The document contains chemical structures represented using SMILES notation and connection tables. It also includes sections on machine learning concepts like neural networks, loss functions, and backpropagation for training models. Graphs, molecules and their representations are discussed in the context of using machine learning for molecular property prediction and generation.

3. ✓

4.
CH3
N
H3C
H
NS
N
O
CH3
N
OH
x ˆy
ˆy = f✓(x)

5. N
NH
OO
HH
H
H H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
O
O
O
O
O
O
Cl
H
H
H
H
H
HH
H
H
H
H
H
H
H
H
H
H
Br
Br O P
O
O Br
Br
O
Br
Br
H
H
H
H
H
H
H
H
H
H
HH
H
HH
N
S
N
N
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
O
N
O
O
H
H
H
O
O
H
H
N
O
O
Cl
ClCl
H
H
H
H
H
H H
N
O
O
H
H
H
H
H
H
H H
H
N
O
O
H
H
H
H
H
H
H
N
H
N
O
O
N
O
O
H
H
H
H
H
H
H
H
N
CH3
O
O
H
N
Cl
Cl
Cl
Cl
Cl
H3C
O O
O
O
O
O
H3C
CH3
CH2
O
HN
O
O
NH
CH3
HO
OH
CH3
N
O
O
CH3
N
N
H
N
H
H3C
N
H3C
H3C
NH
O
N
O
NO
CH3
O N
NH2
O
CH3
Br
CH3
N
H3C
H
NS
N
O
CH3
N
OH
CH3
CH3N
N
N
CH3H3C
H2N NH2
H
OH
O
HO
CH3
H
H
O
CH3
H
O
OH3C HH
H
O
H3C
S
CH3
O
H
H
O
CH3
CH3
OO
HO
H3CH
HO
F
H
O
H3C
NH2
O
N
HO
HO
O
H
H
O
O
OH3C
O
O
O
CH3
O
CH3
HO
CH3
H
O
O
CH3
H
H
N
H
N O
H3C
O
O
O

7. CH3
N
H3C
H
NS
N
O
CH3
N
OH
x ˆy
ˆy = f✓(x)
{(x1, y1), (x2, y2), . . . , (xn, yn)}
n
f✓ ✓
min
✓
nX
i=1
error(yi, ˆyi) ˆyi = f✓(xi)
x 7! y

10. SVM, LogReg,
GPR, RF, etc.
…
…

17. SciTegic12231509382D
13 13 0 0 0 0 999 V2000
-2.5458 -9.4750 0.0000 C 0 0
-3.3708 -9.4750 0.0000 C 0 0
-2.2875 -8.6917 0.0000 C 0 0
-3.6208 -8.6917 0.0000 C 0 0 2 0 0 0
-2.9583 -8.2042 0.0000 O 0 0
-4.3583 -8.3125 0.0000 C 0 0 1 0 0 0
-1.5000 -8.4375 0.0000 O 0 0
-2.0583 -10.1417 0.0000 O 0 0
-3.8500 -10.1417 0.0000 O 0 0
-5.0500 -8.7542 0.0000 O 0 0
-3.6958 -7.0417 0.0000 O 0 0
-4.3958 -7.4875 0.0000 C 0 0
-4.2083 -9.2667 0.0000 H 0 0
2 1 2 0
3 1 1 0
4 2 1 0
5 3 1 0
6 4 1 0
7 3 2 0
8 1 1 0
9 2 1 0
6 10 1 1
11 12 1 0
12 6 1 0
4 13 1 6
5 4 1 0
M END
OC[C@H](O)[C@H]1OC(=O)C(=C1O)O
InChI=1S/C6H8O6/
c7-1-2(8)5-3(9)4(10)6(11)12-5/
h2,5,7-10H,1H2/t2-,5+/m0/s1
CIWBSHSKHKDKBQ-JLAZNSOCSA-N

