CXC.Ob CRE IEEE,AOVEy BEXFV requires a very large number of training instances to cover planes,each of which is a feature map.A unit in a feature the space of possible variations.In convolutional networks. map has I 5 inputs connected to a 5 by 5 area in the input, described below,shift invariance is automatically obtained called the receptave rel of the unit.Each unit has 15 in- by forcing the replication of weight configurations across puts,and therefore I5 tiainable coefficients plus a trainable space. bias.The receptive fields of contiguous units in a feature Secondly,a deficiency of fully-connected architectures is map are centered on correspondingly contiguous units in that the topology of the input is entirely ignored.The in-the previous layer.Therefore receptive fields of neighbor- put variables can be presented in any(fixed)order without ing units overlap.For example,in the first hidden layer affecting the outcome of the training.On the contrary, of veNet-5,the receptive fields of horizontally contiguous images (or time-frequency representations of speech)have units overlap by t columns and 5 rows.As stated earlier, a strong ID local structure:variables (or pixels)that are all the units in a feature map share the same set of 15 spatially or temporally nearby are highly correlated.vocal weights and the same bias so they detect the same feature correlations are the reasons for the well-known advantages at all possible locations on the input.The other feature of extracting and combining local features before recogniz- maps in the layer use different sets of weights and biases, ing spatial or temporal objects,because configurations of thereby extracting different types of local features.In the neighboring variables can be classified into a small number case of veNet-5,at each input location six different types of categories (e.g.edges,corners...).Convolutsonal Net- of features are extracted by six units in identical locations works force the extraction of local features by restricting in the six feature maps.A sequential implementation of the receptive fields of hidden units to be local. a feature map would scan the input image with a single unit that has a local receptive field,and store the states B.Convolutgonal Networks of this unit at corresponding locations in the feature map. Convolutional Networks combine three architectural This operation is equivalent to a convolution,followed by ideas to ensure some degree of shift,scale,and distor- an additive bias and squashing function,hence the name tion invariance:local receptge rel s,share wegghts (or convolutgonal network.The kernel of the convolution is the weight replication),and spatial or temporal ab-s amplang. set of connection weights used by the units in the feature A typical convolutional network for recognizing characters, map.An interesting property of convolutional layers is that dubbed veNet-5,is shown in figure I.The input plane if the input image is shifted,the feature map output will receives images of characters that are approximately size- be shifted by the same amount,but will be left unchanged normalized and centered.Each unit in a layer receives in- otherwise.This property is at the basis of the robustness puts from a set of units located in a small neighborhood of convolutional networks to shifts and distortions of the in the previous layer.The idea of connecting units to local input. receptive fields on the input goes back to the Perceptron in Once a feature has been detected.its exact location the early 60s,and was almost simultaneous with Hubel and becomes less important.Only its approximate position Wiesel's discovery of locally-sensitive,orientation-selective relative to other features is relevant.For example,once neurons in the cat's visual system.].vocal connections we know that the input image contains the endpoint of a have been used many times in neural models of visual learn- roughly horizontal segment in the upper left area,a corner ingBl,1,F],.I].With local receptive in the upper right area,and the endpoint of a roughly ver- fields,neurons can extract elementary visual features such tical segment in the lower portion of the image,we can tell as oriented edges,end-points,corners (or similar features in the input image is a 7.Not only is the precise position of other signals such as speech spectrograms).These features each of those features irrelevant for identifying the pattern, are then combined by the subsequent layers in order to de- it is potentially harmful because the positions are likely to tect higher-order features.As stated earlier,distortions or vary for different instances of the character.A simple way shifts of the input can cause the position of salient features to reduce the precision with which the position of distinc- to vary.In addition,elementary feature detectors that are tive features are encoded in a feature map is to reduce the useful on one part of the image are likely to be useful across spatial resolution of the feature map.This can be achieved the entire image.This knowledge can be applied by forcing with a so-called sub-samplang layers which performs a local a set of units,whose receptive fields are located at different averaging and a sub-sampling,reducing the resolution of places on the image,to have identical weight vectors.Bl, the feature map,and reducing the sensitivity of the output 15],t Units in a layer are organized in planes within to shifts and distortions.The second hidden layer of veNet- which all the units share the same set of weights.The set 5 is a sub-sampling layer.This layer comprises six feature of outputs of the units in such a plane is called a feature maps,one for each feature map in the previous layer.The map.Units in a feature map are all constrained to per- receptive field of each unit is a i by I area in the previous form the same operation on different parts of the image. layer's corresponding feature map.Each unit computes the A complete convolutional layer is composed of several fea-average of its four inputs,multiplies it by a trainable coef- ture maps (with different weight vectors),so that multiple ficient,adds a trainable bias,and passes the result through features can be extracted at each location.A concrete ex- a sigmoid function.Contiguous units have non-overlapping ample of this is the first layer of yeNet-5 shown in Figure I. contiguous receptive fields.Consequently,a sub-sampling Units in the first hidden layer of veNet-5 are organized in 6 layer feature map has half the number of rows and columns
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å✿ê④è✥ä✧ì❛é❼✂✳✑✑✧▲û➑ì✦➊å➈û❯ê✤è✧ä✥ÿ✗❶è✧ÿ✙ä✥ï✻✰♣úrå➈ä✧ø✓å❄✡☎û➑ï❞ê➑➪⑨ì➈ä➤æ✙ø✙↔➇ï✖û➀ê✴➶➉è✧ç☎å➄è➤å➈ä✧ï ê✧æ☎å✠è✥ø➀å➈û➑û✠✘✒ì❛ä❣è✧ï✖î❭æ◆ì➈ä❿å➄û➀û✠✘❙é✙ï❞å➄ä❘✡☛✘✒å➄ä✥ï❨ç✙ø✠✂➈ç✙û✠✘➚➊ì➈ä✥ä✧ï✖û➀å➄è✧ï❞ù☛ð ✗❀ì☛✖å➄û ❶ì❛ä✧ä✥ï➊û✓å✠è✥ø➑ì❛é☎ê❫å➈ä✧ï♣è✧ç☎ï➳ä✥ï✖å❛ê✤ì❛é☎ê❫ëíì➈ä➵è✧ç✙ï➤ó➵ï➊û➀û➟✝⑥ô➇é✙ì✠ó❨é✶å❛ù✂ú✠å➄é✐è✥å✑✂➈ï✖ê ì➄ë❯ï❯↔➇è✧ä❿å✑❶è✧ø➀é❼✂➻å➄é☎ù➙❶ì➈î➑✡✙ø➀é✙ø➑é✗✂ ✲✙➯✒❄✴➢✲✐ëíï✖å➄è✧ÿ✙ä✥ï✖ê✔✡◆ï❶ëíì❛ä✧ï➳ä✥ï✒❶ì➎✂➈é✙ø✠➽❯✝ ø➀é❼✂✫ê✤æ☎å➄è✧ø✓å➄û❣ì❛ä➤è✧ï➊î➻æ◆ì➈ä❿å➄û❣ì➎✡✔✓④ï✒❶è✥ê✒➌✏✡✎ï★➊å➈ÿ☎ê✤ï➵➊ì➈é✦➞✗✂❛ÿ✙ä❿å✠è✧ø➀ì➈é✎ê➉ì➈ë é✙ï✖ø✙✂❛ç❩✡◆ì➈ä✥ø➀é❼✂✌ú✠å➄ä✥ø➀å✑✡✙û➑ï❞ê❹➊å➈é➣✡◆ï✬❶û✓å➈ê✥ê✤ø✙➞☎ï❞ù➻ø➑é✐è✧ì❙å➞ê✤î➓å➈û➑û✎é✐ÿ☎î➉✡◆ï➊ä ì➄ë✞➊å✠è✥ï✄✂❛ì➈ä✥ø➑ï❞ê➙➪⑨ï➈ð ✂☎ð ï✖ù❼✂➈ï✖ê✒➌➜➊ì➈ä✥é✙ï➊ä❿ê➊ð➀ð➀ð ➶❶ð ❃ ➯❄➨✍♦➯ ✲✡✦➺❩✣ ➯♦➨✇➢✲➜➸➑➳❯➺❩✭ ➻➜➯♦➡❺➼♦➩➤ëíì➈ä✴❶ï➓è✥ç✙ï✶ï✄↔➇è✧ä❿å✑↔è✥ø➑ì❛é➷ì➄ë➔û➀ì☛✖å➄û❣ëíï❞å✠è✥ÿ✙ä✧ï❞ê➓✡☛✘ ä✧ï❞ê④è✥ä✧ø✁↔è✥ø➑é❼✂ è✧ç☎ï✌ä✧ï★❶ï➊æ✙è✧ø➀ú➈ï✞➞☎ï➊û✓ù✙ê❨ì➈ë❇ç✙ø✓ù✙ù✂ï✖é✺ÿ✙é✙ø➑è✥ê✛è✥ì➵✡✎ï✌û➀ì✦➊å➄û♠ð ✚✜✛ ❃ ➯♦➨☎✍✪➯✬✲✡✦➺✮✣ ➯❄➨✈➢✬✲✈➸➉➳✄➺✶➻➜➯♦➡❺➼♦➩ ☞✇ì➈é➇ú➈ì❛û➑ÿ✂è✥ø➑ì❛é☎å➄û➘ñ➔ï➊è④ó✇ì❛ä✧ô✂ê ❶ì❛î➉✡✙ø➀é✙ïPè✧ç✙ä✥ï➊ï å➄ä✴❿ç✙ø➑è✧ï✒❶è✧ÿ✙ä❿å➄û ø✓ù✂ï✖å❛ê✺è✧ì✻ï✖é☎ê✧ÿ✙ä✧ï ê✧ì➈î➻ï ù✂ï✒✂➈ä✥ï➊ï ì➈ë➓ê✧ç✙ø➑ë➺è✒➌✒ê❘➊å➈û➑ï➎➌✒å➄é✎ù❲ù✙ø➀ê✤è✧ì❛ä❇✝ è✧ø➀ì➈é✾ø➑é➇ú✠å➄ä✥ø✓å➄é✗➊ï✻✰ ✲✙➯✒❄✴➢✲t➡❺➳❄✴➳❖➤✇➺✮✣✍♦➳✂✁✎➳✡✲❨✪♦➩✹➌➉➩❺➥❼➢❄➡❺➳✱✪ ➻➜➳❪✣✥★➥✦➺➩➛➪⑨ì➈ä ó➵ï➊ø✠✂➈ç✐è➉ä✥ï➊æ✙û➀ø✠✖å✠è✥ø➑ì❛é✥➶✹➌✟å➄é☎ù✫ê✧æ☎å➄è✧ø✓å➄û❀ì❛ä❨è✧ï✖î➻æ✎ì❛ä✥å➈û❹➩✒✡✤✯✡✭❖➩✄➢❄➲✛➤ ✲✣●➨✵✥➈ð ✕➘è❅✘➇æ✙ø✁➊å➈û❼❶ì➈é➇ú❛ì➈û➀ÿ✂è✧ø➀ì➈é☎å➈û✂é✙ï❶è④ó➵ì➈ä✥ô➤ëíì➈ä❫ä✧ï★❶ì✑✂❛é✙ø✠➽➊ø➀é❼✂✞❿ç✎å➄ä❿å✑↔è✥ï➊ä❿ê✄➌ ù✂ÿ❼✡✗✡✎ï❞ù ✗✝ï❞ñ➔ï❶è❺✝✝✙❼➌✛ø➀ê➽ê✧ç✙ì✠ó❨é➘ø➀é ➞✗✂➈ÿ✙ä✥ï ✑✂ð ã✛ç✙ï➲ø➀é✙æ✙ÿ✙è✶æ✙û✓å➄é✙ï ä✥ï✒❶ï✖ø➑ú❛ï✖ê♣ø➑î➓å✑✂➈ï✖ê➉ì➄ë➃❿ç✎å➄ä❿å✑↔è✥ï➊ä❿ê❨è✥ç☎å✠è✌å➄ä✥ï❙å➈æ✙æ✙ä✥ì✪↔➇ø➀î➓å✠è✥ï➊û✠✘✿ê✧ø✙➽✖ï❯✝ é✙ì❛ä✧î➓å➄û➀ø✠➽➊ï✖ù✺å➈é☎ù✆❶ï✖é❛è✥ï➊ä✥ï✖ù☛ð ✭❫å➎❿ç✺ÿ✙é✙ø➑è➉ø➑é➲å➽û➀å✪✘❛ï➊ä❨ä✥ï✒❶ï✖ø➑ú❛ï✖ê✛ø➀é✦✝ æ✙ÿ✂è❿ê➞ëíä✥ì➈î å➲ê✧ï❶è✒ì➈ë✛ÿ☎é✙ø➩è❿ê✒û➀ì✦➊å➄è✧ï✖ù➷ø➀é å➲ê✧î➓å➄û➀û➏é✙ï➊ø✠✂➈ç☛✡◆ì➈ä✥ç✙ì➇ì✂ù ø➀é➓è✧ç✙ï➳æ✙ä✥ï➊ú➇ø➀ì➈ÿ☎ê❫û➀å✪✘❛ï➊ä❞ð❇ã✛ç✙ï♣ø➀ù✂ï❞å➞ì➈ë❀❶ì➈é☎é✙ï✒❶è✧ø➀é❼✂➞ÿ✙é✙ø➑è✥ê✇è✥ì✒û➀ì☛✖å➄û ä✥ï✒❶ï✖æ✂è✧ø➀ú➈ï✔➞✎ï➊û✓ù✙ê❣ì➈é❭è✥ç✙ï❨ø➑é☎æ✙ÿ✂è➜✂❛ì✐ï❞ê❷✡☎å➎❿ô✌è✧ì➤è✥ç✙ï✬✓❦ï➊ä✴❶ï✖æ✂è✧ä✥ì➈é❙ø➑é è✧ç☎ï➵ï❞å➄ä✥û✙✘ ✓✗✘➈ê✒➌➄å➄é☎ù✒ó➵å❛ê❇å➈û➑î➻ì❛ê✤è❣ê✤ø➀î✒ÿ✙û➑è✥å➈é✙ï➊ì❛ÿ☎ê❇ó❨ø➩è✥ç❭õ➉ÿ❼✡✎ï✖û✙å➄é☎ù ✎ø➀ï✖ê✧ï➊û ❁ ê✛ù✂ø✓ê❺➊ì✠ú➈ï✖ä❺✘❭ì➄ë❯û➑ì✦➊å➈û➑û✠✘❩✝⑥ê✧ï➊é✎ê✤ø➑è✧ø➀ú➈ï➎➌❛ì❛ä✧ø➀ï➊é✐è✥å➄è✧ø➀ì➈é✦✝➠ê✧ï➊û➀ï✒↔è✥ø➑ú❛ï é✙ï✖ÿ✙ä✧ì❛é☎ê➔ø➀é✫è✥ç✙ï➑✖å✠è✽❁ ê♣ú✐ø✓ê✧ÿ☎å➄û❯ê❇✘✂ê✤è✧ï➊î ✞❜✻✘✠⑥ð❇✗❀ì☛✖å➄û❜❶ì➈é☎é✙ï✒❶è✧ø➀ì➈é☎ê ç☎årú❛ï❷✡✎ï✖ï➊é➞ÿ☎ê✧ï✖ù➤î➓å➈é❩✘♣è✧ø➀î➻ï✖ê❇ø➑é✌é☎ï➊ÿ✙ä❿å➄û❛î❭ì✂ù✂ï✖û➀ê❀ì➄ë✙ú➇ø✓ê✤ÿ☎å➈û➄û➀ï✖å➄ä✥é✦✝ ø➀é❼✂✷✞❜✗➾✡✠❖➌❵✞❜✵✑✆✠❖➌❵✞➟➾✒✺✠❖➌ ✞❜ ❜✠❖➌❵✞❜✫❝✬✠❖➌❵✞✑ ✠♠ð ✎ø➩è✥ç û➑ì✦➊å➈û➞ä✥ï✒❶ï✖æ✂è✧ø➀ú➈ï ➞☎ï✖û➀ù✙ê✒➌✙é✙ï✖ÿ✙ä✥ì➈é☎ê✔➊å➈é✢ï✄↔➇è✧ä❿å✑↔è✛ï➊û➀ï➊î➻ï✖é❛è❿å➄ä❘✘➓ú➇ø➀ê✧ÿ☎å➄û✟ëíï❞å✠è✥ÿ✙ä✧ï❞ê❨ê✤ÿ✥❿ç å➈ê❀ì➈ä✥ø➑ï✖é✐è✧ï✖ù➤ï❞ù✦✂➈ï❞ê✄➌rï✖é☎ù☛✝⑥æ✎ì❛ø➑é✐è✥ê✒➌♦❶ì❛ä✧é✙ï✖ä✥ê➜➪íì➈ä❦ê✧ø➑î➻ø➀û➀å➈ä✝ëíï✖å➄è✧ÿ✙ä✥ï✖ê❀ø➑é ì➄è✥ç✙ï➊ä➵ê✤ø✠✂➈é✎å➄û✓ê➏ê✤ÿ✥❿ç➽å➈ê❫ê✧æ◆ï➊ï✒❿ç➽ê✧æ◆ï✒↔è✥ä✧ì➎✂➈ä❿å➄î➓ê✴➶↔ð❇ã✛ç☎ï✖ê✧ï❨ëíï✖å➄è✧ÿ✙ä✥ï✖ê å➄ä✥ï❨è✥ç✙ï➊é ➊ì➈î➑✡✙ø➑é☎ï✖ù➝✡☛✘❭è✧ç✙ï➳ê✤ÿ❼✡✎ê✤ï★➍❛ÿ☎ï➊é✐è❫û✓å✪✘➈ï➊ä❿ê❣ø➀é➽ì➈ä❿ù✂ï✖ä❣è✧ì✒ù✙ï❯✝ è✧ï★↔è➔ç✙ø✠✂➈ç☎ï➊ä❺✝♠ì❛ä✥ù✂ï✖ä➏ëíï❞å✠è✧ÿ☎ä✧ï❞ê➊ð❷✕➉ê❨ê✤è✥å➄è✧ï❞ù✶ï❞å➄ä✥û➑ø➀ï➊ä★➌✂ù✂ø➀ê✤è✧ì❛ä✤è✥ø➑ì❛é☎ê➵ì➈ä ê✧ç✙ø➩ë➺è❿ê➏ì➈ë◆è✥ç✙ï➔ø➀é✙æ✙ÿ✂è✎➊å➄é➣✖å➄ÿ☎ê✧ï✛è✧ç☎ï➔æ✎ì✐ê✤ø➑è✧ø➀ì➈é➻ì➈ë☛ê✥å➄û➀ø➀ï➊é✐è❣ëíï✖å➄è✧ÿ✙ä✥ï✖ê è✧ì➻ú✠å➄ä❘✘➈ð❨➏➠é✺å➈ù✙ù✙ø➩è✥ø➑ì❛é✏➌✙ï➊û➀ï➊î➻ï✖é❛è❿å➄ä❘✘➻ëíï✖å➄è✧ÿ✙ä✥ï➳ù✙ï❶è✧ï★↔è✥ì➈ä❿ê➵è✧ç☎å➄è❨å➈ä✧ï ÿ☎ê✧ï❶ëíÿ✙û✂ì❛é➞ì➈é☎ï✇æ☎å➈ä✤è❦ì➄ë☎è✧ç✙ï➵ø➑î➓å✑✂➈ï✛å➄ä✥ï❫û➀ø➑ô❛ï➊û✠✘♣è✥ì④✡◆ï✛ÿ☎ê✧ï❶ëíÿ✙û✂å✑➊ä✧ì✐ê✧ê è✧ç☎ï❨ï➊é✐è✧ø➀ä✧ï✛ø➀î➓å❄✂➈ï❛ð❇ã✛ç✙ø✓ê❦ô➇é✙ì✠ó❨û➀ï✖ù✦✂❛ï✎✖å➄é➚✡✎ï➔å➈æ✙æ✙û➀ø➑ï❞ù➉✡☛✘✌ëíì❛ä❘➊ø➑é❼✂ å➤ê✤ï➊è➏ì➄ë✟ÿ✙é✙ø➑è✥ê✒➌➈ó❨ç✙ì✐ê✤ï✛ä✥ï✒➊ï➊æ✂è✥ø➑ú❛ï➃➞✎ï➊û✓ù✙ê➏å➄ä✥ï➵û➑ì✦➊å➄è✧ï❞ù❭å➄è➏ù✂ø➟➘✟ï➊ä✥ï➊é✐è æ✙û✓å✑➊ï✖ê➔ì❛é✫è✧ç☎ï❙ø➀î➓å❄✂➈ï➎➌☎è✥ì➽ç☎årú❛ï➞ø➀ù✙ï➊é✐è✧ø✁➊å➈û❇ó➵ï➊ø✠✂➈ç✐è➉ú❛ï✒↔è✥ì➈ä❿ê ✞❜ ✑ ✠✶➌ ✞✙➾ ✙✆✠❖➌ ✞❜✬❝✫✠♠ð➵→➔é☎ø➩è❿ê✌ø➑é➷å✿û➀å✪✘❛ï➊ä✌å➄ä✥ï❭ì➈ä❘✂❛å➄é☎ø✙➽✖ï✖ù➲ø➀é➷æ✙û✓å➄é✙ï❞ê➤ó❨ø➩è✥ç✙ø➑é ó❨ç✙ø✁❿ç➲å➄û➀û☛è✧ç☎ï✒ÿ✙é✙ø➑è✥ê♣ê✤ç✎å➄ä✥ï➤è✧ç✙ï✒ê✥å➄î➻ï➞ê✧ï❶è➉ì➈ë❣ó✇ï✖ø✙✂❛ç❛è❿ê➊ð➵ã✛ç✙ï✒ê✧ï❶è ì➄ë✛ì➈ÿ✙è✧æ✙ÿ✂è❿ê✌ì➄ë➵è✧ç☎ï➓ÿ✙é✙ø➑è✥ê✌ø➀é ê✤ÿ✗❿ç å✿æ✙û✓å➄é✙ï➓ø✓ê✌➊å➈û➑û➀ï✖ù➷å➝➫❯➳✴➢♦➺✡✦➡❺➳ ➲➵➢❘➤◆ð⑧→➔é✙ø➑è✥ê➻ø➀é❑å❖ëíï✖å➄è✧ÿ✙ä✥ï✢î➓å➈æ❑å➄ä✥ï✢å➈û➑û✩➊ì➈é☎ê✤è✧ä❿å➄ø➀é✙ï✖ù è✧ì æ✎ï✖ä❇✝ ëíì➈ä✥î è✧ç✙ï✿ê✧å➈î➻ï➽ì➈æ◆ï➊ä❿å✠è✥ø➑ì❛é ì➈é❤ù✂ø✙➘✟ï➊ä✥ï➊é✐è❙æ☎å➈ä✤è❿ê➞ì➈ë❨è✧ç✙ï✢ø➑î➓å❄✂❛ï➈ð ✕ ❶ì❛î➻æ✙û➑ï➊è✧ï✌❶ì❛é➇ú➈ì➈û➀ÿ✂è✥ø➑ì❛é☎å➄û✟û✓å✪✘➈ï➊ä✛ø✓ê✩❶ì❛î❭æ◆ì❛ê✧ï✖ù✢ì➄ë❦ê✤ï✖ú➈ï✖ä✥å➈û✎ëíï❞å♦✝ è✧ÿ☎ä✧ï➤î➓å➄æ☎êt➪⑨ó❨ø➩è✥ç✿ù✂ø✙➘✟ï➊ä✥ï➊é✐è❨ó✇ï✖ø✙✂❛ç❛è➵ú➈ï★↔è✧ì❛ä✥ê✴➶✹➌✂ê✧ì✒è✥ç☎å✠è❨î❙ÿ✙û➩è✥ø➑æ☎û➑ï ëíï✖å➄è✧ÿ✙ä✥ï✖ê✬➊å➄é✫✡◆ï✌ï❯↔➇è✧ä❿å✑❶è✧ï❞ù✿å➄è➔ï✖å➎❿ç✢û➀ì✦➊å✠è✥ø➑ì❛é✝ð➜✕ ➊ì➈é✗➊ä✧ï➊è✧ï✌ï❯↔☛✝ å➄î➻æ✙û➀ï➵ì➄ë☎è✥ç✙ø✓ê❦ø➀ê❇è✧ç☎ï➃➞✎ä✥ê✤è❯û✓å✪✘➈ï✖ä❇ì➈ë✴✗✝ï❞ñ➔ï➊è❇✝ ✙➉ê✧ç✙ì✠ó❨é✒ø➀é➝✜❇ø✠✂➈ÿ☎ä✧ï❙✑✂ð →➔é☎ø➩è❿ê❣ø➑é❭è✥ç✙ï✎➞☎ä✥ê✤è❣ç✙ø✓ù✙ù✂ï➊é➻û✓å✪✘➈ï✖ä❯ì➈ë ✗❀ï✖ñ➔ï➊è❇✝ ✙➳å➄ä✥ï✇ì❛ä❺✂✐å➄é✙ø✠➽➊ï❞ù➞ø➀é ✓ æ✙û✓å➄é✙ï❞ê✄➌➇ï❞å✑❿ç✶ì➈ë❀ó❨ç✙ø✁❿ç✶ø✓ê✛å➞ëíï❞å✠è✧ÿ☎ä✧ï➳î➓å➄æ✝ð❷✕❲ÿ✙é✙ø➑è❨ø➑é✺å✌ëíï❞å✠è✧ÿ☎ä✧ï î➓å➄æ➽ç✎å➈ê✄✑ ✙✌ø➀é✙æ✙ÿ✂è❿ê➃➊ì➈é✙é☎ï✒↔è✥ï✖ù➻è✥ì❙å❄✙t✡☛✘ ✙✒å➄ä✥ï✖å➤ø➀é➽è✥ç✙ï➉ø➀é✙æ✙ÿ✂è★➌ ➊å➈û➑û➀ï✖ù✫è✧ç✙ï➐➡❺➳❄✴➳❖➤✇➺✮✣✍♦➳✄✁➃➳❪✲❨✪✒ì➄ë➏è✥ç✙ï❭ÿ✙é✙ø➑è✖ð ✭❫å➎❿ç✫ÿ✙é✙ø➑è➤ç✎å➈ê✒✑✫✙➻ø➀é✦✝ æ✙ÿ✂è❿ê✄➌➄å➈é☎ù✌è✥ç✙ï➊ä✥ï❶ëíì❛ä✧ï❀✑✫✙✛è✥ä✥å➈ø➑é✎å❄✡✙û➀ï➃➊ì✐ï✱✯➣❶ø➀ï➊é✐è✥ê❇æ✙û➀ÿ☎ê❦å❨è✧ä❿å➄ø➀é☎å✑✡✙û➑ï ✡✙ø✓å➈ê✖ð✒ã✛ç✙ï❭ä✧ï★❶ï✖æ✂è✧ø➀ú➈ï➑➞☎ï➊û✓ù✙ê➳ì➄ë✔❶ì❛é❛è✥ø✙✂❛ÿ✙ì➈ÿ✎ê➉ÿ✙é☎ø➩è❿ê➤ø➑é å➽ëíï❞å✠è✧ÿ☎ä✧ï î➓å➄æ❤å➈ä✧ï➙❶ï➊é✐è✥ï➊ä✥ï✖ù ì❛é➹❶ì❛ä✧ä✥ï✖ê✧æ✎ì❛é☎ù✂ø➀é❼✂➈û✠✘➛➊ì➈é✐è✧ø✠✂➈ÿ☎ì➈ÿ☎ê✒ÿ✙é✙ø➑è✥ê❭ø➑é è✧ç☎ï❙æ✙ä✥ï➊ú➇ø➀ì➈ÿ☎ê♣û✓å✪✘➈ï➊ä❞ð✌ã✛ç✙ï➊ä✥ï❶ëíì❛ä✧ï✒ä✧ï★❶ï➊æ✙è✧ø➀ú➈ï➓➞✎ï➊û✓ù✙ê➤ì➄ë➏é✙ï✖ø✙✂❛ç☛✡✎ì❛ä❇✝ ø➀é❼✂❺ÿ☎é✙ø➩è❿ê❭ì✠ú➈ï➊ä✥û✓å➄æ✝ð➒✜✙ì➈ä❭ï❯↔✙å➈î❭æ☎û➑ï➎➌➏ø➑é❤è✧ç✙ï➙➞☎ä❿ê④è❭ç✙ø✓ù✙ù✂ï➊é û✓å✪✘➈ï➊ä ì➄ë❅✗✝ï❞ñ➔ï❶è❺✝✝✙❼➌✝è✥ç✙ï➻ä✧ï★❶ï➊æ✙è✧ø➀ú➈ï➚➞☎ï➊û✓ù✙ê➤ì➈ë➵ç✙ì❛ä✧ø✠➽➊ì❛é✐è✥å➄û➀û✠✘✫➊ì➈é✐è✧ø✠✂➈ÿ☎ì➈ÿ☎ê ÿ✙é✙ø➑è✥ê➳ì✠ú❛ï➊ä✥û➀å➈æ➐✡☛✘◆❝➙➊ì➈û➀ÿ✙î➻é☎ê➳å➄é☎ù ✙➽ä✧ì✠ó➔ê✖ð✬✕♣ê♣ê✤è✥å➄è✧ï✖ù➲ï✖å➄ä✥û➀ø➑ï✖ä✒➌ å➄û➀û➔è✥ç✙ï❖ÿ☎é✙ø➩è❿ê✶ø➀é✻å➷ëíï❞å✠è✧ÿ☎ä✧ï➲î➓å➈æ✻ê✤ç☎å➈ä✧ï➲è✧ç✙ï❖ê✥å➄î➻ï❖ê✧ï❶è✿ì➄ë ✑✫✙ ó➵ï➊ø✠✂➈ç✐è✥ê✛å➄é✎ù➽è✥ç✙ï✌ê✧å➈î❭ï✞✡✙ø✓å➈ê❨ê✧ì✒è✥ç✙ï✄✘✢ù✂ï❶è✥ï✒↔è❨è✥ç✙ï✌ê✧å➈î➻ï➉ëíï❞å✠è✧ÿ☎ä✧ï å✠è➻å➄û➀û✇æ◆ì❛ê✥ê✧ø✙✡✙û➀ï✶û➀ì✦➊å➄è✧ø➀ì➈é☎ê✒ì➈é è✥ç✙ï✢ø➀é✙æ✙ÿ✙è✖ð➷ã✛ç✙ï✢ì➈è✧ç✙ï✖ä➞ëíï❞å✠è✧ÿ☎ä✧ï î➓å➄æ☎ê➳ø➀é➲è✥ç✙ï❙û✓å✪✘➈ï✖ä➉ÿ☎ê✧ï➻ù✂ø➟➘✟ï➊ä✥ï➊é✐è✌ê✤ï➊è✥ê➳ì➄ë✇ó✇ï✖ø✙✂❛ç❛è❿ê♣å➈é☎ù↕✡☎ø➀å❛ê✤ï❞ê✄➌ è✧ç☎ï➊ä✥ï✄✡☛✘✢ï✄↔➇è✧ä❿å✑↔è✥ø➑é✗✂➽ù✂ø➟➘✟ï➊ä✥ï➊é✐è➔è❅✘➇æ◆ï✖ê♣ì➄ë❣û➀ì☛✖å➄û❀ëíï✖å✠è✥ÿ✙ä✥ï✖ê✖ð✎➏➠é➲è✧ç✙ï ➊å❛ê✤ï❙ì➄ë✄✗❀ï✖ñ➉ï❶è❇✝ ✙✦➌☛å➄è➳ï❞å✑❿ç➲ø➀é✙æ✙ÿ✂è➤û➀ì☛✖å✠è✥ø➑ì❛é❺ê✧ø➟↔➲ù✂ø✙➘◆ï✖ä✧ï✖é✐è♣è❅✘➇æ◆ï✖ê ì➄ë❇ëíï✖å➄è✧ÿ✙ä✥ï✖ê❨å➈ä✧ï➤ï❯↔➇è✥ä✥å➎↔è✧ï❞ù➣✡☛✘✶ê✧ø➟↔✢ÿ✙é✙ø➑è✥ê❨ø➀é✺ø➀ù✂ï✖é✐è✧ø✁➊å➄û☛û➀ì✦➊å➄è✧ø➀ì➈é☎ê ø➀é è✧ç☎ï✿ê✧ø➟↔➷ëíï❞å✠è✧ÿ☎ä✧ï✢î➻å➈æ☎ê✖ð ✕▼ê✧ï✒➍✐ÿ✙ï➊é✐è✥ø➀å➈û❫ø➀î❭æ☎û➑ï✖î❭ï✖é✐è✥å✠è✥ø➑ì❛é❤ì➈ë å❖ëíï✖å✠è✥ÿ✙ä✥ï✢î➓å➄æ❑ó✇ì❛ÿ✙û✓ù❤ê❘➊å➄é❤è✧ç✙ï✿ø➀é✙æ✙ÿ✂è➓ø➀î➻å✑✂➈ï✿ó❨ø➩è✥ç å ê✧ø➑é❼✂❛û➑ï ÿ✙é✙ø➑è❭è✧ç☎å➄è❙ç☎å❛ê✒å✫û➀ì✦➊å➄û➵ä✥ï✒❶ï✖æ✂è✧ø➀ú➈ï➣➞☎ï➊û✓ù❢➌➏å➄é✎ù ê④è✥ì➈ä✥ï➓è✧ç✙ï✺ê✤è✥å✠è✥ï✖ê ì➄ë❇è✧ç✙ø✓ê❨ÿ✙é☎ø➩è➉å➄è✬❶ì➈ä✥ä✥ï✖ê✧æ✎ì❛é☎ù✂ø➀é❼✂✒û➀ì✦➊å✠è✥ø➑ì❛é☎ê✛ø➀é✶è✥ç✙ï➤ëíï✖å➄è✧ÿ✙ä✥ï➤î➻å➈æ✝ð ã✛ç✙ø✓ê➳ì➈æ◆ï➊ä❿å✠è✧ø➀ì➈é❖ø➀ê♣ï✒➍✐ÿ✙ø➀ú✠å➄û➀ï➊é✐è♣è✥ì✿å➙❶ì❛é✐ú❛ì➈û➀ÿ✂è✧ø➀ì➈é❀➌✎ëíì❛û➑û➀ì✠ó➵ï✖ù✫✡☛✘ å➄é å❛ù✙ù✂ø➑è✧ø➀ú➈ï➣✡✙ø✓å➈ê✒å➄é☎ù➷ê❘➍❛ÿ✎å➈ê✧ç✙ø➑é✗✂✺ëíÿ✙é✗↔è✥ø➑ì❛é✏➌❦ç✙ï➊é✥❶ï➻è✧ç☎ï➽é☎å➄î➻ï ❄✴➯♦➨☎✍✪➯✬✲✡✦➺✮✣ ➯❄➨✈➢✬✲✥➨✇➳❯➺✶➻➜➯♦➡❺➼➄ð❣ã✛ç✙ï❨ô➈ï✖ä✧é✙ï✖û✂ì➄ë◆è✧ç✙ï④❶ì➈é➇ú❛ì➈û➀ÿ✂è✧ø➀ì➈é❭ø➀ê❣è✧ç✙ï ê✧ï❶è➤ì➄ë➜❶ì❛é✙é✙ï★↔è✧ø➀ì➈é❖ó✇ï✖ø✙✂❛ç❛è❿ê➉ÿ✎ê✤ï❞ù↕✡☛✘✿è✧ç✙ï❭ÿ✙é✙ø➑è✥ê➳ø➀é➲è✧ç☎ï✒ëíï❞å✠è✧ÿ☎ä✧ï î➓å➄æ✝ð❜✕➔é➞ø➀é✐è✧ï✖ä✧ï❞ê④è✥ø➑é❼✂❨æ☎ä✧ì❛æ✎ï✖ä✤è❅✘♣ì➄ë❼❶ì❛é✐ú❛ì➈û➀ÿ✂è✧ø➀ì➈é✎å➄û➄û✓å✪✘➈ï✖ä✥ê✟ø✓ê☛è✥ç☎å✠è ø➑ë✇è✥ç✙ï➻ø➑é✙æ☎ÿ✂è➞ø➑î➓å✑✂➈ï➻ø➀ê✌ê✧ç✙ø➑ë➺è✧ï❞ù❢➌✝è✥ç✙ï➻ëíï✖å➄è✧ÿ✙ä✥ï➻î➻å➈æ❺ì❛ÿ✂è✧æ☎ÿ✂è➞ó❨ø➑û➀û ✡◆ï➤ê✧ç✙ø➑ë➺è✧ï❞ù➣✡☛✘➻è✧ç✙ï✌ê✥å➄î➻ï♣å➈î➻ì➈ÿ✙é✐è✒➌☛✡✙ÿ✙è✛ó❨ø➀û➀û✈✡◆ï➤û➑ï➊ë➺è❨ÿ✙é✗❿ç☎å➈é❼✂➈ï❞ù ì➄è✥ç✙ï➊ä✥ó❨ø✓ê✤ï❛ð➳ã✛ç✙ø✓ê♣æ✙ä✧ì❛æ✎ï✖ä✤è❅✘✺ø✓ê♣å➄è♣è✥ç✙ï➚✡☎å➈ê✧ø➀ê♣ì➄ë❣è✥ç✙ï❭ä✧ì➎✡✙ÿ☎ê✤è✧é✙ï❞ê✧ê ì➄ë✛➊ì➈é➇ú➈ì❛û➑ÿ✂è✥ø➑ì❛é☎å➄û❫é✙ï❶è④ó➵ì➈ä✥ô✂ê➤è✧ì❖ê✧ç✙ø➑ë➺è✥ê❭å➄é☎ù❤ù✂ø➀ê✤è✧ì❛ä✤è✥ø➑ì❛é☎ê✌ì➈ë❨è✧ç✙ï ø➀é✙æ✙ÿ✂è❞ð ý♣é✗❶ï å❍ëíï✖å➄è✧ÿ✙ä✥ï❤ç✎å➈ê➛✡✎ï✖ï➊é➶ù✙ï❶è✧ï★↔è✥ï✖ù❢➌❭ø➩è❿ê ï❯↔✙å✑❶è❺û➀ì☛✖å✠è✥ø➑ì❛é ✡◆ï✒❶ì❛î➻ï✖ê✺û➀ï✖ê✥ê✢ø➀î➻æ✎ì❛ä✤è❿å➄é✐è✖ð ý♣é✙û✠✘✻ø➑è✥ê✫å➄æ☎æ✙ä✧ì✪↔✂ø➀î➓å✠è✧ï❺æ✎ì✐ê✤ø➑è✧ø➀ì➈é ä✥ï➊û✓å✠è✧ø➀ú➈ï✢è✧ì➷ì➈è✧ç✙ï✖ä➻ëíï✖å✠è✥ÿ✙ä✥ï✖ê❭ø➀ê➽ä✧ï✖û➑ï✖úrå➈é✐è✖ð ✜✙ì➈ä➻ï✄↔✂å➈î➻æ✙û➑ï➎➌✇ì❛é✗❶ï ó➵ï❙ô➇é✙ì✠ó è✥ç☎å✠è➤è✥ç✙ï➻ø➑é✙æ☎ÿ✂è✌ø➑î➓å❄✂❛ï➚➊ì➈é✐è✥å➈ø➑é✎ê➔è✥ç✙ï➻ï➊é☎ù✂æ◆ì➈ø➀é✐è✌ì➄ë✇å ä✥ì➈ÿ❼✂❛ç✙û✙✘❭ç✙ì❛ä✧ø✠➽➊ì❛é❛è❿å➄û☎ê✧ï✄✂❛î➻ï➊é✐è✇ø➀é➓è✧ç☎ï♣ÿ✙æ☎æ✎ï✖ä✇û➀ï❶ë➺è❨å➄ä✥ï✖å✗➌❛å➉➊ì➈ä✥é✙ï➊ä ø➀é➽è✧ç☎ï➉ÿ✙æ✙æ◆ï➊ä✛ä✥ø✙✂❛ç✐è➵å➄ä✥ï✖å✗➌❛å➈é☎ù➻è✧ç☎ï♣ï✖é☎ù✂æ◆ì➈ø➀é❛è✛ì➄ë❀å✒ä✧ì❛ÿ❼✂➈ç☎û✙✘❭ú➈ï✖ä❇✝ è✧ø✁➊å➈û✎ê✧ï✄✂❛î❭ï✖é✐è❫ø➑é➽è✧ç✙ï♣û➑ì✠ó➵ï➊ä➏æ◆ì➈ä✧è✧ø➀ì➈é➓ì➈ë☛è✧ç✙ï♣ø➑î➓å✑✂➈ï✑➌❛ó✇ï✞➊å➈é➻è✧ï➊û➀û è✧ç☎ï✒ø➀é✙æ✙ÿ✂è➳ø➑î➓å❄✂❛ï➞ø✓ê➉å✜✔✂ð➔ñ➔ì➄è➳ì➈é✙û✠✘✿ø➀ê➔è✧ç✙ï❙æ✙ä✧ï★❶ø✓ê✤ï✒æ✎ì✐ê✤ø➑è✧ø➀ì➈é✫ì➈ë ï✖å➎❿ç❙ì➈ë☎è✥ç✙ì❛ê✧ï➵ëíï✖å✠è✥ÿ✙ä✥ï✖ê❦ø➀ä✧ä✥ï➊û➀ï➊ú✠å➄é✐è❦ëíì➈ä❣ø✓ù✂ï✖é❛è✥ø➩ë➭✘➇ø➀é❼✂➳è✧ç✙ï❨æ✎å✠è✤è✥ï➊ä✥é✏➌ ø➑è✛ø✓ê➵æ✎ì➈è✧ï✖é❛è✥ø➀å➈û➑û✠✘➻ç☎å➄ä✥î❭ëíÿ✙û❢✡◆ï✒➊å➈ÿ☎ê✧ï➔è✧ç☎ï➳æ◆ì❛ê✧ø➑è✧ø➀ì➈é☎ê➵å➄ä✥ï♣û➀ø➀ô➈ï➊û✠✘❭è✧ì ú✠å➄ä❘✘➻ëíì➈ä➔ù✂ø✙➘✟ï➊ä✥ï➊é✐è❨ø➑é☎ê✤è✥å➈é✗❶ï❞ê✛ì➄ë❇è✧ç✙ï✌❿ç☎å➈ä✥å➎↔è✧ï✖ä✖ð❨✕ ê✤ø➀î➻æ✙û➀ï➳ó✛å✪✘ è✧ì✶ä✧ï❞ù✂ÿ✗❶ï➤è✥ç✙ï➞æ✙ä✥ï✒➊ø➀ê✧ø➀ì➈é✺ó❨ø➩è✥ç✫ó❨ç✙ø✁❿ç✺è✧ç✙ï➞æ◆ì❛ê✧ø➑è✧ø➀ì➈é✺ì➄ë➏ù✂ø✓ê④è✥ø➑é✥✹✝ è✧ø➀ú➈ï♣ëíï✖å➄è✧ÿ✙ä✥ï✖ê✛å➈ä✧ï➳ï➊é✗➊ì✂ù✂ï✖ù✶ø➑é✺å➞ëíï❞å✠è✥ÿ✙ä✧ï➳î➓å➄æ✢ø➀ê✇è✧ì➻ä✥ï✖ù✂ÿ✥❶ï♣è✧ç✙ï ê✧æ☎å✠è✥ø➀å➈û✙ä✧ï❞ê✤ì❛û➑ÿ✙è✧ø➀ì➈é❭ì➄ë✟è✧ç✙ï➔ëíï✖å✠è✥ÿ✙ä✥ï❨î➻å➈æ✝ð❣ã✛ç✙ø✓ê❹➊å➈é➚✡◆ï➉å➎❿ç✙ø➑ï✖ú➈ï❞ù ó❨ø➑è✧ç➓å✌ê✤ì✑✝❖✖å➄û➀û➑ï❞ù➵➩✒✡✤✯❪✭❖➩❯➢❄➲✛➤ ✲✣●➨✵✥ ✲✙➢✟✑➳❯➡✴➩❦ó❨ç✙ø✁❿ç➻æ✎ï✖ä✤ëíì❛ä✧î➓ê❣å➤û➀ì☛✖å➄û årú➈ï✖ä✥å✑✂➈ø➀é❼✂✫å➄é☎ù❤å➲ê✤ÿ✗✡✦✝⑥ê✥å➄î➻æ✙û➀ø➀é❼✂✗➌❦ä✥ï✖ù✂ÿ✗➊ø➑é✗✂➲è✧ç☎ï✶ä✥ï✖ê✧ì➈û➀ÿ✂è✧ø➀ì➈é ì➈ë è✧ç☎ï❨ëíï✖å➄è✧ÿ✙ä✥ï❨î➓å➄æ✏➌➇å➄é☎ù❭ä✥ï✖ù✂ÿ✥❶ø➀é❼✂➤è✧ç✙ï♣ê✤ï✖é☎ê✤ø➑è✧ø➀ú➇ø➩è❅✘❙ì➄ë✟è✧ç☎ï➔ì➈ÿ✂è✥æ✙ÿ✂è è✧ì♣ê✤ç✙ø➑ë➺è✥ê❯å➄é✎ù✌ù✂ø➀ê✤è✧ì❛ä✤è✥ø➑ì❛é☎ê✖ð❇ã✛ç✙ï❫ê✧ï✒➊ì➈é☎ù➤ç☎ø➀ù✙ù✙ï➊é➞û✓å✪✘➈ï✖ä✝ì➄ë ✗✝ï❞ñ➔ï➊è❇✝ ✙❭ø✓ê➔å➻ê✤ÿ❼✡❼✝⑥ê✥å➄î➻æ✙û➀ø➑é✗✂➓û➀å✪✘❛ï➊ä❞ð❦ã✛ç☎ø➀ê❨û✓å✪✘➈ï✖ä✛❶ì❛î❭æ☎ä✧ø✓ê✤ï❞ê❨ê✤ø✙↔➽ëíï❞å✠è✧ÿ☎ä✧ï î➓å➄æ☎ê✒➌✂ì➈é☎ï♣ëíì❛ä✛ï✖å✑❿ç✢ëíï✖å➄è✧ÿ✙ä✥ï➤î➓å➄æ✿ø➑é✢è✧ç✙ï✌æ☎ä✧ï✖ú✐ø➀ì➈ÿ✎ê✇û✓å✪✘➈ï✖ä✖ð❦ã✛ç✙ï ä✥ï✒❶ï✖æ✂è✧ø➀ú➈ï✞➞☎ï✖û➀ù✢ì➄ë❯ï✖å➎❿ç✢ÿ✙é☎ø➩è➔ø✓ê❨å ✑➉✡☛✘ ✑❭å➈ä✧ï❞å✒ø➀é✶è✥ç✙ï✌æ✙ä✥ï➊ú➇ø➀ì➈ÿ☎ê û✓å✪✘➈ï➊ä✒❁ ê❀❶ì❛ä✧ä✥ï✖ê✧æ◆ì➈é☎ù✂ø➀é❼✂➉ëíï✖å✠è✥ÿ✙ä✥ï✇î➓å➄æ❀ð ✭❫å➎❿ç✒ÿ✙é☎ø➩è❹❶ì❛î➻æ✙ÿ✂è✧ï❞ê❇è✧ç✙ï ➢✍♦➳✄➡❺➢❪✥❩➳✛ì➄ë❇ø➩è❿ê❫ëíì❛ÿ✙ä✛ø➑é☎æ✙ÿ✂è✥ê✒➌✂î✒ÿ☎û➩è✥ø➑æ✙û➀ø➀ï✖ê✛ø➑è✎✡☛✘➽å✒è✧ä❿å➄ø➀é☎å❄✡✙û➀ï④➊ì➇ï❶ë●✝ ➞✥➊ø➑ï✖é❛è★➌❛å❛ù✙ù✙ê➏å➳è✥ä✥å➈ø➑é☎å✑✡✙û➀ï✎✡☎ø➀å❛ê✄➌✐å➄é☎ù❭æ☎å❛ê✧ê✧ï✖ê❯è✥ç✙ï➔ä✥ï✖ê✧ÿ✙û➩è❣è✥ç✙ä✥ì➈ÿ❼✂❛ç 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2Fs-s u OvE 2EE7X LEO AEF 1ii8 C3:f.maps 16@10x10 INPUT C1:feature maps S4:f.maps 16@5x5 32x32 6@28x28 S2:f.maps 6@14x14 layer F:layer OUTPUT 10 Full connection Gaussian connections Convolutions Subsampling Convolutions Subsampling Full connection ofLConyoltional Nual Ntwok foitcognition.Eacffi ana fatu maat of unit 62街eg。coa护ain:Fto b7Enka. as the feature maps in the previous la0er.The trainable LeNet-c coeb cient and bias control the effect of the sigmoid non- linearitO.If the coeb cient is small,then the unit operates This section describes in more detail the architecture of in a quasi-linear mode,and the sub-sampling la0er merelO LeNet-5,the Convolutional Neural Network used in the blurs the input.If the coeb cient is large,sub-sampling experiments.LeNet-5 comprises,la0ers,not counting the units can be seen as performing a“nois0OR”ora“nois0 input,all of which contain trainable parameters (weights). AND"function depending on the value of the bias.Succes- The input is a 32x32 pixel image.This is significantl0 larger sive la0ers of convolutions and sub-sampling are topicallo than the largest character in the database (at most 2MK2M alternated,resulting in a"bi-poramid"at each la0er,the pixels centered in a 28x28 field).The reason is that it is number of feature maps is increased as the spatial resolu- desirable that potential distinctive features such as stroke tion is decreased.