DeepLearning on FPGAs - Introduction to Deep Learning

e−βz )−1 = (−1) ( 1 + e−βz )−2 (−β)e−βz = βe−βz (1 + e−βz) 2 = β e−βz 1 + e−βz 1 1 + e−βz = β e−βz + 1− 1 1 + e−βz 1 1 + e−βz = β ( 1 + e−βz 1 + e−βz − 1 1 + e−βz ) 1 1 + e−βz = β(1− σ(z))σ(z) DeepLearning [...] σ(z) = 1 1+e−β·z , β ∈ R>0 Derivative ∂σ(z) ∂z = ∂ ∂z ( 1 + e−βz )−1 = (−1) ( 1 + e−βz )−2 (−β)e−βz = βe−βz (1 + e−βz) 2 = β e−βz 1 + e−βz 1 1 + e−βz = β e−βz + 1− 1 1 + e−βz 1 1 + e−βz = β ( 1 + e−βz [...] e−βz )−2 (−β)e−βz = βe−βz (1 + e−βz) 2 = β e−βz 1 + e−βz 1 1 + e−βz = β e−βz + 1− 1 1 + e−βz 1 1 + e−βz = β ( 1 + e−βz 1 + e−βz − 1 1 + e−βz ) 1 1 + e−βz = β(1− σ(z))σ(z) DeepLearning on FPGAs 23 Data Mining …

Slide 1

layers x1 x2 y1 y2 z 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 ≥ 1 ≥ 1 x1 x2 -1 1 1 y1 z ≥ 1 1 y2 1 -1 without AND gate in 2nd layer Multi-Layer Perceptron (MLP) x1 – x2 ≥ 1 x2 – x1 ≥ 1 x2 ≤ x1 – 1 x2 ≥ x1 [...] e ▪ Winter Term 2018/19 13 XOR with 3 neurons in 2 steps x1 x2 y1 y2 z 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 ≥ 2 x1 x2 -1 1 -1 y1 z 1 y2 1 1 convex set Multi-Layer Perceptron (MLP) Lecture 02 G. Rudolph: [...] x1 + 1 , 1 1 Lecture 02 G. Rudolph: Computational Intelligence ▪ Winter Term 2018/19 15 XOR can be realized with only 2 neurons! ≥ 2 ≥ 1 x1 x2 1 1 -2 1 1 y z x1 x2 y -2y x1-2y+x2 z 0 0 0 0 0 0 0 1 0 0 1 …

Slide 1

layers x1 x2 y1 y2 z 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 ≥ 1 ≥ 1 x1 x2 -1 1 1 y1 z ≥ 1 1 y2 1 -1 without AND gate in 2nd layer Multi-Layer Perceptron (MLP) x1 – x2 ≥ 1 x2 – x1 ≥ 1 x2 ≤ x1 – 1 x2 ≥ x1 [...] e ▪ Winter Term 2015/16 13 XOR with 3 neurons in 2 steps x1 x2 y1 y2 z 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 ≥ 2 x1 x2 -1 1 -1 y1 z 1 y2 1 1 convex set Multi-Layer Perceptron (MLP) Lecture 02 G. Rudolph: [...] x1 + 1 , 1 1 Lecture 02 G. Rudolph: Computational Intelligence ▪ Winter Term 2015/16 15 XOR can be realized with only 2 neurons! ≥ 2 ≥ 1 x1 x2 1 1 -2 1 1 y z x1 x2 y -2y x1-2y+x2 z 0 0 0 0 0 0 0 1 0 0 1 …

Slide 1

layers x1 x2 y1 y2 z 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 ≥ 1 ≥ 1 x1 x2 -1 1 1 y1 z ≥ 1 1 y2 1 -1 without AND gate in 2nd layer Multi-Layer Perceptron (MLP) x1 – x2 ≥ 1 x2 – x1 ≥ 1 x2 ≤ x1 – 1 x2 ≥ x1 [...] e ▪ Winter Term 2016/17 13 XOR with 3 neurons in 2 steps x1 x2 y1 y2 z 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 ≥ 2 x1 x2 -1 1 -1 y1 z 1 y2 1 1 convex set Multi-Layer Perceptron (MLP) Lecture 02 G. Rudolph: [...] x1 + 1 , 1 1 Lecture 02 G. Rudolph: Computational Intelligence ▪ Winter Term 2016/17 15 XOR can be realized with only 2 neurons! ≥ 2 ≥ 1 x1 x2 1 1 -2 1 1 y z x1 x2 y -2y x1-2y+x2 z 0 0 0 0 0 0 0 1 0 0 1 …

Slide 1

layers x1 x2 y1 y2 z 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 ≥ 1 ≥ 1 x1 x2 -1 1 1 y1 z ≥ 1 1 y2 1 -1 without AND gate in 2nd layer Multi-Layer Perceptron (MLP) x1 – x2 ≥ 1 x2 – x1 ≥ 1 x2 ≤ x1 – 1 x2 ≥ x1 [...] e ▪ Winter Term 2017/18 13 XOR with 3 neurons in 2 steps x1 x2 y1 y2 z 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 ≥ 2 x1 x2 -1 1 -1 y1 z 1 y2 1 1 convex set Multi-Layer Perceptron (MLP) Lecture 02 G. Rudolph: [...] x1 + 1 , 1 1 Lecture 02 G. Rudolph: Computational Intelligence ▪ Winter Term 2017/18 15 XOR can be realized with only 2 neurons! ≥ 2 ≥ 1 x1 x2 1 1 -2 1 1 y z x1 x2 y -2y x1-2y+x2 z 0 0 0 0 0 0 0 1 0 0 1 …

