US 2025/0029016 A1 · LINEAR MACHINE LEARNING METHOD BASED ON DNA HYBRIDIZATION REACTION TECHNOLOGY

Abstract

A new linear machine learning method based on DNA hybridization reaction technology, includes a machine learning training part, an algorithm part, and a testing part. This machine learning method has the ability to learn linear functions. Unlike silicon circuits, the learning algorithm is implemented through the synchronization of DNA hybridization reactions. Therefore, the calculation mode of this machine learning method is a parallel computing model, and the weights of this machine learning are obtained through training without the involvement of electronic computers. Through the method, it is possible to learn multivariable linear functions without any limitation on the number of input terms. Due to the non-negative DNA concentration, the method used a dual track model for negative data processing operations.

A linear machine learning method based on deoxyribonucleic acid (DNA) hybridization reaction technology, comprising:

a training part, an algorithm part and a testing part;
wherein,
(1) reaction expressions of the training part are as follows:
X
1
+
+
W
1
+
→
k
1
I
+
+
X
1
+
+
W
1
+
(
1
⁢
a
)
X
1
-
+
W
1
-
→
k
1
I
+
+
X
1
-
+
W
1
-
(
1
⁢
b
)
X
1
+
+
W
1
-
→
k
1
I
-
+
X
1
+
+
W
1
-
(
1
⁢
c
)
X
1
-
+
W
1
+
→
k
1
I
-
+
X
1
-
+
W
1
+
(
1
⁢
d
)
X
2
+
+
W
2
+
→
k
1
I
+
+
X
2
+
+
W
2
+
(
2
⁢
a
)
X
2
-
+
W
2
-
→
k
1
I
+
+
X
2
-
+
W
2
-
(
2
⁢
b
)
X
2
+
+
W
2
-
→
k
1
I
-
+
X
2
+
+
W
2
-
(
2
⁢
c
)
X
2
-
+
W
2
+
→
k
1
I
-
+
X
2
-
+
W
2
+
(
2
⁢
d
)
⋮
X
N
+
+
W
N
+
→
k
1
I
+
+
X
N
+
+
W
N
+
(
3
⁢
a
)
X
N
-
+
W
N
-
→
k
1
I
+
+
X
N
-
+
W
N
-
(
3
⁢
b
)
X
N
+
+
W
N
-
→
k
1
I
-
+
X
N
+
+
W
N
-
(
3
⁢
c
)
X
N
-
+
W
N
+
→
k
1
I
-
+
X
N
-
+
W
N
+
(
3
⁢
d
)
Y
+
+
H
+
→
k
1
I
-
+
H
+
(
4
⁢
a
)
Y
-
+
H
-
→
k
1
I
+
+
H
-
(
4
⁢
b
)
I
+
+
C
+
→
k
1
I
+
+
C
+
+
Y
+
(
4
⁢
c
)
I
-
+
C
-
→
k
1
I
-
+
C
-
+
Y
-
(
4
⁢
d
)
X
1
+
+
X
1
-
→
k
2
Φ
(
5
⁢
a
)
W
1
+
+
W
1
-
→
k
2
Φ
(
5
⁢
b
)
X
2
+
+
X
2
-
→
k
2
Φ
(
5
⁢
c
)
W
2
+
+
W
2
-
→
k
2
Φ
(
5
⁢
d
)
⋮
X
i
+
+
X
i
-
→
k
2
Φ
(
6
⁢
a
)
W
i
+
+
W
i
-
→
k
2
Φ
(
6
⁢
b
)
Y
+
+
Y
-
→
k
2
Φ
(
6
⁢
c
)
C
+
+
C
-
→
k
2
Φ
(
6
⁢
d
)
H
+
+
H
-
→
k
2
Φ
(