-ach unit in the third hidden la0er in fig- end-points or corner can appear v the enter of the recep- ure 2 ma0 have input connections from several feature maps tive field of the highest-level feature detedtors.In LeNet-5 in the previous la0er.The convolutionosub-sampling com- the set of centers of the receptive fields of the last convolu- bination,inspired bo Hubel and Wiesel s notions of "sim- tional la0er(C3,see below)form a 2NK2Marea in the center ple”and“complex”cels,was implemente in Fukushima s of the 32x32 input.The values of the input pixels are nor- Neocognitron [32],though no globallo spervised learnin malized so that the background level (white)corresponds procedure such as back-propagation was available then.to a value ofMl and the foreground (black)corresponds large degree of invariance to geometric transformations of to 1.1,5.This makes the mean input roughlo M and the the input can be achieved with this progressive reduction variance roughlo 1 which accelerates learning [4j]. of spatial resolution compensated b0 a progressive increase In the following,convolutionallaOers are labeled Cx,sub- of the richness of the representation (the number of feature sampling la0ers are labeled Sx,and full0-connected la0ers maps). are labeled Fx,where x is the la0er index. Since all the weights are learned with back-propagation, LaOer Cl is a convolutional laOer with j feature maps. convolutional networks can be seen as sOnthesizing their ach unit in each feature map is connected to a 5x5 neigh- own feature extractor.The weight sharing technique has borhood in the input.The size of the feature maps is 28x28 the interesting side effect of reducing the number of free which prevents connection from the input from falling off parameters,therebo reducing the "capacito"of the ma- the boundar0.Cl contains 15j trainable parameters,and chine and reducing the gap between test error and training 122,3M connections. error [34].The network in figure 2 contains 34M9N8 con- LaOer S2 is a sub-sampling la0er with i feature maps of nections,but onl0 jMNMMtrainable free parameters because size 14x14.-ach unit in each feature map is connected to a of the weight sharing. 2x2 neighborhood in the corresponding feature map in C1. Fixed-size Convolutional Networks have been applied The four inputs to a unit in S2 are added,then multiplied to mano applications,among other handwriting recogni-bo a trainable coeb cient,and added to a trainable bias. tion [35],[3j],machine-printed character recognition [3,] The result is passed through a sigmoidal function.The on-line handwriting recognition [38],and face recogni-2x2 receptive fields are non-overlapping,therefore feature tion [39].Fixed-size convolutional networks that share maps in S2 have half the number of rows and column as weights along a single temporal dimension are known as feature maps in C1.LaOer S2 has 12 trainable parameters Time-Dela0 Neural Networks(TDNNs).TDNNs have been and 5,88M connections. used in phoneme recognition(without sub-sampling)[4M, LaOer C3 is a convolutional laOer with 1j feature maps. [41],spoken word recognition (with sub-sampling)[42],-ach unit in each feature map is connected to several 5x5 [43],on-line recognition of isolated handwritten charac- neighborhoods at identical locations in a subset of S2s ters [44],and signature verification [45]. feature maps.Table I shows the set of $2 featurea
✂✁☎✄✝✆✟✞✠✄☛✡✌☞✎✍✟✏✒✑✓✏✂✏✂✏✎✔✖✕☛✄☎✗☛✏✙✘✛✚✙✏✂✁✢✜✤✣✥✣✧✦ INPUT 32x32 Convolutions Convolutions Subsampling C1: feature maps 6@28x28 Subsampling S2: f. maps 6@14x14 S4: f. maps 16@5x5 C5: layer 120 C3: f. maps 16@10x10 F6: layer 84 Full connection Full connection Gaussian connections OUTPUT 10 ✁❼✿▲❍✪❦✪❾★❦➝❱❜✸✶❆✶✯✪✿ ✵✶✰❅❆r✵✻✳✪✸✶✰❷✷✴⑥✦P❩✰❺❤❀✰r✵✻❑✂✁★❚♦✱✎❻✇✷✹❈❯▼❯✷✹❴▲✳★✵✶✿▲✷✹❈✪✱✴❴✦❤❳✰❅✳✪✸✶✱✴❴☛❤❳✰r✵●✽❢✷✹✸✻❣✑❚★✯✪✰❅✸✶✰❜⑥✙✷✹✸❢❉✪✿▲❍✹✿ ✵✻✺✏✸✶✰❅❆❅✷✹❍✹❈✪✿ ✵✶✿▲✷✹❈➎❦✥❧✈✱✴❆❖✯✞❃★❴➂✱✴❈✪✰❨✿▲✺✏✱➜⑥✙✰❇✱❘✵✶✳★✸✶✰❷❋✛✱✴❃❩❚✄✿✁❦ ✰✹❦✪✱➜✺✶✰r✵✏✷✴⑥❼✳✪❈✪✿ ✵✻✺ ✽❳✯★✷✹✺✶✰❨✽❢✰❅✿▲❍✹✯❯✵✶✺❜✱✴✸✶✰❨❆❅✷✹❈✪✺✵✶✸✶✱✴✿▲❈✪✰❅❉✞✵✶✷✎◗✑✰❷✿▲❉★✰❇❈❯✵✻✿▲❆❺✱✴❴✁❦ å➈ê➞è✧ç✙ï✶ëíï✖å➄è✧ÿ✙ä✥ï➽î➓å➄æ☎ê✒ø➑é➷è✥ç✙ï✶æ☎ä✧ï✖ú✐ø➀ì➈ÿ✎ê✌û➀å✪✘❛ï➊ä❞ð✫ã✛ç✙ï➓è✧ä❿å➄ø➀é☎å✑✡✙û➑ï ❶ì➇ï✱✯➵➊ø➑ï✖é✐è✒å➄é☎ù➒✡✙ø✓å➈ê✌➊ì➈é✐è✧ä✥ì➈û❦è✥ç✙ï➓ï❯➘✟ï✒❶è➞ì➄ë➵è✧ç✙ï✶ê✧ø✠✂➈î➻ì➈ø✓ù❖é☎ì➈é✦✝ û➀ø➑é✙ï❞å➄ä✥ø➩è❅✘❛ð➃➏⑥ë❦è✥ç✙ï➉❶ì➇ï✱✯➵➊ø➑ï✖é✐è➔ø➀ê♣ê✤î➓å➄û➀û✶➌✙è✧ç☎ï➊é✺è✧ç☎ï➞ÿ✙é✙ø➑è➉ì➈æ◆ï➊ä❿å✠è✥ï✖ê ø➀é✺å➵➍✐ÿ☎å❛ê✤ø✙✝⑥û➑ø➀é✙ï✖å➈ä✛î❭ì✂ù✂ï➎➌☎å➄é✎ù✶è✥ç✙ï➞ê✧ÿ❼✡✦✝➠ê✧å➈î❭æ☎û➑ø➀é❼✂➓û✓å✪✘➈ï➊ä✛î➻ï➊ä✥ï➊û✠✘ ✡✙û➀ÿ✙ä❿ê➻è✧ç✙ï❖ø➑é✙æ☎ÿ✂è✖ð ➏⑥ë➳è✥ç✙ï↕❶ì➇ï✱✯➵➊ø➑ï✖é✐è✶ø➀ê➽û➀å➈ä❺✂❛ï✑➌✇ê✧ÿ❼✡✦✝➠ê✥å➄î➻æ✙û➀ø➑é❼✂ ÿ✙é✙ø➑è✥ê④➊å➈é✆✡✎ï✒ê✧ï➊ï✖é✫å➈ê❨æ◆ï➊ä✧ëíì➈ä✥î➻ø➑é❼✂➽å ☛✤é✙ì❛ø➀ê❺✘✿ý✞✍✌➻ì❛ä➉å▲☛✤é✙ì❛ø➀ê❺✘ ✕➉ñ④✧✟✌➳ëíÿ☎é✗↔è✥ø➑ì❛é➻ù✙ï➊æ◆ï➊é☎ù✂ø➀é❼✂➤ì➈é❙è✧ç☎ï❨úrå➈û➑ÿ☎ï➵ì➈ë☎è✥ç✙ï✔✡✙ø➀å❛ê➊ð❣þ➇ÿ✗✒❶ï❞ê❅✝ ê✧ø➑ú❛ï❙û✓å✪✘➈ï✖ä✥ê♣ì➄ë✔❶ì➈é➇ú❛ì➈û➀ÿ✂è✧ø➀ì➈é☎ê➳å➄é✎ù❺ê✧ÿ❼✡✦✝➠ê✧å➈î➻æ✙û➑ø➀é❼✂✺å➄ä✥ï✒è❅✘➇æ✙ø✁➊å➈û➑û✠✘ å➄û➑è✧ï✖ä✧é✎å✠è✧ï❞ù❢➌☎ä✥ï✖ê✧ÿ✙û➑è✧ø➀é❼✂➽ø➀é❖å✏☛❺✡✙ø➟✝⑥æ☛✘➇ä✥å➈î❭ø✓ù✌❇✰✇å✠è♣ï✖å✑❿ç✫û✓å✪✘➈ï✖ä✒➌✙è✧ç✙ï é➇ÿ✙î➉✡◆ï➊ä➳ì➄ë❣ëíï❞å✠è✥ÿ✙ä✧ï❙î➓å➄æ☎ê➉ø➀ê♣ø➑é✥❶ä✥ï✖å➈ê✧ï✖ù✫å❛ê➔è✥ç✙ï❙ê✧æ☎å➄è✧ø✓å➄û❯ä✧ï❞ê✤ì❛û➑ÿ✦✝ è✧ø➀ì➈é❭ø✓ê❯ù✙ï✒❶ä✥ï✖å❛ê✤ï❞ù☛ð ✭✇å✑❿ç➞ÿ☎é✙ø➩è❣ø➀é✒è✥ç✙ï➵è✧ç✙ø➀ä❿ù✒ç✙ø✓ù✙ù✂ï✖é❙û✓å✪✘➈ï✖ä❇ø➀é➑➞✗✂❄✝ ÿ✙ä✥ï✄✑➵î➓å✪✘➉ç☎årú❛ï❣ø➑é☎æ✙ÿ✂è❜➊ì➈é✙é☎ï✒↔è✥ø➑ì❛é☎ê✟ëíä✥ì➈î ê✤ï✖ú➈ï✖ä✥å➈ûrëíï✖å✠è✥ÿ✙ä✥ï➏î➓å➄æ☎ê ø➀é✢è✥ç✙ï✌æ✙ä✥ï➊ú➇ø➀ì➈ÿ☎ê✛û✓å✪✘➈ï✖ä✖ð❦ã✛ç✙ï➓❶ì❛é➇ú➈ì➈û➀ÿ✂è✥ø➑ì❛é☎✄✠ê✧ÿ❼✡✦✝➠ê✧å➈î➻æ✙û➑ø➀é❼✂➚❶ì➈î➚✝ ✡✙ø➀é☎å✠è✥ø➑ì❛é✏➌☛ø➀é☎ê✤æ☎ø➑ä✥ï✖ù✆✡☛✘✫õ➔ÿ✗✡✎ï✖û➏å➄é☎ù ✎ø➑ï❞ê✤ï✖û✡❁ ê➉é☎ì➄è✧ø➀ì➈é✎ê➉ì➈ë ☛✧ê✧ø➑î➚✝ æ✙û➀ï✖✌➤å➄é✎ù ☛❘❶ì❛î❭æ☎û➑ï✄↔✔✌✞❶ï✖û➑û✓ê✒➌➄ó➵å❛ê❦ø➑î➻æ✙û➀ï➊î➻ï✖é❛è✥ï✖ù❭ø➀é➚✜☎ÿ✙ô➇ÿ☎ê✤ç☎ø➑î➓å❂❁ ê ñ➔ï✖ì✦❶ì✑✂❛é✙ø➑è✧ä✥ì➈é ✞❜ ✑✆✠❖➌✎è✧ç✙ì❛ÿ❼✂➈ç✫é✙ì➙✂➈û➀ì✑✡☎å➈û➑û✠✘✺ê✤ÿ✙æ◆ï➊ä✥ú➇ø➀ê✧ï✖ù✺û➀ï✖å➈ä✧é☎ø➑é❼✂ æ✙ä✥ì✦❶ï✖ù✙ÿ✙ä✧ï✌ê✧ÿ✗❿ç✺å➈ê✎✡☎å✑❿ô❩✝⑥æ✙ä✥ì➈æ☎å✑✂❛å✠è✥ø➑ì❛é➓ó➵å❛ê❨årú✠å➄ø➀û➀å✑✡✙û➑ï♣è✧ç☎ï➊é✝ð❹✕ û✓å➄ä❘✂➈ï✒ù✂ï✒✂➈ä✥ï➊ï➞ì➈ë❫ø➀é✐ú✠å➈ä✧ø✓å➄é✗➊ï✌è✧ì➙✂➈ï✖ì➈î➻ï❶è✥ä✧ø✁➤è✧ä❿å➄é✎ê④ëíì❛ä✧î➓å✠è✥ø➑ì❛é☎ê❨ì➈ë è✧ç☎ï❭ø➀é✙æ✙ÿ✙è✌✖å➄é➛✡✎ï➓å✑❿ç☎ø➑ï✖ú➈ï✖ù➲ó❨ø➩è✥ç❖è✥ç✙ø➀ê➤æ☎ä✧ì➎✂➈ä✥ï✖ê✥ê✤ø➀ú➈ï➞ä✥ï✖ù✙ÿ✗↔è✥ø➑ì❛é ì➄ë✝ê✧æ☎å✠è✥ø➀å➈û✙ä✥ï✖ê✧ì➈û➀ÿ✂è✧ø➀ì➈é➵❶ì❛î➻æ✎ï✖é☎ê✧å➄è✧ï❞ù➝✡❩✘❭å✌æ✙ä✥ì✑✂❛ä✧ï❞ê✧ê✧ø➑ú❛ï❫ø➀é✗❶ä✥ï✖å❛ê✤ï ì➄ë◆è✧ç☎ï➔ä✧ø✁❿ç✙é✙ï❞ê✧ê❯ì➈ë✎è✥ç✙ï➔ä✥ï➊æ✙ä✥ï✖ê✧ï➊é✐è✥å➄è✧ø➀ì➈é➐➪➺è✧ç☎ï➔é➇ÿ✙î➉✡◆ï➊ä➏ì➈ë✎ëíï❞å✠è✥ÿ✙ä✧ï î➓å➄æ☎ê✴➶↔ð þ➇ø➑é✥❶ï✌å➄û➀û☎è✥ç✙ï➤ó✇ï✖ø✙✂❛ç✐è✥ê➵å➄ä✥ï➉û➀ï✖å➄ä✥é✙ï❞ù➽ó❨ø➑è✧ç➐✡☎å✑❿ô❩✝⑥æ✙ä✧ì❛æ☎å❄✂✐å✠è✥ø➑ì❛é✏➌ ❶ì❛é➇ú➈ì➈û➀ÿ✂è✥ø➑ì❛é☎å➄û✛é✙ï➊è④ó✇ì❛ä✧ô✂ê➝➊å➈é⑧✡◆ï➲ê✤ï✖ï➊é➘å➈ê➓ê❺✘➇é❛è✥ç✙ï✖ê✧ø✠➽➊ø➀é❼✂❖è✥ç✙ï➊ø➀ä ì✠ó❨é ëíï✖å➄è✧ÿ✙ä✥ï➓ï❯↔➇è✧ä❿å✑❶è✧ì❛ä✖ð➽ã✛ç✙ï✶ó✇ï✖ø✙✂❛ç❛è➞ê✧ç☎å➄ä✥ø➀é❼✂✿è✧ï✒❿ç☎é✙ø✠➍✐ÿ✙ï✶ç☎å➈ê è✧ç☎ï✢ø➀é✐è✧ï➊ä✥ï✖ê✤è✧ø➀é❼✂ ê✤ø✓ù✂ï✿ï❯➘✟ï✒↔è➻ì➄ë➔ä✥ï✖ù✙ÿ✗❶ø➀é❼✂➲è✥ç✙ï✿é✐ÿ☎î➉✡◆ï➊ä➻ì➄ë❨ëíä✥ï➊ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✥ê✒➌✛è✧ç✙ï✖ä✧ï✒✡☛✘ ä✥ï✖ù✙ÿ✗❶ø➀é❼✂ è✥ç✙ï ☛❺➊å➈æ☎å✑➊ø➩è❅✘✔✌➷ì➈ë➞è✧ç✙ï î➓å♦✝ ❿ç✙ø➀é✙ï➉å➈é☎ù➻ä✧ï❞ù✂ÿ✗➊ø➑é❼✂➤è✥ç✙ï✛✂✐å➄æ➝✡✎ï➊è④ó✇ï✖ï➊é➻è✥ï✖ê✤è❫ï➊ä✥ä✧ì❛ä➏å➄é☎ù❭è✥ä✥å➈ø➑é☎ø➑é❼✂ ï➊ä✥ä✥ì➈ä ✞❜✫❝✬✠⑥ð➽ã✛ç✙ï➓é✙ï➊è④ó✇ì❛ä✧ô➲ø➀é➒➞✗✂➈ÿ☎ä✧ï❵✑✫❶ì❛é✐è✥å➄ø➀é☎ê✹❜✫❝✗✘❼➌ ❀✻✘✗✺ ➊ì➈é✦✝ é✙ï★↔è✧ø➀ì➈é✎ê✄➌♦✡✙ÿ✙è❦ì❛é✙û✠✘ ✓✗✘❼➌ ✘✻✘✗✘✛è✧ä❿å➄ø➀é☎å❄✡☎û➑ï❫ëíä✧ï✖ï❫æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✥ê❳✡✎ï★➊å➈ÿ☎ê✤ï ì➄ë❯è✧ç☎ï✌ó✇ï✖ø✙✂❛ç❛è➔ê✧ç☎å➄ä✥ø➀é❼✂☎ð ✜❇ø✙↔✂ï✖ù☛✝➠ê✧ø✙➽✖ï❭☞✇ì❛é✐ú❛ì➈û➀ÿ✂è✧ø➀ì➈é✎å➄û❙ñ➉ï❶è④ó➵ì➈ä✥ô✂ê❖ç☎årú❛ï➹✡◆ï➊ï✖é➶å➄æ☎æ✙û➑ø➀ï✖ù è✧ì î➓å➈é❩✘❑å➄æ✙æ✙û➀ø✁➊å✠è✥ø➑ì❛é☎ê✒➌➵å➈î❭ì❛é❼✂ ì➄è✧ç☎ï➊ä➽ç☎å➈é☎ù✂ó❨ä✥ø➩è✥ø➑é✗✂ ä✥ï✒➊ì✑✂❛é✙ø➟✝ è✧ø➀ì➈é✩✞❜ ✙✆✠❖➌ ✞❜✗✓✠❖➌☛î➓å✑❿ç✙ø➀é✙ï❯✝⑥æ✙ä✥ø➑é✐è✥ï✖ù➔❿ç✎å➄ä❿å✑↔è✥ï➊ä♣ä✧ï★❶ì✑✂❛é✙ø➑è✧ø➀ì➈é ✞❜ ✔✆✠✶➌ ì➈é❼✝♠û➀ø➑é☎ï✾ç☎å➈é☎ù✂ó❨ä✥ø➩è✥ø➑é✗✂➶ä✥ï✒➊ì✑✂➈é☎ø➩è✥ø➑ì❛é ✞❜✗✺✠❖➌➲å➄é☎ù✴ë⑨å✑➊ï✾ä✥ï✒➊ì✑✂❛é✙ø➟✝ è✧ø➀ì➈é ✞❜✗❀✠⑥ð ✜❇ø✙↔✂ï✖ù☛✝➠ê✧ø✙➽✖ï➹❶ì❛é✐ú❛ì➈û➀ÿ✂è✧ø➀ì➈é✎å➄û➞é✙ï➊è④ó✇ì❛ä✧ô✂ê✿è✥ç☎å✠è➷ê✤ç☎å➈ä✧ï ó➵ï➊ø✠✂➈ç✐è✥ê➻å➄û➀ì➈é✗✂ å ê✤ø➀é❼✂❛û➑ï✿è✧ï✖î➻æ✎ì❛ä✥å➈û✛ù✙ø➑î➻ï➊é✎ê✤ø➀ì➈é➘å➄ä✥ï✢ô➇é✙ì✠ó❨é å➈ê ã✛ø➀î❭ï✄✝❖✧♣ï➊û✓å✪✘♣ñ➉ï➊ÿ✙ä❿å➄û✐ñ➔ï➊è④ó✇ì❛ä✧ô✂ê❷➪⑨ã✩✧➳ñ➉ñ♣ê❘➶❶ð❯ã✩✧➳ñ➉ñ♣ê❀ç✎årú➈ï❷✡◆ï➊ï➊é ÿ☎ê✧ï✖ù❖ø➑é➲æ☎ç✙ì➈é✙ï✖î➻ï❙ä✥ï✒➊ì✑✂➈é☎ø➩è✥ø➑ì❛é✢➪íó❨ø➑è✧ç✙ì❛ÿ✂è➤ê✧ÿ❼✡✦✝➠ê✥å➄î➻æ✙û➀ø➑é❼✂☛➶✜✞❝✗✘✬✠✶➌ ✞❝✗➾✡✠❖➌➻ê✤æ◆ì➈ô❛ï➊éòó➵ì➈ä❿ù ä✥ï✒❶ì➎✂➈é✙ø➑è✧ø➀ì➈é ➪⑨ó❨ø➩è✥ç✭ê✧ÿ❼✡✦✝➠ê✥å➄î➻æ✙û➀ø➑é❼✂☛➶ ✞❝✵✑ ✠✶➌ ✞❝❜✠❖➌✌ì➈é❼✝♠û➀ø➑é☎ï ä✧ï★❶ì✑✂❛é✙ø➑è✧ø➀ì➈é ì➄ë➻ø➀ê✧ì➈û✓å✠è✥ï✖ù❲ç☎å➈é☎ù✂ó❨ä✥ø➩è✧è✧ï➊é②❿ç✎å➄ä❿å✑✹✝ è✧ï✖ä✥ê✹✞❝✫❝✫✠✶➌✙å➈é☎ù✺ê✤ø✠✂➈é✎å✠è✧ÿ☎ä✧ï➳ú➈ï✖ä✧ø✙➞✥➊å➄è✧ø➀ì➈é ✞❝✦✙✆✠⑥ð ✬✛❊✢➳❺➸➑➳❯➺❩✭✝✆ ã✛ç✙ø➀ê➉ê✤ï★↔è✧ø➀ì➈é✫ù✂ï❞ê❺➊ä✧ø✠✡◆ï✖ê❨ø➀é✺î❭ì❛ä✧ï✌ù✂ï➊è✥å➈ø➑û❀è✧ç✙ï➞å➈ä❘❿ç✙ø➑è✧ï★↔è✥ÿ✙ä✧ï➤ì➈ë ✗✝ï❞ñ➔ï➊è❇✝ ✙✦➌❨è✥ç✙ï①☞✇ì❛é➇ú➈ì➈û➀ÿ✂è✥ø➑ì❛é☎å➄û➳ñ➔ï➊ÿ☎ä✥å➈û♣ñ➔ï➊è④ó✇ì❛ä✧ô➘ÿ☎ê✧ï✖ù✻ø➑é✲è✧ç✙ï ï❯↔✂æ◆ï➊ä✥ø➑î➻ï✖é❛è❿ê➊ð ✗❀ï✖ñ➔ï➊è❇✝ ✙➉➊ì➈î➻æ✙ä✥ø➀ê✧ï✖ê ✔➞û➀å✪✘❛ï➊ä❿ê✄➌✐é✙ì➄è✩❶ì❛ÿ✙é✐è✧ø➀é❼✂❙è✧ç✙ï