Document (#42905)

Author

Bischoff, M.

Title

KI lernt die Sprache der Mathematik

Source

Spektrum der Wissenschaft. 2020, H.7, S.27-28

Year

2020

Series

Informatik

Abstract

Bisher konnten neuronale Netze bloß einfache Ausdrücke addieren und multiplizieren. Nun haben Informatiker einen selbstlernenden Algorithmus vorgestellt, der Differenzialgleichungen löst und Stammfunktionen berechnet - und dabei alle bisherigen Methoden übertrifft.

Content

Verweis auf: Lample, G., Charton, F.: Deep learning for symbolic mathematics. ArXiv: 11912.01412, 2019.

Field

Informatik
Mathematik

Similar documents (author)

1. Bischoff, U.: ¬Die Informationslawine : wie ist die Nachrichtenfülle zu bewältigen? (1967) 5.76

   5.7574883 = sum of:
     5.7574883 = weight(author_txt:bischoff in 4975) [ClassicSimilarity], result of:
       5.7574883 = fieldWeight in 4975, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.211981 = idf(docFreq=11, maxDocs=44218)
         0.625 = fieldNorm(doc=4975)
   

2. Bischoff, M.: ¬Das grosse Experiment (2021) 5.76

   5.7574883 = sum of:
     5.7574883 = weight(author_txt:bischoff in 329) [ClassicSimilarity], result of:
       5.7574883 = fieldWeight in 329, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.211981 = idf(docFreq=11, maxDocs=44218)
         0.625 = fieldNorm(doc=329)
   

3. Bischoff, M.: Eine (fast) unlösbare Aufgabe mit tragischem Ende : die fabelhafte Welt der Mathematik (2023) 5.76

   5.7574883 = sum of:
     5.7574883 = weight(author_txt:bischoff in 932) [ClassicSimilarity], result of:
       5.7574883 = fieldWeight in 932, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.211981 = idf(docFreq=11, maxDocs=44218)
         0.625 = fieldNorm(doc=932)
   

4. Bischoff, M.: Hobby-Mathematiker findet die lang ersehnte Einstein-Kachel : Mathematisches Mosaik (2023) 5.76

   5.7574883 = sum of:
     5.7574883 = weight(author_txt:bischoff in 936) [ClassicSimilarity], result of:
       5.7574883 = fieldWeight in 936, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.211981 = idf(docFreq=11, maxDocs=44218)
         0.625 = fieldNorm(doc=936)
   

5. Bischoff, M.: ¬Das Dornröschen-Problem spaltet die Mathewelt : Die fabelhafte Welt der Mathematik (2023) 5.76

   5.7574883 = sum of:
     5.7574883 = weight(author_txt:bischoff in 940) [ClassicSimilarity], result of:
       5.7574883 = fieldWeight in 940, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         9.211981 = idf(docFreq=11, maxDocs=44218)
         0.625 = fieldNorm(doc=940)
   

Similar documents (content)

