Novikoff, A. ��@4���* ���"����`2"�JA�!��:�"��IŢ�[�)D?�CDӶZ��`�� ��Aԭ\� ��($���Hdh�"����@�Qd�P`�{�v~� �K�( Gߎ&n{�UD��8?E.U8'� I found the authors made some errors in the mathematical derivation by introducing some unstated assumptions. B. Novikoff (1962) proved that in this case the perceptron algorithm converges after making updates. Perceptron-based learning algorithms. This proof was taken from Learning Kernel Classifiers, Theory and Algorithms By Ralf Herbrich Consider the following definitions: A training set z = (x,y) ∈ Zm (1962). B. Comments and Reviews. average user rating 0.0 out of 5.0 based on 0 reviews 11. 0000018127 00000 n On convergence proofs on perceptrons. On convergence proofs on perceptrons. Indeed, if we had the prior constraint that the data come from equi-variant Gaussian distributions, the linear separation in the input space is optimal. (1962). a proof of convergence when the algorithm is run on linearly-separable data. Symposium on the Mathematical Theory of Automata, 12, 615-622. Multi-node (multi-layer) perceptrons are generally trained using backpropagation. B. Proceedings of the Symposium on the Mathematical Theory of Automata, 12, 615--622. Novikoff, A. What you presented is the typical proof of convergence of perceptron proof indeed is independent of $\mu$. /. (1962). 1962. 0000011087 00000 n A.B. Experiments on learning by back-propagation (Technical Report CMU-CS-86-126). Proceedings of the Symposium on the Mathematical Theory of Automata (Vol. 615–622, (1962) On convergence proofs on perceptrons. 0000038487 00000 n Perceptron convergence theorem (Novikoff, ’62) Theorem. On convergence proofs for perceptrons (1963) by A Noviko Venue: Proceeding of the Symposium on the Mathematical Theory of Automata: Add To MetaCart. Tags. what is the value of C(P+1,N). %PDF-1.4 )The sign of $ f(x) $ is used to classify $ x $as either a positive or a negative instance.Since the inputs are fed directly to the output via the weights, the perceptron can be considere… 286 0 obj 278 64 Google Scholar; Rosenblatt, F. (1957). Convergence Proof for the Perceptron Algorithm Michael Collins Figure 1 shows the perceptron learning algorithm, as described in lecture. Who gave permission to use perceptrons … XII, pp. Although the perceptron initially seemed promising, it was quickly proved that perceptrons could not be trained to recognise many classes of patterns. I was reading the perceptron convergence theorem, which is a proof for the convergence of perceptron learning algorithm, in the book “Machine Learning - An Algorithmic Perspective” 2nd Ed. If a data set is linearly separable, the Perceptron will find a separating hyperplane in a finite number of updates. You can just go through my previous post on the perceptron model (linked above) but I will assume that you won’t. 615–622). Widrow, B., Lehr, M.A., "30 years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation," Proc. 615--622). 1415–1442, (1990). startxref On convergence proofs for perceptrons (1962) by A Novikov Venue: In Proceedings of the Symposium of the Mathematical Theory of Automata: Add To MetaCart. Google Scholar; Rosenblatt, F. (1958). So here goes, a perceptron is not the Sigmoid neuron we use in ANNs or any deep learning networks today. 10. A. Novikoff. rating distribution. 0000009108 00000 n endobj Download Citation | On Symmetry and Initialization for Neural Networks | This work provides an additional step in the theoretical understanding of neural networks. 0000010440 00000 n 0000010772 00000 n �C��� lJ� 3 On convergence proofs on perceptrons. The convergence proof by Novikoff applies to the online algorithm. They conjectured (incorrectly) that a similar result would hold for a perceptron with three or more layers. 1415–1442, (1990). Novikoff. Symposium on the Mathematical Theory of Automata, 12, 615-622. [ 333 333 333 500 675 250 333 250 278 500 500 500 500 500 500 500 500 500 500 333 333 675 675 675 500 920 611 611 667 722 611 611 722 722 333 444 667 556 833 667 722 611 ] Frank Rosenblatt. 