6
⁢
e
)
I
+
+
I
-
→
k
2
Φ
(
6
⁢
f
)
where the reaction expressions (1a) to (3d) belong to a first catalytic reaction module;
the reaction expressions (4a) and (4b) belong to a second catalytic reaction module;
the reaction expressions (4c) and (4d) belong to the first catalytic reaction module;
the reaction expressions (5a) to (6f) belong to an annihilation reaction module;
k1 and k2 represent different reaction rates;
and Φ represents a waste;
Xi(t)=[Xi+]t−[Xi−]t, i=1, 2, . . . , N, N represents the number of input items, [*]t represents a concentration of a substance * at a time t, and Xi represents an i-th input item;
Xi+ and Xi− respectively represent a positive part and a negative part of Xi;
Wi(t)=[Wi+]t−[Wi−]t, Wi represents an i-th weight corresponding to the i-th input item, Wi+ and Wi− respectively represent a positive part and a negative part of Wi;
I+ and I− respectively represent a positive part and a negative part of a substance I;
H+ and H− respectively represent a positive part and a negative part of a substance H;
C+ and C− respectively represent a positive part and a negative part of a substance C;
supposing [H+]t=[H−]t=1 nanomoles per liter (nM), differential equations of concentrations varying over time of I+ and I− are as follows:
{
d
[
I
+
]
t
dt
=
k
1
(
[
W
1
+
]
t
[
X
1
+
]
t
+
[
W
2
+
]
t
[
X
2
+
]
t
+
…
+
[
W
N
+
]
t
[
X
N
+
]
t
+
[
W
1
-
]
t
[
X
1
-
]
t
+
[
W
2
-
]
t
[
X
2
-
]
t
+
…
+
[
W
N
-
]
t
[
X
N
-
]
t
+
[
Y
-
]
t
[
H
-
]
t
)
d
[
I
-
]
t
dt
=
k
1
(
[
W
1
+
]
t
[
X
1
-
]
t
+
[
W
2
+
]
t
[
X
2
-
]
t
+
…
+
[
W
N
+
]
t
[
X
N
-
]
t
+
[
W
1
-
]
t
[
X
1
+
]
t
+
[
W
2
-
]
t
[
X
2
+
]
t
+
…
+
[
W
N
-
]
t
[
X
N
+
]
t
+
[
Y
+
]
t
[
H
+
]
t
)
(
7
)
the differential equations (7) are simplified as follows:
{
d
[
I
+
]
t
dt
=
k
1
(
∑
i
=
1
N
(
[
W
i
+
]
t
[
X
i
+
]
t
+
[
W
i
-
]
t
[
X
i
-
]
t
)
+
[
Y
-
]
t
[
H
]
t
)
d
[
I
-
]
t
dt
=
k
1
(
∑
i
=
1
N
(
[
W
t
+
]
t
[
X
i
-
]
t
+
[
W
i
-
]
t
[
X
i
+
]
t
)
+
[
Y
+
]
t
[
H
+
]
t
)
and
dI
⁢
(
t
)
dt
=
d
[
I
+
]
t
dt
-
d
[
I
-
]
t
dt
=
k
1
[
∑
i
=
1
N
(
[
W
i
+
]
t
[
X
i
+
]
t
+
[
W
i
-
]
t
[
X
i
-
]
t
-
[
W
i
+
]
t
[
X
i
-
]
t
-
[
W
i
-
]
t
[
X
i
+
]
t
)
+
[
Y
-
]
t
[
H
-
]
t
-
[
Y
+
]
t
[
H
+
]
t
]