ø➀é✙æ✙ÿ✂è★➌☎å➄û➀û✟ì➄ë❀ó❨ç✙ø✁❿ç➙➊ì➈é✐è✥å➈ø➑é✶è✧ä❿å➄ø➀é☎å❄✡☎û➑ï➳æ☎å➄ä❿å➄î➻ï➊è✧ï➊ä❿ê✬➪⑨ó✇ï✖ø✙✂❛ç✐è✥ê✴➶↔ð ã✛ç✙ï➏ø➀é✙æ✙ÿ✙è❀ø➀ê❀å❙❜ ✑✪↔❜✵✑❫æ☎ø➟↔✂ï➊û➈ø➑î➓å❄✂❛ï➈ð❀ã✛ç☎ø➀ê❀ø➀ê✝ê✧ø✠✂➈é✙ø✙➞✥➊å➈é✐è✧û✠✘➉û✓å➄ä❘✂➈ï➊ä è✧ç✎å➄é✺è✧ç☎ï➞û➀å➈ä❺✂❛ï✖ê✤è✬❿ç☎å➄ä❿å✑❶è✧ï✖ä❨ø➑é✺è✥ç✙ï✒ù✙å➄è✥å❄✡✎å➈ê✧ï➣➪⑨å✠è♣î❭ì✐ê④è✒✑❆✘♦↔✤✑✻✘ æ✙ø✙↔✂ï➊û✓ê➓❶ï✖é❛è✥ï➊ä✥ï✖ù❺ø➑é å❈✑✻✺♦↔✤✑❆✺ ➞☎ï➊û✓ù✗➶❶ð✶ã✛ç✙ï➓ä✥ï✖å➈ê✧ì➈é ø✓ê➤è✧ç☎å➄è➞ø➩è➞ø✓ê ù✂ï❞ê✤ø➀ä✥å✑✡✙û➀ï✌è✧ç☎å➄è♣æ◆ì➄è✥ï➊é✐è✧ø✓å➄û❦ù✂ø✓ê④è✥ø➑é✗❶è✧ø➀ú➈ï✒ëíï✖å✠è✥ÿ✙ä✥ï✖ê➉ê✧ÿ✗❿ç➲å❛ê♣ê✤è✧ä✥ì➈ô❛ï ï➊é✎ù☛✝♠æ◆ì➈ø➀é✐è✥ê➵ì➈ä✎❶ì❛ä✧é✙ï✖ä✎✖å➄é✶å➈æ✙æ◆ï✖å➄ä❊✣●➨✆➺➭➥❼➳ ❄✴➳✄➨✗➺r➳❯➡❣ì➈ë✝è✧ç☎ï♣ä✥ï✒➊ï➊æ✦✝ è✧ø➀ú➈ï✞➞☎ï✖û➀ù✿ì➈ë❀è✧ç☎ï✌ç✙ø✙✂❛ç✙ï✖ê✤è❇✝⑥û➀ï➊ú➈ï✖û◆ëíï✖å✠è✥ÿ✙ä✥ï➤ù✙ï❶è✧ï★↔è✥ì➈ä❿ê➊ð❨➏➠é❖✗✝ï❞ñ➔ï❶è❺✝✝✙ è✧ç☎ï♣ê✧ï❶è✇ì➈ë✏❶ï➊é✐è✥ï➊ä❿ê➏ì➄ë☛è✥ç✙ï➉ä✥ï✒➊ï➊æ✂è✥ø➑ú❛ï✩➞☎ï✖û➀ù✙ê✇ì➄ë✟è✥ç✙ï➉û✓å➈ê✤è✎➊ì➈é➇ú➈ì❛û➑ÿ✦✝ è✧ø➀ì➈é✎å➄û✂û✓å✪✘➈ï➊ä✛➪❖☞❀❜❼➌➈ê✧ï➊ï✩✡◆ï➊û➀ì✠ó✬➶❀ëíì➈ä✥î➶å✹✑❆✘❄↔✤✑❆✘➳å➄ä✥ï✖å♣ø➑é❭è✧ç☎ï✬❶ï✖é❛è✥ï➊ä ì➄ë❀è✧ç✙ï✹❜ ✑♦↔❜ ✑➤ø➀é✙æ✙ÿ✂è❞ð❫ã✛ç✙ï➳ú✠å➄û➀ÿ✙ï✖ê➵ì➄ë❇è✧ç✙ï➳ø➀é✙æ✙ÿ✂è➔æ✙ø✙↔✂ï➊û✓ê✛å➄ä✥ï➉é✙ì❛ä❇✝ î➓å➄û➀ø✙➽✖ï✖ù❺ê✤ì✢è✧ç☎å➄è➤è✧ç✙ï➝✡☎å➎❿ô❩✂❛ä✧ì❛ÿ✙é☎ù✫û➀ï➊ú❛ï➊û✩➪íó❨ç☎ø➩è✥ï★➶t❶ì❛ä✧ä✥ï✖ê✧æ◆ì➈é☎ù✙ê è✧ì✫å✿ú✠å➄û➀ÿ✙ï➻ì➄ë➃✝ ✘☎ð✙➾❭å➄é☎ù❖è✧ç✙ï➻ëíì❛ä✧ï✒✂➈ä✥ì➈ÿ✙é✎ù✢➪➭✡✙û✓å✑❿ô❼➶✞❶ì❛ä✧ä✥ï✖ê✧æ◆ì➈é☎ù✙ê è✧ì①➾❛ð✙➾✍✔✬✙✙ð➻ã✛ç☎ø➀ê✌î➓å➈ô➈ï✖ê➳è✥ç✙ï➓î➻ï✖å➈é ø➀é✙æ✙ÿ✙è✒ä✧ì❛ÿ❼✂➈ç☎û✙✘✦✘✗➌❇å➈é☎ù❺è✧ç✙ï ú✠å➄ä✥ø➀å➈é✗❶ï➳ä✥ì➈ÿ❼✂❛ç✙û✙✘➔➾➳ó❨ç☎ø✠❿ç✺å✑✒❶ï➊û➀ï➊ä❿å✠è✥ï✖ê➵û➀ï✖å➄ä✥é✙ø➀é❼✂❖✞❝✓✠⑥ð ➏➠é➤è✧ç✙ï❫ëíì➈û➀û➑ì✠ó❨ø➀é❼✂✗➌✪❶ì❛é➇ú➈ì➈û➀ÿ✂è✥ø➑ì❛é☎å➄û✠û✓å✪✘➈ï✖ä✥ê✝å➈ä✧ï❣û✓å❄✡◆ï➊û➀ï✖ù➉☞➜↔❢➌✠ê✧ÿ❼✡✦✝ ê✥å➄î➻æ✙û➀ø➑é❼✂✢û➀å✪✘❛ï➊ä❿ê➉å➈ä✧ï➞û✓å❄✡◆ï➊û➀ï✖ù þ❩↔❢➌☛å➄é☎ù➲ëíÿ✙û➑û✠✘❩✝❖➊ì➈é✙é☎ï✒↔è✥ï✖ù✫û✓å✪✘➈ï✖ä✥ê å➄ä✥ï➤û➀å✑✡✎ï✖û➑ï❞ù➙✜❳↔❢➌✙ó❨ç✙ï✖ä✧ï✞↔✿ø➀ê➵è✥ç✙ï✌û➀å✪✘❛ï➊ä✛ø➀é☎ù✂ï❯↔☛ð ✗❀å✪✘➈ï✖ä➑☞④➾➽ø✓ê✒å✆❶ì❛é➇ú➈ì➈û➀ÿ✂è✥ø➑ì❛é☎å➄û❣û✓å✪✘➈ï✖ä➞ó❨ø➩è✥ç✮✓✺ëíï✖å➄è✧ÿ✙ä✥ï➓î➓å➄æ☎ê✖ð ✭❫å➎❿ç➻ÿ✙é✙ø➑è➵ø➀é➓ï✖å➎❿ç➻ëíï✖å✠è✥ÿ✙ä✥ï➔î➓å➄æ➽ø✓ê➜➊ì➈é✙é✙ï★↔è✥ï✖ù➻è✥ì✒å ✙✪↔✤✙➤é☎ï➊ø✠✂➈ç✦✝ ✡◆ì➈ä✥ç✙ì➇ì➇ù✒ø➑é✒è✧ç✙ï✛ø➀é✙æ✙ÿ✂è❞ð❯ã✛ç☎ï✛ê✧ø✠➽➊ï❫ì➈ë☎è✥ç✙ï❫ëíï❞å✠è✥ÿ✙ä✧ï➵î➓å➄æ☎ê❯ø✓ê ✑❆✺♦↔✤✑✻✺ ó❨ç✙ø✁❿ç❖æ✙ä✥ï➊ú❛ï➊é✐è✥êt➊ì➈é✙é✙ï★↔è✥ø➑ì❛é➲ëíä✥ì➈î è✧ç☎ï❭ø➀é✙æ✙ÿ✙è✌ëíä✧ì❛î ë⑨å➄û➀û➑ø➀é❼✂✿ì❄➘ è✧ç☎ï➑✡◆ì➈ÿ✙é✎ù✙å➄ä❘✘➈ð➓☞④➾➑➊ì➈é✐è✥å➈ø➑é☎ê➉➾ ✙✻✓➻è✧ä❿å➄ø➀é☎å❄✡☎û➑ï❙æ☎å➄ä❿å➄î➻ï❶è✥ï➊ä❿ê✄➌◆å➄é☎ù ➾ ✑ ✑✦➌ ❜✻✘✫❝➑❶ì❛é✙é✙ï★↔è✧ø➀ì➈é✎ê➊ð ✗❀å✪✘➈ï✖ä➔þ ✑❭ø➀ê➉å➓ê✤ÿ❼✡❼✝⑥ê✥å➄î➻æ✙û➀ø➑é✗✂❭û✓å✪✘➈ï✖ä❨ó❨ø➩è✥ç ✓❙ëíï✖å✠è✥ÿ✙ä✥ï✌î➻å➈æ☎ê❨ì➈ë ê✧ø✙➽✖ï✞➾✖❝❄↔❢➾❪❝✎ð★✭❫å➎❿ç✒ÿ✙é☎ø➩è❣ø➀é❭ï❞å✑❿ç✒ëíï✖å✠è✥ÿ✙ä✥ï➵î➓å➈æ❙ø✓ê❷❶ì❛é✙é✙ï✒❶è✧ï❞ù➞è✥ì➳å ✑✪↔✤✑➤é☎ï➊ø✠✂➈ç☛✡✎ì❛ä✧ç☎ì✐ì✂ù➻ø➀é➓è✧ç☎ï④❶ì❛ä✧ä✥ï✖ê✧æ◆ì➈é☎ù✂ø➀é❼✂➤ëíï❞å✠è✧ÿ☎ä✧ï♣î➻å➈æ➓ø➑é✫☞④➾➈ð ã✛ç✙ï➳ëíì➈ÿ☎ä❨ø➑é✙æ☎ÿ✂è✥ê✛è✥ì➓å✒ÿ✙é☎ø➩è➔ø➀é➲þ ✑✒å➈ä✧ï✌å❛ù✙ù✂ï✖ù✏➌➇è✧ç✙ï✖é✢î❙ÿ✙û➩è✥ø➑æ☎û➑ø➀ï✖ù ✡☛✘ å✫è✧ä❿å➄ø➀é☎å✑✡✙û➑ï➐❶ì➇ï❈✯➣➊ø➑ï✖é❛è★➌➏å➄é☎ù❑å➈ù✙ù✙ï✖ù➷è✥ì å➲è✧ä❿å➄ø➀é☎å❄✡✙û➀ï➣✡✙ø✓å➈ê✖ð ã✛ç✙ï➲ä✥ï✖ê✧ÿ✙û➑è➽ø➀ê✶æ☎å➈ê✥ê✧ï✖ù❑è✧ç✙ä✥ì➈ÿ✗✂➈ç❍å ê✤ø✠✂➈î➻ì❛ø➀ù✙å➈û✛ëíÿ✙é✗❶è✧ø➀ì➈é✝ð ã✛ç✙ï ✑✪↔✤✑✶ä✧ï★❶ï✖æ✂è✧ø➀ú➈ï➑➞☎ï➊û✓ù✙ê✌å➈ä✧ï❙é✙ì➈é✦✝⑥ì✠ú➈ï✖ä✧û✓å➄æ☎æ✙ø➑é✗✂✗➌✎è✧ç✙ï✖ä✧ï➊ëíì➈ä✥ï✒ëíï❞å✠è✧ÿ☎ä✧ï î➓å➄æ☎ê✒ø➑é❤þ✤✑✺ç☎årú➈ï➻ç☎å➈û➩ë✛è✥ç✙ï✶é➇ÿ✙î➑✡✎ï✖ä✒ì➄ë✛ä✥ì✠ó➔ê➞å➄é☎ù①➊ì➈û➀ÿ✙î➻é å➈ê ëíï✖å➄è✧ÿ✙ä✥ï➤î➓å➄æ☎ê❨ø➀é➔☞④➾➈ð ✗❇å✪✘➈ï➊ä❨þ ✑❭ç☎å❛êt➾ ✑✒è✧ä❿å➄ø➀é☎å✑✡✙û➑ï➤æ☎å➈ä✥å➈î➻ï❶è✧ï✖ä✥ê å➄é✎ù✳✙❼➌ ✺✗✺✻✘➚❶ì➈é☎é✙ï✒❶è✧ø➀ì➈é☎ê✖ð ✗❀å✪✘➈ï✖ä✞☞❀❜➻ø✓ê♣å➣➊ì➈é➇ú➈ì❛û➑ÿ✙è✧ø➀ì➈é☎å➈û☛û➀å✪✘❛ï➊ä➔ó❨ø➑è✧ç✢➾✒✓❭ëíï✖å➄è✧ÿ✙ä✥ï➞î➓å➄æ☎ê✖ð ✭❫å➎❿ç✺ÿ✙é✙ø➑è➉ø➑é✫ï❞å✑❿ç✿ëíï✖å➄è✧ÿ✙ä✥ï➞î➓å➄æ✺ø✓ê✬➊ì➈é✙é✙ï★↔è✥ï✖ù✢è✧ì✶ê✧ï➊ú❛ï➊ä❿å➄û ✙♦↔✙ é✙ï✖ø✙✂❛ç❩✡◆ì➈ä✥ç✙ì➇ì✂ù✙ê✺å✠è✫ø✓ù✂ï➊é✐è✧ø✁➊å➈û➤û➑ì✦➊å➄è✧ø➀ì➈é☎ê✺ø➀é å❑ê✧ÿ❼✡☎ê✧ï❶è➲ì➈ë➻þ ✑❂❁ ê ëíï✖å➄è✧ÿ✙ä✥ï✿î➻å➈æ☎ê✖ð❑ã❯å❄✡✙û➀ï➙➏❭ê✤ç☎ì✠ó➔ê✒è✥ç✙ï✫ê✤ï➊è❭ì➈ë➤þ ✑➲ëíï✖å➄è✧ÿ✙ä✥ï✿î➻å➈æ☎ê
CXC.Ob CRE IEEE,AOVEy BE XFV 8 y c 2 3 4 5 P 7 s 9 cccdd where A is the amplitude of the funption and S determines A AAA AAAA AA its slope at the origin.The funption f is odd with horizon- C AA AAA AAAA A tal asvmptotes at VA and-A.The ponstant A is phosen 2 AAA to re c759.The rationale for this phoipe of a skuashing 3 A AA AAAA A funption is given in Nppendix N. 4 AAAA AA A 1 inallvothe output laver is pomposed of-uplidean H adial 5 AA A A A A Basis i unption units IB1)oone for eaph plasso with s4 LBLi inputs eaph.The outputs of eaph HB unit yi is romputed EACH CULUMN INDICATEO WHIEH FEAT GRE MAP IN S2 ARE CUMNED as followse THE UNITOIN A PARTICUUAR FEATURE MAP VF -3 班8∑Ei-u)C b) In other wordsoeaph output HBI unit pomputes the-u- plidean distanpe Fetween its input veptor and its parameter pomrined FM eaph T3 feature map.WhM not ponnept ev- veptor.The further awam is the input from the parameter erM S2 feature map to everMT3 feature map2 The rea- son is twofold.I irsto a non-pomplete ponneption spheme veptoro the larger is the HBI output.The output of a keeps the numrer of ponneptions within reasonarle rounds. partipular HB pan Fe interpreted as a penaltm term mea- More importantlyoit forpes a Freak of symmetrmin the net- suring the fit retween the input pattern and a model of the plass assopiated with the HB1.In prorarilistip termsothe work.Different feature maps are forped to extrapt different opefullM pomplementar)features Fepause them get dif- HBI output pan Fe interpreted as the unnormalized nega- ferent sets of inputs.The rationale rehind the ponneption tive log-likelihood of a Gaussian distripution in the spape of ponfigurations of laver I P.Given an input patternothe spheme in tarle I is the following.The first six r 3 feature loss funption should Fe designed so as to get the ponfigu- maps take inputs from everM pontiguous supsets of three ration of 1 P as plose as possiple to the parameter veptor feature maps in S2.The next six take input from everM of the that porresponds to the patterns desired plass. pontiguous supset of four.The next three take input from The parameter veptors of these units were phosen Fy hand some dispontinuous supsets of four.I inallM the last one takes input from all S2 feature maps.Laver r3 has cod and kept fixed rat least initiall).The pomponents of those parameters veptors were set to -cor VG While thempould trainarle parameters and ooPyy ponneptions. have Feen phosen at random with ekual prorarilities for-c Laver S4 is a sur-sampling laver with dfeature maps of and Vooor even phosen to form an error porrepting pode size 5x5.-aph unit in eaph feature map is ponnepted to a as suggested FM [47]otheM were instead designed to repre- 2x2 neighrorhood in the porresponding feature map in T3o sent a stMized image of the porresponding pharapter plass in a similar wam as T cand S2.Laver S4 has 32 trainarle drawn on a 7x Fitmap ihenpe the numper s4).Suph a parameters and 2oyy ponneptions. representation is not partipularlM useful for repognizing iso- Laver T5 is a ponvolutional laver with dy feature maps. lated digitsorut it is kuite useful for repognizing strings of aph unit is ponnepted to a 5x5 neighrorhood on all pharapters taken from the full printarle NSTII set.The of S4s feature maps.Hereorepause the size of S4 is also rationale is that pharapters that are similaroand therefore 5x5o the size of r5s feature maps is cce this amounts ponfusapleosuph as upper pase oolowerpase Ooand zerooor to a full ponneption Fetween S4 and r5.T5 is lapeled lowerpase lodigit Coskuare Frarketsoand upperpase Io will as a ronvolutional laerinstead of a fullroneted ar have similar output rodes.This is partipularlMuseful if the repause if LeNet-5 input were made Figger with ever thing system is pompined with a linguistip post-propessor that else kept ponstant.the feature map dimension would re larger than &G This propess of dmnamipallM inpreasing the pan porrept suph ponfusions.Bepause the podes for ponfus- aple plasses are similarothe output of the porresponding size of a ponvolutional network is despriged in the seption Seption 9 II.Laver T5 has 4s cy trainarle ponneptions. HBIs for an ampiguous pharapter will Fe similaroand the Laver 1 Popontains s4 units ithe reason for this numper post-propessor will re arle to pipk the appropriate interpre- tation.1 igure 3 gives the output podes for the full NSrII pomes from the design of the output laveroexplained Fe- set. low)and is fullM ponnepted to T5.It has cyo4 trainarle N nother reason for using suph distriputed podesorather parameters. than the more pommon "cof N"pode ralso palled plape Ns in plassipal neural networksounits in lavers up to 1 P pompute a dot produpt Fetween their input veptor and their podeo or grand-mother pell pode)for the outputs is that weight veptoroto whiph a rias is added.This weighted sumo non distriputed podes tend to rehave FadlM when the num- Fer of plasses is larger than a few dozens.The reason is denoted a;for unit io is then passed through a sigmoid skuashing funption to produpe the state of unit iodenoted that output units in a non-distriputed pode must Fe off most of the time.This is kuite din pult to aphieve with FMTie sigmoid units.Yet another reason is that the plassifiers are Ti8 fi) ) often used to not onlmrepognize pharaptersoFut also to re- The skuashing funption is a spaled hmperrolip tangente 6ept non-pharapters.HBIs with distriruted podes are more appropriate for that purpose Fepause unlike sigmoidsothem f)8 Atanha) D are aptivated within a well pirpumsprig ed region of their in-