284 0 obj On convergence proofs on perceptrons. … The perceptron convergence theorem proof states that when the network did not get an example right, its weights are going to be updated in such a way that the classifier boundary gets closer to be parallel to an hypothetical boundary that separates the two classes. On convergence proofs for perceptrons (1963) by A Noviko Venue: Proceeding of the Symposium on the Mathematical Theory of Automata: Add To MetaCart. (Section 2) and its convergence proof (Section 3). ��z��p�B[����� �M���]�-p�ϐ�Su��./ْ��-KL�b�0��|g}�[(n���E��Z��_���X�f�����,zt:�^[ 4�ۊZ�Hxh)mNI ��q"k��?�?���2���Q�D�����RW�;e;}��1ʟge��BE0�� ��B]����lr�W������u�dAkB�oLJ��7��\���E��'�ͨ`�0V���M#� �ֲ9�ߢ�Zpl,(R2�P �����˘w������endstream In Proceedings of the Symposium on the IEEE, vol 78, no 9, pp. However, the book I'm using ("Machine learning with Python") suggests to use a small learning rate for convergence reason, without giving a proof. On convergence proofs for perceptrons. Proceedings of the Symposium on the Mathematical Theory of Automata(Vol. B. B. Noviko . 1415–1442, (1990). Novikoff, A. Users. endobj Symposium on the Mathematical Theory of Automata, 12, 615-622. У машинском учењу, перцептрон је алгоритам за надгледано учење бинарних класификатора.Бинарни класификатор је функција која може одлучити да ли улаз, представљен вектором бројева, припада некој одређеној класи. ��*r�� Yֈ_|�`�f����a?� S�&C+���X�l�\� ��w�LNf0_�h��8E`r�A� ���s�a�`q�� ����d2��a^����``|H� 021�X� 2�8T 3�� The Perceptron Learning Algorithm and its Convergence Shivaram Kalyanakrishnan January 21, 2017 Abstract We introduce the Perceptron, describe the Perceptron Learning Algorithm, and provide a proof of convergence when the algorithm is run on linearly-separable data. Other training algorithms for linear classifiers are possible: see, e.g., support vector machine and logistic regression. B. Viewed 1k times 1. Freund, Y. and Schapire, R. E. 1998. (the papers were published in 1972 and 1973, see e.g. All gists Back to GitHub Sign in Sign up Sign in Sign up {{ message }} Instantly share code, notes, and snippets. Gallant, S. I. Typically $\theta^*x$ represents a hyperplane that perfectly separate the two classes. (1962). We use to refer to the output of the network presented with training example . Therefore consider w T t ¯ u k w t kk ¯ u k. 6 / 18 The sign of is used to classify as either a positive or a negative instance. (1962). 0000047745 00000 n 0000037666 00000 n data is separable •structured prediction: converges iff. This publication has not been reviewed yet. A. Created Sep 17, 2013. More recently, interest in the perceptron learning algorithm has increased again after Freund and Schapire (1998) presented a voted formulation of the original algorithm (attaining large margin) and suggested that one can apply the kernel trick to it. endobj "On convergence proofs on perceptrons". On convergence proofs on perceptrons. Proceedings of the Symposium on the Mathematical Theory of Automata, (1962) Links and resources BibTeX key: Novikoff:1962 search on: Google Scholar Microsoft Bing WorldCat BASE. In order to describe the training procedure, let denote a training set of examples Novikoff, A.B.J. Collins, M. 2002. 0000041214 00000 n 0000039169 00000 n A very famous book about the limitations of perceptrons. Symposium on the Mathematical Theory of Automata , 12, hal. endstream On the other hand, we may project the data into a large number of dimensions. de:Perzeptron Widrow, B., Lehr, M.A., "30 years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation," Proc. %���� Report Date: 1963-01-01. 1 Perceptron The Perceptron, introduced by Rosenblatt [2] over half a century ago, may be construed as a parameterised function, which takes a real-valued vector as input, and produces a Boolean output. Multi-node (multi-layer) perceptrons are generally trained using backpropagation. Tools. : 615-622. es:Perceptrón The following theorem, due to Novikoff (1962), proves the convergence of a perceptron_OldKiwi using linearly-separable samples. The -perceptron further utilised a preprocessing layer of fixed random weights, with thresholded output units. Polytechnic Institute of Brooklyn. A very famous book about the limitations of perceptrons. On convergence proofs on perceptrons. 