1. Lexikon der Mathematik (2000-2003) 0.20

   0.19805962 = sum of:
     0.19805962 = product of:
       0.7262186 = sum of:
         0.022660648 = weight(abstract_txt:einen in 4614) [ClassicSimilarity], result of:
           0.022660648 = score(doc=4614,freq=1.0), product of:
             0.06799915 = queryWeight, product of:
               4.2655873 = idf(docFreq=1687, maxDocs=44218)
               0.015941333 = queryNorm
             0.333249 = fieldWeight in 4614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.2655873 = idf(docFreq=1687, maxDocs=44218)
               0.078125 = fieldNorm(doc=4614)
         0.056478344 = weight(abstract_txt:methoden in 4614) [ClassicSimilarity], result of:
           0.056478344 = score(doc=4614,freq=1.0), product of:
             0.12499996 = queryWeight, product of:
               1.3558236 = boost
               5.7833843 = idf(docFreq=369, maxDocs=44218)
               0.015941333 = queryNorm
             0.4518269 = fieldWeight in 4614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.7833843 = idf(docFreq=369, maxDocs=44218)
               0.078125 = fieldNorm(doc=4614)
         0.22101697 = weight(abstract_txt:mathematik in 4614) [ClassicSimilarity], result of:
           0.22101697 = score(doc=4614,freq=5.0), product of:
             0.18153024 = queryWeight, product of:
               1.6338898 = boost
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.015941333 = queryNorm
             1.2175215 = fieldWeight in 4614, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.078125 = fieldNorm(doc=4614)
         0.11369452 = weight(abstract_txt:netze in 4614) [ClassicSimilarity], result of:
           0.11369452 = score(doc=4614,freq=1.0), product of:
             0.1992882 = queryWeight, product of:
               1.7119421 = boost
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.015941333 = queryNorm
             0.570503 = fieldWeight in 4614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.078125 = fieldNorm(doc=4614)
         0.15136375 = weight(abstract_txt:algorithmus in 4614) [ClassicSimilarity], result of:
           0.15136375 = score(doc=4614,freq=1.0), product of:
             0.24117734 = queryWeight, product of:
               1.883287 = boost
               8.033325 = idf(docFreq=38, maxDocs=44218)
               0.015941333 = queryNorm
             0.62760353 = fieldWeight in 4614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.033325 = idf(docFreq=38, maxDocs=44218)
               0.078125 = fieldNorm(doc=4614)
         0.16100436 = weight(abstract_txt:neuronale in 4614) [ClassicSimilarity], result of:
           0.16100436 = score(doc=4614,freq=1.0), product of:
             0.25131226 = queryWeight, product of:
               1.9224502 = boost
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.015941333 = queryNorm
             0.6406546 = fieldWeight in 4614, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.078125 = fieldNorm(doc=4614)
       0.27272728 = coord(6/22)
   

2. Devlin, K.: ¬Das Mathe-Gen : oder wie sich das mathematische Denken entwickelt und warum Sie Zahlen ruhig vergessen können (2001) 0.16

   0.15502091 = sum of:
     0.15502091 = product of:
       0.56841 = sum of:
         0.015862454 = weight(abstract_txt:einen in 4019) [ClassicSimilarity], result of:
           0.015862454 = score(doc=4019,freq=1.0), product of:
             0.06799915 = queryWeight, product of:
               4.2655873 = idf(docFreq=1687, maxDocs=44218)
               0.015941333 = queryNorm
             0.23327431 = fieldWeight in 4019, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.2655873 = idf(docFreq=1687, maxDocs=44218)
               0.0546875 = fieldNorm(doc=4019)
         0.029295793 = weight(abstract_txt:haben in 4019) [ClassicSimilarity], result of:
           0.029295793 = score(doc=4019,freq=2.0), product of:
             0.08124252 = queryWeight, product of:
               1.0930498 = boost
               4.6624994 = idf(docFreq=1134, maxDocs=44218)
               0.015941333 = queryNorm
             0.3605968 = fieldWeight in 4019, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               4.6624994 = idf(docFreq=1134, maxDocs=44218)
               0.0546875 = fieldNorm(doc=4019)
         0.046102207 = weight(abstract_txt:alle in 4019) [ClassicSimilarity], result of:
           0.046102207 = score(doc=4019,freq=3.0), product of:
             0.0960205 = queryWeight, product of:
               1.1883113 = boost
               5.0688457 = idf(docFreq=755, maxDocs=44218)
               0.015941333 = queryNorm
             0.4801288 = fieldWeight in 4019, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               5.0688457 = idf(docFreq=755, maxDocs=44218)
               0.0546875 = fieldNorm(doc=4019)
         0.0978835 = weight(abstract_txt:sprache in 4019) [ClassicSimilarity], result of:
           0.0978835 = score(doc=4019,freq=5.0), product of:
             0.13378462 = queryWeight, product of:
               1.4026567 = boost
               5.9831543 = idf(docFreq=302, maxDocs=44218)
               0.015941333 = queryNorm
             0.7316499 = fieldWeight in 4019, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               5.9831543 = idf(docFreq=302, maxDocs=44218)
               0.0546875 = fieldNorm(doc=4019)
         0.2396786 = weight(abstract_txt:mathematik in 4019) [ClassicSimilarity], result of:
           0.2396786 = score(doc=4019,freq=12.0), product of:
             0.18153024 = queryWeight, product of:
               1.6338898 = boost
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.015941333 = queryNorm
             1.3203233 = fieldWeight in 4019, product of:
               3.4641016 = tf(freq=12.0), with freq of:
                 12.0 = termFreq=12.0
               6.9694996 = idf(docFreq=112, maxDocs=44218)
               0.0546875 = fieldNorm(doc=4019)
         0.1395874 = weight(abstract_txt:löst in 4019) [ClassicSimilarity], result of:
           0.1395874 = score(doc=4019,freq=1.0), product of:
             0.28983715 = queryWeight, product of:
               2.0645494 = boost
               8.806516 = idf(docFreq=17, maxDocs=44218)
               0.015941333 = queryNorm
             0.48160633 = fieldWeight in 4019, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.806516 = idf(docFreq=17, maxDocs=44218)
               0.0546875 = fieldNorm(doc=4019)
       0.27272728 = coord(6/22)
   