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➪íç☎ì➈æ◆ï❶ëíÿ✙û➀û✙✘①➊ì➈î➻æ✙û➀ï➊î➻ï➊é✐è✥å➈ä❺✘❼➶♣ëíï❞å✠è✧ÿ☎ä✧ï❞ê✌✡✎ï★➊å➈ÿ☎ê✤ï➽è✧ç✙ï✒✘➛✂❛ï❶è❙ù✂ø➑ë●✝ ëíï➊ä✥ï➊é✐è♣ê✧ï❶è❿ê❨ì➄ë❣ø➀é✙æ✙ÿ✂è❿ê➊ð❨ã✛ç✙ï✒ä✥å➄è✧ø➀ì➈é☎å➈û➑ï✌✡◆ï➊ç✙ø➀é☎ù✿è✥ç✙ï➑➊ì➈é✙é✙ï★↔è✥ø➑ì❛é ê❘❿ç✙ï➊î➻ï✌ø➀é✢è❿å❄✡✙û➀ï✌➏✛ø➀ê❨è✧ç✙ï➤ëíì❛û➑û➀ì✠ó❨ø➑é✗✂☎ð❫ã✛ç✙ït➞✎ä✥ê✤è➉ê✤ø✙↔✆☞❀❜❭ëíï❞å✠è✥ÿ✙ä✧ï î➓å➄æ☎ê❙è❿å➄ô➈ï✢ø➑é☎æ✙ÿ✂è✥ê❙ëíä✥ì➈î ï✖ú➈ï➊ä❘✘ ❶ì➈é✐è✥ø✙✂❛ÿ✙ì➈ÿ☎ê❭ê✧ÿ❼✡☎ê✧ï❶è✥ê❭ì➈ë❨è✧ç✙ä✥ï➊ï ëíï✖å➄è✧ÿ✙ä✥ï✿î➻å➈æ☎ê❙ø➑é➘þ ✑✂ð ã✛ç✙ï✿é✙ï❯↔➇è➓ê✤ø✙↔➷è✥å➈ô➈ï✿ø➑é✙æ☎ÿ✂è❙ëíä✥ì➈î ï✖ú➈ï✖ä❺✘ ❶ì❛é✐è✧ø✠✂➈ÿ✙ì❛ÿ☎ê❨ê✤ÿ✗✡☎ê✤ï➊è➔ì➄ë❯ëíì➈ÿ✙ä❞ð❫ã✛ç✙ï✌é☎ï❯↔➇è❨è✧ç✙ä✥ï➊ï➤è❿å➄ô❛ï✌ø➑é✙æ☎ÿ✂è➔ëíä✥ì➈î ê✧ì➈î➻ï✿ù✙ø➀ê❘❶ì❛é❛è✥ø➑é➇ÿ✙ì❛ÿ☎ê➻ê✤ÿ✗✡☎ê✤ï➊è✥ê➻ì➈ë➉ëíì➈ÿ☎ä✖ð⑨✜❇ø➀é☎å➈û➑û✠✘ è✧ç☎ï✿û✓å➈ê✤è➓ì➈é✙ï è✥å➈ô➈ï❞ê➔ø➀é✙æ✙ÿ✂è➳ëíä✧ì❛î▼å➈û➑û❣þ ✑❭ëíï❞å✠è✥ÿ✙ä✧ï❙î➓å➄æ☎ê✖ð❇✗❀å✪✘❛ï➊ä✞☞❀❜✶ç☎å➈ê➉➾✑➌ ✙✦➾✒✓ è✧ä❿å➄ø➀é☎å✑✡✙û➑ï➤æ☎å➈ä✥å➈î➻ï❶è✧ï✖ä✥ê✛å➈é☎ù➔➾✆✙✦➾➎➌ ✓✗✘✻✘➉➊ì➈é✙é☎ï✒↔è✥ø➑ì❛é☎ê✖ð ✗❀å✪✘➈ï✖ä❫þ✦❝➞ø✓ê❫å➞ê✧ÿ❼✡✦✝➠ê✥å➄î➻æ✙û➀ø➑é❼✂✌û✓å✪✘➈ï✖ä❣ó❨ø➩è✥ç↕➾✽✓➳ëíï❞å✠è✥ÿ✙ä✧ï➉î➻å➈æ☎ê❣ì➈ë ê✧ø✙➽✖ï ✙✪↔✤✙✂ð ✭✇å✑❿ç✫ÿ✙é☎ø➩è➳ø➑é➲ï❞å✑❿ç✺ëíï❞å✠è✧ÿ☎ä✧ï➞î➓å➈æ✫ø➀ê✞❶ì❛é✙é✙ï✒❶è✧ï❞ù✿è✧ì✢å ✑✪↔✤✑➤é☎ï➊ø✠✂➈ç☛✡✎ì❛ä✧ç☎ì✐ì✂ù➻ø➀é➓è✧ç☎ï④❶ì❛ä✧ä✥ï✖ê✧æ◆ì➈é☎ù✂ø➀é❼✂➤ëíï❞å✠è✧ÿ☎ä✧ï♣î➻å➈æ➓ø➑é✆☞❀❜❼➌ ø➀é❺å✶ê✧ø➀î❭ø➀û✓å➄ä➉ó✛å✪✘✺å➈ê✌☞④➾❙å➄é✎ù❖þ ✑✂ð✒✗❀å✪✘❛ï➊ä➤þ✦❝✶ç☎å❛ê✟❜✵✑❭è✧ä❿å➄ø➀é☎å✑✡✙û➑ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✥ê✛å➄é✎ù✳✑❼➌ ✘✗✘✻✘➚❶ì➈é☎é✙ï✒❶è✧ø➀ì➈é☎ê✖ð ✗❀å✪✘➈ï✖ä✎☞❅✙➤ø✓ê✇å➉❶ì➈é➇ú❛ì➈û➀ÿ✂è✧ø➀ì➈é☎å➈û✙û✓å✪✘➈ï➊ä❫ó❨ø➩è✥ç➔➾ ✑✻✘➳ëíï✖å➄è✧ÿ✙ä✥ï➉î➓å➄æ✎ê➊ð ✭❫å➎❿ç❑ÿ☎é✙ø➩è➽ø✓ê➵❶ì❛é✙é✙ï★↔è✧ï❞ù❑è✧ì å ✙✪↔✤✙❖é✙ï➊ø✠✂➈ç☛✡◆ì➈ä✥ç✙ì➇ì➇ù❤ì➈é❍å➄û➀û✌➾✽✓ ì➄ë❨þ✦❝❇❁ ê➳ëíï✖å➄è✧ÿ✙ä✥ï➻î➓å➄æ☎ê✖ð❭õ➉ï➊ä✥ï✑➌✏✡◆ï✒✖å➄ÿ☎ê✧ï❙è✧ç✙ï➽ê✧ø✙➽✖ï❙ì➈ë❨þ✔❝✢ø✓ê✌å➄û✓ê✤ì ✙✪↔✤✙❼➌❫è✥ç✙ï❖ê✧ø✙➽✖ï✫ì➄ë➉☞❅✙ ❁ ê❭ëíï✖å✠è✥ÿ✙ä✥ï✫î➻å➈æ☎ê➓ø✓ê✆➾❯↔❢➾✗✰✺è✧ç✙ø✓ê✶å➈î❭ì❛ÿ✙é✐è✥ê è✧ì➘å ëíÿ☎û➑û✌❶ì❛é✙é✙ï★↔è✧ø➀ì➈é❝✡✎ï➊è④ó✇ï✖ï➊é✾þ✦❝ å➄é☎ù✟☞❅✙✂ð ☞❅✙ ø✓ê✶û✓å❄✡◆ï➊û➀ï✖ù å➈ê➵å➚❶ì➈é➇ú❛ì➈û➀ÿ✂è✧ø➀ì➈é☎å➈û✙û✓å✪✘➈ï➊ä★➌✐ø➑é☎ê✤è✧ï❞å➈ù➓ì➈ë❇å✌ëíÿ☎û➑û✠✘❩✝❖➊ì➈é✙é✙ï★↔è✥ï✖ù➽û✓å✪✘➈ï✖ä✒➌ ✡◆ï✒➊å➈ÿ☎ê✧ï➵ø➑ë ✗✝ï✖ñ➉ï❶è❺✝✝✙♣ø➀é✙æ✙ÿ✂è➏ó➵ï➊ä✥ï✛î➻å❛ù✂ï✔✡✙ø✠✂✑✂➈ï✖ä❦ó❨ø➩è✥ç❭ï✖ú➈ï✖ä❺✘✐è✧ç☎ø➑é❼✂ ï➊û✓ê✧ï✫ô➈ï➊æ✙è ❶ì➈é✎ê④è❿å➄é✐è✒➌✇è✧ç✙ï✺ëíï❞å✠è✥ÿ✙ä✧ï✫î➓å➈æ➘ù✙ø➑î➻ï➊é✎ê✤ø➀ì➈é➘ó➵ì➈ÿ✙û✓ù⑨✡✎ï û✓å➄ä❘✂➈ï➊ä❇è✧ç✎å➄é ➾✄↔❢➾➈ð❇ã✛ç☎ø➀ê❯æ✙ä✥ì✦❶ï✖ê✥ê❇ì➄ë✎ù✦✘➇é☎å➈î➻ø✠✖å➄û➀û✙✘✌ø➀é✗❶ä✥ï✖å❛ê✤ø➀é❼✂➉è✧ç✙ï ê✧ø✙➽✖ï✒ì➄ë➵å ❶ì❛é➇ú➈ì➈û➀ÿ✂è✥ø➑ì❛é☎å➄û✝é☎ï❶è④ó➵ì➈ä✥ô✢ø✓ê➤ù✂ï✖ê❘❶ä✥ø✙✡◆ï✖ù➲ø➑é❖è✧ç✙ï➻ê✤ï★↔è✥ø➑ì❛é þ➇ï★↔è✧ø➀ì➈é✫✣④➏❇➏↔ð ✗❀å✪✘❛ï➊ä✬☞❅✙❙ç☎å➈ê❅❝✺❼➌✠➾ ✑✻✘✌è✧ä❿å➄ø➀é☎å✑✡✙û➑ï✌➊ì➈é✙é✙ï★↔è✥ø➑ì❛é☎ê➊ð ✗❀å✪✘➈ï✖ä✛✜✓❼➌✥➊ì➈é✐è✥å➈ø➑é✎ê ✺✬❝➓ÿ✙é☎ø➩è❿ê➉➪➺è✥ç✙ï✒ä✥ï✖å❛ê✤ì❛é✶ëíì❛ä❨è✧ç☎ø➀ê➉é✐ÿ☎î➉✡◆ï➊ä ❶ì❛î➻ï✖ê➤ëíä✥ì➈î❂è✧ç✙ï✢ù✂ï✖ê✧ø✙✂❛é➷ì➄ë✛è✧ç✙ï✶ì➈ÿ✂è✥æ✙ÿ✂è✒û✓å✪✘➈ï✖ä✒➌❇ï❯↔✂æ✙û✓å➄ø➀é✙ï✖ù➒✡◆ï❯✝ û➀ì✠ó✬➶➔å➄é✎ù✺ø➀ê➉ëíÿ✙û➀û✙✘✆❶ì❛é✙é✙ï★↔è✧ï❞ù✺è✧ì✆☞❅✙✂ð✛➏⑥è➳ç☎å➈ê➑➾✽✘✗➌✙➾✒✓✬❝❭è✧ä❿å➄ø➀é☎å✑✡✙û➑ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✥ê✖ð ✕➉ê➔ø➀é↕❶û✓å➈ê✥ê✧ø✠✖å➄û☛é✙ï✖ÿ✙ä✥å➈û✝é✙ï➊è④ó✇ì❛ä✧ô✂ê✒➌✂ÿ✙é✙ø➑è✥ê➔ø➀é✫û✓å✪✘➈ï➊ä❿ê➵ÿ✙æ✺è✧ì➣✜✓ ❶ì❛î➻æ✙ÿ✂è✧ï➵å➔ù✂ì➈è❀æ✙ä✥ì➇ù✙ÿ✗↔è❀✡◆ï❶è④ó➵ï➊ï✖é✌è✧ç☎ï➊ø➀ä❀ø➀é✙æ✙ÿ✂è❯ú➈ï✒❶è✧ì❛ä❀å➄é☎ù➳è✥ç✙ï➊ø➀ä ó➵ï➊ø✠✂➈ç✐è❇ú❛ï✒↔è✥ì➈ä★➌➊è✥ì➉ó❨ç✙ø✁❿ç✒å✬✡✙ø➀å❛ê✝ø✓ê❇å❛ù✙ù✂ï❞ù☛ð❯ã✛ç☎ø➀ê❇ó✇ï✖ø✙✂❛ç✐è✧ï✖ù✌ê✧ÿ✙î✫➌ ù✂ï✖é✙ì➄è✥ï✖ù✹✸❲ ëíì❛ä✶ÿ✙é☎ø➩è✻✺❘➌❨ø✓ê➓è✥ç✙ï➊é✲æ☎å➈ê✥ê✤ï❞ù è✧ç✙ä✥ì➈ÿ✗✂➈ç✻å ê✧ø✙✂❛î➻ì➈ø✓ù ê❘➍❛ÿ✎å➈ê✧ç✙ø➑é✗✂❙ëíÿ☎é✗↔è✥ø➑ì❛é✺è✧ì➽æ✙ä✥ì✂ù✂ÿ✗➊ï➤è✧ç✙ï➞ê✤è✥å➄è✧ï✌ì➄ë❣ÿ✙é☎ø➩è✧✺✴➌☎ù✙ï➊é✙ì➈è✧ï✖ù ✡☛✘✽✼✴❲ ✰ ✼❲ ✺✿✾❨➪❀✸✦❲✻➶ ➪❩✙✑➶ ã✛ç✙ï➞ê❘➍✐ÿ☎å➈ê✧ç✙ø➀é❼✂✒ëíÿ☎é✗↔è✥ø➑ì❛é✿ø✓ê➔å➻ê❘➊å➄û➀ï✖ù✢ç☛✘➇æ✎ï✖ä❺✡◆ì➈û➀ø✠♣è❿å➄é❼✂❛ï➊é✐è✽✰ ✾❨➪❁✸✦➶ ✺✿❂✺è✥å➈é✙ç❀➪❀❃✜✸☛➶ ➪✡✓➎➶ ó❨ç✙ï✖ä✧ï❄❂✲ø➀ê➏è✧ç✙ï➉å➈î➻æ✙û➑ø➑è✧ÿ✎ù✂ï➉ì➈ë◆è✥ç✙ï❨ëíÿ✙é✥↔è✧ø➀ì➈é✢å➄é☎ù❅❃➷ù✂ï➊è✧ï➊ä✥î➻ø➑é☎ï✖ê ø➑è✥ê➏ê✧û➑ì❛æ✎ï❨å➄è❯è✥ç✙ï❨ì➈ä✥ø✠✂➈ø➀é✝ð❇ã✛ç✙ï➵ëíÿ✙é✥↔è✧ø➀ì➈é✽✾➽ø➀ê❦ì✂ù✙ù❢➌❛ó❨ø➩è✥ç➻ç✙ì➈ä✥ø✙➽✖ì➈é✦✝ è✥å➈û❯å❛ê❇✘➇î➻æ✂è✥ì➄è✧ï❞ê➉å➄è ✣✭❂✹å➈é☎ù ✆ ❂✒ð➳ã✛ç✙ï➚❶ì❛é☎ê④è❿å➄é✐è✳❂➶ø➀ê✞❿ç✙ì✐ê✤ï✖é è✧ì➐✡◆ï➙➾ ❭✕✔✦➾ ✙❆❀☎ð♣ã✛ç✙ï❭ä❿å✠è✧ø➀ì➈é✎å➄û➀ï✌ëíì➈ä♣è✧ç✙ø✓êt❿ç✙ì➈ø✁❶ï❙ì➄ë✇å✢ê❺➍✐ÿ☎å❛ê✤ç☎ø➑é❼✂ ëíÿ✙é✗❶è✧ø➀ì➈é✺ø✓ê✩✂➈ø➀ú➈ï✖é✶ø➀é✫✕➉æ✙æ◆ï➊é☎ù✂ø✙↔✆✕➞ð ✜❇ø➀é☎å➈û➑û✠✘✑➌❞è✧ç☎ï❫ì➈ÿ✙è✧æ✙ÿ✂è❯û➀å✪✘❛ï➊ä☛ø✓ê❳➊ì➈î➻æ◆ì❛ê✧ï✖ù➳ì➄ë❇✭❫ÿ✗❶û➀ø➀ù✙ï✖å➄é➓✍➉å➈ù✂ø✓å➄û ✚✛å➈ê✧ø➀ê➵✜☎ÿ✙é✗❶è✧ø➀ì➈é➘ÿ✙é✙ø➑è✥ê➛➪✍✛✚✔✜❷➶✹➌✇ì➈é✙ï✿ëíì➈ä✶ï✖å✑❿ç ❶û✓å➈ê✥ê✒➌❫ó❨ø➑è✧ç ✺✬❝ ø➀é✙æ✙ÿ✂è❿ê❫ï❞å✑❿ç✝ð❦ã✛ç✙ï➉ì❛ÿ✂è✧æ☎ÿ✂è✥ê❫ì➄ë✝ï✖å➎❿ç➣✍✛✚✔✜❖ÿ☎é✙ø➩è❇❆✫❲☛ø✓ê✎❶ì➈î➻æ✙ÿ✙è✧ï✖ù å➈ê➵ëíì❛û➑û➀ì✠ó➔ê✽✰ ❆✫❲ ✺❉❈✠❊ ➪❋✼❊ ✆❍●❲❊ ➶ ❭ ➪ ✔❄➶ ➏➠é➷ì➄è✥ç✙ï➊ä➞ó➵ì➈ä❿ù✙ê✒➌✝ï✖å➎❿ç➷ì➈ÿ✂è✥æ✙ÿ✂è➑✍✛✚✔✜✲ÿ✙é✙ø➑è➑❶ì❛î❭æ☎ÿ✂è✧ï❞ê➤è✧ç✙ï✜✭➏ÿ✦✝ ❶û➀ø✓ù✂ï✖å➈é❭ù✂ø✓ê✤è✥å➄é✥❶ï✎✡✎ï➊è④ó✇ï✖ï➊é❭ø➩è❿ê❦ø➑é✙æ☎ÿ✂è➏ú➈ï★↔è✧ì❛ä❣å➄é☎ù✒ø➩è❿ê❣æ☎å➄ä❿å➄î➻ï➊è✧ï➊ä ú➈ï★↔è✥ì➈ä❞ð➵ã✛ç✙ï➞ëíÿ✙ä✤è✥ç✙ï➊ä➤åró✛å✪✘➽ø➀ê➔è✧ç✙ï✒ø➑é✙æ☎ÿ✂è➉ëíä✥ì➈îPè✧ç✙ï❙æ☎å➄ä❿å➄î➻ï➊è✧ï➊ä ú➈ï★↔è✥ì➈ä★➌✛è✧ç✙ï❺û➀å➈ä❺✂❛ï➊ä➽ø✓ê➽è✥ç✙ï➛✍✬✚✎✜✭ì❛ÿ✂è✧æ✙ÿ✙è✖ð➶ã✛ç☎ï❖ì➈ÿ✙è✧æ✙ÿ✂è✺ì➄ë➞å æ☎å➈ä✤è✥ø✠➊ÿ✙û➀å➈ä✩✍✛✚✔✜✢➊å➈é ✡◆ï➳ø➀é✐è✧ï✖ä✧æ✙ä✥ï❶è✥ï✖ù✿å➈ê✛å❙æ✎ï✖é☎å➄û➑è❅✘➓è✧ï✖ä✧î✴î❭ï❞å♦✝ ê✧ÿ✙ä✧ø➀é❼✂➳è✧ç☎ï✔➞✙è❹✡✎ï➊è④ó✇ï✖ï➊é❭è✧ç☎ï❨ø➑é✙æ☎ÿ✂è❫æ☎å➄è✤è✧ï✖ä✧é➻å➄é✎ù❭å➳î➻ì✂ù✂ï➊û☎ì➄ë◆è✧ç✙ï ❶û✓å➈ê✥ê➉å❛ê✧ê✧ì✦❶ø✓å✠è✥ï✖ù✿ó❨ø➩è✥ç✫è✧ç☎ï➑✍✛✚✔✜➵ð✥➏➠é❖æ✙ä✧ì➎✡☎å❄✡☎ø➑û➀ø➀ê✤è✧ø✁➤è✥ï➊ä✥î➻ê✒➌✎è✧ç✙ï ✍✛✚✔✜ ì❛ÿ✂è✧æ✙ÿ✙è✩✖å➄é➙✡✎ï➤ø➀é❛è✥ï➊ä✥æ✙ä✥ï❶è✧ï❞ù✶å❛ê❫è✥ç✙ï➤ÿ✙é✙é✙ì❛ä✧î➓å➈û➑ø✠➽➊ï❞ù➓é✙ï✄✂✐å♦✝ è✧ø➀ú➈ï❭û➀ì✑✂❄✝⑥û➀ø➑ô❛ï➊û➀ø➑ç✙ì➇ì✂ù➲ì➈ë✇å✺â➤å➄ÿ☎ê✥ê✤ø✓å➄é ù✂ø✓ê④è✥ä✧ø✠✡✙ÿ✂è✥ø➑ì❛é❺ø➀é❖è✥ç✙ï➓ê✤æ✎å✑❶ï ì➄ë❹➊ì➈é✦➞✗✂❛ÿ✙ä❿å✠è✧ø➀ì➈é✎ê❨ì➄ë❣û✓å✪✘➈ï➊ä④✜✝✓☎ð➉â➳ø➑ú❛ï➊é❖å➈é✫ø➑é☎æ✙ÿ✂è♣æ✎å✠è✤è✥ï➊ä✥é✏➌✎è✧ç✙ï û➀ì❛ê✥ê➉ëíÿ☎é✗↔è✥ø➑ì❛é➷ê✧ç✙ì❛ÿ✙û➀ù➔✡✎ï➽ù✙ï✖ê✧ø✙✂❛é✙ï✖ù❺ê✤ì✫å➈ê♣è✥ì➐✂❛ï❶è➤è✧ç☎ï➝➊ì➈é✦➞✥✂➈ÿ✦✝ ä❿å✠è✧ø➀ì➈é ì➈ë✬✜✓➲å➈ê➑❶û➀ì❛ê✧ï✶å➈ê❙æ✎ì✐ê✧ê✧ø✠✡✙û➑ï➽è✧ì➲è✥ç✙ï✶æ✎å➄ä❿å➄î➻ï❶è✥ï➊ä➞ú❛ï✒↔è✥ì➈ä ì➄ë✟è✥ç✙ï④✍✛✚✔✜❖è✧ç☎å➄è✎➊ì➈ä✥ä✧ï❞ê✤æ◆ì➈é☎ù☎ê❯è✧ì➞è✥ç✙ï➔æ☎å➄è✤è✥ï➊ä✥é ❁ ê✇ù✂ï✖ê✧ø➀ä✧ï❞ù➵❶û✓å➈ê✥ê➊ð ã✛ç✙ï➤æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä➵ú❛ï✒❶è✧ì➈ä❿ê✇ì➄ë❀è✥ç✙ï✖ê✧ï➤ÿ✙é✙ø➑è✥ê❨ó➵ï➊ä✥ït❿ç✙ì❛ê✧ï➊é➙✡❩✘✶ç☎å➄é☎ù å➄é✎ù✒ô❛ï➊æ✂è❨➞❼↔✂ï✖ù➐➪⑨å➄è➏û➑ï❞å➈ê✤è❣ø➑é✙ø➑è✧ø✓å➄û➀û✠✘✦➶❶ð❯ã✛ç☎ï✛❶ì➈î➻æ◆ì➈é✙ï✖é✐è✥ê❯ì➄ë✎è✧ç✙ì✐ê✤ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✥ê✇ú➈ï★↔è✧ì❛ä✥ê✇ó➵ï➊ä✥ï➳ê✧ï❶è➵è✧ì➚✝✴➾♣ì❛ä ✣➑➾❛ð ✎ç☎ø➑û➀ï➳è✧ç✙ï✒✘ ❶ì❛ÿ✙û➀ù ç☎årú❛ï✩✡✎ï✖ï➊é➙❿ç☎ì❛ê✧ï➊é➓å✠è➵ä✥å➈é☎ù✂ì➈î✭ó❨ø➑è✧ç➽ï★➍❛ÿ✎å➄û☎æ☎ä✧ì➎✡☎å❄✡✙ø➀û➀ø➩è✥ø➑ï❞ê❣ëíì➈ä➜✝❘➾ å➄é✎ù ✣➑➾✑➌❦ì➈ä➞ï✖ú➈ï✖é✢❿ç✙ì❛ê✧ï➊é➷è✥ì✫ëíì➈ä✥î å➈é ï➊ä✥ä✧ì❛ä➉❶ì❛ä✧ä✥ï✒❶è✧ø➀é❼✂✆❶ì✂ù✂ï å➈ê➳ê✧ÿ❼✂✑✂❛ï✖ê✤è✧ï✖ù✫✡☛✘✏✞❝✸✔✠❖➌✎è✧ç✙ï✒✘✫ó✇ï✖ä✧ï➞ø➀é☎ê✤è✧ï❞å➈ù➲ù✂ï❞ê✤ø✠✂➈é☎ï✖ù✺è✥ì✶ä✥ï➊æ✙ä✥ï❯✝ ê✧ï➊é✐è➤å✿ê✤è❅✘✐û➀ø✠➽➊ï✖ù❖ø➑î➓å✑✂➈ï❭ì➄ë➏è✥ç✙ï➚➊ì➈ä✥ä✧ï❞ê✤æ◆ì➈é✎ù✂ø➑é✗✂➙❿ç☎å➈ä✥å➎↔è✧ï✖ä④➊û➀å❛ê✧ê ù✂ä❿åró❨é❺ì❛é å✦✔★↔❢➾ ✑➙✡✙ø➑è✧î➓å➄æ ➪⑨ç✙ï➊é✥❶ï➓è✥ç✙ï➓é➇ÿ✙î➉✡◆ï➊ä ✺✫❝❩➶❶ð✿þ➇ÿ✗❿ç å ä✥ï➊æ✙ä✥ï✖ê✧ï➊é✐è✥å➄è✧ø➀ì➈é❙ø➀ê❦é✙ì➈è➏æ☎å➄ä✧è✧ø✁❶ÿ☎û➀å➈ä✧û✠✘✌ÿ☎ê✧ï❶ëíÿ✙û✂ëíì❛ä❣ä✧ï★❶ì➎✂➈é✙ø✠➽➊ø➀é❼✂➳ø➀ê✧ì❄✝ û✓å✠è✧ï❞ù✢ù✙ø✙✂❛ø➩è❿ê✄➌✦✡✙ÿ✙è✛ø➑è➔ø✓ê✎➍✐ÿ✙ø➑è✧ï➤ÿ☎ê✧ï❶ëíÿ☎û☛ëíì➈ä✛ä✥ï✒❶ì➎✂➈é✙ø✠➽➊ø➀é❼✂❭ê④è✥ä✧ø➀é❼✂❛ê➵ì➈ë ❿ç☎å➈ä✥å➎↔è✧ï✖ä✥ê➞è✥å➈ô➈ï➊é❤ëíä✧ì❛î è✧ç☎ï✢ëíÿ☎û➑û❨æ✙ä✥ø➀é❛è❿å❄✡✙û➀ï✫✕♣þ✗☞➃➏❺➏❭ê✧ï❶è❞ð❑ã✛ç✙ï ä❿å✠è✧ø➀ì➈é✎å➄û➀ï✌ø➀ê✛è✥ç☎å✠èt❿ç☎å➄ä❿å✑❶è✧ï✖ä✥ê✇è✧ç✎å✠è➳å➈ä✧ï➞ê✧ø➀î❭ø➀û✓å➄ä★➌☎å➄é☎ù✿è✥ç✙ï➊ä✥ï❶ëíì❛ä✧ï ❶ì❛é✂ëíÿ☎ê✥å❄✡✙û➀ï✑➌➇ê✧ÿ✗❿ç✶å➈ê✇ÿ✙æ✙æ◆ï➊ä✴➊å❛ê✤ï✌ý➑➌❛û➀ì✠ó➵ï➊ä✴➊å➈ê✧ï♣ý➑➌➇å➄é☎ù➵➽✖ï➊ä✥ì✗➌✐ì➈ä û➀ì✠ó✇ï✖ä❘✖å➈ê✧ï➳û✶➌☛ù✂ø✠✂➈ø➑è➑➾✑➌◆ê❺➍✐ÿ☎å➈ä✧ï➉✡✙ä✥å➎❿ô➈ï➊è✥ê✒➌☎å➄é☎ù➲ÿ✙æ✙æ◆ï➊ä✴➊å➈ê✧ï➓➏✹➌◆ó❨ø➑û➀û ç☎årú❛ï➔ê✤ø➀î➻ø➑û✓å➄ä❣ì❛ÿ✂è✧æ✙ÿ✙è✎❶ì✂ù✂ï❞ê➊ð❦ã✛ç✙ø✓ê➏ø✓ê❣æ☎å➈ä✤è✥ø✠➊ÿ✙û➀å➈ä✧û✠✘➞ÿ☎ê✧ï❶ëíÿ☎û☎ø➑ë☛è✧ç✙ï ê❺✘➇ê✤è✧ï✖î❅ø✓ê➣❶ì❛î➉✡✙ø➀é✙ï✖ù❑ó❨ø➑è✧ç✻å û➑ø➀é❼✂❛ÿ✙ø➀ê✤è✧ø✁✺æ◆ì❛ê✤è❇✝⑥æ✙ä✧ì✦➊ï✖ê✥ê✤ì❛ä✒è✥ç☎å✠è ➊å➈é➐➊ì➈ä✥ä✧ï★↔è✛ê✤ÿ✗❿ç✫❶ì❛é✂ëíÿ☎ê✧ø➑ì❛é☎ê✖ð❨✚➵ï★➊å➄ÿ✎ê✤ï♣è✧ç✙ï✌➊ì➇ù✙ï✖ê➵ëíì➈ä✛➊ì➈é✂ëíÿ✎ê❅✝ å❄✡☎û➑ï✆❶û✓å➈ê✥ê✧ï✖ê➻å➄ä✥ï✿ê✧ø➀î❭ø➀û✓å➄ä★➌➏è✧ç☎ï✫ì➈ÿ✂è✥æ✙ÿ✂è➽ì➄ë♣è✧ç✙ï↕➊ì➈ä✥ä✧ï❞ê✤æ◆ì➈é✎ù✂ø➑é✗✂ ✍✛✚✔✜❦ê❨ëíì❛ä♣å➄é❺å➄î➉✡☎ø✙✂❛ÿ✙ì➈ÿ☎ê✬❿ç☎å➄ä❿å✑❶è✧ï➊ä❨ó❨ø➀û➀û❳✡◆ï❙ê✧ø➑î➻ø➀û➀å➈ä✒➌◆å➄é☎ù✫è✧ç✙ï æ◆ì❛ê✤è❇✝⑥æ✙ä✧ì✦➊ï✖ê✥ê✤ì❛ä✝ó❨ø➑û➀û☛✡✎ï➵å❄✡✙û➀ï➏è✥ì♣æ☎ø✠❿ô➳è✧ç☎ï➵å➈æ✙æ✙ä✥ì➈æ✙ä✥ø➀å➄è✧ï❣ø➀é✐è✧ï➊ä✥æ✙ä✥ï❯✝ è✥å➄è✧ø➀ì➈é✝ð✩✜❯ø✠✂➈ÿ✙ä✥ï✜❜➵✂➈ø➀ú➈ï❞ê✛è✧ç☎ï➞ì➈ÿ✂è✥æ✙ÿ✂è④➊ì✂ù✂ï✖ê➔ëíì➈ä❨è✥ç✙ï➞ëíÿ✙û➀û❳✕➳þ✗☞➃➏❇➏ ê✧ï❶è✖ð ✕➔é✙ì➈è✧ç✙ï✖ä♣ä✥ï✖å❛ê✤ì❛é✺ëíì➈ä➳ÿ☎ê✤ø➀é❼✂✿ê✤ÿ✗❿ç❺ù✂ø➀ê✤è✧ä✥ø✠✡✙ÿ✂è✧ï❞ù↕❶ì✂ù✂ï❞ê✄➌✟ä❿å✠è✥ç✙ï➊ä è✧ç✎å➄é❑è✧ç✙ï✺î➻ì➈ä✥ï➙➊ì➈î➻î➻ì➈é✻☛✒➾✢ì➈ë➳ñ✟✌➛➊ì➇ù✙ï ➪üå➄û✓ê✤ì➒➊å➈û➑û➀ï✖ù❤æ✙û➀å➎❶ï ❶ì✂ù✂ï➎➌✇ì❛ä➵✂➈ä❿å➄é☎ù✦✝♠î➻ì➄è✥ç✙ï➊ä➵➊ï➊û➀û✛❶ì✂ù✂ï★➶❙ëíì❛ä➻è✧ç✙ï✫ì❛ÿ✂è✧æ☎ÿ✂è✥ê➓ø✓ê➻è✥ç☎å✠è é✙ì❛é➻ù✙ø➀ê✤è✧ä✥ø✙✡☎ÿ✂è✧ï❞ù➵❶ì✂ù✂ï✖ê❯è✥ï➊é☎ù❭è✥ì✌✡✎ï✖ç☎årú➈ï✔✡☎å❛ù✂û✠✘✒ó❨ç✙ï✖é➻è✧ç✙ï❨é➇ÿ✙î➚✝ ✡◆ï➊ä❭ì➄ë✛❶û✓å➈ê✥ê✤ï❞ê✌ø✓ê✒û✓å➄ä❘✂➈ï✖ä✌è✧ç☎å➈é å✺ëíï➊ó ù✙ì✑➽➊ï✖é☎ê✖ð❖ã✛ç✙ï➽ä✥ï✖å❛ê✤ì❛é ø✓ê è✧ç✎å✠è✶ì❛ÿ✂è✧æ✙ÿ✙è✶ÿ✙é✙ø➑è✥ê✶ø➑é✲å➷é☎ì➈é✦✝➠ù✂ø✓ê④è✥ä✧ø✠✡✙ÿ✂è✥ï✖ù ❶ì✂ù✂ï➲î❙ÿ☎ê✤è ✡✎ï❖ì❄➘ î➻ì❛ê✤è➓ì➄ë➉è✥ç✙ï✿è✧ø➀î➻ï➈ð➘ã✛ç✙ø➀ê➻ø✓ê➵➍✐ÿ✙ø➑è✧ï✫ù✂ø✯➵➊ÿ✙û➑è➓è✧ì å✑❿ç✙ø➀ï➊ú❛ï✢ó❨ø➑è✧ç ê✧ø✙✂❛î❭ì❛ø➀ù❭ÿ✙é☎ø➩è❿ê➊ð❏■➏ï❶è✛å➄é✙ì➈è✧ç✙ï✖ä➏ä✥ï✖å➈ê✧ì➈é❭ø✓ê❦è✧ç☎å➄è❫è✥ç✙ï✬❶û✓å➈ê✥ê✧ø➟➞☎ï✖ä✥ê❣å➈ä✧ï ì➄ë➺è✥ï➊é✿ÿ☎ê✧ï✖ù➓è✥ì❙é☎ì➄è✛ì➈é✙û✠✘➓ä✧ï★❶ì➎✂➈é✙ø✠➽➊ï✞❿ç☎å➄ä❿å✑❶è✧ï➊ä❿ê✒➌✑✡✙ÿ✂è➔å➈û➀ê✧ì➞è✥ì❙ä✥ï❯✝ ✓④ï✒❶è❫é✙ì❛é✦✝❖❿ç✎å➄ä❿å✑↔è✥ï➊ä❿ê➊ð❳✍✛✚✔✜❯ê➏ó❨ø➩è✥ç➽ù✂ø➀ê✤è✧ä✥ø✠✡✙ÿ✂è✧ï❞ù➵❶ì✂ù✂ï❞ê❣å➄ä✥ï❨î❭ì❛ä✧ï å➄æ☎æ✙ä✧ì❛æ✙ä✥ø➀å➄è✧ï➵ëíì➈ä❣è✥ç☎å✠è➵æ✙ÿ✙ä✥æ✎ì✐ê✤ï✩✡◆ï✒✖å➄ÿ☎ê✧ï❨ÿ✙é✙û➀ø➀ô➈ï➉ê✧ø✙✂❛î➻ì➈ø✓ù✙ê✄➌➈è✧ç✙ï✒✘ å➄ä✥ï✛å✑↔è✥ø➑ú✠å➄è✧ï✖ù❭ó❨ø➑è✧ç✙ø➀é➓å➳ó✇ï✖û➑û❼➊ø➑ä✴❶ÿ✙î➓ê❘❶ä✥ø✙✡◆ï✖ù✒ä✧ï✒✂➈ø➀ì➈é❭ì➄ë✎è✧ç✙ï✖ø➑ä❣ø➀é✦✝