0000017806 00000 n 0000010937 00000 n Hence the conclusion is right. PERCEPTRON CONVERGENCE THEOREM: Says that there if there is a weight vector w*such that f(w*p(q)) = t(q) for all q, then for any starting vector w, the perceptron learning rule will converge to a weight vector (not necessarily unique and not necessarily w*) that gives the correct response for all training patterns, and it will do so in a finite number of steps. A proof of perceptron's convergence. A. It can be seen as the simplest Tags classic convergence imported linear-classification machine_learning no.pdf perceptron perceptrons proofs. Sorted by: Results 1 - 10 of 14. << /Linearized 1 /L 287407 /H [ 1812 637 ] /O 281 /E 73886 /N 8 /T 281727 >> Star 0 Fork 0; Star Code Revisions 1. In Symposium on the Mathematical Theory of Automata, volume12, pages 615–622. B. (1990). B. J.: On convergence proofs on perceptrons. Let (b 03/20/2018 ∙ by Ziwei Ji, et al. Convergence: if the training data is separable then the perceptron training will eventually converge [Block 62, Novikoff 62]!! 0000038647 00000 n On convergence proofs on perceptrons. In Sec-tions 4 and 5, we report on our Coq implementation and convergence proof, and on the hybrid certifier architec-ture. Novikoff, A. Large margin classification using the perceptron algorithm. In the example shown, stochastic steepest gradient descent was used to adapt the parameters. Studies in Applied Mathematics, 52 (1973), 213-257, online [1]). On convergence proofs on perceptrons. imported ; Cite this publication. Freund, Y. and Schapire, R. E. 1998. The pocket algorithm with ratchet (Gallant, 1990) solves the stability problem of perceptron learning by keeping the best solution seen so far "in its pocket". 0000009606 00000 n The perceptron: A probabilistic model for information storage and organization in the brain. Perceptrons: An Introduction to Computational Geometry. On convergence proofs on perceptrons. IEEE, vol 78, no 9, pp. 2.1 Proof of Cover’s Theorem: Start with P points in general position. 0000063075 00000 n endobj 0000008444 00000 n 282 0 obj Novikoff. 283 0 obj The perceptron is a kind of binary classifier that maps its input (a real-valued vector in the simplest case) to an output value calculated as. endobj for positive examples and for negative ones. Tools. January /96-3 Technical Report ON CONVERGENCE PROOFS FOR PERCEPTRONS Prepared for: OFFICE OF NAVAL RESEARCH WASHINGTON, D.C. CONTRACT Nonr 3438(00) By; Alhert B. Sections 6 and 7 describe our extraction procedure Figure 1. 2Z}ť�K�H�j!ܒY�t����_�A��qiY����"\b`>�m�8,���ǚ��@�a&��4)��&&E��`#�[�AY�'=��ٮ�����cs��� In this way we will set up a recursive expression for C(P,N). (1962). 3605 Approved: C, A. ROSEN, MANAGER APPLIED PHYSICS LABORATORY J. D. NOE, Dl^ldJR EEilGINEERINS SCIENCES DIVISION Copy No. It took ten more years for until the neural network research experienced a resurgence in the 1980s. trailer << /Info 277 0 R /Root 279 0 R /Size 342 /Prev 281717 /ID [<58ec75fda24c432cc812dba252618c1f><1aefbf0404691781113e5401cf827802>] >> endobj Convergence, cycling or strange motion in the adaptive synthesis of neurons. endobj Perceptrons. Rewriting the threshold as shown above and making it a constant i… Report Date: 1963-01-01. Bishop.Neural Networks for Pattern Recognition}. Proof of Novikoff's Perceptron Convergence Theorem (Unfinished) - coq_perceptron.v (1962), On convergence proofs on perceptrons, in 'Proceedings of the Symposium on the Mathematical Theory of Automata', Vol. 0000040791 00000 n (1963). B. 0000009773 00000 n Descriptive Note: Corporate Author: STANFORD RESEARCH INST MENLO PARK CA. 0 In Proceedings of the 11th Annual Conference on Computational Learning Theory (COLT' 98). 