%PDF-1.4 % 1 0 obj << /S /GoTo /D (section.1) >> endobj 4 0 obj (Introduction) endobj 5 0 obj << /S /GoTo /D (section.2) >> endobj 8 0 obj (RBM networks) endobj 9 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 12 0 obj (Free energy function) endobj 13 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 16 0 obj (RBM networks) endobj 17 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 20 0 obj (Hardplus RBM networks) endobj 21 0 obj << /S /GoTo /D (subsection.2.4) >> endobj 24 0 obj (Hardplus RBM networks versus \(Softplus\) RBM networks) endobj 25 0 obj << /S /GoTo /D (subsection.2.5) >> endobj 28 0 obj (Thresholded Networks and Boolean Functions) endobj 29 0 obj << /S /GoTo /D (subsection.2.6) >> endobj 32 0 obj (RBM networks versus standard neural networks) endobj 33 0 obj << /S /GoTo /D (subsection.2.7) >> endobj 36 0 obj (Simulating hardplus RBM networks by a one-hidden-layer threshold network) endobj 37 0 obj << /S /GoTo /D (section.3) >> endobj 40 0 obj (n2 + 1-sized RBM networks can compute any symmetric function) endobj 41 0 obj << /S /GoTo /D (section.4) >> endobj 44 0 obj (Lower bounds on the size of RBM networks for certain functions) endobj 45 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 48 0 obj (Existential results) endobj 49 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 52 0 obj (Qualified lower bound results for the IP function) endobj 53 0 obj << /S /GoTo /D (section.5) >> endobj 56 0 obj (Conclusions and Future Work) endobj 57 0 obj << /S /GoTo /D (appendix.A) >> endobj 60 0 obj (Appendix) endobj 61 0 obj << /S /GoTo /D (subsection.A.1) >> endobj 64 0 obj (Free-energy derivation) endobj 65 0 obj << /S /GoTo /D (subsection.A.2) >> endobj 68 0 obj (Proofs for Section 2.4 ) endobj 69 0 obj << /S /GoTo /D (subsection.A.3) >> endobj 72 0 obj (Proofs for Section 2.5) endobj 73 0 obj << /S /GoTo /D (subsection.A.4) >> endobj 76 0 obj (Proofs for Section 2.7) endobj 77 0 obj << /S /GoTo /D (subsection.A.5) >> endobj 80 0 obj (Proof of Theorem 7) endobj 81 0 obj << /S /GoTo /D (subsection.A.6) >> endobj 84 0 obj (Proofs for Section 4) endobj 85 0 obj << /S /GoTo /D (subsubsection.A.6.1) >> endobj 88 0 obj (Proof of Theorem 8) endobj 89 0 obj << /S /GoTo /D (subsubsection.A.6.2) >> endobj 92 0 obj (Proof of Theorem 9) endobj 93 0 obj << /S /GoTo /D (subsubsection.A.6.3) >> endobj 96 0 obj (Proof of Theorem 10) endobj 97 0 obj << /S /GoTo /D [98 0 R /Fit ] >> endobj 120 0 obj << /Length 3841 /Filter /FlateDecode >> stream xْܶ]_1Ole&.'>"%qEGڔ|
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