The document contains chemical structures and mathematical equations. It discusses machine learning methods for predicting molecular properties from graph-based representations of molecules using node and edge descriptors without quantum chemistry calculations. Random forest, support vector machines, and other models are mentioned for making predictions from molecular graph encodings.

2. 😊
😆
😊

4. ✓

5.
CH3
N
H3C
H
NS
N
O
CH3
N
OH
x ˆyˆy = f✓(x)

6. 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
n
f✓ ✓
x 7! y
x ˆyˆy = f✓(x)
(x1, y1), (x2, y2), . . . , (xn, yn)
ˆyi = f✓(xi)min
✓
nX
i=1
error(yi, ˆyi)
yiˆyi

8. CH3
N
H3C
H
NS
N
O
CH3
N
OH
x ˆyˆy = f✓(x)
@<TRIPOS>MOLECULE
*****
13 13 0 0 0
SMALL
GASTEIGER
@<TRIPOS>ATOM
1 C -2.5458 -9.4750 0.0000 C.2 1 UNL1 0.3080
2 C -3.3708 -9.4750 0.0000 C.2 1 UNL1 0.2529
3 C -2.2875 -8.6917 0.0000 C.2 1 UNL1 0.3838
4 C -3.6208 -8.6917 0.0000 C.3 1 UNL1 0.2067
5 O -2.9583 -8.2042 0.0000 O.3 1 UNL1 -0.4441
6 C -4.3583 -8.3125 0.0000 C.3 1 UNL1 0.2245
7 O -1.5000 -8.4375 0.0000 O.2 1 UNL1 -0.2412
8 O -2.0583 -10.1417 0.0000 O.2 1 UNL1 -0.2764
9 O -3.8500 -10.1417 0.0000 O.2 1 UNL1 -0.2843
10 O -5.0500 -8.7542 0.0000 O.3 1 UNL1 -0.2164
11 O -3.6958 -7.0417 0.0000 O.3 1 UNL1 -0.2174
12 C -4.3958 -7.4875 0.0000 C.3 1 UNL1 0.2185
13 H -4.2083 -9.2667 0.0000 H 1 UNL1 0.0853
@<TRIPOS>BOND
1 2 1 2
2 3 1 1
3 4 2 1
4 5 3 1
5 6 4 1
6 7 3 2
7 8 1 1
8 9 2 1
9 6 10 1
10 11 12 1
11 12 6 1
12 4 13 1
13 5 4 1
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
1
2
3
4
5
6
7 8
9
10
11
12
13

9. O
N
N
NH
NHN
N
N
CH3
CH3
1
2
3
284
Atom + Bond SYBYL MOL2 Pharmacophore
分⼦グラフ表現
…

10. 物性値構造式 基底状態構造 電⼦状態計算
原⼦化エネルギ
電⼦状態
基本振動
電⼦の空間分布
分⼦グラフ
•頂点に原⼦不変量
•辺や頂点対に原⼦対不変量
記述⼦
量⼦化学計算なしでML予測したい
(3次元や表⾯形状の幾何的量など)
(表⾯や堆積など⽴体依存量など)
(原⼦の種類,電⼦配置,電荷など)
(原⼦間の距離,結合の種類など)
エネルギーや
⽴体選択性?

13. SVM, LogReg,
GPR, RF, etc.
…
…

15. • Descriptors
• Descriptors3D
• GraphDescriptors
• Fingerprints
• ChemicalFeatures
• ChemicalForceFields
rdkit.Chem
rdkit.ML.Descriptors

18. x =

x1
x2
y
x1
x2
y
1
1
w0
ji
w00
i
wkj
1
x
b
W
h
h = ReLU(Wx + b)
bk b0
j
b00
i

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

23. ✓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)

24. 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
✓

25. 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

26. 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
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

28. 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)
⇥ +
⇥
tanh(·)
(·)tanh(·)(·)(·)
⇥
y(t)
x(t)
(·)(·) tanh(·)
1 · ⇥
+⇥
⇥
y(t)
x(t)
{x(t)} 7! {y(t)}

29.
w1
i j
w1
w2
w3
w4
i j

30. f : Rn
! Rm
x yx y
✓
f✓
f✓
✓

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

37. Donor 1 0 1 0 0
Acceptor 0 1 1 0 0
Aromatic 0 0 0 1 0
Halogen 0 0 0 0 0
Basic 0 0 1 0 0
Acidic 0 0 0 0 1
例) アントラニル酸 トポロジ (グラフ構造)
原⼦不変量の例 (FCFP-like)原⼦不変量の例 (ECFP-like)
• By Chemical Features: Donor, Acceptor,
Aromatic, Halogen, Basic, Acidic
頂点や頂点対/辺の不変量(多変量)： RDKitの例
• By Connectivity: atomic number, total
degree, #Hs, formal charge, isotope, inRing
Implicit Hydrogens Explicit HydrogensStructural Formula
分⼦グラフへ
エンコーディング
atomic number 8 8 7 6 6 6
total degree 2 1 3 3 3 3
#Hs 1 0 2 0 0 1
formal charge 0 0 0 0 0 0
isotope 0 0 0 0 0 0
in Ring? 0 0 0 1 0 1

38. • the number of immediate neighbors who are
“heavy” (non-hydrogen) atoms
• the valence minus the number of hydrogens
• the atomic number
• the atomic mass
• the atomic charge
• the number of attached hydrogens
• whether the atom is contained in at least one ring
• hydrogen-bond acceptor or not?
• hydrogen-bond donor or not?
• negatively ionizable or not?
• positively ionizable or not?
• aromatic or not?
• halogen or not?
Rogers+, Extended-Connectivity Fingerprints. J. Chem. Inf. Model., 2010, 50 (5), pp 742–754
Faber+, Prediction Errors of Molecular Machine Learning Models Lower than Hybrid DFT Error. J. Chem. Theory Comput., 2017, 13 (11), pp 5255–5264

39. 000100001010001000000010000100100101000010010001010010002
1
0
3
4
5
6
7
8
9
Layer-0 (直径 0) Layer-1 (直径 2) Layer-2 (直径 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
予め決めた⻑さ(例えば2048bit)でfolding

42. 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)
!
yv
zv

h
(T )
v
xv

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

44. American Chemical Society