supposing [H+]t=[H−]t≡1 nM, and
dI
⁢
(
t
)
dt
=
k
1
(
∑
i
=
1
N
W
i
(
t
)
⁢
X
i
(
t
)
-
Y
⁡
(
t
)
)
,
when a DNA hybridization reaction network reaches dynamic equilibrium, i.e.,
dI
⁢
(
t
)
dt
=
0
,
then:
Y
=
∑
i
=
1
N
W
i
⁢
X
i
where Y(t)=[Y+]t−[Y−]t, Y represents an output value of a system;
(2) reaction expressions of the algorithm part are as follows:
D
+
+
X
1
+
→
k
3
D
+
+
X
1
+
+
W
1
+
(
8
⁢
a
)
D
-
+
X
1
-
→
k
3
D
-
+
X
1
-
+
W
1
+
(
8
⁢
b
)
Y
+
+
X
1
-
→
k
3
Y
+
+
X
1
-
+
W
1
+
(
8
⁢
c
)
Y
-
+
X
1
+
→
k
3
D
-
+
X
1
+
+
W
1
+
(
8
⁢
d
)
D
+
+
X
1
-
→
k
3
D
+
+
X
1
-
+
W
1
-
(
8
⁢
e
)
D
-
+
X
1
+
→
k
3
D
-
+
X
1
+
+
W
1
-
(
8
⁢
f
)
Y
+
+
X
1
+
→
k
3
Y
+
+
X
1
+
+
W
1
-
(
8
⁢
g
)
Y
-
+
X
1
-
→
k
3
D
-
+
X
1
-
+
W
1
-
(
8
⁢
h
)
D
+
+
X
2
+
→
k
3
D
+
+
X
2
+
+
W
2
+
(
9
⁢
a
)
D
-
+
X
2
-
→
k
3
D
-
+
X
2
-
+
W
2
+
(
9
⁢
b
)
Y
+
+
X
2
+
→
k
3
Y
+
+
X
2
-
+
W
2
+
(
9
⁢
c
)
Y
-
+
X
2
+
→
k
3
D
-
+
X
2
+
+
W
2
+
(
9
⁢
d
)
D
+
+
X
2
-
→
k
3
D
+
+
X
2
-
+
W
2
-
(
9
⁢
e
)
D
-
+
X
2
+
→
k
3
D
-
+
X
2
+
+
W
2
-
(
9
⁢
f
)
Y
+
+
X
2
+
→
k
3
Y
+
+
X
2
+
+
W
2
-
(
9
⁢
g
)
Y
-
+
X
2
-
→
k
3
D
-
+
X
2
-
+
W
2
-
(
9
⁢
h
)
⋮
D
+
+
X
N
+
→
k
3
D
+
+
X
N
+
+
W
N
+
(
10
⁢
a
)
D
-
+
X
N
-
→
k
3
D
-
+
X
N
-
+
W
N
+
(
10
⁢
b
)
Y
+
+
X
N
-
→
k
3
Y
+
+
X
N
-
+
W
N
+
(
10
⁢
c
)
Y
-
+
X
N
+
→
k
3
D
-
+
X
N
+
+
W
N
+
(
10
⁢
d
)
D
+
+
X
N
-
→
k
3
D
+
+
X
N
-
+
W
N
-
(
10
⁢
e
)
D
-
+
X
N
+
→
k
3
D
-
+
X
N
+
+
W
N
-
(
10
⁢
f
)
Y
+
+
X
N
+
→
k
3
Y
+
+
X
N
+
+
W
N
-
(
10
⁢
g
)
Y
-
+
X
N
+
→
k
3
D
-
+
X
N
-
+
W
N
-
(
10
⁢
h
)
where the reaction expressions (8) to (10) belong to the first catalytic reaction module;
D+ and D− respectively represent a positive part and a negative part of D;
and k3 represents a reaction rate which is different from k1 and k2;
differential equations of concentrations varying over time of Wi+ and Wi− are as follows:
{
d
[
W
1
+
]
dt
=
k
3
(
[
D
+
]
t
[
X
1
+
]
t
+
[
D
-
]
t
[
X
1
-
]
t
+
[
Y
+
]
t
[
X
1
-
]
t
+
[
Y
-
]
t
[
X
1
+
]
t
)
d
[
W
1
-
]
dt
=
k
3
(
[
D
+
]
t
[
X
1
-
]
t
+
[
D
-
]
t
[
X
1
+
]
t
+
[
Y
+
]
t
[
X
1
+
]
t
+
[
Y
-
]
t
[
X
1
-
]
t
)
(
11
)
{
d
[
W
2
+
]
dt
=
k
3
(
[
D
+
]
t
[
X
2
+
]
t
+
[
D
-
]
t
[
X
2
-
]
t
+
[
Y
+
]
t
[
X
2
-
]
t
+
[
Y
-
]
t
[
X
2
+
]
t
)