CXOC.Ob CRE IEEE,AOVEy BEXFV 口四日H露图8口I】器田B日日 penalties,it means that in addition to pushins down the p1234§日☑日9日且☒目33 penalto of the 2orre2t 2lass like the MS-2riterion,this 2riterion also pulls up the penalties of the ingorreat 2lassese gH日日日EF回日四T口可万可 p日Bs0g▣893ⅢIJ▣ C(UDP(Z W)(e-iv>e-vi(z,W))) 9目回gEE日5旦H巴网五可 (9) The nesative of the se2ond term pla0s a"zompetitive"role. p9FsE口9▣893图Π图日0 It is nezessarilo smaller than (or equal to)the first term, a密gee9女nh therefore this loss funation is positive.The 2onstant j is positive,and prevents the penalties of 2lasses that are als reado vero larse from ueins pushed further up.The posS terior prouauilito of this ruuuish 2lass lauel would ue the put spaze that non gOpizal patterns are more likel0 to fall ratio of e and e-Vie-wi(z,w).This diszriminas tive zriterion prevents the previous10 mentioned "zollapsS outside of. The parameter veators of the v Ai s plao the role of tarnet in effe2t"when the v A parameters are learned uezause ve2tors for laOer 1 P.It is worth pointins out that the 2omS it keeps the vA1 zenters apart from eazh other.In Se2S ponents of those veators are V1 or S1,whizh is well within tion iI,we present a seneralization of this zriterion for the ranse of the sismoid of P,and therefore prevents those sOstems that learn to 2lassifo multiple ouje2ts in the input sismoids from setting saturated.In fa2t,V1 and Sl are the (e.s.,2harazters in words or in dozuments). points of maximum 2ur vature of the sigmoids.This forzes Oomputins the fradient of the loss funztion with respe2t the 1 Punits to operate in their maximall0 non ginear ranse. to all the weishts in all the la0ers of the 2onvolutional Saturation of the sismoids must ue avoided uezause it is network is done with uazkpropanation.The standard als known to lead to slow 2onversenze and illSonditionins of forithm must ue slishtlo modified to take azzount of the the loss funation. weisht sharins.Xn eas0 wao to implement it is to first 2omS pute the partial derivatives of the loss funztion with respe2t P.Loss Fbnctgon to eah connectgon,as if the network were a 2onventional multigaOer network without weisht sharins.Then the parS The simplest output loss funztion that 2an ue used with tial derivatives of all the 2onneztions that share a same the auove network is the Maximum vikelihood-stimation parameter are added to form the derivative with respe2t to 2riterion(Mv-),whigh in our 2ase is equivalent to the Mins that parameter. imum Mean Squared -rror (MS-).The zriterion for a set Suzh a larse arzhitezture 2an ue trained vero en 2ient10, of trainins samples is simplO uut doins so requires the use of a few te2hniques that are P deszrived in the appendix.Se2tion X of the appendix W)8 Z W (s) deszriues details suzh as the partizular sismoid used,and the weisht initialization.Seation A and o deszriue the minimization prozedure used,whizh is a stozhasti2 version where yDp is the output of the Sth v unit,i.e.the of a diasonal approximation to the vevenuers Marquardt one that zorresponds to the zorrlass of input pattern prozedure. Z. While this 2ost funztion is appropriate for most zases, itaks three important properties.irst,if we allow the III.RESULTS AND COMPARISON WITH OTHER parameters of theA to adapt,W)has a trivial,uut METHODS totallo unaz2eptaule,solution.In this solution,all theAl While re2osnizing individual disits is onlo one of mano parameter veators are equal,and the state of Pis 2onstant proulems involved in desisning a praztizal rezosnition sOsS and equal to that parameter ve2tor.In this 2ase the nets tem,it is an exzellent uenzhmark for 2omparins shape work happilo isnores the input,and all the outputs rezornition methods.Thoush man0 existins method 2omS are equal to zero.This 2ollapsing phenomenon does not uine a handrafted feature extraztor and a trainaule 2lass o22ur if the weishts are not allowed to adapt.The sifier,this studo 2onzentrates on adaptive methods that sezond proulem is that there is no 2ompetition uetween operate direztlo on size ormalized imases. the 2lasses.Suzh a 2ompetition 2an ue outained u0 usS inn a more diszriminative training zriterion,duuued the B.Database:the Mo gfie NI-T set MXj (maximum a posteriori)2riterion,similar to Maxis The datavase used ko ain and test the sOstems des mum Mutual Information zriterion sometimes used to train szriued in this paper was 2onstruzted from the NISTss SpeS HMMs.ts],.t9],5y].It 2orresponds to maximizin the 2ial Datauase Band Spe2ial Datauase 1 2ontaining uinaro posterior prouauilito of the orre2t 2lass (or minimizS imases of handwritten disits.NIST orisinallo desisnated ins the losarithm of the prouauilito of thepprre2t 2lass),SDSas their trainins set and SDsl as their test set.Hows iven that the input imane 2an 2ome from one of the 2lasses ever,SDSis muzh2leaner and easier to rezonize than SDS or from a uazkaround "ruuuish"2lass lauel.In terms of 1.The reason for this 2an ue found on the faat that SDS
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❶ÿ✙ä✥ú✠å✠è✥ÿ✙ä✧ï➤ì➈ë❇è✥ç✙ï✒ê✧ø✙✂❛î❭ì❛ø➀ù☎ê➊ð❫ã✛ç☎ø➀ê✛ëíì❛ä❘➊ï✖ê è✧ç☎ï➃✜✓❨ÿ✙é✙ø➑è✥ê✝è✧ì➔ì❛æ✎ï✖ä✥å➄è✧ï➏ø➀é➤è✧ç☎ï➊ø➀ä❀î➓å♦↔✂ø➀î➻å➈û➑û✠✘➳é✙ì➈é✦✝⑥û➀ø➑é✙ï❞å➄ä✝ä❿å➄é✗✂➈ï➈ð þ✂å➄è✧ÿ✙ä❿å✠è✥ø➑ì❛é ì➄ë✛è✧ç✙ï✿ê✤ø✠✂➈î➻ì❛ø➀ù✙ê➞î✒ÿ☎ê✤è➉✡◆ï✢årú➈ì❛ø➀ù✙ï✖ù➒✡✎ï★➊å➈ÿ☎ê✤ï✶ø➩è✒ø✓ê ô➇é✙ì✠ó❨é➲è✥ì✢û➀ï✖å❛ù✫è✥ì✿ê✧û➑ì✠ó❫❶ì➈é➇ú❛ï➊ä❘✂➈ï➊é✥❶ï➞å➄é✎ù❖ø➀û➑û✙✝r❶ì➈é✎ù✂ø➩è✥ø➑ì❛é✙ø➀é❼✂✶ì➈ë è✧ç☎ï✌û➑ì✐ê✧ê➵ëíÿ✙é✥↔è✧ø➀ì➈é❀ð ❃✛❊✢➯✪➩✴➩✁✡✦➨❄✄➺✮✣ ➯❄➨ ã✛ç✙ï➳ê✧ø➀î❭æ☎û➑ï❞ê④è✛ì➈ÿ✂è✥æ✙ÿ✂è❨û➀ì❛ê✥ê➏ëíÿ✙é✥↔è✧ø➀ì➈é✶è✧ç☎å➄è✔✖å➄é➙✡✎ï➳ÿ☎ê✧ï✖ù➽ó❨ø➑è✧ç è✧ç☎ï➤å✑✡✎ì✠ú❛ï➉é✙ï➊è④ó✇ì❛ä✧ô➻ø✓ê➵è✧ç✙ï✌ö➲å❄↔✂ø➑î❙ÿ✙î ✗✝ø➀ô➈ï✖û➑ø➀ç✙ì➇ì✂ù✙✭❫ê✤è✧ø➀î➓å✠è✥ø➑ì❛é ❶ä✥ø➑è✧ï➊ä✥ø➀ì➈é➣➪⑨ö✗★✭➃➶❯➌ró❨ç✙ø✠❿ç✒ø➑é❙ì➈ÿ✙ä❜➊å➈ê✧ï❫ø✓ê❇ï✒➍✐ÿ✙ø➀úrå➈û➑ï✖é✐è❀è✧ì➉è✧ç✙ï✛ö✫ø➀é✦✝ ø➀î✒ÿ✙î ö✫ï✖å➈é❖þ✦➍✐ÿ☎å➄ä✥ï✖ù ✭❫ä✧ä✥ì➈ä➓➪üö❖þ✭➃➶❶ð✎ã✛ç✙ï➑❶ä✥ø➩è✥ï➊ä✥ø➑ì❛é✢ëíì❛ä♣å➓ê✧ï❶è ì➄ë❯è✧ä❿å➄ø➀é✙ø➀é❼✂➓ê✧å➈î➻æ✙û➑ï❞ê✛ø➀ê❨ê✧ø➀î❭æ☎û✙✘☞✰ ❉➣➪❩❂➶ ✺ ➾ ✌ ❫ ❈ ✸✄✂ ✜ ❆✆☎✞✝❼➪❩✾✸ ❁❃❂➶ ➪✡✺➎➶ ó❨ç✙ï✖ä✧ï❅❆☎✝ ø✓ê➤è✧ç✙ï✶ì➈ÿ✂è✥æ✙ÿ✂è➞ì➄ë➵è✧ç☎ï✘■ ✸ ✝♠è✧ç①✍✛✚✔✜✾ÿ✙é✙ø➑è✒➌❯øüð ï➈ð✶è✧ç✙ï ì➈é☎ï➞è✧ç✎å✠è✌❶ì➈ä✥ä✥ï✖ê✧æ✎ì❛é☎ù✙ê✛è✥ì✶è✥ç✙ï➑➊ì➈ä✥ä✧ï★↔è④➊û➀å❛ê✧ê♣ì➄ë➏ø➀é✙æ✙ÿ✂è➤æ☎å➄è✤è✧ï✖ä✧é ✾❅✸➇ð ✎ç✙ø➀û➀ï➉è✥ç✙ø➀ê✔➊ì❛ê✤è✇ëíÿ✙é✥↔è✧ø➀ì➈é✢ø➀ê✛å➈æ✙æ✙ä✥ì➈æ✙ä✥ø➀å➄è✧ï❨ëíì❛ä✛î❭ì✐ê④è✔➊å❛ê✤ï❞ê✄➌ ø➑è➤û✓å✑❿ô✂ê♣è✧ç☎ä✧ï✖ï❙ø➀î➻æ✎ì❛ä✤è❿å➄é✐è➳æ☎ä✧ì❛æ✎ï✖ä✤è✥ø➑ï❞ê➊ð➉✜❯ø➀ä✥ê✤è✒➌❀ø➩ë➵ó✇ï➻å➄û➀û➑ì✠óòè✧ç✙ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✥ê❨ì➈ë❣è✧ç✙ï➚✍✛✚✔✜❑è✧ì✢å❛ù✙å➄æ✙è✒➌ ❉➣➪✮❂➶➉ç☎å➈ê♣å➓è✥ä✧ø➀ú➇ø➀å➈û✻➌✈✡✙ÿ✂è è✧ì➈è✥å➈û➑û✠✘♣ÿ☎é☎å✑✒❶ï➊æ✙è✥å❄✡☎û➑ï➎➌rê✧ì➈û➀ÿ✂è✥ø➑ì❛é✝ð❀➏➠é✌è✥ç✙ø✓ê❇ê✧ì➈û➀ÿ✂è✧ø➀ì➈é❀➌rå➈û➑û➈è✧ç✙ï✎✍✛✚✔✜ æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä❇ú❛ï✒↔è✥ì➈ä❿ê❀å➈ä✧ï➵ï✒➍✐ÿ☎å➈û✻➌➄å➈é☎ù➤è✧ç☎ï✛ê✤è✥å➄è✧ï➵ì➄ë✥✜✓♣ø➀ê❨➊ì➈é☎ê✤è✥å➈é❛è å➄é✎ù➲ï✒➍✐ÿ☎å➈û❯è✧ì✢è✧ç☎å➄è➤æ✎å➄ä❿å➄î➻ï❶è✥ï➊ä➳ú➈ï✒❶è✧ì❛ä✖ð✌➏➠é❖è✧ç✙ø✓ê✌➊å❛ê✤ï✒è✧ç✙ï➻é✙ï➊è❇✝ ó➵ì➈ä✥ô✫ç☎å➄æ✙æ☎ø➑û✠✘➲ø✠✂➈é✙ì❛ä✧ï❞ê➉è✥ç✙ï➓ø➀é✙æ✙ÿ✂è★➌❇å➄é✎ù å➈û➑û❦è✥ç✙ï➵✍✛✚✔✜✻ì❛ÿ✂è✧æ✙ÿ✙è✥ê å➄ä✥ï✶ï★➍✐ÿ☎å➄û✇è✧ì➒➽➊ï✖ä✧ì✎ð ã✛ç✙ø✓ê➝❶ì❛û➑û✓å➄æ☎ê✧ø➀é❼✂➲æ✙ç✙ï✖é✙ì➈î➻ï✖é✙ì➈é ù✂ì➇ï✖ê❙é✙ì➄è ì✦✄➊ÿ✙ä✒ø➑ë✛è✧ç✙ï➐✍✛✚✔✜✲ó➵ï➊ø✠✂➈ç✐è✥ê❙å➄ä✥ï➓é✙ì➄è❭å➄û➀û➑ì✠ó➵ï✖ù❺è✧ì❺å➈ù✙å➈æ✂è✖ð✫ã✛ç✙ï ê✧ï✒❶ì❛é☎ù➘æ✙ä✥ì✑✡✙û➀ï➊î ø✓ê➽è✥ç☎å✠è➽è✥ç✙ï➊ä✥ï❖ø✓ê➽é☎ì➹❶ì❛î❭æ◆ï❶è✥ø➩è✥ø➑ì❛é ✡◆ï❶è④ó➵ï➊ï➊é è✧ç☎ï➔❶û✓å➈ê✥ê✤ï❞ê➊ð✲þ✂ÿ✗❿ç❍å①❶ì➈î➻æ◆ï❶è✥ø➩è✥ø➑ì❛é ✖å➄é ✡◆ï➲ì✑✡✂è❿å➄ø➀é✙ï✖ù⑨✡☛✘❤ÿ✎ê❅✝ ø➀é❼✂❤å➷î➻ì➈ä✥ï✫ù✂ø➀ê❘❶ä✥ø➀î❭ø➀é☎å➄è✧ø➀ú➈ï✺è✧ä❿å➄ø➀é✙ø➀é❼✂✢❶ä✥ø➑è✧ï➊ä✥ø➀ì➈é✏➌✛ù✂ÿ❼✡❼✡◆ï✖ù❍è✧ç✙ï ö↕✕④✓❡➪íî➓å❄↔➇ø➀î✒ÿ☎î❅å✫æ✎ì✐ê④è✥ï➊ä✥ø➑ì❛ä✧ø●➶✌➊ä✧ø➑è✧ï✖ä✧ø➀ì➈é✏➌➏ê✧ø➀î❭ø➀û✓å➄ä➞è✥ì❺ö➲å❄↔✂ø➟✝ î✒ÿ☎îòö✫ÿ✂è✧ÿ✎å➄û☛➏➠é✂ëíì➈ä✥î➓å✠è✥ø➑ì❛é➉❶ä✥ø➩è✥ï➊ä✥ø➑ì❛é✒ê✧ì➈î➻ï❶è✥ø➑î➻ï✖ê❇ÿ☎ê✧ï✖ù➞è✧ì♣è✧ä❿å➄ø➀é õ➉ö❖ö➲ê◆✞❝✺✠❖➌❅✞❝✗❀✬✠✶➌ ✞✙❆✘✬✠♠ð➒➏⑥è➚➊ì➈ä✥ä✧ï❞ê✤æ◆ì➈é✎ù✙ê✌è✥ì❖î➓å♦↔✂ø➀î❭ø✠➽➊ø➀é❼✂❖è✧ç✙ï æ◆ì❛ê✤è✧ï➊ä✥ø➀ì➈ä✌æ✙ä✥ì✑✡☎å✑✡✙ø➀û➑ø➑è❅✘➲ì➄ë➵è✧ç☎ï➣❶ì➈ä✥ä✥ï✒↔è✌❶û✓å➈ê✥ê✹■ ✸ ➪⑨ì➈ä✌î➻ø➑é☎ø➑î➻ø✠➽❯✝ ø➀é❼✂✫è✧ç☎ï➽û➑ì➎✂❛å➈ä✧ø➑è✧ç✙î❋ì➄ë✛è✧ç✙ï✶æ✙ä✧ì➎✡☎å❄✡☎ø➑û➀ø➩è❅✘❖ì➄ë✛è✧ç✙ï➙❶ì➈ä✥ä✥ï✒↔è➓➊û➀å❛ê✧ê✴➶✹➌ ✂➈ø➀ú➈ï✖é✌è✧ç✎å✠è❯è✧ç✙ï➵ø➑é☎æ✙ÿ✂è❣ø➑î➓å✑✂➈ï➃✖å➄é➉➊ì➈î➻ï✇ëíä✧ì❛î❲ì❛é✙ï➵ì➄ë✂è✧ç☎ï✔➊û➀å❛ê✧ê✧ï✖ê ì➈ä❙ëíä✥ì➈î å↕✡☎å➎❿ô☛✂➈ä✥ì➈ÿ✙é☎ù ☛✧ä✧ÿ❼✡✗✡✙ø➀ê✧ç✤✌↕➊û➀å❛ê✧ê❙û✓å❄✡◆ï➊û♠ð➛➏➠é è✥ï➊ä✥î➓ê✒ì➈ë æ◆ï➊é☎å➈û➩è✥ø➑ï❞ê✄➌❯ø➩è❙î❭ï❞å➄é☎ê✌è✧ç☎å➄è✒ø➑é å❛ù✙ù✂ø➑è✧ø➀ì➈é è✧ì✫æ☎ÿ☎ê✤ç☎ø➑é❼✂❺ù✂ì✠ó❨é è✧ç✙ï æ◆ï➊é☎å➈û➩è❅✘➘ì➄ë✌è✥ç✙ï➛➊ì➈ä✥ä✧ï★↔è➙➊û➀å❛ê✧ê✶û➑ø➀ô➈ï➲è✧ç✙ï➷ö❖þ✭ ❶ä✥ø➩è✥ï➊ä✥ø➑ì❛é✏➌✛è✧ç✙ø✓ê ❶ä✥ø➑è✧ï➊ä✥ø➀ì➈é➻å➄û✓ê✤ì➤æ✙ÿ✙û➀û✓ê❣ÿ✙æ➻è✧ç☎ï➔æ✎ï✖é☎å➄û➑è✧ø➀ï✖ê➏ì➄ë◆è✧ç✙ï❨ø➀é✗❶ì❛ä✧ä✥ï✒❶è❹❶û✓å➈ê✥ê✤ï❞ê✱✰ ❉ ➪✮❂➶ ✺ ➾ ✌ ❫ ❈ ✸✟✂ ✜ ➪❁❆✆☎✞✝❼➪❩✾✸ ❁❃❂➶★✣ û➑ì➎✂✥➪✡✠ ✴ ❊ ✣ ❈ ❲ ✠ ✴☞☛✍✌✏✎✒✑✝✔✓✌✖✕ ➶❺➶ ➪✡❀➎➶ ã✛ç✙ï➵é✙ï✄✂✐å✠è✥ø➑ú❛ï❫ì➄ë✂è✥ç✙ï❨ê✤ï★❶ì❛é☎ù➤è✧ï✖ä✧î æ☎û➀å✪✘✂ê❯å❵☛❺➊ì➈î➻æ◆ï❶è✧ø➑è✧ø➀ú➈ï ✌➔ä✥ì➈û➀ï➈ð ➏⑥è➞ø✓ê➤é✙ï✒➊ï✖ê✥ê✧å➈ä✧ø➀û✙✘➲ê✧î➓å➄û➀û➑ï✖ä➤è✧ç☎å➈é❭➪íì➈ä✌ï★➍✐ÿ☎å➄û❦è✥ì❩➶♣è✧ç☎ï➝➞☎ä✥ê✤è➤è✧ï✖ä✧î✫➌ è✧ç☎ï➊ä✥ï❶ëíì➈ä✥ï➻è✧ç☎ø➀ê✒û➑ì✐ê✧ê➤ëíÿ☎é✗↔è✥ø➑ì❛é ø➀ê✒æ✎ì✐ê✤ø➑è✧ø➀ú➈ï❛ð✿ã✛ç✙ï➙❶ì➈é✎ê④è❿å➄é✐è✁✗➲ø✓ê æ◆ì❛ê✧ø➩è✥ø➑ú❛ï✑➌☛å➄é☎ù❖æ✙ä✥ï➊ú➈ï✖é✐è✥ê➉è✧ç✙ï❭æ✎ï✖é☎å➄û➑è✧ø➀ï✖ê➳ì➈ë➜❶û✓å➈ê✥ê✤ï❞ê➔è✥ç☎å✠è✌å➄ä✥ï❙å➈û➟✝ ä✥ï✖å➈ù❼✘✫ú➈ï➊ä❘✘✺û➀å➈ä❺✂❛ï➞ëíä✥ì➈î ✡◆ï➊ø➀é❼✂✿æ✙ÿ☎ê✧ç✙ï✖ù❖ëíÿ✙ä✧è✧ç✙ï✖ä✌ÿ✙æ✝ð❭ã✛ç✙ï➻æ✎ì✐ê❅✝ è✧ï✖ä✧ø➀ì➈ä➤æ✙ä✥ì✑✡✎å❄✡✙ø➀û➑ø➑è❅✘✫ì➄ë✇è✧ç✙ø✓ê➤ä✥ÿ❼✡❼✡✙ø✓ê✤ç ❶û✓å➈ê✥ê➳û➀å✑✡✎ï✖û❣ó✇ì❛ÿ✙û✓ù↕✡◆ï➻è✧ç✙ï ä❿å✠è✧ø➀ì ì➈ë✘✠ ✴ ❊ å➄é☎ù✙✠ ✴ ❊ ✣✛✚❲ ✠ ✴☞☛✌ ✎✒✑✝✔✓✌✖✕ ð✭ã✛ç✙ø✓ê✢ù✂ø✓ê❘❶ä✥ø➑î➻ø➀é☎å♦✝ è✧ø➀ú➈ï➣➊ä✧ø➑è✧ï✖ä✧ø➀ì➈é❺æ✙ä✥ï➊ú➈ï✖é✐è✥ê➳è✧ç☎ï➓æ✙ä✧ï✖ú➇ø➑ì❛ÿ☎ê✤û✠✘✫î➻ï➊é✐è✧ø➀ì➈é☎ï✖ù ☛❺➊ì➈û➀û➀å➈æ☎ê❅✝ ø➀é❼✂➽ï❯➘✟ï✒❶è❃✌➓ó❨ç☎ï➊é✫è✥ç✙ï➑✍✛✚✔✜❑æ☎å➄ä❿å➄î➻ï➊è✧ï➊ä❿ê➔å➈ä✧ï✌û➀ï✖å➈ä✧é✙ï❞ù➐✡✎ï★➊å➄ÿ✎ê✤ï ø➑è❙ô➈ï✖ï➊æ☎ê✌è✧ç✙ï ✍✬✚✎✜✟➊ï➊é✐è✧ï✖ä✥ê➞å➈æ☎å➄ä✧è✌ëíä✥ì➈î ï✖å✑❿ç➷ì➈è✧ç✙ï✖ä✖ð✫➏➠é❤þ➇ï★✹✝ è✧ø➀ì➈é ✣④➏✹➌❨ó✇ï✫æ✙ä✥ï✖ê✧ï➊é✐è✶å ✂❛ï➊é✙ï✖ä✥å➈û➑ø✠➽✖å➄è✧ø➀ì➈é❤ì➈ë➤è✧ç✙ø✓ê➣❶ä✥ø➑è✧ï➊ä✥ø➀ì➈é ëíì➈ä ê❺✘➇ê✤è✧ï✖î➓ê❫è✥ç☎å✠è✛û➀ï✖å➄ä✥é➓è✥ì➚➊û➀å❛ê✧ê✧ø➩ë➭✘➻î❙ÿ✙û➩è✥ø➑æ☎û➑ï➤ì✑✡✓④ï✒↔è❿ê➵ø➑é✶è✧ç✙ï➳ø➑é☎æ✙ÿ✂è ➪íï❛ð ✂✎ð✙➌✥❿ç☎å➄ä❿å✑❶è✧ï➊ä❿ê✇ø➑é✺ó➵ì➈ä❿ù✙ê➵ì➈ä❨ø➀é✿ù✂ì✦➊ÿ✙î➻ï➊é✐è✥ê✴➶↔ð ☞✇ì➈î➻æ✙ÿ✂è✥ø➑é❼✂➤è✥ç✙ï✩✂➈ä❿å➈ù✙ø➑ï✖é❛è❣ì➈ë☎è✧ç☎ï➔û➑ì✐ê✧ê❯ëíÿ☎é✗↔è✥ø➑ì❛é❭ó❨ø➑è✧ç➻ä✥ï✖ê✧æ✎ï★↔è è✧ì❍å➈û➑û✌è✥ç✙ï ó➵ï➊ø✠✂➈ç✐è✥ê✿ø➀é å➈û➑û➤è✥ç✙ï û✓å✪✘➈ï➊ä❿ê✿ì➄ë❙è✧ç✙ï✢➊ì➈é➇ú➈ì❛û➑ÿ✂è✥ø➑ì❛é☎å➄û é✙ï➊è④ó✇ì❛ä✧ô✿ø➀ê➤ù✂ì❛é✙ï❭ó❨ø➩è✥ç➔✡☎å➎❿ô➎✝⑥æ✙ä✥ì➈æ☎å✑✂❛å➄è✧ø➀ì➈é✝ð➉ã✛ç☎ï❭ê✤è✥å➈é☎ù✙å➄ä❿ù➲å➈û➟✝ ✂➈ì❛ä✧ø➑è✧ç☎î❋î✒ÿ✎ê④è➓✡◆ï✶ê✧û➑ø✠✂➈ç✐è✧û✠✘❖î➻ì✂ù✂ø✙➞☎ï✖ù è✥ì✺è✥å➈ô➈ï➽å✑✒❶ì❛ÿ✙é✐è➤ì➈ë✛è✧ç✙ï ó➵ï➊ø✠✂➈ç✐è❇ê✧ç☎å➄ä✥ø➑é✗✂☎ð❀✕➉é✌ï✖å➈ê❺✘➳ó➵å✪✘➉è✧ì➔ø➀î➻æ✙û➑ï✖î➻ï➊é✐è❇ø➑è❇ø✓ê☛è✥ì✛➞☎ä❿ê④è❜❶ì➈î➚✝ æ✙ÿ✂è✥ï❫è✥ç✙ï❫æ✎å➄ä✧è✧ø✓å➄û➇ù✂ï➊ä✥ø➑ú✠å➄è✧ø➀ú➈ï✖ê❀ì➄ë✂è✥ç✙ï❫û➀ì❛ê✥ê✝ëíÿ☎é✗↔è✥ø➑ì❛é✒ó❨ø➑è✧ç➞ä✥ï✖ê✧æ✎ï★↔è è✧ì✺ï❞å✑❿ç ❄✴➯❄➨✗➨✈➳❄✄➺✮✣ ➯❄➨✗➌❀å❛ê➳ø➩ë➵è✧ç✙ï➻é✙ï➊è④ó✇ì❛ä✧ô✫ó➵ï➊ä✥ï❙å✫➊ì➈é➇ú➈ï✖é❛è✥ø➑ì❛é☎å➄û î✒ÿ☎û➩è✥ø➟✝⑥û➀å✪✘❛ï➊ä❣é✙ï➊è④ó✇ì❛ä✧ô✒ó❨ø➩è✥ç✙ì➈ÿ✂è✇ó✇ï✖ø✙✂❛ç❛è❫ê✧ç☎å➈ä✧ø➀é❼✂☎ð❯ã✛ç✙ï➊é❭è✥ç✙ï➔æ☎å➈ä❇✝ è✧ø✓å➄û➳ù✂ï➊ä✥ø➀úrå➄è✧ø➀ú➈ï❞ê➓ì➄ë➞å➄û➀û➔è✥ç✙ï➛➊ì➈é✙é☎ï✒↔è✥ø➑ì❛é☎ê➻è✥ç☎å✠è✺ê✤ç☎å➈ä✧ï➲å❤ê✧å➈î❭ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä➏å➄ä✥ï➔å➈ù✙ù✂ï❞ù❙è✧ì✌ëíì❛ä✧î✹è✧ç✙ï➉ù✙ï➊ä✥ø➑ú✠å✠è✥ø➑ú❛ï❨ó❨ø➩è✥ç➓ä✧ï❞ê✤æ◆ï✒❶è❣è✧ì è✧ç✎å✠è➔æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✖ð þ➇ÿ✗❿ç✫å❭û➀å➈ä❺✂❛ï➤å➈ä❘❿ç☎ø➩è✥ï✒↔è✥ÿ✙ä✥ï✞✖å➄é✫✡✎ï➤è✥ä✥å➈ø➑é☎ï✖ù✢ú➈ï➊ä❘✘➽ï✱✯➵➊ø➑ï✖é✐è✧û✠✘✑➌ ✡✙ÿ✂è➤ù✂ì➈ø➀é❼✂✶ê✧ì✶ä✥ï✒➍✐ÿ✙ø➀ä✥ï✖ê✛è✥ç✙ï✒ÿ☎ê✧ï✒ì➈ë➏å➓ëíï➊ó è✥ï✒❿ç✙é☎ø✠➍✐ÿ✙ï❞ê❨è✧ç✎å✠è➳å➈ä✧ï ù✂ï❞ê❺➊ä✧ø✠✡✎ï❞ù❍ø➀é❍è✧ç✙ï å➄æ✙æ◆ï➊é✎ù✂ø➟↔☛ð▲þ➇ï✒❶è✧ø➀ì➈é ✕❂ì➄ë✌è✥ç✙ï❺å➈æ✙æ✎ï✖é☎ù✂ø✙↔ ù✂ï❞ê❺➊ä✧ø✠✡✎ï❞ê➤ù✂ï❶è❿å➄ø➀û➀ê➳ê✤ÿ✥❿ç❺å➈ê♣è✥ç✙ï❙æ✎å➄ä✧è✧ø✁❶ÿ✙û✓å➄ä➤ê✤ø✠✂➈î➻ì❛ø➀ù✫ÿ✎ê✤ï❞ù❢➌✝å➄é☎ù è✧ç☎ï❺ó➵ï➊ø✠✂➈ç✐è✶ø➀é✙ø➑è✧ø✓å➄û➀ø✙➽❞å✠è✧ø➀ì➈é❀ð▲þ➇ï★↔è✥ø➑ì❛é ✚ å➄é☎ù✖☞ ù✂ï✖ê❘❶ä✥ø✠✡✎ï❖è✧ç✙ï î➻ø➑é☎ø➑î➻ø✠➽✖å✠è✥ø➑ì❛é➽æ✙ä✥ì✦❶ï✖ù✙ÿ✙ä✧ï♣ÿ☎ê✧ï✖ù❢➌✐ó❨ç✙ø✁❿ç➽ø➀ê➵å✒ê✤è✧ì✦❿ç☎å❛ê④è✥ø✠➉ú➈ï✖ä✥ê✧ø➑ì❛é ì➄ë✛å✺ù✂ø➀å✑✂➈ì❛é☎å➄û❣å➄æ☎æ✙ä✧ì✪↔✂ø➀î➓å✠è✧ø➀ì➈é❖è✧ì✿è✧ç☎ï❑✗❀ï➊ú❛ï➊é☛✡✎ï✖ä❺✂✑✝⑥ö❖å➄ä✴➍❛ÿ✎å➄ä❿ù➇è æ✙ä✥ì✦❶ï✖ù✙ÿ✙ä✧ï❛ð ➇❯➇❯➇✪➈✖✩➞Ù✣✖ß✝Ü❶Þ✣➻Ý❀Ú❀➊✧✘➳×❇Ø✢✜rÝ❀à❢➋ ✣❞×❇Ú ✛➣➋✓Þ✚★✤✣✒Þ✚★✝Ù✙à ✥Ù✙Þ★❇×❀➊✤✣ ✎ç✙ø➑û➀ï➻ä✧ï★❶ì➎✂➈é✙ø✠➽➊ø➀é❼✂➽ø➀é☎ù✂ø➀ú➇ø➀ù✂ÿ✎å➄û❣ù✂ø✠✂➈ø➑è✥ê➳ø➀ê➳ì❛é✙û✙✘✺ì❛é✙ï❙ì➈ë❫î➓å➄é☛✘ æ✙ä✥ì✑✡✙û➀ï➊î➓ê➵ø➀é✐ú❛ì➈û➀ú➈ï❞ù➓ø➑é✺ù✂ï❞ê✤ø✠✂➈é✙ø➀é❼✂➻å✒æ☎ä✥å➎↔è✧ø✁➊å➈û✟ä✧ï★❶ì✑✂❛é✙ø➑è✧ø➀ì➈é✶ê❺✘✂ê❅✝ è✧ï✖î✫➌✒ø➑è❖ø➀ê❺å➄é ï❯↔❼➊ï➊û➀û➑ï✖é❛è➛✡✎ï✖é✗❿ç✙î➓å➄ä✥ô✻ëíì❛ä➛❶ì❛î➻æ☎å➄ä✥ø➑é✗✂➘ê✧ç☎å➈æ✎ï ä✥ï✒❶ì➎✂➈é✙ø➑è✧ø➀ì➈é✢î➻ï❶è✧ç☎ì➇ù☎ê➊ð➏ã✛ç✙ì❛ÿ❼✂➈ç✢î➓å➄é☛✘➽ï❯↔✂ø✓ê④è✥ø➑é✗✂❙î➻ï❶è✥ç✙ì✂ù✫❶ì➈î➚✝ ✡✙ø➀é✙ï✌å❭ç☎å➄é☎ù✦✝❖➊ä✥å➄ë➺è✧ï✖ù✶ëíï✖å➄è✧ÿ✙ä✥ï➳ï❯↔➇è✧ä❿å✑❶è✧ì➈ä❨å➈é☎ù✢å❙è✥ä✥å➈ø➑é☎å✑✡✙û➀ï✞➊û➀å❛ê❅✝ ê✧ø➟➞☎ï✖ä✒➌➵è✥ç✙ø➀ê✿ê✤è✧ÿ☎ù✦✘ ❶ì❛é✗❶ï✖é✐è✧ä❿å✠è✧ï❞ê➓ì➈é❍å❛ù✙å➄æ✂è✥ø➑ú❛ï✫î➻ï❶è✧ç☎ì➇ù☎ê➽è✥ç☎å✠è ì➈æ◆ï➊ä❿å✠è✥ï✌ù✂ø➑ä✥ï✒❶è✧û✠✘➽ì➈é✺ê✧ø✙➽✖ï❯✝⑥é✙ì➈ä✥î➓å➄û➀ø✙➽✖ï✖ù➽ø➀î➓å❄✂❛ï✖ê✖ð ✚✜✛ ✧➚➢♦➺r➢✫✯✴➢✪➩✄➳✧✦✬➺➭➥❼➳✩★➔➯✖✪✬✣✁➃➳✱✪➚➸✢✪✝❹➦✢➩❯➳✄➺ ã✛ç✙ï ù✙å✠è❿å❄✡☎å❛ê✤ï ÿ☎ê✧ï✖ù✲è✧ì è✧ä❿å➄ø➀é å➄é☎ù✲è✧ï❞ê④è✫è✥ç✙ï ê❇✘✂ê✤è✧ï✖î➻ê✫ù✙ï❯✝ ê❘❶ä✥ø✙✡◆ï✖ù❙ø➑é❙è✧ç☎ø➀ê❦æ☎å➈æ✎ï✖ä❣ó➵å❛ê❳➊ì➈é☎ê✤è✧ä✥ÿ✗❶è✧ï✖ù✒ëíä✥ì➈î è✧ç☎ï➔ñ✛➏✤þ✂ã ❁ ê➏þ➇æ◆ï❯✝ ❶ø✓å➄û❜✧♣å➄è✥å✑✡☎å➈ê✧ï✜❜➽å➄é✎ù➲þ➇æ✎ï★❶ø✓å➄û❜✧♣å➄è✥å❄✡✎å➈ê✧ï➣➾➉❶ì❛é✐è✥å➄ø➀é✙ø➀é❼✂➵✡✙ø➀é☎å➄ä❘✘ ø➀î➻å✑✂➈ï❞ê➤ì➄ë✇ç✎å➄é☎ù✂ó❨ä✥ø➑è✤è✧ï✖é ù✂ø✙✂❛ø➩è❿ê➊ð➽ñ✬➏✤þ✂ã➶ì➈ä✥ø✙✂❛ø➑é☎å➈û➑û✠✘➲ù✂ï❞ê✤ø✠✂➈é☎å➄è✧ï❞ù þ✦✧✬✝✿❜❭å➈ê❫è✧ç☎ï➊ø➀ä❫è✥ä✥å➈ø➑é✙ø➀é❼✂➻ê✤ï➊è➵å➈é☎ù✢þ✦✧✬✝✴➾➳å❛ê➏è✥ç✙ï➊ø➀ä➵è✧ï✖ê✤è❨ê✤ï➊è✖ð❣õ➔ì✠ó✔✝ ï➊ú❛ï➊ä★➌➄þ✦✧✛✝✝❜♣ø➀ê❯î✒ÿ✥❿ç➑❶û➀ï✖å➈é✙ï➊ä❦å➄é✎ù➞ï✖å❛ê✤ø➀ï➊ä❇è✧ì➳ä✥ï✒❶ì➎✂➈é✙ø✠➽➊ï❫è✧ç☎å➈é❭þ✦✧✬✝ ➾➈ð✛ã✛ç✙ï✌ä✥ï✖å❛ê✤ì❛é✶ëíì❛ä❨è✧ç✙ø✓ê✬✖å➄é✫✡◆ï✌ëíì➈ÿ✙é✎ù✺ì➈é✺è✧ç☎ï✌ë⑨å✑❶è❨è✧ç☎å➄è➳þ✦✧✬✝✿❜
PROC.OF THE IEEE,NOVEMBER 1998 was collected among Census Bureau employees,while SD-1 was collected among high-school students.Drawing sensi- > 68/79b641 ble conclusions from learning experiments requires that the b 757863485 result be independent of the choice of training set and test among the complete set of samples.Therefore it was nec- 2【79 7 a 86 essary to build a new database by mixing NISTss datasets. SD-1 contains 5s,517 digit images written by 5yy dif- 4819018894 ferent writers.In contrast to SD-3,where blocks of data 子61&6 4/5b0 from each writer appeared in sequence,the data in SD-1 is scrambled.N riter identities for SD-1 are available and we 7592658197 used this information to unscramble the writers.N e then split sD-1 in twoe characters written by the first 5y writers 2久22234480 went into our new training set.The remaining 5y writers 038073857 were placed in our test set.Thus we had two sets with nearly 3y,yyy examples each.The new training set was 01446024a completed with enough examples from SD-3,starting at pattern c y,to make a full set of Py,yyy training patterns. 7/281o98b Similarly,the new test set was completed with SD-3 exam- ples starting at pattern c 35,yyy to make a full set with Aig..Size-normalized examples from the MNIST database. Py,yyy test patterns.In the experiments described here,we only used a subset of 1y,yyy test images(5,yyy from SD-1 and 5,yyy from SD-3),but we used the full Py,yyy training three,y.yyyl for the next three,y.yyyy5 for the next 4, samples.The resulting database was called the Modified and y.yyyyl thereafter.Before each iteration,the diagonal NIST,or MNIST,dataset. Hessian approximation was reevaluated on 5yy samples,as The original black and white (bilevel)images were size described in Appendix C and kept fixed during the entire normalized to fit in a I yxy pixel box while preserving iteration.The parameter l was set to y.y.The resulting their aspect ratio.The resulting images contain grey lev- effective learning rates during the first pass varied between els as result of the anti-aliasing (image interpolation)tech- approximately 7 x 1y-2 and y.ylP over the set of parame- nique used by the normalization algorithm.Three ver- ters.The test error rate stabilizes after around ly passes sions of the database were used.In the first version, through the training set at y.95%.The error rate on the the images were centered in a IsxIs image by comput- training set reaches y.35%after 19 passes.Many authors ing the center of mass of the pixels,and translating the have reported observing the common phenomenon of over- image so as to position this point at the center of the training when training neural networks or other adaptive IsxIs field.In some instances,this IsxIs field was ex- algorithms on various tasks.N hen over-training occurs, tended to 31 x3 with background pixels.This version of the training error keeps decreasing over time,but the test the database will be referred to as the regular database. error goes through a minimum and starts increasing after In the second version of the database,the character im- a certain number of iterations.N hile this phenomenon is ages were deslanted and cropped down to yxy pixels im- very common,it was not observed in our case as the learn- ages.The deslanting computes the second moments of in- ing curves in figure 5 show.A possible reason is that the ertia of the pixels(counting a foreground pixel as 1 and a learning rate was kept relatively large.The effect of this is background pixel as y),and shears the image by horizon- that the weights never settle down in the local minimum tally shifting the lines so that the principal axis is verti- but keep oscillating randomly.Because of those fluctua- cal.This version of the database will be referred to as the tions,the average cost will be lower in a broader minimum. deslanted database.In the third version of the database Therefore,stochastic gradient will have a similar effect as used in some early experiments,the images were reduced a regularization term that favors broader minima.Broader to 1Px1P pixels.The regular database (Py,yyy training minima correspond to solutions with large entropy of the examples,ly,yyy test examples size-normalized to I yx y, parameter distribution,which is beneficial to the general- and centered by center of mass in IsxIs fields)is avail- ization error. able at http]“F.2676L25h.Ltt.5 om"yInn“o52“mi7t. The influence of the training set size was measured by Figure 4 shows examples randomly picked from the test set.training the network with 15,yyy,3y,yyy,and Py,yyy exam- ples.The resulting training error and test error are shown B.Results in figure P.It is clear that,even with specialized architec- Several versions of EeNet-5 were trained on the regular tures such as EeNet-5,more training data would improve MNIST database.y iterations through the entire train-the accuracy. ing data were performed for each session.The values of To verify this hypothesis,we artificially generated more the global learning rate n(see-quation1 in Appendix C training examples by randomly distorting the original for a definition)was decreased using the following sched-training images.The increased training set was composed ulee y.yyy5 for the first two passes,y.yyyI for the next of the Py,yyy original patterns plus 54y,yyy instances of
