What Can Neural Networks Reason About?

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8IBUDBOOFVSBMOFUXPSL SFBTPOBCPVU ҳ࢚ળ .-4DJFOUJTU 1JOHQPOH

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ݾର ݾର • Introduction: Reasoning • Algorithmic Alignment • Conclusion

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*OUSPEVDUJPO3FBTPOJOH

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8IBUJT3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • “୶ܻ”

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8IBUJT3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • ୶ܻ: ঌҊ ੓ח Ѫਵ۽ࠗఠ ঌ૑ ޅೞח Ѫਸ ࢎҊೣ • ীಘ఑਷ ౵ܻী ੓যਃ -> ౵ܻח ೐یझ੄ ࣻبীਃ -> ীಘ఑਷ যו աۄী ੓ਸө? • ੿ࠁܳ ઱঻ਸ ٸ, Ӓ ੿ࠁ۽ࠗఠ ҙ଴ೞ૑ ޅೠ Ѫী ؀ೠ ࢜۽਍ ੿ࠁܳ ب୹೧ղח ੘স

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8IBUJT3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • ੿ࠁܳ ઱঻ਸ ٸ, Ӓ ੿ࠁ۽ࠗఠ ҙ଴ೞ૑ ޅೠ Ѫী ؀ೠ ࢜۽਍ ੿ࠁܳ ب୹೧ղח ੘স • न҃ݎ੄ ୶ܻ ޙઁ: ੿ࠁ/ࣁ࢚ਸ ҳઑചೞҊ Ӓ ҳઑ۽ࠗఠ Ѿҗܳ ৘ஏೞب۾ ೟णदఇ • GNN, Neural Symbolic Programs (Semantic Parsing), Deep Sets

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%FGJOJUJPOPG3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • ޛ୓ ૘೤ s ∈ Sо ੓যࢲ п sܳ Xۄח ߭ఠ۽ ಴അೡ ࣻ ੓׮Ҋ о੿ • ࢚ട {S1, S2, S3, …} ী ؀೧ࢲ ੿׹ ۄ߰ {y1, y2, y3, …} о ੓ਸ ٸ • ੐੄੄ ࠁ૑ ޅೠ ࢚ട Sী ؀ೠ ੿׹ ۄ߰ yܳ ب୹ೞח ೣࣻ y=g(S)ܳ ঳ח Ѫ੉ ݾ಴੐

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4USVDUVSFTGPS3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • Deep Sets • S = {ࡈр ҕ, ౵ۆ ҕ, ֢ۆ ҕ} ੉ۄҊ о੿೧ࠁݶ, • ࢎۈ ੑ੢ীࢲח ࣽࢲо ࢚ҙ হ਺ {ࡈр ҕ, ౵ۆ ҕ, ֢ۆ ҕ} = {౵ۆ ҕ, ֢ۆ ҕ, ࡈр ҕ} • Permutation Invariant ೞѱ ೣࣻ gܳ ࢸ҅ೠ Ѫ੉ Deep set੐ • য۰ਕ ࠁ੉૑݅ Ӓր MLP ೤੄ MLPۄҊ ࢤп • যڃ ࣽࢲ۽ ৬ب ࢚ҙ হ਺

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4USVDUVSFTGPS3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • GNN (Graph Neural Network) • Aggregate৬ Concatܳ ഝਊೞৈ Graph ҳઑܳ Networkܳ ಴അ

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,JOEPG3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • ੷੗ٜ਷ ୶ܻ ޙઁܳ դ੉ب৬ ౠ૚ী ٮۄࢲ ֎ о૑۽ ࠙ܨೣ • ా҅ ਃড (Summary Statistics): ઱য૓ ੑ۱ਸ ‘ࣁח’ ޙઁ • ৘द) ز੹੉ ࢎ૓ী ݻ ѐ ੓ա? Ҋন੉ی ѐ઺ী যڃ Ѫ੉ ݆ա? • ҙ҅ ࢲৌ (Relational Argmax): ઱য૓ ੑ۱ীࢲ ࢚؀੸ ҙ҅ܳ ٮ૑ח ޙઁ • ৘द) о੢ ݣܻ ڄযઉ ੓ח ޛ୓ ह਷ যڃ ࢝ӭੋо? • ز੸ ೐۽Ӓې߁ (Dynamic Programming): Ѿҗܳ ੷੢ೞݴ ಹח ޙઁ • ৘द) ೖࠁա஖, ઁੌ ૣ਷ ӡ ଺ӝ • NP-Hard Problem: ??? • ৘द) ઱য૓ ૘೤ী ؀೧ࢲ Ӓ ೤੉ 0੉غח ࠗ࠙ ૘೤ਸ ଺ਸ ࣻ ੓ਸө?