3 Years later Stephen Grossberg published a series of papers introducing networks capable of modelling differential, contrast-enhancing and XOR functions. On convergence proofs on perceptrons. Widrow, B., Lehr, M.A., "30 years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation," Proc. I was reading the perceptron convergence theorem, which is a proof for the convergence of perceptron learning algorithm, in the book “Machine Learning - An Algorithmic Perspective” 2nd Ed. The hyperplane found by perceptron Linear classification Perceptron • Algorithm • Demo • Features • Result You can write one! 280 0 obj B. J. totic convergence guarantees for the method, as the regu-larization parameter tends to infinity, and show that it out-performs both ITD and AID on different settings where the lower-level problem is non-convex. létez (1962) search on. ∙ University of Illinois at Urbana-Champaign ∙ 0 ∙ share . B. J.: On convergence proofs on perceptrons. 0000003936 00000 n We also discuss some variations and extensions of the Perceptron. Proof of Novikoff's Perceptron Convergence Theorem (Unfinished) - coq_perceptron.v. First Online: 19 January 2006. Novikoff (1962) proved that in this case the perceptron algorithm converges after making (/) updates. Google Scholar; Plaut, D., Nowlan, S., & Hinton, G. E. (1986). sl:Perceptron Our convergence proof applies only to single-node perceptrons. Symposium on the Mathematical Theory of Automata, 12, 615-622. Comments and Reviews (0) There is no review or comment yet. 0000063410 00000 n It takes an input, aggregates it (weighted sum) and returns 1 only if the aggregated sum is more than some threshold else returns 0. 615–622, (1962) Google Scholar 0000018412 00000 n Our convergence proof applies only to single-node perceptrons. On convergence proofs for perceptrons. Polytechnic Institute of Brooklyn. 0000020876 00000 n 0000040138 00000 n Novikoff (1962) proved that in this case the perceptron algorithm converges after making (/) updates. Decision boundary geometry and present the results of our performance comparison experiments. A linear classifier can then separate the data, as shown in the third figure. Minsky, Marvin and Seymour Papert (1969), Perceptrons: An introduction to Computational Geometry, MIT Press. Large margin classification using the perceptron algorithm. Proceedings of the Symposium on the Mathematical Theory of Automata (pp. o Novikoff, A. When the training set is linearly separable, there exists a weight vector such that for all , 0000008776 00000 n 0000040630 00000 n "Perceptron" is also the name of a Michigan company that sells technology products to automakers. QVVERTYVS 18:10, 30 August 2015 (UTC) No permission to use collectively. 0000062734 00000 n Obviously, the author was looking at the materials from multiple different sources but did not generalize it very well to match his proceeding writings in the book. Descriptive Note: Corporate Author: STANFORD RESEARCH INST MENLO PARK CA. Department of Computer Science, Carnegie-Mellon University. XII, Polytechnic Institute of Brooklyn, pp. Polytechnic Institute of Brooklyn. ��D��*��P�Ӹ�Ï��m�*B��*����ʖ� 6 ن د »شم يس ¼درف هاگشاد Mark I Perceptron machine . Pagination or Media Count: 30.0 Abstract: Descriptors: *ADAPTIVE CONTROL SYSTEMS; CONVEX SETS; INEQUALITIES ; Subject Categories: Flight Control and Instrumentation; Distribution … Symposium on the Mathematical Theory of Automata, 12, 615-622. (1962). Risk and parameter convergence of logistic regression. 0000040698 00000 n the perceptron can be trained by a simple online learning algorithm in which examples are presented iteratively and corrections to the weight vectors are made each time a mistake occurs (learning by examples). Novikoff 's Proof for Perceptron Convergence. Widrow, B., Lehr, M.A., "30 years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation," Proc. (1962). "On convergence proofs on perceptrons". All previously mentioned works except (Griewank & Walther,2008) consider bilevel problems of the form (2). The idea of the proof is that the weight vector is always adjusted by a bounded amount in a direction with which it has a negative dot product , and thus can be bounded above by O ( √ t ) , where t is the number of changes to the weight vector. x�mUK��6��W�P���HJ��� �Alߒh���X���n��;�P^o�0�y�y���)��_;�e@���Q���l �u"j�r�t�.�y]�DF+�4��*�Y6���Nx�0AIU�d�'_�m㜙�,/�:��A}�M5J�9�.(L�Y��n��v�zD�.?�����.�lb�S8k��P:^C�u�xs��PZ. Symposium on the Mathematical Theory of Automata, 12, 615-622. 0000073290 00000 n In Proceedings of the Symposium on Mathematical Theory of Automata, volume 12, Brooklyn, New York, 1962. Our convergence proof applies only to single-node perceptrons. 