-
Notifications
You must be signed in to change notification settings - Fork 1
/
deepll.aux
186 lines (186 loc) · 7.8 KB
/
deepll.aux
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
\relax
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\@writefile{toc}{\contentsline {section}{\numberline {1}Warning}{1}{section.1}}
\citation{sorensen}
\citation{minsky}
\citation{girard}
\citation{ehrhard-survey}
\citation{blutecon}
\citation{murfetclift}
\citation{elman}
\citation{joulin}
\citation{sutskever}
\citation{ntm}
\@writefile{toc}{\contentsline {section}{\numberline {2}Introduction}{2}{section.2}}
\citation{dlbook}
\citation{elman}
\@writefile{toc}{\contentsline {section}{\numberline {3}Background}{3}{section.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Recurrent Neural Network}{3}{subsection.3.1}}
\newlabel{eq:update_eqn}{{3.4}{3}{}{equation.3.4}{}}
\newlabel{eq:output_rnn}{{3.5}{3}{}{equation.3.5}{}}
\citation{highorderrec}
\citation{pollack}
\citation{firstvsecond}
\citation{secondorder}
\citation{sutskever}
\citation{highorderrec}
\citation{pollack}
\citation{sutskever}
\citation{sutskever}
\citation{irsoy}
\citation{yuhai}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Second-order Recurrent Neural Network}{4}{subsection.3.2}}
\newlabel{eq:2ndorderrnn}{{3.6}{4}{Second-order Recurrent Neural Network}{equation.3.6}{}}
\newlabel{eq:input_to_operator}{{3.7}{4}{Second-order Recurrent Neural Network}{equation.3.7}{}}
\newlabel{eq:second_order_evolution}{{3.8}{4}{}{equation.3.8}{}}
\newlabel{eq:threelinearmaps}{{3.9}{4}{}{equation.3.9}{}}
\newlabel{eq:new_term_mRNN}{{3.10}{4}{}{equation.3.10}{}}
\citation{irsoy}
\citation{ntm}
\citation{ntm}
\citation{ntm}
\citation{ntm}
\citation{ntm}
\citation{ntm}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Neural Turing Machine}{5}{subsection.3.3}}
\newlabel{example:ntm}{{3.3}{5}{Neural Turing Machine}{subsection.3.3}{}}
\newlabel{eq:decomp}{{3.11}{5}{Neural Turing Machine}{equation.3.11}{}}
\newlabel{eq:ntm_update2}{{3.12}{6}{Neural Turing Machine}{equation.3.12}{}}
\newlabel{eq:ntm_update3}{{3.13}{6}{Neural Turing Machine}{equation.3.13}{}}
\newlabel{eq:NTMequation}{{3.14}{6}{Neural Turing Machine}{equation.3.14}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}Abstract reformulation}{6}{subsubsection.3.3.1}}
\newlabel{section:abstract_ntm}{{3.3.1}{6}{Abstract reformulation}{subsubsection.3.3.1}{}}
\citation{ntm}
\newlabel{defn:psimap}{{3.15}{7}{}{equation.3.15}{}}
\citation{ntm}
\citation{ntm}
\citation{dnc}
\citation{dnc}
\citation{murfet_ll}
\citation{murfetclift}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Linear Logic}{9}{subsection.3.4}}
\citation{benton_etal}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.4.1}Types}{10}{subsubsection.3.4.1}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.4.2}Terms}{10}{subsubsection.3.4.2}}
\newlabel{eq:example_lambda_1}{{3.20}{10}{Terms}{equation.3.20}{}}
\newlabel{eq:example_lambda_2}{{3.21}{10}{Terms}{equation.3.21}{}}
\newlabel{eq:example_lambda_3}{{3.22}{10}{Terms}{equation.3.22}{}}
\citation{murfet_ll}
\newlabel{remark:atu}{{3.11}{11}{}{theorem.3.11}{}}
\newlabel{eq:church_2_linearlambda}{{3.23}{11}{Terms}{equation.3.23}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.4.3}Semantics}{11}{subsubsection.3.4.3}}
\citation{murfet_ll}
\citation{murfetclift}
\newlabel{eq:vtobangv}{{3.24}{12}{Semantics}{equation.3.24}{}}
\newlabel{example:denotation_intaphi}{{3.12}{12}{}{theorem.3.12}{}}
\newlabel{eq:defnnl}{{3.25}{12}{Semantics}{equation.3.25}{}}
\newlabel{example_1}{{3.13}{12}{}{theorem.3.13}{}}
\citation{murfetclift}
\newlabel{example_2}{{3.14}{13}{}{theorem.3.14}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}The Linear Logic Recurrent Neural Network}{13}{section.4}}