18. Mrv0541 04051115152D
10 10 0 0 0 0 999 V2000
-0.9408 0.3707 0.0000 C 0 0 0 0 0 0 0 0 0 0 0 0
-1.6552 -0.0418 0.0000 O 0 0 0 0 0 0 0 0 0 0 0 0
-0.9408 1.1957 0.0000 O 0 0 0 0 0 0 0 0 0 0 0 0
-0.2263 -0.0418 0.0000 C 0 0 0 0 0 0 0 0 0 0 0 0
0.4882 0.3707 0.0000 C 0 0 0 0 0 0 0 0 0 0 0 0
1.2027 -0.0418 0.0000 C 0 0 0 0 0 0 0 0 0 0 0 0
0.4882 1.1957 0.0000 N 0 0 0 0 0 0 0 0 0 0 0 0
1.2027 -0.8668 0.0000 C 0 0 0 0 0 0 0 0 0 0 0 0
0.4882 -1.2793 0.0000 C 0 0 0 0 0 0 0 0 0 0 0 0
-0.2263 -0.8668 0.0000 C 0 0 0 0 0 0 0 0 0 0 0 0
1 2 2 0 0 0 0
1 3 1 0 0 0 0
1 4 1 0 0 0 0
4 5 2 0 0 0 0
4 10 1 0 0 0 0
5 6 1 0 0 0 0
5 7 1 0 0 0 0
6 8 2 0 0 0 0
8 9 1 0 0 0 0
9 10 2 0 0 0 0
M END
1
2
3
4
5
6
7
8
9
102
C
1
2 3
4
5
6
7
8
9
10
1
1
2 1
2
2 1
1
1
C
O O
C
C
N
C
C
C

19. @<TRIPOS>MOLECULE
*****
10 10 0 0 0
SMALL
GASTEIGER
@<TRIPOS>ATOM
1 C -0.9408 0.3707 0.0000 C.2 1 UNL1 0.3891
2 O -1.6552 -0.0418 0.0000 O.co2 1 UNL1 -0.2405
3 O -0.9408 1.1957 0.0000 O.co2 1 UNL1 -0.2405
4 C -0.2263 -0.0418 0.0000 C.ar 1 UNL1 0.0965
5 C 0.4882 0.3707 0.0000 C.ar 1 UNL1 0.0954
6 C 1.2027 -0.0418 0.0000 C.ar 1 UNL1 0.0183
7 N 0.4882 1.1957 0.0000 N.pl3 1 UNL1 -0.1278
8 C 1.2027 -0.8668 0.0000 C.ar 1 UNL1 0.0014
9 C 0.4882 -1.2793 0.0000 C.ar 1 UNL1 0.0003
10 C -0.2263 -0.8668 0.0000 C.ar 1 UNL1 0.0079
@<TRIPOS>BOND
1 1 2 ar
2 1 3 ar
3 1 4 1
4 4 5 ar
5 4 10 ar
6 5 6 ar
7 5 7 1
8 6 8 ar
9 8 9 ar
10 9 10 ar
C.2
ar
ar
ar
ar
ar
ar
1
ar
1
ar
O.co2 O.co2
C.ar
C.ar
C.ar
C.ar
C.ar
C.ar
N.pl3
1
2 3
4
5
6
7
8
9
10

20. a
h
h
h
h
d
h
h
a
h
r
r
r
r
r
r
r
rr
r
r
r
C
O
N
S
CC
C
C C
C
C
C
C
C
C
C
C
C
C C
C
C
O2x
C1x
C1x
C1x
C1x
N1x
C1b C1b
S2a
C1c
C8y
C8y
C8x
C8x
C8x
C8x
C8x
C8xC8x
C8x
C8x
C8x
RA
L
L
Ar
Ar
A
Structure
diagram
Skeletal
topology
Atom/bond
labeled graph
KEGG atom
labeled graph
(KCF)
Pharmacophore
type labeled graph
(ChemAxon Screen)
Reduced graph
1
1
1 1
1
1
1
1
1
1 1
2
1
1
1
1
1
2
2
2
2
2
1
1

21. …
…
…
…
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱
…
⋮ ⋮
y g

25. CH3
N
H3C
H
NS
N
O
CH3
N
OH
x ˆy
ˆy = f✓(x)
{(x1, y1), (x2, y2), . . . , (xn, yn)}
n
f✓ ✓
min
✓
nX
i=1
error(yi, ˆyi) ˆyi = f✓(xi)
x 7! y

26. x =

x1
x2
y
(z)
z
+1
1
tanh(z) 2 ( 1, 1)
x1
x2
y
11
h0
1
h0
2
h1
h2
h3
w0
ji
w00
i
wkj
i
0
j
ijk
✓ = (wkj, w0
ji, w00
i , 0
j, i)
y =
2X
i
w00
i (h0
i i) =
2X
i
w00
i
0
@
3X
j
w0
ji (hj
0
j) i
1
A
=
2X
i
w00
i
0
@
3X
j
w0
ji
2X
k=1
wkjxk
0
j
!
i
1
A

27. min
✓
L(✓)
L(✓) =
nX
i=1
error(yi, f✓(xi))
r✓L(✓t) =
2
6
4
@L(✓)/@✓1 |✓=✓t
@L(✓)/@✓2 |✓=✓t
...
3
7
5
✓t+1 ✓t ⌘ · r✓L(✓t)