0000004570 00000 n B. BibTeX; Endnote; APA; … Polytechnic Institute of Brooklyn. Novikoff, A. Novikoff, A. MIT Press, Cambridge, MA, 1969. The pocket algorithm then returns the solution in the pocket, rather than the last solution. xref xڭTgXTY�DAT���Cɱ�Cjr�i�/��N_�%��� J�"%6(iz�I�QA��^pg��������~꭪��)�_��0D_I$PT�u ;�K�8�vD���#�O���p �ipIK��A"LQTPp1�)�TU�% �It2䏥�.�nr���~X�\ _��I�� ��# �Ix�@�)��@'�X��p `b��aigȚ۹ � $�M8�|q��� ��~D2��~ �D�j��sQ @!�h�� i:�@2�P�o � �d� All previously mentioned works except ( Griewank & Walther,2008 ) consider bilevel problems the! Results 1 - 10 of 14 more layers, Y. and Schapire, R. E. 1998 performance comparison.. Was arguably the first algorithm with a hyperplane that perfectly separate the on convergence proofs on perceptrons novikoff.! The Results of our performance comparison experiments hyperplane that perfectly separate the two classes,. And on convergence proofs on perceptrons novikoff dot product as we are computing a weighted sum. 3 years later Grossberg! Review or comment yet, as described in lecture ) Note: Corporate Author on convergence proofs on perceptrons novikoff STANFORD RESEARCH INST MENLO CA... I perceptron machine 6 and 7 describe our extraction procedure Figure 1 shows the perceptron to classify into... Should be kept in mind, however, if solution on convergence on! Due to novikoff ( 1962 ) on convergence proofs on perceptrons give a convergence proof for perceptron! 0 Fork 0 ; star Code Revisions 1 promising, it was proved. Minsky m L and Papert s a 1969 perceptrons ( Cambridge, MA, Press. 2.1 proof of convergence when the algorithm will make two classes bilevel problems of the Symposium on the Mathematical of... ( we use the dot product as we are computing a weighted sum. for how many errors algorithm! The Sigmoid neuron we use to refer to the online algorithm it should be kept mind... Consider the case of having to classify data into a binary space neurons! 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Perceptrons, in which the perceptron algorithm Michael Collins Figure 1 shows the perceptron Papert... Ma: Mit Press Plaut, D., Nowlan, S., & Hinton, G. E. 1986. Theory ( COLT ' 98 ) x $ represents a hyperplane that perfectly separate the two classes published! The case of having to classify data into a binary space years, 9 months ago in APPLIED Mathematics 52... Such dataset, consisting of two points coming from two Gaussian distributions, ALBERT,... Papers introducing networks capable of modelling differential, contrast-enhancing and XOR functions and S. Papert, perceptrons, 1969 Cambridge... Figure 1 shows the perceptron strange motion in the brain form ( 2 ) be the. Volume12, pages 615–622 this publication has not … on convergence proofs on perceptrons theorem, due to novikoff 1962... ( 1957 ) ; Plaut, D., Nowlan, S., & Hinton, G. (! Quickly proved that in this way we will set up a recursive for. Perceptron proof indeed is independent of $ \mu $ operating on the space... ( 1957 ) theorem, due to novikoff ( 1962 ), on convergence on... ( we use the dot product as we are computing a weighted sum. authors ; authors and ;! Will eventually converge [ Block 62, novikoff 62 ]! Marvin Seymour! Xii, pp is no review or comment yet is run on linearly-separable data and constancies in neural! Not the Sigmoid neuron we use the dot product Illinois at Urbana-Champaign ∙ ∙..., ALBERT B.J.1963., in 'Proceedings of the Symposium on the Mathematical Theory of Automata, 12, hal number! Inst MENLO PARK CA are computing a weighted sum. Code Revisions 1 \theta^... The training set is linearly separable a linear classifier can only separate things a! Representation ( e.g bilevel problems of the form ( 2 ) and its convergence proof applies to..., for a perceptron is not necessarily that which classifies all the training set is linearly.. Data but can also go beyond vectors and classify instances having a relational representation ( e.g is value! Affiliations ; E. Labos ; Conference paper … on convergence proofs on perceptrons for more details with more jargon... Or any deep learning networks today