\newlabel{eq:masterh}{{4.1}{14}{The Linear Logic Recurrent Neural Network}{equation.4.1}{}}
\newlabel{eq:masterz}{{4.2}{14}{The Linear Logic Recurrent Neural Network}{equation.4.2}{}}
\citation{murfetclift}
\citation{murfet_ll}
\newlabel{remark:sequentbang}{{4.3}{15}{}{theorem.4.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Examples}{15}{subsection.4.1}}
\citation{benton_etal}
\newlabel{eq:secondorderRNNinLLRNN}{{4.6}{16}{(Second-order RNN)}{equation.4.6}{}}
\newlabel{eq:higherorderRNN}{{4.7}{16}{(Higher-order RNN)}{equation.4.7}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}NTM as an LLRNN}{17}{subsection.4.2}}
\newlabel{section:ntmasllrnn}{{4.2}{17}{NTM as an LLRNN}{subsection.4.2}{}}
\newlabel{example:dihedral}{{4.6}{18}{(Dihedral NTM)}{theorem.4.6}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Generalisations of the NTM}{18}{section.5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Pattern NTM}{19}{subsection.5.1}}
\newlabel{example:ntm_extended}{{5.1}{19}{Pattern NTM}{subsection.5.1}{}}
\newlabel{eq:deliver_iterators}{{5.1}{19}{Pattern NTM}{equation.5.1}{}}
\newlabel{eq:patternntm_state}{{5.2}{20}{Pattern NTM}{equation.5.2}{}}
\newlabel{remark:alt_presentation}{{5.1}{21}{}{theorem.5.1}{}}
\newlabel{eq:pattern_ntm_distinction}{{5.8}{21}{}{equation.5.8}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Multiple pattern NTM}{21}{subsection.5.2}}
\newlabel{example:ntm_super}{{5.2}{21}{Multiple pattern NTM}{subsection.5.2}{}}
\newlabel{eq:example_seq_func}{{5.12}{22}{Multiple pattern NTM}{equation.5.12}{}}
\newlabel{eq:summerevening}{{5.13}{22}{Multiple pattern NTM}{equation.5.13}{}}
\newlabel{eq:summerevening_after}{{5.14}{22}{Multiple pattern NTM}{equation.5.14}{}}
\newlabel{eq:crazyhorse}{{5.15}{23}{Multiple pattern NTM}{equation.5.15}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Polynomial step NTM}{24}{subsection.5.3}}
\newlabel{section:polynomialntm}{{5.3}{24}{Polynomial step NTM}{subsection.5.3}{}}
\newlabel{eq:summerevening2}{{5.19}{24}{Polynomial step NTM}{equation.5.19}{}}
\newlabel{eq:crazyhorse2}{{5.20}{24}{Polynomial step NTM}{equation.5.20}{}}
\citation{murfetclift}
\citation{alemi}
\citation{ntp}
\citation{proofsearch}
\citation{tarlow}
\citation{difflambda}
\citation{ehrhard-survey}
\citation{griewank}
\citation{tensorflow}
\citation{manzyuk}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.1}Dihedral polynomial step NTM}{25}{subsubsection.5.3.1}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Unpolished remarks}{25}{section.6}}
\citation{cho}
\citation{cho}
\citation{sutskever2}
\bibstyle{amsalpha}
\bibcite{bahdanau}{1}
\bibcite{cho}{2}
\bibcite{neuralprog}{3}
\bibcite{freitas}{4}
\bibcite{dnc}{5}
\bibcite{frege}{6}
\bibcite{blutecon}{7}
\bibcite{sorensen}{8}
\bibcite{dlnature}{9}
\bibcite{elman}{10}
\bibcite{ntm}{11}
\bibcite{armmik}{12}
\bibcite{graves_etal}{13}
\bibcite{yuhai}{14}
\bibcite{irsoy}{15}
\bibcite{sutskever}{16}
\bibcite{sutskever2}{17}
\bibcite{firstvsecond}{18}
\bibcite{secondorder}{19}
\bibcite{highorderrec}{20}
\bibcite{pollack}{21}
\bibcite{murfet_ll}{22}
\bibcite{murfet_coalg}{23}
\bibcite{girard}{24}
\bibcite{joulin}{25}
\bibcite{grefen}{26}
\bibcite{weston}{27}
\bibcite{zaremba2}{28}
\bibcite{mellies}{29}
\bibcite{alemi}{30}
\bibcite{tarlow}{31}
\bibcite{ntp}{32}
\bibcite{ehrhard-survey}{33}
\bibcite{murfetclift}{34}
\bibcite{tensorflow}{35}
\bibcite{tensorflow2}{36}
\bibcite{griewank}{37}
\bibcite{difflambda}{38}
\bibcite{manzyuk}{39}
\bibcite{minsky}{40}
\bibcite{prooftypes}{41}
\bibcite{benton_etal}{42}
\bibcite{dlbook}{43}
\bibcite{proofsearch}{44}
\bibcite{mikolovmemory}{45}