d
[
W
2
-
]
dt
=
k
3
(
[
D
+
]
t
[
X
2
-
]
t
+
[
D
-
]
t
[
X
2
+
]
t
+
[
Y
+
]
t
[
X
2
+
]
t
+
[
Y
-
]
t
[
X
2
-
]
t
)
(
12
)
{
d
[
W
N
+
]
dt
=
k
3
(
[
D
+
]
t
[
X
N
+
]
t
+
[
D
-
]
t
[
X
N
-
]
t
+
[
Y
+
]
t
[
X
N
-
]
t
+
[
Y
-
]
t
[
X
N
+
]
t
)
d
[
W
N
-
]
dt
=
k
3
(
[
D
+
]
t
[
X
N
-
]
t
+
[
D
-
]
t
[
X
N
+
]
t
+
[
Y
+
]
t
[
X
N
+
]
t
+
[
Y
-
]
t
[
X
N
-
]
t
)
(
13
)
wherein D(t)=[D+]t−[D−]t, D represents an expectation value;
based on the differential equations (11) to (13), expressions are obtained as follows:
dW
1
⁢
(
t
)
dt
=
d
[
W
1
+
]
t
dt
-
d
[
W
1
]
t
dt
=
k
3
(
[
D
+
]
t
[
X
1
+
]
t
+
[
D
-
]
t
[
X
1
-
]
t
-
[
D
+
]
t
[
X
1
-
]
t
-
[
D
-
]
t
[
X
1
+
]
t
)
+
k
2
(
[
Y
+
]
t
[
X
1
-
]
t
+
[
Y
-
]
t
[
X
1
+
]
t
-
[
Y
+
]
t
[
X
1
+
]
t
+
[
Y
-
]
t
[
X
1
-
]
t
)
=
k
3
[
(
[
D
+
]
t
-
[
D
-
]
t
)
-
(
[
Y
+
]
t
-
[
Y
-
]
t
)
]
×
(
[
X
1
+
]
t
-
[
X
1
-
]
t
)
=
k
3
(
[
D
]
t
-
[
Y
]
t
)
[
X
1
]
t
dW
2
(
t
)
dt
=
d
[
W
2
+
]
t
dt
-
d
[
W
2
]
t
dt
=
k
3
(
[
D
+
]
t
[
X
2
+
]
t
+
[
D
-
]
t
[
X
2
-
]
t
-
[
D
+
]
t
[
X
2
-
]
t
-
[
D
-
]
t
[
X
2
+
]
t
)
+
k
2
(
[
Y
+
]
t
[
X
2
-
]
t
+
[
Y
-
]
t
[
X
2
+
]
t
-
[
Y
+
]
t
[
X
2
+
]
t
+
[
Y
-
]
t
[
X
2
-
]
t
)
=
k
3
[
(
[
D
+
]
t
-
[
D
-
]
t
)
-
(
[
Y
+
]
t
-
[
Y
-
]
t
)
]
×
(
[
X
2
+
]
t
-
[
X
2
-
]
t
)
=
k
3
(
[
D
]
t
-
[
Y
]
t
)
[
X
2
]
t
⋮
dW
N
(
t
)
dt
=
d
[
W
N
+
]
t
dt
-
d
[
W
N
-
]
t
dt
=
k
3
(
[
D
+
]
t
[
X
N
+
]
t
+
[
D
-
]
t
[
X
N
-
]
t
-
[
D
+
]
t
[
X
N
-
]
t
-
[
D
-
]
t
[
X
N
*
]
t
)
+
k
2
(
[
Y
+
]
t
[
X
N
-
]
t
+
[
Y
-
]
t
[
X
N
*
]
t
=
k
3
[
(
[
D
+
]
t
-
[
D
-
]
t
)
-
(
[
Y
+
]
t
-
[
Y
-
]
f
)
]
×
(
[
X
N
+
]
t
-
[
X
N
-
]
t
)
=
k
3
(
[
D
]
t
-
[
Y
]
t
)
[
X
N
]
t
;
(3) reaction expressions of the testing part are as follows:
X
1
+
+
W
ˆ
1
+
→
k
1
I
^
+
+
X
1
+
+
W
ˆ
1
+
(
14
⁢
a
)
X
1
-
+
W
ˆ
1
-
→
k
1
I
^
+
+
X
1
-
+
W
ˆ
1
+
(
14
⁢
b
)
X
1
+
+
W
ˆ
1
-
→
k
1
I
^
-
+
X
1
+
+
W
ˆ
1
-
(
14
⁢
c
)
X
1
-
+
W
ˆ
1
+
→
k
1
I
^
-
+
X
1
-
+
W
ˆ
1
+
(
14
⁢
d
)
X
2
+
+
W
ˆ
2
+
→
k
1
I
^
+
+
X
2
+
+
W
ˆ
2
+
(
15
⁢
a
)
X
2
+
+
W
ˆ
2
+
→
k
1
I
^
+
+
X
2
+
+
W
ˆ
2
+
(
15
⁢
b
)
X
2
+
+
W
ˆ
2
-
→
k
1
I
^
-
+
X
2
+
+
W
ˆ
2
-
(
15
⁢
c
)
X
2
-
+
W
ˆ
2
+
→
k
1
I
^
-
+
X
2
-
+
W
ˆ
2
+
(
15
⁢
d
)
⋮
X
N
+
+
W
ˆ
N
+
→
k
1
I
ˆ
+
+
X