3. Krause, J.: Integration von Ansätzen neuronaler Netzwerke in die Systemarchitektur von ViBSoz und CARMEN (2001) 0.15

   0.14674576 = sum of:
     0.14674576 = product of:
       0.6456813 = sum of:
         0.031724907 = weight(abstract_txt:einen in 1698) [ClassicSimilarity], result of:
           0.031724907 = score(doc=1698,freq=1.0), product of:
             0.06799915 = queryWeight, product of:
               4.2655873 = idf(docFreq=1687, maxDocs=44218)
               0.015941333 = queryNorm
             0.46654862 = fieldWeight in 1698, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.2655873 = idf(docFreq=1687, maxDocs=44218)
               0.109375 = fieldNorm(doc=1698)
         0.07906968 = weight(abstract_txt:methoden in 1698) [ClassicSimilarity], result of:
           0.07906968 = score(doc=1698,freq=1.0), product of:
             0.12499996 = queryWeight, product of:
               1.3558236 = boost
               5.7833843 = idf(docFreq=369, maxDocs=44218)
               0.015941333 = queryNorm
             0.63255763 = fieldWeight in 1698, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.7833843 = idf(docFreq=369, maxDocs=44218)
               0.109375 = fieldNorm(doc=1698)
         0.084377 = weight(abstract_txt:bisher in 1698) [ClassicSimilarity], result of:
           0.084377 = score(doc=1698,freq=1.0), product of:
             0.13053268 = queryWeight, product of:
               1.3855044 = boost
               5.90999 = idf(docFreq=325, maxDocs=44218)
               0.015941333 = queryNorm
             0.64640516 = fieldWeight in 1698, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.90999 = idf(docFreq=325, maxDocs=44218)
               0.109375 = fieldNorm(doc=1698)
         0.22510363 = weight(abstract_txt:netze in 1698) [ClassicSimilarity], result of:
           0.22510363 = score(doc=1698,freq=2.0), product of:
             0.1992882 = queryWeight, product of:
               1.7119421 = boost
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.015941333 = queryNorm
             1.1295382 = fieldWeight in 1698, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.109375 = fieldNorm(doc=1698)
         0.22540611 = weight(abstract_txt:neuronale in 1698) [ClassicSimilarity], result of:
           0.22540611 = score(doc=1698,freq=1.0), product of:
             0.25131226 = queryWeight, product of:
               1.9224502 = boost
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.015941333 = queryNorm
             0.8969165 = fieldWeight in 1698, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.109375 = fieldNorm(doc=1698)
       0.22727273 = coord(5/22)
   