31. ✓t+1 ✓t ⌘ · r✓L(✓t) L(✓) =
Pn
i=1 error(yi, f✓(xi))
Li(✓) = error(yi, f✓(xi))✓t+1 ✓t ⌘ · r✓Li(✓t)
Lm
i (✓) =
Pi+m
k=i error(yk, f✓(xk))✓t+1 ✓t ⌘ · r✓Lm
i (✓t)

32. x =
2
6
6
6
6
4
x1
x2
x3
x4
x5
3
7
7
7
7
5
y =
2
4
y1
y2
y3
3
5
x 7! y
y = f✓(x)
x1
x2
x3
x4
x5
y1
y2
y3
wij ! wij + w yk ! yk + y
wij
@f✓(x)
@wij
=
@yk
@wij

33. a
c
b
d
e
add
mult
add
1
c = a + b
d = b + 1
e = c ⇤ d
add
mult
add
1
a 2
b 1
a = 2 b = 1
c = 3 d = 2
e = 6

34. add
mult
add
1a = 2 b = 1
c = 3 d = 2
e = 6
@e
@c
= 2
@c
@a
= 1
@c
@b
= 1
@d
@b
= 1
@e
@d
= 3
c = a + b
d = b + 1
e = c ⇤ d
add
mult
add
1
@e
@c
= 2
@c
@a
= 1
@c
@b
= 1
@d
@b
= 1
@e
@d
= 3
add
mult
add
1
@e
@c
= 2
@c
@a
= 1
@c
@b
= 1
@d
@b
= 1
@e
@d
= 3
@a
@b
= 0
@c
@b
= 1
@b
@b
= 1
@d
@b
= 1
@e
@b
= 5
@e
@e
= 1
@e
@c
= 2
@e
@d
= 3
@e
@b
= 5
@e
@a
= 2
@e
@b
=
@e
@c
@c
@b
+
@e
@d
@d
@b

36. x(1), x(2), . . . , x(t) y(1), y(2), . . . , y(t)7!
x(t)
h(t)
y(t)
x(1) x(2)
y(2)y(1)
h(0) h(1) h(2)
x(t)
y(t)
h(t)
h(t)
y(t)
x(t)
h(t 1)
x(t)
h(t 1)
⇥ +
⇥
tanh(·)
(·)tanh(·)(·)(·)
⇥
y(t)
x(t)
(·)(·) tanh(·)
1 · ⇥
+⇥
⇥
y(t)
x(t)

37. w1
w2
w3
w4
i j

39. f : Rn
! Rm
f✓
f✓
✓
x yx y
✓

41. CH3
N
H3C
H
NS
N
O
CH3
N
OH
x ˆy
ˆy = f✓(x)
{(x1, y1), (x2, y2), . . . , (xn, yn)}
n
f✓ ✓
min
✓
nX
i=1
error(yi, ˆyi) ˆyi = f✓(xi)
x 7! y

42. Vector Annotations for Atoms (RDKit defaults)

43. 000100001010001000000010000100100101000010010001010010002
1
0
3
4
5
6
7
8
9
Layer-0 (diameter 0) Layer-1 (diameter 2) Layer-2 (diameter 4)
0 1 2
3 4 5 6
7 8 9
3
0
4
7
1
5
8
2
6
9
847957139 3217380708 3218693969
3218693969 3218693969 3218693969
864942730 2246699815 864662311
3217380708
1510328189 2784506312 1533864325
4158944142 2309124039 951226070
951226070 98513984 98513984
1083852209
2784506312 132611095 2784506312
916604632 3450167988 2987120039
1171638766 3999906991 3999906991
4158944142
folding into a fixed length

48. a1
a2
a3
a4
a5
a1 a2 a3 a4 a5 (a1, a2) (a1, a3) (a4, a5)
A P
(ai, aj)
ai aj
ai
fA fP
(A ! A)0
(A ! A)1
(A ! P)0 (P ! P)0
(P ! P)1
(P ! A)0
A P

49. v
hv
h(t 1)
v
a(t)
v
h(t 1)
v
a(t)
v
h(t)
v
v
tanh
X
v2V
(yv) tanh(zv)
!

hT
v
xv
yv
zv

50. M
M
vv
hv
N(v)
m
U
U
R

52. G = (V, E, W), L = diag(d) W, di =
P
j Wij
x 2 R|V |
ˆx = U0
x, L = U⇤U0
g✓ ⇤ x = Ug✓(⇤)U0
x