequence(meaningthatpossibledependenciesbetweensuccessive
lineswereignored).Inordertomaximisetheamountoftrainingdata,weused
thetrainingset,test setandthelarger ofthevalidationsetsfortrainingand
thesmallervalidationset for early-stopping. . Thelackofindependenttestset
meansthattherecordedresultsmaybesomewhatovertonthevalidationset;
howeverthevalidationresultsareofsecondaryimportance,sincenobenchmark
resultsexistandthemaingoalwastogenerateconvincing-lookinghandwriting.
Theprincipalchallengeinapplyingthepredictionnetworktoonlinehand-
writingdatawas determiningapredictivedistributionsuitableforreal-valued
inputs.Thefollowingsectiondescribeshowthiswasdone.
18
Figure9:TrainingsamplesfromtheIAMonlinehandwritingdatabase.
Noticethewiderangeofwritingstyles,thevariationinlineangleandcharacter
sizes,andthewritingandrecordingerrors,suchasthescribbledoutlettersin
therstlineandtherepeatedwordinthenalline.
4.1 MixtureDensityOutputs
The ideaofmixture densitynetworks [2, 3] is to use the outputs of aneural
network toparameterise amixturedistribution. . Asubsetof f the outputsare
usedto denethe mixture weights,whilethe remainingoutputs s are usedto
parameterisetheindividualmixturecomponents. Themixtureweightoutputs
arenormalisedwithasoftmaxfunctiontoensuretheyformavaliddiscretedis-
tribution,andtheotheroutputsarepassedthroughsuitablefunctionstokeep
their valueswithinmeaningfulrange (for exampletheexponentialfunctionis
typicallyappliedtooutputsusedasscaleparameters,whichmustbepositive).
Mixture density network k are e trained d by y maximising the log probability den-
sityofthetargetsundertheinduceddistributions. Notethatthedensitiesare
normalised(uptoaxedconstant)andarethereforestraightforwardtodier-
entiateandpickunbiasedsamplefrom,incontrastwithrestrictedBoltzmann
machines[14]andotherundirectedmodels.
Mixturedensityoutputscanalsobeusedwithrecurrentneuralnetworks[28].
Inthiscasetheoutputdistributionisconditionednotonlyonthecurrentinput,
butonthehistoryofpreviousinputs.Intuitively,thenumberofcomponentsis
thenumberofchoicesthenetworkhasforthenextoutputgiventheinputsso
far.
Forthehandwritingexperimentsinthispaper,thebasicRNNarchitecture
andupdateequationsremainunchangedfromSection2. Eachinputvectorx
t
consistsofareal-valuedpairx
1
;x
2
thatdenesthepenosetfromtheprevious
19
input,alongwithabinaryx
3
thathasvalue1ifthevectorendsastroke(that
is,ifthepenwasliftedotheboardbeforethenextvectorwasrecorded)and
value 0 otherwise. . Amixture e of bivariate Gaussians s was usedtopredict t x
1
andx
2
,whileaBernoullidistributionwas usedfor x
3
. Eachoutputvectory
t
thereforeconsistsoftheendofstrokeprobabilitye,alongwithasetofmeans
j,standarddeviationsj,correlationsandmixtureweights for theM
mixturecomponents.Thatis
x
t
2RRf0;1g
(15)
y
t
=
e
t
;f
j
t
;
j
t
;
j
t
;
j
t
g
M
j=1
(16)
Notethatthemeanandstandarddeviationaretwodimensionalvectors,whereas
thecomponentweight,correlationandend-of-strokeprobabilityarescalar.The
vectorsy
t
areobtainedfromthenetworkoutputs^y
t
,where
^y
t
=
^e
t
;fw^
j
t
;^
j
t
;^
j
t
;^
j
t
g
M
j=1
=b
y
+
XN
n=1
W
hny
h
n
t
(17)
asfollows:
e
t
=
1
1+exp(^e
t
)
=) e
t
2(0;1)
(18)
j
t
=
exp
^
j
t
P
M
j0=1
exp
^
j0
t
=) 
j
t
2(0;1);
X
j
j
t
=1
(19)
j
t
=^
j
t
=) 
j
t
2R
(20)
j
t
=exp
^
j
t
=) 
j
t
>0
(21)
j
t
=tanh(^
j
t
)
=) 
j
t
2( 1;1)
(22)
The probability density Pr(x
t+1
jy
t
) of the next input x
t+1
giventheoutput
vectory
t
isdenedasfollows:
Pr(x
t+1
jy
t
)=
XM
j=1
j
t
N(x
t+1
j
j
t
;
j
t
;
j
t
)
(
e
t
if(x
t+1
)
3
=1
1 e
t
otherwise
(23)
where
N(xj;;)=
1
2
1
2
p
1 2
exp
Z
2(1 2)
(24)
with
Z=
(x
1
1
)
2
2
1
+
(x
2
2
)
2
2
2
2(x
1
1
)(x
2
2
)
1
2
(25)
20
Documents you may be interested
Documents you may be interested