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,JOEPG3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • ੷੗ٜ਷ ୶ܻ ޙઁܳ դ੉ب৬ ౠ૚ী ٮۄࢲ ֎ о૑۽ ࠙ܨೣ • ా҅ ਃড (Summary Statistics): ઱য૓ ੑ۱ਸ ‘ࣁח’ ޙઁ • ৘द) ز੹੉ ࢎ૓ী ݻ ѐ ੓ա? Ҋন੉ی ѐ઺ী যڃ Ѫ੉ ݆ա? • ҙ҅ ࢲৌ (Relational Argmax): ઱য૓ ੑ۱ীࢲ ࢚؀੸ ҙ҅ܳ ٮ૑ח ޙઁ • ৘द) о੢ ݣܻ ڄযઉ ੓ח ޛ୓ ह਷ যڃ ࢝ӭੋо? • ز੸ ೐۽Ӓې߁ (Dynamic Programming): Ѿҗܳ ੷੢ೞݴ ಹח ޙઁ • ৘द) ೖࠁա஖, ઁੌ ૣ਷ ӡ ଺ӝ • NP-Hard Problem: ࠺Ѿ੿੸ ౚ݂ӝ҅о ׮೦दрী ಽ ࣻ ੓ח ޙઁܳ ೧׼ ޙઁٜ۽ ׮೦ दрী ജਗೡ ࣻ ੓ח ૘೤ • ৘द) ઱য૓ ૘೤ী ؀೧ࢲ Ӓ ೤੉ 0੉غח ࠗ࠙ ૘೤ਸ ଺ਸ ࣻ ੓ਸө?

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,JOEPG3FBTPOJOH *OUSPEVDUJPO3FBTPOJOH • ੷੗ٜ਷ п ޙઁٜী ؀೧ࢲ যڃ न҃ݎ ҳઑ۽ ಽ ࣻ ੓ח૑ ׹ೞҊ੗ ೞ৓਺ • ా҅ ਃড (Summary Statistics): ઱য૓ ੑ۱ਸ ‘ࣁח’ ޙઁ • ৘द) GNNҗ Deep Setਵ۽ח ੜ ಽ ࣻ ੓૑݅, MLP۽ח ಽӝ য۰਑ • ҙ҅ ࢲৌ (Relational Argmax): ઱য૓ ੑ۱ীࢲ ࢚؀੸ ҙ҅ܳ ٮ૑ח ޙઁ • ৘द) GNNਵ۽ח ಽ ࣻ ੓૑݅, Deep Setਵ۽ח ಽӝ য۰਑ • ز੸ ೐۽Ӓې߁ (Dynamic Programming): Ѿҗܳ ੷੢ೞݴ ಹח ޙઁ • ৘द) GNNਵ۽ ಽ ࣻ ੓਺ • NP-Hard Problem: ࠺Ѿ੿੸ ౚ݂ӝ҅о ׮೦दрী ಽ ࣻ ੓ח ޙઁܳ ೧׼ ޙઁٜ۽ ׮೦ दрী ജਗೡ ࣻ ੓ח ૘೤ • ৘द) Exhaustive Searchо ೙ਃೣ

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"MHPSJUIN"MJHONFOU

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4USVDUVSF$PNQMFYJUZPG1SPCMFN "MHPSJUINJD"MJHONFOU • ޙઁ৬ Ӓ ޙઁܳ ಹח न҃ݎ ҳઑܳ о੿೧ࠁӝ • ݅ডী ޙઁ੄ ҳઑܳ न҃ݎ੄ ҳઑী ؀਽दఆ ࣻ ੓׮ݶ?