N
+
+
W
ˆ
N
+
(
16
⁢
a
)
X
N
-
+
W
ˆ
N
-
→
k
1
I
ˆ
+
+
X
N
-
+
W
ˆ
N
-
(
16
⁢
b
)
X
N
+
+
W
ˆ
N
-
→
k
1
I
ˆ
-
+
X
N
+
+
W
ˆ
N
-
(
16
⁢
c
)
X
N
-
+
W
ˆ
N
+
→
k
1
I
ˆ
-
+
X
N
-
+
W
ˆ
N
+
(
16
⁢
d
)
Y
ˆ
-
+
H
ˆ
-
→
k
1
I
ˆ
-
+
H
ˆ
-
(
17
⁢
a
)
Y
ˆ
-
+
H
ˆ
-
→
k
1
I
ˆ
-
+
H
ˆ
+
(
17
⁢
b
)
I
ˆ
+
+
C
ˆ
+
→
k
1
I
ˆ
+
+
C
ˆ
+
+
Y
ˆ
+
(
17
⁢
c
)
I
ˆ
-
+
C
ˆ
-
→
k
1
I
ˆ
-
+
C
ˆ
-
+
Y
ˆ
+
(
17
⁢
d
)
X
i
+
+
X
i
-
→
k
2
Φ
(
18
⁢
a
)
W
ˆ
i
+
+
W
ˆ
i
-
→
k
2
Φ
(
18
⁢
b
)
Y
ˆ
+
+
Y
ˆ
-
→
k
2
Φ
(
18
⁢
c
)
C
ˆ
+
+
C
ˆ
-
→
k
2
Φ
(
18
⁢
d
)
H
ˆ
+
+
H
ˆ
-
→
k
2
Φ
(
18
⁢
e
)
I
ˆ
+
+
I
ˆ
-
→
k
2
Φ
(
18
⁢
f
)
where the reaction expressions (14d) to (16d) belong to the first catalytic reaction module;
the reaction expressions (17a) and (17b) belong to the second catalytic reaction module;
the reaction expressions (17c) and (17d) belong to the first catalytic reaction module;
and the reaction expressions (18a) to (18f) belong to the annihilation reaction module;
Ŵi represents a weight obtained after a plurality of rounds of learning;
Ŵi+ and {tilde over (W)}i− respectively represent a positive part and a negative part of Ŵi;
Ŷ represents an output of the testing part;
Ŷ+ and Ŷ− respectively represent a positive part and a negative part of Ŷ;
Î, Ĥ and Ĉ represent substances involved in a chemical reaction in the testing part;
Ĥ+ and Ĥ− respectively represent a positive part and a negative part of Ĥ;
Ĉ+ and Ĉ− respectively represent a positive part and a negative part of Ĉ;
Î+ and Î− respectively represent a positive part and a negative part of Î;
the linear machine learning method comprises following steps S1-S3:
S1, normalizing training data;
wherein training of machine learning comprises a plurality of rounds of training;
each of the plurality of rounds of training comprises:
K sets of training data, each set of training data comprises N data, and the machine learning has N inputs and i=1, 2, 3, . . . , N;
shuffling the K sets of training data to obtain another round of training data, and normalizing the another round of training data as follows:
{
x
^
i
(
k
,
l
)
=
ρ
⁢
x
i
(
k
,
l
)
/
η
d
^
l
(
k
)
=
ρ
⁢
d
~
l
(
k
)
/
η
(
19
)
where:
{
ε
i
=
max
⁡
(
Θ
i
)
-
min
⁡
(
Θ
i
)
η
=
max
⁡
(
[
ε
1
,