414 96.9 78 3.1 Saarland 471 461 97.9 10 2.1 Sachsen 2,358 2,356 99.9 2 0.1 Sachsen-Anhalt 1,411 1,410 99.9 1 0.1 Schleswig-Holstein 1,789 1,474 82.4 315 17.6 Thüringen 1,335 1,334 99.9 1 0.1 Westdeutschland [...] 393 96.9 77 3.1 Saarland 470 458 97.4 12 2.6 Sachsen 2,348 2,336 99.5 12 0.5 Sachsen-Anhalt 1,414 1,412 99.9 2 0.1 Schleswig-Holstein 1,774 1,437 81.0 337 19.0 Thüringen 1,330 1,329 99.9 1 0.1 Westdeutschland [...] 96.3 90 3.7 Saarland 464 455 98.1 9 1.9 Sachsen 2,341 2,331 99.6 10 0.4 Sachsen-Anhalt 1,418 1,417 99.9 1 0.1 Schleswig-Holstein 1,768 1,445 81.7 323 18.3 Thüringen 1,328 1,328 100.0 0 0.0 Westdeutschland …

tu-dortmund.de/bitstreams/1af1d3e1-5eaf-42a0-9494-1f5ee83a8695/download> ; rel="item" ; type="application/pdf" ; anchor="https://eldorado.tu-dortmund.de/items/e6a9a602-a1bb-462e-8e29-1bd3d742481b" , <https [...] /eldorado.tu-dortmund.de/bitstreams/1af1d3e1-5eaf-42a0-9494-1f5ee83a8695/download" , <https://eldorado.tu-dortmund.de/signposting/linksets/e6a9a602-a1bb-462e-8e29-1bd3d742481b/json> ; rel="linkset" ; [...] anchor="https://eldorado.tu-dortmund.de/bitstreams/1af1d3e1-5eaf-42a0-9494-1f5ee83a8695/download" , <https://eldorado.tu-dortmund.de/items/e6a9a602-a1bb-462e-8e29-1bd3d742481b> ; rel="collection" ; type="text/html" …

dby/3a8d05f1-f7a0-4af4-bdc2-3bc4e1c1a60c> ; rel="describedby" ; type="application/vnd.datacite.datacite+xml" ; anchor="https://eldorado.tu-dortmund.de/items/3a8d05f1-f7a0-4af4-bdc2-3bc4e1c1a60c" , <http://hdl [...] ://eldorado.tu-dortmund.de/items/3a8d05f1-f7a0-4af4-bdc2-3bc4e1c1a60c" , <https://eldorado.tu-dortmund.de/signposting/linksets/3a8d05f1-f7a0-4af4-bdc2-3bc4e1c1a60c> ; rel="linkset" ; type="application/linkset" [...] ://eldorado.tu-dortmund.de/items/3a8d05f1-f7a0-4af4-bdc2-3bc4e1c1a60c" , <https://eldorado.tu-dortmund.de/signposting/linksets/3a8d05f1-f7a0-4af4-bdc2-3bc4e1c1a60c/json> ; rel="linkset" ; type="applic …

Evaluation-Sommersemester-2015-Ueberblick

ng 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 Ü bu ng sl ei tu ng (1 = se hr g ut , . .., 6 = se hr s ch le ch t) Übungszettel (1=sehr [...] ausgesprochen hat. 1,00 1,50 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 0 20 40 60 80 100 120 140 160 180 200 1 = s eh r gu t, .. .., 6 = s eh r sc hl ec ht Anzahl Fragebögen (n=1 bis 200 (ca.) oder [...] Veranstaltungen) 1,00 2,00 3,00 4,00 5,00 6,00 1,00 2,00 3,00 4,00 5,00 6,00 G es am tn ot e D oz en t/ in b zw . B et re uu ng 1 = s eh r gu t, .. ., 6 = s eh r sc hl ec ht Gesamtnote Veranstaltung 1 = sehr gut …

n-graph3.fig

∪ {ei1 , ei2} Setze E1 = E1 \ (E1 ∩ F ′1) und E2 = E2 \ (E2 ∩ F ′1) Falls n1 6= 0 Für j = 1, . . . , n1 Setze V1 := V1 ∪ {uj} und E1 = E1 ∪ {ej1 , ej2} Falls n1 6= m1 Für j = n1 + 1, . . . ,m1 Setze [...] mit 1 ≤ a ≤ 3. Diese hat die Form P(H) = {C1. . . . , Ck1} ∪ {Ck1+1, . . . , Ck1+k2} ∪ {C ′1, . . . , C ′a} mit {C1. . . . , Ck1} ⊆ H1, {Ck1+1, . . . , Ck1+k2} ⊆ H2 und ν(H) = k1 +k2 +a. Es gilt k1 ≤ ν(H1) [...] v12 , . . . , v1k−1 , x, v1k+1 , . . . , v1d(C1) ) mit {v12 , . . . , v1k−1 } ⊆ V (H1) und {v1k+1 , . . . , v1d(C1) } ⊆ V (H2). Folglich hätte der Knoten x in C1 einen Knotengrad von vier, was der Definition …