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4USVDUVSF$PNQMFYJUZPG1SPCMFN "MHPSJUINJD"MJHONFOU • ޙઁ ಽ੉੄ ҙ੼ীࢲ ֤ޙ਷ ׮਺ਸ ੹ઁೣ

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4USVDUVSF$PNQMFYJUZPG1SPCMFN "MHPSJUINJD"MJHONFOU • ޙઁ ಽ੉੄ ҙ੼ীࢲ ֤ޙ਷ ׮਺ਸ ੹ઁೣ

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4USVDUVSF$PNQMFYJUZPG1SPCMFN "MHPSJUINJD"MJHONFOU • ޙઁ ಽ੉੄ ҙ੼ীࢲ ֤ޙਸ ׮਺ਸ ੹ઁೣ • ೧ࢳ: • ׮਺ ઑѤਸ ݅઒ೞח ޙઁח GNNਵ۽ ؀਽दఆ ࣻ ੓׮ • Ӓ ޙઁী աఋաח ޛ୓ח ୭؀ Nѐө૑݅ оמೞҊ, • Ӓ ޙઁ੄ ޛ୓੄ ࣽࢲח ޙઁܳ ಹחؘ ޖҙೞ׮

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4USVDUVSF$PNQMFYJUZPG1SPCMFN "MHPSJUINJD"MJHONFOU • ޙઁ ಽ੉੄ ҙ੼ীࢲ ֤ޙਸ ׮਺ਸ ੹ઁೣ • ೧ࢳ: • ׮਺ ઑѤਸ ݅઒ೞח ޙઁח GNNਵ۽ ؀਽दఆ ࣻ ੓׮ • ӒܻҊ ੐੄੄ GNN਷ MLP۽ ؀਽दఆ ࣻ ੓׮

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4USVDUVSF$PNQMFYJUZPG1SPCMFN "MHPSJUINJD"MJHONFOU • ޙઁ ಽ੉੄ ҙ੼ীࢲ ֤ޙਸ ׮਺ਸ ੹ઁೣ • ೧ࢳ: • ׮਺ ઑѤਸ ݅઒ೞח ޙઁח GNNਵ۽ ؀਽दఆ ࣻ ੓׮ • ӒܻҊ ੐੄੄ GNN਷ MLP۽ ؀਽दఆ ࣻ ੓׮ • ޙઁ: “ޙઁ ೟ण”੄ ҃਋ب Ӓۡө???

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4USVDUVSF$PNQMFYJUZPG1SPCMFN "MHPSJUINJD"MJHONFOU • ޙઁ : ޙઁ ೟णী ؀೧ࢲب Ӓۡө? • ೧ࠁݶ MLPח ੜ ޅ ߓ਋ח Ѫ э਺: ҳઑ੸ਵ۽ ޙઁܳ ୶࢚ചೞח מ۱੉ ࠗ઒೧ࢲ • GNN਷ п ױ҅ܳ ߓ਎ ࣻ ੓૑݅, MLPۄݶ ܖ೐ ੹୓੄ Ѿҗޛਸ ೞա۽ ߓਕঠ ೣ

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1"$-FBSOBCJMJUZBOE"MJHONFOU "MHPSJUINJD"MJHONFOU • Probably approximately correct learning (Ѣ੄ ੿ഛೠ ೟ण) • ੑ۱җ ୹۱हਸ ࢠ೒݂೧ࢲ ೟णೞח ঌҊ્ܻਸ ࢤп೧ࠁݶ • Probably: ֫਷ ഛܫ۽ • Approximately Correct: ݽ؛੄ ী۞о Threshold ޷݅ੌѢ׮

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1"$-FBSOBCJMJUZ "MHPSJUINJD"MJHONFOU • Probably approximately correct learning (Ѣ੄ ੿ഛೠ ೟ण) • ೧ࢳ: • ਋ܻ ݽ؛੉ ࢠ೒݂ਸ ా೧ࢲ ೟णदఆ ࣻ ੓׮Ҋ о੿೧ࠁ੗ (PAC ઑѤ) • Ӓ۞ݶ ী۞بܳ ઁೠೞӝ ਤ೧ࢲח ݆੉ ࡳইঠ ೠ׮ (୭ࣗ M ݅ఀ੄ ࠂ੟ب۽ ࡳইঠೣ)

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1"$-FBSOBCJMJUZ "MHPSJUINJD"MJHONFOU • Probably approximately correct learning (Ѣ੄ ੿ഛೠ ೟ण) • ؊ ए਍ ೧ࢳ: • ࢠ೒݂ਵ۽ ೟णदఆ ٸ, ࢿמ ֫੉۰ݶ ݆੉ ࡳইঠೠ׮!