ε
2
,
…
⁢
ε
N
]
)
y
~
l
(
k
)
=
∑
i
=
1
N
⁢
w
i
⁢
x
i
(
l
,
k
)
;
xi(k,l) represents an i-th data of a k-th set of an l-th round of training, k=1, 2, . . . , K, l=1, 2, . . . , ∧, ρ represents a positive adjustment parameter, Θi=[xi(1), xi(2), . . . , xi(K)] and {circumflex over (d)}l (k) meeting {circumflex over (x)}i(k,l)=[Xi+]0−[Xi−]0, and {circumflex over (d)}l(k)=[D+]0−[D−]0;
S2, assessing the training of the machine learning;
defining a relative error el(k) in the l-th round of training as follows:
e
l
(
k
)
=
y
~
l
(
k
)
-
d
^
l
(
k
)
d
^
l
(
k
)
(
20
)
where:
y
^
n
(
k
)
=
∑
i
=
1
N
W
^
i
⁢
χ
i
(
k
)
;
assessing a result of the round of training and defining an average relative error as follows:
e
_
l
=
1
K
⁢
∑
k
=
1
K
❘
"\[LeftBracketingBar]"
e
l
(
k
)
❘
"\[RightBracketingBar]"
(
21
)
performing the plurality of rounds of trainings, and stopping training after the average relative error reaches a target value;
S3, assessing and testing of the machine learning;
the testing of machine learning comprising a plurality of rounds of testing;
one of the plurality of rounds of testing comprising P sets of test data;
shuffling the P sets of test data to obtain another round of test data, and normalizing the another round of test data as follows:
{
x
^
i
′
(
p
,
g
)
=
ρβ
i
(
p
,
g
)
/
θ
d
^
g
′
(
p
)
=
ρ
⁢
d
~
g
′
(
p
)
/
θ
βi(p,g) represents an i-th data of a p-th set of a g-th round of testing, p=1, 2, . . . , P, g=1,2, . . . ,G;
θi=max(Φi)−min(Φi), θ=max ([θ1, θ2, . . . θN]), and {tilde over (d)}′g(p)=Σi=1Nwixi(g,p);
in the g-th round of testing, defining a relative error e′g (p) as follows:
e
g
′
(
p
)
=
y
~
g
′
(
p
)
-
d
^
g
′
(
p
)
d
^
l
′
(
p
)
,
where:
y
^
g
(
p
)
=
∑
i
=
1
N
W
^
i
⁢
x
^
i
′
(
k
)
;
assessing a result of the round of training, and defining an average relative error in the testing as follows:
e
_
g
′
=
1
P
⁢
∑
p
=
1
P
❘
"\[LeftBracketingBar]"
e
g
(
k
)
❘
"\[RightBracketingBar]"
.

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Linear machine learning method based on dna hybridization reaction technology

Life of this patent

Linear machine learning method based on dna hybridization reaction technology

Life of this patent

Abstract

Claims3