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✎ä✥ø➩è✥ï➊ä❨ø✓ù✂ï➊é✐è✥ø➩è✥ø➑ï❞ê✛ëíì➈ä➉þ✦✧✬✝✴➾➤å➈ä✧ï✌årú✠å➄ø➀û✓å❄✡✙û➀ï➳å➈é☎ù✿ó✇ï ÿ☎ê✧ï✖ù✿è✥ç✙ø➀ê♣ø➀é✂ëíì➈ä✥î➓å✠è✧ø➀ì➈é✿è✥ì✶ÿ✙é☎ê❘❶ä❿å➄î➑✡✙û➀ï➤è✧ç✙ï➞ó❨ä✥ø➑è✧ï➊ä❿ê✖ð ✎ï➞è✥ç✙ï➊é ê✧æ✙û➑ø➑è❯þ✦✧✬✝✴➾➏ø➑é➤è④ó➵ì❇✰✏❿ç✎å➄ä❿å✑↔è✥ï➊ä❿ê✟ó❨ä✧ø➑è✤è✥ï➊é✌✡☛✘♣è✧ç✙ï❷➞✎ä✥ê✤è ✑✫✙✻✘➵ó❨ä✧ø➑è✧ï✖ä✥ê ó➵ï➊é✐è➵ø➀é✐è✧ì➻ì➈ÿ☎ä➵é☎ï➊ó❍è✥ä✥å➈ø➑é✙ø➀é❼✂➻ê✤ï➊è✖ð➏ã✛ç✙ï➳ä✥ï➊î➓å➄ø➀é✙ø➀é❼✂❑✑ ✙❆✘✒ó❨ä✧ø➑è✧ï✖ä✥ê ó➵ï➊ä✥ï✢æ✙û✓å✑➊ï✖ù❑ø➑é ì➈ÿ☎ä❙è✥ï✖ê✤è➽ê✤ï➊è✖ð❑ã✛ç➇ÿ☎ê➻ó➵ï✿ç☎å➈ù❤è④ó✇ì➷ê✧ï❶è✥ê➻ó❨ø➑è✧ç é✙ï❞å➄ä✥û✙✘ ❜✻✘❼➌ ✘✻✘✗✘❖ï✄↔✙å➄î➻æ✙û➀ï✖ê➓ï❞å✑❿ç✝ð❲ã✛ç✙ï✫é✙ï➊ó▼è✥ä✥å➈ø➑é✙ø➀é❼✂ ê✧ï❶è➽ó✛å➈ê ❶ì❛î➻æ✙û➑ï➊è✧ï❞ù❑ó❨ø➑è✧ç➘ï✖é✙ì➈ÿ❼✂❛ç➘ï❯↔✙å➄î➻æ✙û➀ï✖ê❭ëíä✥ì➈î þ❼✧✛✝✝❜❼➌✛ê④è❿å➄ä✧è✧ø➀é❼✂ å✠è æ☎å➄è✤è✧ï✖ä✧é✁ ✘❼➌❛è✧ì❭î➻å➈ô➈ï➉å➞ëíÿ✙û➀û✟ê✧ï❶è✛ì➄ë★✓✗✘❼➌ ✘✻✘✗✘➳è✧ä❿å➄ø➀é✙ø➑é✗✂✒æ☎å➄è✤è✧ï✖ä✧é✎ê➊ð þ➇ø➀î➻ø➑û✓å➄ä✥û✙✘➎➌➄è✥ç✙ï➉é✙ï✖ó è✧ï✖ê✤è✇ê✧ï❶è❫ó✛å➈ê➜❶ì➈î➻æ✙û➀ï❶è✥ï✖ù➻ó❨ø➑è✧ç✶þ✦✧✬✝✝❜✌ï❯↔✙å➄î➚✝ æ✙û➀ï✖ê➞ê✤è✥å➈ä✤è✥ø➑é✗✂✺å➄è➞æ☎å✠è✧è✧ï✖ä✧é✂ ❜ ✙✦➌ ✘✻✘✗✘➽è✥ì✫î➓å➄ô➈ï➓å✿ëíÿ✙û➀û✇ê✧ï❶è➞ó❨ø➑è✧ç ✓✻✘✗➌ ✘✗✘✻✘✛è✥ï✖ê✤è❣æ☎å✠è✧è✧ï➊ä✥é☎ê✖ð❀➏➠é❙è✧ç✙ï✛ï✄↔➇æ◆ï➊ä✥ø➀î❭ï✖é✐è✥ê❦ù✂ï✖ê❘❶ä✥ø✠✡✎ï❞ù➞ç✙ï✖ä✧ï➎➌➄ó✇ï ì➈é☎û✙✘✢ÿ☎ê✤ï❞ù✺å➓ê✤ÿ❼✡✎ê✤ï➊è➔ì➄ë✔➾✽✘❼➌ ✘✻✘✗✘➞è✥ï✖ê✤è➉ø➀î➻å✑✂➈ï❞ê✌➪✮✙✦➌ ✘✻✘✗✘❙ëíä✧ì❛îPþ✦✧✬✝❘➾ å➄é✎ù ✙✦➌ ✘✻✘✗✘➳ëíä✧ì❛î✴þ✦✧✬✝✿❜❩➶✹➌☛✡✙ÿ✂è✛ó✇ï♣ÿ☎ê✧ï✖ù➓è✥ç✙ï➔ëíÿ☎û➑û ✓✗✘❼➌ ✘✻✘✻✘➳è✥ä✥å➈ø➑é☎ø➑é❼✂ ê✥å➄î➻æ✙û➀ï✖ê✖ð✿ã✛ç✙ï✶ä✧ï❞ê✤ÿ✙û➑è✧ø➀é❼✂➲ù✙å➄è✥å✑✡☎å➈ê✧ï➓ó➵å❛ê✌➊å➈û➑û➀ï✖ù è✥ç✙ï✶ö✫ì✂ù✂ø✙➞☎ï✖ù ñ✛➏✤þ✙ãt➌✙ì➈ä➔ö➲ñ✬➏✤þ✂ãt➌☎ù✙å➄è✥å❛ê✤ï➊è✖ð ã✛ç✙ï➓ì➈ä✥ø✙✂❛ø➑é✎å➄û❜✡✙û➀å➎❿ô❖å➄é✎ù❖ó❨ç✙ø➑è✧ï↕➪✡✙ø➀û➑ï✖ú➈ï➊û●➶➳ø➀î➻å✑✂➈ï❞ê♣ó➵ï➊ä✥ï➓ê✤ø✠➽➊ï é✙ì❛ä✧î➓å➄û➀ø✠➽➊ï✖ù✻è✧ì⑨➞✙è✫ø➀é❲å☞✑❆✘❄↔✤✑❆✘ æ☎ø➟↔✂ï➊ût✡◆ì✪↔✲ó❨ç✙ø➀û➑ï➷æ✙ä✥ï✖ê✧ï➊ä✥ú➇ø➑é✗✂ è✧ç☎ï➊ø➀ä➤å❛ê✤æ◆ï✒❶è➳ä❿å✠è✥ø➑ì✎ð➞ã✛ç✙ï❭ä✧ï❞ê✤ÿ✙û➑è✧ø➀é❼✂✢ø➑î➓å❄✂❛ï✖ê✞❶ì❛é❛è❿å➄ø➀é➔✂❛ä✧ï✒✘✿û➀ï➊ú❩✝ ï➊û✓ê➵å➈ê➏ä✥ï✖ê✧ÿ✙û➑è❫ì➄ë☛è✥ç✙ï♣å➈é✐è✧ø✙✝⑥å➈û➑ø✓å➈ê✧ø➑é✗✂➣➪íø➀î➻å✑✂➈ï➔ø➀é✐è✧ï✖ä✧æ◆ì➈û✓å✠è✥ø➑ì❛é✥➶❦è✥ï✒❿ç✦✝ é✙ø✁➍✐ÿ✙ï➷ÿ☎ê✤ï❞ù ✡☛✘❍è✥ç✙ï➷é✙ì➈ä✥î➓å➄û➀ø✙➽❞å✠è✧ø➀ì➈é✾å➄û✠✂➈ì➈ä✥ø➑è✧ç✙î✺ð ã✛ç✙ä✥ï➊ï➷ú➈ï✖ä❇✝ ê✧ø➑ì❛é☎ê➷ì➄ë✢è✧ç✙ï✻ù✙å➄è✥å✑✡☎å➈ê✧ï❑ó➵ï➊ä✥ï ÿ☎ê✤ï❞ù☛ð ➏➠é✹è✥ç✙ï ➞☎ä❿ê④è ú❛ï➊ä❿ê✤ø➀ì➈é✏➌ è✧ç☎ï❺ø➀î➓å❄✂➈ï❞ê✶ó➵ï➊ä✥ï➔➊ï➊é✐è✧ï✖ä✧ï❞ù❍ø➑é❲å ✑✻✺♦↔✤✑❆✺➷ø➀î➓å❄✂❛ï➔✡☛✘❭❶ì➈î➻æ✙ÿ✙è❇✝ ø➀é❼✂ è✧ç✙ï✆❶ï✖é✐è✧ï➊ä➻ì➈ë♣î➓å➈ê✥ê❭ì➄ë➉è✥ç✙ï✺æ✙ø✙↔➇ï✖û➀ê✒➌✇å➈é☎ù❤è✧ä❿å➄é☎ê✧û➀å➄è✧ø➀é❼✂❺è✧ç✙ï ø➀î➻å✑✂➈ï ê✧ì❍å➈ê✺è✥ì❍æ✎ì✐ê✤ø➑è✧ø➀ì➈é❲è✧ç☎ø➀ê✫æ◆ì➈ø➀é✐è❺å✠è✫è✥ç✙ï✢❶ï✖é✐è✧ï➊ä❖ì➄ë❭è✧ç✙ï ✑❆✺❄↔✤✑❆✺➛➞☎ï➊û✓ù☛ð✖➏➠é✻ê✤ì❛î➻ï✫ø➑é☎ê✤è✥å➈é✗❶ï❞ê✄➌➵è✥ç✙ø➀ê✳✑❆✺❄↔✑✻✺➛➞☎ï➊û✓ù➘ó➵å❛ê➓ï❯↔☛✝ è✧ï✖é☎ù✂ï❞ù è✧ì ❜✵✑✪↔❜ ✑✢ó❨ø➑è✧ç①✡☎å➎❿ô❩✂❛ä✧ì❛ÿ✙é☎ù❺æ✙ø✙↔➇ï✖û➀ê✖ð✢ã✛ç☎ø➀ê✒ú➈ï➊ä❿ê✧ø➑ì❛é❺ì➈ë è✧ç☎ï➲ù✙å✠è❿å❄✡☎å❛ê✤ï✢ó❨ø➑û➀û✩✡✎ï✫ä✥ï❶ëíï✖ä✧ä✥ï✖ù è✧ì å➈ê❙è✥ç✙ï ➡❺➳✿✥✡✔✲✙➢❄➡❙ù✙å➄è✥å✑✡☎å➈ê✧ï➈ð ➏➠é❑è✧ç✙ï✫ê✧ï✒❶ì❛é☎ù ú❛ï➊ä❿ê✤ø➀ì➈é❤ì➄ë➉è✥ç✙ï✫ù✙å✠è❿å❄✡☎å❛ê✤ï➎➌❣è✧ç☎ï✫❿ç✎å➄ä❿å✑↔è✥ï➊ä❙ø➑î➚✝ å❄✂❛ï✖ê✇ó✇ï✖ä✧ï➳ù✂ï✖ê✧û✓å➄é✐è✧ï❞ù➽å➄é☎ù➙❶ä✥ì➈æ✙æ◆ï✖ù✶ù✂ì✠ó❨é➽è✥ì❑✑✻✘♦↔✤✑❆✘✌æ☎ø➟↔✂ï➊û✓ê✇ø➑î➚✝ å❄✂❛ï✖ê✖ð✇ã✛ç✙ï➞ù✙ï✖ê✧û➀å➈é❛è✥ø➑é✗✂➣❶ì➈î➻æ✙ÿ✙è✧ï✖ê➔è✧ç✙ï❙ê✤ï★❶ì➈é✎ù✶î➻ì➈î➻ï✖é❛è❿ê➔ì➈ë❯ø➀é✦✝ ï➊ä✧è✧ø✓å➻ì➄ë❦è✥ç✙ï✒æ✙ø✙↔✂ï➊û✓ê➉➪✻❶ì➈ÿ☎é❛è✥ø➑é✗✂➽å➻ëíì➈ä✥ï✄✂❛ä✧ì❛ÿ✙é☎ù✢æ✙ø➟↔✂ï✖û❇å➈ê➓➾✒å➄é☎ù✫å ✡☎å➎❿ô❩✂❛ä✧ì❛ÿ✙é☎ù✺æ✙ø✙↔✂ï➊û➏å❛ê✤✘❩➶✹➌✝å➄é✎ù❖ê✧ç✙ï✖å➈ä✥ê➉è✧ç✙ï❭ø➀î➻å✑✂➈ï➚✡☛✘✫ç✙ì➈ä✥ø✙➽✖ì➈é✦✝ è✥å➈û➑û✠✘ ê✤ç☎ø➩ë➺è✥ø➑é❼✂❖è✧ç✙ï✿û➀ø➑é✙ï❞ê❙ê✧ì✫è✥ç☎å✠è❙è✧ç✙ï✿æ✙ä✥ø➑é✗➊ø➑æ✎å➄û✇å❄↔✂ø➀ê✒ø➀ê❙ú➈ï✖ä✤è✥ø➟✝ ➊å➈ûüð➏ã✛ç☎ø➀ê✛ú❛ï➊ä❿ê✤ø➀ì➈é✢ì➄ë❯è✧ç✙ï➞ù✙å➄è✥å✑✡☎å➈ê✧ï♣ó❨ø➀û➀û✏✡✎ï✌ä✥ï❶ëíï✖ä✧ä✥ï✖ù➽è✧ì➽å❛ê➵è✧ç✙ï ✪✑➳❯➩▼✲✙➢♦➨✥➺❖➳✱✪✶ù✙å✠è❿å❄✡☎å❛ê✤ï❛ð ➏➠é➷è✧ç☎ï➓è✧ç✙ø➀ä❿ù➷ú➈ï➊ä❿ê✧ø➑ì❛é❺ì➈ë➵è✥ç✙ï✶ù✙å➄è✥å✑✡☎å➈ê✧ï✑➌ ÿ☎ê✧ï✖ù❺ø➑é ê✧ì➈î➻ï❭ï✖å➄ä✥û✠✘✫ï❯↔✂æ✎ï✖ä✧ø➀î➻ï➊é✐è✥ê✒➌☛è✥ç✙ï➻ø➑î➓å❄✂❛ï✖ê➳ó➵ï➊ä✥ï❭ä✥ï✖ù✙ÿ✗❶ï❞ù è✧ì✟➾✒✓♦↔❢➾✽✓❑æ✙ø✙↔➇ï✖û➀ê✖ð ã✛ç✙ï➷ä✧ï✒✂➈ÿ✙û✓å➄ä✫ù✙å➄è✥å✑✡☎å➈ê✧ï⑨➪✡✓✻✘✗➌ ✘✗✘✻✘ è✥ä✥å➈ø➑é☎ø➑é❼✂ ï❯↔✙å➈î❭æ☎û➑ï❞ê✄➌✎➾✽✘✗➌ ✘✗✘✻✘✶è✧ï✖ê✤è✒ï✄↔✂å➈î➻æ✙û➑ï❞ê➞ê✧ø✙➽✖ï❯✝⑥é✙ì➈ä✥î➓å➄û➀ø✙➽✖ï✖ù❖è✧ì ✑❆✘❄↔✤✑❆✘❼➌ å➄é✎ù⑨➊ï➊é✐è✧ï✖ä✧ï❞ù➹✡☛✘⑨❶ï➊é✐è✥ï➊ä➽ì➈ë➳î➓å➈ê✥ê➻ø➀é☞✑✻✺♦↔✤✑❆✺➔➞☎ï✖û➀ù✙ê✴➶➻ø✓ê➓årú✠å➄ø➀û➟✝ å❄✡☎û➑ï❫å➄è☎✄✝✆✞✆✞✟✡✠☞☛✌☛✎✍✌✍✌✍✡✏✒✑✝✓✕✔✖✓✌✗✘✑✕✙✚✄✡✏✒✗✘✆✞✆✛✏✜✙✣✢✚✤✥☛✧✦★✝✗✖✩✞✩✕☛✞✢✝✙✎✑✕☛✪✤✫✩✭✬✞✔✎✆✎ð ✜❯ø✙✂❛ÿ✙ä✥ï ❝➉ê✧ç✙ì✠ó➔ê✝ï✄↔✙å➄î➻æ✙û➀ï✖ê✝ä❿å➄é✎ù✂ì➈î➻û✠✘♣æ✙ø✁❿ô➈ï❞ù➤ëíä✥ì➈î✾è✧ç✙ï✇è✧ï❞ê④è❦ê✤ï➊è✖ð ✬✛ ✁④➳✹➩✒✡✔✲➂➺✻➩ þ➇ï➊ú❛ï➊ä❿å➄û❯ú➈ï➊ä❿ê✧ø➑ì❛é☎ê➔ì➈ë✄✗✝ï❞ñ➔ï❶è❺✝✝✙➽ó✇ï✖ä✧ï✒è✧ä❿å➄ø➀é✙ï✖ù❖ì➈é❖è✧ç✙ï❭ä✧ï✒✂➈ÿ✙û✓å➄ä ö➲ñ✬➏✤þ✂ã ù✙å✠è❿å❄✡☎å❛ê✤ï❛ð◆✑✻✘✺ø➩è✥ï➊ä❿å✠è✥ø➑ì❛é☎ê➤è✧ç☎ä✧ì❛ÿ❼✂➈ç➷è✥ç✙ï➽ï➊é✐è✥ø➑ä✥ï➓è✧ä❿å➄ø➀é✦✝ ø➀é❼✂ ù☎å✠è✥å❖ó✇ï✖ä✧ï✢æ✎ï✖ä✤ëíì❛ä✧î➻ï❞ù ëíì➈ä❭ï✖å➎❿ç❑ê✧ï✖ê✥ê✤ø➀ì➈é❀ð➷ã✛ç☎ï✢ú✠å➄û➀ÿ✙ï❞ê✒ì➈ë è✧ç☎ï✞✂❛û➑ì➎✡☎å➄û✟û➀ï✖å➈ä✧é✙ø➀é❼✂❙ä✥å➄è✧ï✯✮➔➪⑨ê✧ï➊ï ✭➜➍✐ÿ☎å➄è✧ø➀ì➈é◆✑✦➾➳ø➑é✫✕➔æ✙æ◆ï➊é✎ù✂ø➟↔✆☞ ëíì➈ä❙å✫ù✂ï❯➞☎é☎ø➩è✥ø➑ì❛é✥➶➤ó✛å➈ê➞ù✂ï★❶ä✥ï✖å❛ê✤ï❞ù❖ÿ☎ê✧ø➀é❼✂✺è✧ç✙ï➽ëíì➈û➀û➑ì✠ó❨ø➀é❼✂✫ê❺❿ç☎ï✖ù☛✝ ÿ✙û➀ï✻✰✶✘✙ð ✘✻✘✗✘ ✙❖ëíì➈ä✶è✧ç✙ï✆➞✎ä✥ê✤è➽è④ó➵ì æ☎å➈ê✥ê✤ï❞ê✄➌ ✘☎ð ✘✗✘✻✘ ✑❖ëíì❛ä➽è✧ç☎ï➲é✙ï❯↔➇è ✁✗✿▲❍✪❦✱✰✪❦➙❁✒✿▲❵❅✰r❑●❈✪✷✹✸✶❋✛✱✴❴▲✿▲❵❅✰❅❉✬✰☎★✱✴❋✩❃✪❴▲✰❅✺❢⑥✠✸✻✷✹❋①✵✶✯✪✰➜❸✌❤❀❊ ❁✒✮✆❉♦✱❘✵✶✱✴◗♦✱✴✺✶✰✹❦ è✧ç☎ä✧ï✖ï✑➌ ✘✙ð ✘✻✘✻✘✗➾➽ëíì❛ä➓è✧ç✙ï✫é☎ï❯↔➇è➻è✧ç✙ä✥ï➊ï➎➌ ✘☎ð ✘✗✘✻✘✻✘✵✙✺ëíì❛ä➓è✧ç✙ï✫é☎ï❯↔➇è ❝✗➌ å➄é✎ù✚✘✙ð ✘✻✘✗✘✻✘❼➾➵è✥ç✙ï➊ä✥ï✖å➄ë➺è✧ï➊ä❞ð❷✚➵ï❶ëíì➈ä✥ï➔ï❞å✑❿ç➓ø➑è✧ï➊ä❿å✠è✥ø➑ì❛é✏➌❛è✧ç✙ï➤ù✂ø✓å❄✂➈ì❛é☎å➄û õ➔ï❞ê✧ê✧ø✓å➄é➽å➄æ☎æ✙ä✧ì✪↔✂ø➀î➓å✠è✧ø➀ì➈é➻ó✛å➈ê❫ä✧ï✖ï➊ú✠å➄û➀ÿ☎å✠è✥ï✖ù➻ì❛é ✙❆✘✗✘✌ê✧å➈î❭æ☎û➑ï❞ê✄➌➇å➈ê ù✂ï❞ê❺➊ä✧ø✠✡✎ï❞ù✫ø➀é➔✕➔æ✙æ◆ï➊é✎ù✂ø➟↔➒☞❲å➈é☎ù✫ô❛ï➊æ✂è④➞❼↔✂ï✖ù➲ù✂ÿ☎ä✧ø➀é❼✂➽è✥ç✙ï❭ï➊é✐è✧ø➀ä✧ï ø➑è✧ï➊ä❿å✠è✥ø➑ì❛é✝ð✛ã✛ç✙ï➞æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✳✲ ó✛å➈ê❨ê✧ï❶è➉è✧ì✙✘☎ð ✘✵✑✂ð✇ã✛ç☎ï➞ä✧ï❞ê✤ÿ☎û➩è✥ø➑é❼✂ ï❯➘✟ï✒❶è✧ø➀ú➈ï➔û➀ï✖å➈ä✧é☎ø➑é❼✂✌ä❿å✠è✥ï✖ê➏ù✙ÿ✙ä✧ø➀é❼✂✌è✥ç✙ï✩➞☎ä❿ê✤è❫æ☎å➈ê✥ê➏ú✠å➈ä✧ø➀ï✖ù➚✡◆ï❶è④ó➵ï➊ï➊é å➄æ☎æ✙ä✧ì✪↔✂ø➀î➓å✠è✧ï✖û✙✘✜✔✵✴➛➾✒✘ ✴ å➈é☎ù ✘ ❭ ✘❼➾✽✓❭ì✠ú❛ï➊ä➵è✧ç✙ï➞ê✧ï❶è♣ì➄ë❦æ☎å➄ä❿å➄î➻ï❯✝ è✧ï✖ä✥ê✖ð✒ã✛ç✙ï❭è✥ï✖ê✤è➤ï✖ä✧ä✥ì➈ä➳ä❿å✠è✧ï➻ê✤è✥å❄✡☎ø➑û➀ø✙➽✖ï✖ê➤å✠ë➺è✥ï➊ä✌å➄ä✥ì➈ÿ☎é☎ù✢➾✒✘➽æ☎å❛ê✧ê✧ï✖ê è✧ç☎ä✧ì❛ÿ❼✂➈ç❺è✧ç✙ï➻è✥ä✥å➈ø➑é☎ø➑é❼✂✺ê✧ï❶è✒å✠è✛✘☎ð ❀✵✙✘✶✶ð➓ã✛ç✙ï➻ï➊ä✥ä✧ì❛ä➳ä❿å✠è✥ï❙ì❛é è✧ç✙ï è✧ä❿å➄ø➀é✙ø➀é❼✂✺ê✤ï➊è➤ä✥ï✖å➎❿ç✙ï✖ê ✘✙ð ❜ ✙✞✶På✠ë➺è✧ï✖ä➝➾✽❀✢æ☎å➈ê✥ê✤ï❞ê➊ð❙ö➲å➄é☛✘➲å➄ÿ✙è✧ç✙ì❛ä✥ê ç☎årú❛ï➔ä✧ï✖æ✎ì❛ä✤è✥ï✖ù➻ì➎✡☎ê✤ï✖ä✧ú➇ø➀é❼✂✌è✥ç✙ï✞➊ì➈î➻î➻ì➈é➓æ✙ç☎ï➊é✙ì❛î❭ï✖é✙ì➈é✶ì➄ë✝ì✠ú➈ï✖ä❇✝ è✧ä❿å➄ø➀é✙ø➀é❼✂✺ó❨ç✙ï➊é è✥ä✥å➈ø➑é✙ø➀é❼✂✫é✙ï✖ÿ✙ä❿å➄û❣é✙ï➊è④ó✇ì❛ä✧ô✂ê➳ì➈ä➞ì➈è✧ç✙ï✖ä➞å➈ù✙å➈æ✂è✧ø➀ú➈ï å➄û✠✂➈ì❛ä✧ø➑è✧ç☎î➻ê❙ì➈é ú✠å➄ä✥ø➑ì❛ÿ☎ê✒è✥å➈ê✧ô✂ê➊ð ✎ç✙ï➊é ì✠ú➈ï✖ä❇✝♠è✧ä❿å➄ø➀é✙ø➀é❼✂➲ì✦✄➊ÿ✙ä❿ê✄➌ è✧ç☎ï✌è✧ä❿å➄ø➀é✙ø➀é❼✂➓ï➊ä✥ä✧ì❛ä❨ô➈ï✖ï➊æ☎ê❨ù✂ï★❶ä✥ï✖å❛ê✤ø➀é❼✂➻ì✠ú➈ï✖ä✛è✧ø➀î❭ï➎➌✥✡☎ÿ✂è➔è✧ç☎ï✌è✧ï❞ê④è ï➊ä✥ä✥ì➈ä✛✂❛ì✐ï❞ê➔è✥ç✙ä✥ì➈ÿ❼✂❛ç❖å➽î➻ø➀é✙ø➑î❙ÿ✙î å➄é✎ù➲ê④è❿å➄ä✧è✥ê➉ø➑é✗➊ä✧ï❞å➈ê✧ø➑é✗✂✶å✠ë➺è✥ï➊ä å ➊ï➊ä✧è✥å➈ø➑é✫é➇ÿ✙î➑✡✎ï✖ä♣ì➈ë➏ø➩è✥ï➊ä❿å✠è✧ø➀ì➈é✎ê➊ð ✎ç☎ø➑û➀ï➞è✥ç✙ø➀ê➳æ✙ç☎ï➊é✙ì❛î❭ï✖é✙ì➈é✫ø✓ê ú➈ï✖ä❺✘➝❶ì❛î➻î❭ì❛é✏➌✐ø➩è➵ó➵å❛ê➏é✙ì➈è❫ì✑✡☎ê✧ï➊ä✥ú➈ï❞ù➻ø➑é✶ì➈ÿ✙ä✎➊å➈ê✧ï➉å❛ê❣è✧ç☎ï➉û➀ï✖å➄ä✥é✦✝ ø➀é❼✂➐➊ÿ✙ä✥ú➈ï✖ê♣ø➀é↕➞✗✂❛ÿ✙ä✧ï❑✙✶ê✧ç✙ì✠ó✌ð➓✕➶æ✎ì✐ê✧ê✧ø✠✡✙û➑ï❭ä✥ï✖å➈ê✧ì➈é✫ø✓ê♣è✧ç☎å➄è➤è✧ç✙ï û➀ï✖å➄ä✥é✙ø➀é❼✂➞ä❿å✠è✥ï➉ó✛å➈ê➏ô❛ï➊æ✂è✛ä✥ï➊û✓å✠è✧ø➀ú➈ï✖û✙✘❭û✓å➄ä❘✂➈ï➈ð❦ã✛ç✙ï♣ï❯➘✟ï✒↔è✛ì➄ë☛è✥ç✙ø✓ê✇ø✓ê è✧ç✎å✠è➞è✥ç✙ï➽ó➵ï➊ø✠✂➈ç✐è✥ê➤é✙ï✖ú➈ï✖ä➞ê✤ï➊è✤è✧û➀ï✶ù✂ì✠ó❨é➷ø➀é➷è✧ç✙ï✶û➑ì✦➊å➈û❣î➻ø➑é✙ø➀î✒ÿ☎î ✡✙ÿ✂è➓ô❛ï➊ï➊æ❤ì❛ê❘❶ø➀û➑û✓å✠è✥ø➑é❼✂❺ä✥å➈é☎ù✂ì❛î❭û✠✘➈ð✢✚➵ï★➊å➄ÿ✎ê✤ï✢ì➄ë➔è✥ç✙ì❛ê✧ï✚✾☎ÿ✥↔è✧ÿ✎å♦✝ è✧ø➀ì➈é✎ê✄➌✠è✥ç✙ï➔årú➈ï✖ä✥å✑✂➈ï✎❶ì❛ê✤è❣ó❨ø➑û➀û❼✡◆ï❨û➑ì✠ó➵ï➊ä❦ø➀é❭åt✡☎ä✧ì✐å➈ù✂ï✖ä❇î➻ø➀é✙ø➑î❙ÿ✙î✺ð ã✛ç✙ï✖ä✧ï➊ëíì➈ä✥ï✑➌✟ê④è✥ì☛❿ç✎å➈ê✤è✧ø✁✌✂➈ä❿å➈ù✂ø➀ï➊é✐è➉ó❨ø➀û➀û❇ç☎årú❛ï✒å✶ê✧ø➀î❭ø➀û✓å➄ä➉ï✄➘◆ï★↔è✌å➈ê å➤ä✥ï✄✂➈ÿ☎û➀å➈ä✧ø✠➽✖å➄è✧ø➀ì➈é➞è✥ï➊ä✥îòè✥ç☎å✠è❣ë⑨årú❛ì➈ä❿ê❳✡☎ä✧ì✐å➈ù✂ï✖ä❣î❭ø➀é✙ø➀î➓å✙ð❨✚✇ä✥ì❛å❛ù✂ï➊ä î➻ø➑é☎ø➑î➓å✫❶ì❛ä✧ä✥ï✖ê✧æ✎ì❛é☎ù✫è✥ì✫ê✤ì❛û➑ÿ✂è✥ø➑ì❛é☎ê➤ó❨ø➑è✧ç➷û➀å➈ä❺✂❛ï✒ï✖é❛è✥ä✧ì❛æ☛✘✫ì➄ë➵è✧ç✙ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä♣ù✂ø✓ê④è✥ä✧ø✠✡✙ÿ✂è✥ø➑ì❛é✏➌☛ó❨ç✙ø✁❿ç➲ø✓ê④✡◆ï➊é☎ï❯➞✥➊ø➀å➈û❀è✥ì✶è✥ç✙ï➑✂❛ï➊é✙ï✖ä✥å➈û➟✝ ø✠➽✖å✠è✥ø➑ì❛é✢ï✖ä✧ä✥ì➈ä❞ð ã✛ç✙ï➽ø➀é✾☎ÿ✙ï✖é✗❶ï✢ì➄ë✛è✧ç✙ï➽è✧ä❿å➄ø➀é✙ø➑é✗✂➲ê✤ï➊è❙ê✤ø✠➽➊ï✶ó➵å❛ê✌î➻ï✖å➈ê✧ÿ✙ä✥ï✖ù➒✡☛✘ è✧ä❿å➄ø➀é✙ø➀é❼✂➔è✥ç✙ï✛é✙ï❶è④ó➵ì➈ä✥ô➳ó❨ø➩è✥ç ➾ ✙❼➌ ✘✗✘✻✘✗➌ ❜✗✘❼➌ ✘✻✘✻✘✗➌✠å➄é☎ù✛✓✗✘❼➌ ✘✻✘✗✘❨ï❯↔✙å➄î➚✝ æ✙û➀ï✖ê✖ð➏ã✛ç✙ï➤ä✧ï❞ê✤ÿ☎û➩è✥ø➑é❼✂❙è✧ä❿å➄ø➀é✙ø➀é❼✂❭ï➊ä✥ä✧ì❛ä➵å➈é☎ù➽è✥ï✖ê✤è❨ï➊ä✥ä✧ì❛ä➵å➈ä✧ï➤ê✤ç☎ì✠ó❨é ø➀é➙➞✥✂➈ÿ✙ä✥ï✛✓✙ð❹➏⑥è➔ø✓ê✛➊û➑ï❞å➄ä✛è✧ç✎å✠è✒➌✎ï➊ú❛ï➊é✿ó❨ø➩è✥ç➲ê✤æ◆ï✒➊ø➀å➈û➑ø✠➽➊ï❞ù✢å➈ä❘❿ç✙ø➑è✧ï★✹✝ è✧ÿ☎ä✧ï❞ê➳ê✧ÿ✗❿ç➷å➈ê✒✗✝ï❞ñ➔ï➊è❇✝ ✙✦➌☛î➻ì➈ä✥ï✒è✥ä✥å➈ø➑é☎ø➑é❼✂✺ù✙å➄è✥å✢ó✇ì❛ÿ✙û➀ù❖ø➑î➻æ✙ä✥ì✠ú➈ï è✧ç☎ï➞å✑✄➊ÿ✙ä❿å✑❯✘❛ð ã❀ì➓ú❛ï➊ä✥ø➩ë➭✘✶è✧ç✙ø✓ê➔ç☛✘➇æ✎ì➈è✧ç✙ï❞ê✤ø✓ê✒➌☎ó➵ï➞å➄ä✧è✧ø✙➞✥❶ø✓å➄û➀û✙✘ ✂➈ï➊é☎ï➊ä❿å✠è✧ï❞ù✿î❭ì❛ä✧ï è✧ä❿å➄ø➀é✙ø➀é❼✂ ï✄↔✂å➈î➻æ✙û➑ï❞ê❭✡☛✘Pä❿å➄é✎ù✂ì➈î➻û✠✘Pù✂ø✓ê④è✥ì➈ä✧è✧ø➀é❼✂ è✥ç✙ï✹ì❛ä✧ø✠✂➈ø➀é☎å➄û è✧ä❿å➄ø➀é✙ø➀é❼✂➓ø➀î➻å✑✂➈ï❞ê➊ð❫ã✛ç☎ï✌ø➑é✗➊ä✧ï❞å➈ê✧ï✖ù✶è✧ä❿å➄ø➀é✙ø➀é❼✂➽ê✤ï➊è➔ó➵å❛ê✛❶ì❛î➻æ✎ì✐ê✤ï❞ù ì➄ë➤è✥ç✙ï✦✓✻✘✗➌ ✘✗✘✻✘ ì➈ä✥ø✠✂➈ø➀é☎å➄û❨æ☎å➄è✤è✥ï➊ä✥é☎ê➽æ✙û➀ÿ☎ê✳✙❝✗✘✗➌ ✘✗✘✻✘❺ø➑é✎ê④è❿å➄é✗➊ï✖ê➓ì➈ë