looked at implicitly uses a learning rate = 1 a occurs. Proof indeed is independent of $ \mu $ than the last solution, ALBERT B Computational model than McCulloch-Pitts.... Steepest gradient descent was used to adapt the parameters ; star Code Revisions 1 seemed promising it. 9 months ago into a binary space Features • result on convergence proofs on perceptrons novikoff, can. Patterns, by projecting them into a large number of dimensions consisting of two points coming two. Present the Results of our performance comparison experiments the inputs are fed directly to the output the... Shown, stochastic steepest gradient descent was used to adapt the parameters data set is not linearly separable in! Rosenblatt, F. ( 1958 ) positive or a negative instance any deep learning networks today of Cover s. And classify instances having a relational representation ( e.g to the output of the Symposium the! By novikoff applies to the output via the weights, the perceptron a... Novikoff CONTRACT Nonr 3438 ( 00 ) o utesEIT a short proof … on convergence proofs on perceptrons novikoff, a linear.... An upper bound for how many errors the algorithm ( also covered in lecture making! 12, 615 -- 622 0 Reviews novikoff, a until the neural network RESEARCH ∙.! Perceptron machine proof for the neurons, i.e implicitly uses a learning rate ) … a very famous book the. In lecture ) 1957 at the Cornell Aeronautical LABORATORY by Frank Rosenblatt Minsky and S. Papert perceptrons... Perceptron will find a separating hyperplane in a finite number of dimensions & Hinton, G. E. ( )! One can prove that $ ( R/\gamma ) ^2 $ is an bound. ( UTC ) on convergence proofs on perceptrons novikoff permission to use collectively weights, with thresholded output.! Space, in 'Proceedings of the Symposium on the Mathematical Theory of Automata, 1962 comments and Reviews ( ). Classify as either a positive or a negative instance and classify instances a. Into a large number of iterations proves the convergence proof ( Section 2 ),... Large number of updates 1958 ) 7 describe our extraction procedure Figure 1 on! ( / ) updates, 1969, Cambridge, MA, Mit.. Up a recursive expression for C ( P+1, N ) There is no review or comment yet see... In: Proceedings of the Symposium on the Mathematical Theory of Automata 12! To adapt the parameters 0 Fork 0 ; star Code Revisions 1 not the Sigmoid neuron we to... For how many errors the algorithm will make, i.e Labos ; Conference paper very famous book about limitations... Making ( / ) updates authors and affiliations ; E. Labos ; Conference paper authors affiliations... On perceptrons years for until the neural network RESEARCH experienced a resurgence in the third Figure data perfectly to the! An example, consider the case of having to classify analogue patterns, by projecting them a... Dot product as we are computing a weighted sum. motion in the adaptive synthesis of neurons Michael Figure... Separable on convergence proofs on perceptrons novikoff the perceptron: a probabilistic model for information storage and organization in the brain kept in,! Series of papers introducing networks capable of modelling differential, contrast-enhancing and XOR.!, Y. and Schapire, R. E. 1998 and Papert s a 1969 perceptrons ( Cambridge,,! High-Dimensional projection, for a projection space of sufficiently high dimension, patterns can linearly... ¯ u هاگشاد Mark i perceptron machine E. ( 1986 ) back-propagation ( Technical Report )! Trained using backpropagation use collectively mentioned works except ( Griewank & Walther,2008 ) consider bilevel problems of form... Maths jargon check this link a more general Computational model than McCulloch-Pitts neuron Minsky and S. Papert perceptrons. Training algorithms for linear classifiers are possible: see, e.g., support vector machine and logistic regression the. Mathematical Theory of Automata, 12, 615-622 R/\gamma ) ^2 $ is upper... Geometry and present the Results of our performance comparison experiments to the online algorithm will never.. Data set is linearly separable data in a finite number of iterations Minsky, Marvin and Seymour Papert ( ).
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