
이미지 텍스트 확인
Accuracy of gpt-40-2024-08-06
Digits
Number
10 11 12 13 14 15 16 17 18
19
20
‘100
100-00
100}
zooJioo po 2/96 Joo Ba gp2.3/z00/38 3/84.5/92 3p6 392
1001 100
50.053.8
42 350 0
‘100
165.4
10.010.0
100
00
00
0,0
10 0
0,0
‘100
0.0
10.010.0
‘100
0,0| 0.0
0.0
0.0 100
‘100165,4
10.0
0.0
0.0
001 0,0
틀
50,039
100
0.0
0.0
0.0
?
001 0.0
0.0
‘
57,7
몸
53,8
00
00
0,0
100
‘
57.7
10.0
0.0
I0.0
45 ?
0.00C
10.0
9
10.0
00
IO.0
10.0
001 0.0
10.010,0
f
46.2
[0.0l0,0
53,8
10 0
0,0
0.0
00
00
[ooToo
8
10.010,0
0.01 0.010.0
가로 세로는 1~20 자리수고
중앙은 가로 세로 곱한거 정확도임
40는 처참한수준
Accuracy of 01-mini
Digits
‘Number
10
1 ]
12
13 14
15 16 17 18 19
100/ 1o0/ 100|1o0 36 2/100/96 2100/96.2/100
[oo/88.592.306.2/88.5/92.3/30.802.3/883
1oo/1oo]100
[ooliooliooliool
[100/32 3100
69 2
65,430 880 8/46,2
IoolIOO
Ioo
IIOO
176 9 84 6
57.7 57,765,4 53,834,6 42,3
100
‘100 100
100
[oo} 100/ 100/92 3192.338.322 3134.073.153,8 42.3 50,0 46,2 46.230,8 1 5126 5
‘J00 J00
106
‘88,5
76,969,257,7 33 565,4613
26,930,8다Eg
p6
796
IDO
61.5 57.7615
‘154
교soosa
96 2100/92 3
67,5
50.0 57746,2 46 2
n 5
38n313.9
06.2700
34369,265.4 61.557.7 61.5
00138/0.0
0.0
oOo0
10C
57.7 57.750.0 50.053
19239.
38/38
DO
[olooloo
96.296 290 ?
73.1 50,0 30.,8 34,6
10.0
0.0 38
0.010.01 0.0
10.010.0
196.2846/73.157.7 42,.3
26 9
38
7.7
O00.0
10 010.0
{
=
3923e
69 2
50.0
00
0.01 0.00,0
몸
88 5130,9/84.6
42 7
10.0
Da
0.0) 0.0
P
76,9 73.165.4
380
0.0
느
64673 1
16,9
10,0
100
0,0
20
88.5/76.9 57.7
77177
0.0
0.0 10.0
BdBB76s 9 38.5
hisi 3
O010.0
Io 00.0
02.369,2 53.8
11 5
381 0.0
10.0
00
0.0
[olooloo
80 8/61,5
38 38 | 0.0
10.010.0
0o
001 0.0
10.0| 0.0
%
61,5
0.010.0
10,0
0,0
0.0
0.0
000 0
10.0
Accuracy of 01-mini-2024-09-12
Diqits
Numbet
11
12 13
14 15 16
18
20
[1o0| 100 | 1oD| 100 97.5 100192.595.이1o0 95.0/95.0 100/95.0p97 5
95.092.595.035 0/9o 0
(100) 100lJ00
1001700
097535,0
‘0195 0 90,0/75,.0
72,5725300155,0
10D
Ioo
97,5
%ps
900
67,562,5
55.0 47,5 32
50O
100
(1o0| 100/ 100/97.595.097.5187
60 0pz.557.565.0 37.5 42.5 45.0 42.5 32.5 35.0
(100) 100
597,5
‘090.0
57,5
500 50 0
27.52231
97,51
1975
592,5197,5187,570.0
60.057,5 42,525072
[5,oiz 515.0
075ioo/1o0/100
80 0/375
47,5 55.060.0V75k00
UPD 0
75
Oo1
[25
90.092.502 5
72.5187.572.565.0 50.0 47,5 425
32500 0
0,0
12 :
50
2517 5
D5.092.585
375
52.5 42.5 37.535.0
30.0
0.0
5.0
25
0.010.0
@
요
075 100
70.0 700 50.0 47,5
30.0 17 55.0
25
0,0
0.01 0.0
10.01 0.0 |0.0
‘
05,0/975
60,0 425
70.0
10.0
25
00
[010.01oo
흘
95,0/92.575.0 67 5
47,5 32.515 0z0.0/15,0
0.0
0010.01 0,0
0.0 000.0 00|0.0
’40
185.065.0 60.0 35.oi5.O2-10 O5.0
10.0
0O