4. Braun, H.: Neuronale Netze : Optimierung durch Lernen und Evolution (1997) 0.14

   0.13999672 = sum of:
     0.13999672 = product of:
       0.7699819 = sum of:
         0.07906968 = weight(abstract_txt:methoden in 730) [ClassicSimilarity], result of:
           0.07906968 = score(doc=730,freq=1.0), product of:
             0.12499996 = queryWeight, product of:
               1.3558236 = boost
               5.7833843 = idf(docFreq=369, maxDocs=44218)
               0.015941333 = queryNorm
             0.63255763 = fieldWeight in 730, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.7833843 = idf(docFreq=369, maxDocs=44218)
               0.109375 = fieldNorm(doc=730)
         0.14703625 = weight(abstract_txt:bisherigen in 730) [ClassicSimilarity], result of:
           0.14703625 = score(doc=730,freq=1.0), product of:
             0.18902512 = queryWeight, product of:
               1.667278 = boost
               7.11192 = idf(docFreq=97, maxDocs=44218)
               0.015941333 = queryNorm
             0.77786624 = fieldWeight in 730, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.11192 = idf(docFreq=97, maxDocs=44218)
               0.109375 = fieldNorm(doc=730)
         0.22510363 = weight(abstract_txt:netze in 730) [ClassicSimilarity], result of:
           0.22510363 = score(doc=730,freq=2.0), product of:
             0.1992882 = queryWeight, product of:
               1.7119421 = boost
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.015941333 = queryNorm
             1.1295382 = fieldWeight in 730, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.109375 = fieldNorm(doc=730)
         0.31877238 = weight(abstract_txt:neuronale in 730) [ClassicSimilarity], result of:
           0.31877238 = score(doc=730,freq=2.0), product of:
             0.25131226 = queryWeight, product of:
               1.9224502 = boost
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.015941333 = queryNorm
             1.2684314 = fieldWeight in 730, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.109375 = fieldNorm(doc=730)
       0.18181819 = coord(4/22)
   

5. Eurich, C.W.; Wilke, S.: Künstliches Gedächtnis : Neurotheorie für Anfänger (I) (2002) 0.13

   0.12961583 = sum of:
     0.12961583 = product of:
       0.95051605 = sum of:
         0.27286685 = weight(abstract_txt:netze in 1311) [ClassicSimilarity], result of:
           0.27286685 = score(doc=1311,freq=1.0), product of:
             0.1992882 = queryWeight, product of:
               1.7119421 = boost
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.015941333 = queryNorm
             1.3692071 = fieldWeight in 1311, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.3024383 = idf(docFreq=80, maxDocs=44218)
               0.1875 = fieldNorm(doc=1311)
         0.29123873 = weight(abstract_txt:einfache in 1311) [ClassicSimilarity], result of:
           0.29123873 = score(doc=1311,freq=1.0), product of:
             0.20813598 = queryWeight, product of:
               1.7495319 = boost
               7.462781 = idf(docFreq=68, maxDocs=44218)
               0.015941333 = queryNorm
             1.3992715 = fieldWeight in 1311, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.462781 = idf(docFreq=68, maxDocs=44218)
               0.1875 = fieldNorm(doc=1311)
         0.38641047 = weight(abstract_txt:neuronale in 1311) [ClassicSimilarity], result of:
           0.38641047 = score(doc=1311,freq=1.0), product of:
             0.25131226 = queryWeight, product of:
               1.9224502 = boost
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.015941333 = queryNorm
             1.5375712 = fieldWeight in 1311, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.200379 = idf(docFreq=32, maxDocs=44218)
               0.1875 = fieldNorm(doc=1311)
       0.13636364 = coord(3/22)