(1oo)
50.0
10.0
00 |0.0
p5.0
55,.0
Oolo.0
092,3
47,5 40.0
10.이5.0
0.0
00|o.0
90.0/32562.5 475
0.0
50
00
[00.0
85.062.5 60.0
170.0
5.0
0.0 0 C
10.0
10.0 0.0| 0.0
틀
35,0/625 47,5 5.0 1ioa
25
[o
00
00l00
00
[0l0o|o.0
42 520 (
110050 |25
0o
00
100| 0.0
Oo
00
00
100
‘0o
10 0
00 |0.0
이후 조금 발전하다가
Accuracy of 03-mini-2025-01-31
Digits in Numnber
10
11
12 13 14 15 16 17 18 19
20
(100] 100} 100/ 100
100}100
100| 100 97 5 100/ 100| 100 37.5 100| 100/97.595.0 100 | 100)
(100) 100| 100
97,5100
1oo 100/97 5197 :
100
9925p75/100
(100) 100
oo IoO 109/97 ,597.537,532,5/95,090. 0/32,395.0/95 (
100
[00/97-S00
5975
p7.5100/90.097 5190.0/87,5135.0/92.585 0/5 0/72.5/35 (
[07.5/100
‘100
5197,51 100197,5 100197 5
1p7.5/97.392,5/92 5/92.575.0 75.0/30.0/5,067.5/75.0
[100
100/100 92 5197,51100/92.5195.이100 95.0/95.087 5192 5187 5195.0/77,567,5 77557.5 55,0
80
[00/ 100
597
D5,0/97
87.5195.037 5192.567,562,567,5
60.0 CD.0 40.0 45
097,397.3 100
90.037.5197,592.537,597.575.0 62 5185.080 06O.0 57
‘40.0
30.040,0
100197 5
100
0100
95 O100
173
‘70.0 57 5
55,0
12.5
@
9
1100
5197.
[97.5p5.0/95
87.5195.0/77.5130.080,0/70.0 50.0 50.0 32.5 27.5 30.0 15.이
[100
[100 97 5/92,392,595
90.0I9D 090.0/67,5
50.0 50,0 42.5
[o027.5 15.0/25
물
[100/97.995.095.092,995,09s
87 5
65.067,5
062,5
30,0
112.515,050 2.5
’40
돌
[100/97.5100
552
5187
85.0/37 560.045.0
75 015.0
25125/25|00
097,5197.
167 5
62.5 72 5
55.045,0
32.5 10.0i7 5/115 010.02 5
0.0| 0.0
oo
0p50375/300
175.0
675 525 30,0 375
0 07 5
50125
5010.0
(100
097.535 0
67.570.0 6O.057.5 37.5
20 (
0.0 I0.0
25 5.0
0.010.0
물
[700
[90.037.5
62.560
45.057,570 0
75 |10.0/2 51 5015.0125 |0.0
07,5197.587,537.577,567,572,5
35,.0 30.0 30,0 45,0/12.5125 0,01 25 50175.02510.0
의
[100]90.087 5
62.530.0 35.0 45.0
2510.0
75
12
50500.0 |0.0
8
195.0
70 0
45.0 45.0
P5 0
5.0
0.0|0.01 0.0
50
10.0
03 mini 까지오면서 10자리 수 곱셈 거의 정복 성공
1234567890 X 1234567890=?
이런거 잘하다는 소리임
대단 드드
Accuracy of Implicit CoT (Stepwise Internalization)
Digits in Number
10 11 12 13 14 15 16 17 18 19 20
(100) 1001 100| 100
1oo/ 100/ 1o0| 100 | 100
100 1o0) 100 |IOC
[100) 100
100) 100 1OC
(100| 100
11001 100| 100
100| 100) 100
[100/100
100/100 100
‘I00’ 1oC
100
100
’10O
JOO
100
Lioo
100) 100 100
1o0
I00
1o00o0
IoC
100
Jo
80
Iooloooo
틀
‘100
60
10
100
‘100 100
11
‘100
돈 i2
’10o
40
흙
13
100
름
14
99 9100
15
IJDo
1001100 1OO
20
16
100
17
‘Iooou
18
I100
1100
100/99 939
19
IIoC
100
I00
100 100
100
‘100
‘100
[99,8/99,8/39,999,6
20
Mo
iooiono
Ioo
Ioo
100l99 9
수학전용 Ai 모델은 20자리까지도 정복 완료햇음
50
2자리수 곱셈 넘어가면 계산도 못하던 4o에서
10자리수 거의 정복하는데 까지 고작 8개월 걸림