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1"$-FBSOBCJMJUZ&YBNQMF "MHPSJUINJD"MJHONFOU • MLPח ݽٚ ੄ࢎѾ੿ җ੿ਸ ೞա੄ ܖ೐۽ р઱ೡ ࣻ ߆ী হਵ޲۽

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1"$-FBSOBCJMJUZ&YBNQMF "MHPSJUINJD"MJHONFOU • MLPח ݽٚ ੄ࢎѾ੿ җ੿ਸ ೞա੄ ܖ೐۽ р઱ೡ ࣻ ߆ী হਵ޲۽ • ೧ࢳ: • MLP۽ ޙઁܳ ಽѱ दః۰ݶ • ୭ࣗೠ ୐ Layer੄ ௼ӝ ী ؀೧ ੑ۱ ରਗ੄ ௼ӝ ݅ఀ Ѣٟઁғೠ Ѫ • ӒѪਸ فߣ૩ Layer੄ ௼ӝী ؀೧ ғೠ Ѫ • ݅ఀ਷ ࢠ೒݂೧ঠ ೟णदఆ ࣻ ੓ਸ Ѫ

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1"$-FBSOBCJMJUZBOE"MJHONFOU "MHPSJUINJD"MJHONFOU • ݽ؛੉ PAC ള۲ оמ ઑѤਸ ݅઒ೠ׮ݶ ׮਺੄ Alignment ܳ ࣻधਵ۽ ॶ ࣻ ੓਺ • ೧ࢳ: • ੐੄੄ ޙઁী ؀೧ࢲ Ӓ ޙઁܳ f1, f2, f3,..ਵ۽ ଂѓ ࣻ ੓׮Ҋ о੿ೞҊ • Ӓ ଂѐ૓ ٜࠗ࠙ਸ пп੄ न҃ݎਵ۽ ؀਽दఆ ࣻ ੓׮Ҋ о੿ೞݶ • Alignment ػ׮ח Ѫ਷ • пп ݽ؛ਸ ള۲दఆ ٸ, ӝઓী Mѐ ࡳ਷ Ѫࠁ׮ ੸ѱ ࡳইب غח ҃਋

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1"$-FBSOBCJMJUZBOE"MJHONFOU "MHPSJUINJD"MJHONFOU • ݽ؛੉ PAC ള۲ оמ ઑѤਸ ݅઒ೠ׮ݶ ׮਺੄ Alignment ܳ ࣻधਵ۽ ॶ ࣻ ੓਺ • ؊ ए਍ ೧ࢳ: • য۰਍ ޙઁܳ ए਍ ࣁࠗ ޙઁ۽ ଂѐࢲ ೟णदௌਸ ٸ, • Ӓ ए਍ ࣁࠗ ޙઁ пп੉ ੸਷ ؘ੉ఠ۽ب ੜ ߓ਎ ࣻ ੓঻ਵݶ જѷ׮!

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#FUUFS"MJHONFOU#FUUFS(FOFSBMJ[BUJPO "MHPSJUINJD"MJHONFOU • Alignmentܳ ੜ ೡ ࣻ ੓ח ݽ؛਷ ੜ ߓ਎ ࣻ ੓਺ • ׮਺ ઑѤਸ ݅઒ೠ׮ח о੿ ೞীࢲ….

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#FUUFS"MJHONFOU#FUUFS(FOFSBMJ[BUJPO "MHPSJUINJD"MJHONFOU • Alignmentܳ ੜ ೡ ࣻ ੓ח ݽ؛਷ ੜ ߓ਎ ࣻ ੓਺ • ׮਺ ઑѤਸ ݅઒ೠ׮ח о੿ ೞীࢲ….

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#FUUFS"MJHONFOU#FUUFS(FOFSBMJ[BUJPO "MHPSJUINJD"MJHONFOU • Alignmentܳ ੜ ೡ ࣻ ੓ח ݽ؛਷ ੜ ߓ਎ ࣻ ੓਺ • ппਸ ੜ ଂѐࢲ ߓ਋ח ੘স੉ ੜ ഛ݀ػ׮ݶ Ӓۧѱ ػ׮ח ܻࣗ • ցޖ ׼োೠ ݈ੋ٠ • ਋ܻ੄ ҙ੼ীࢲ BERTо MLP ա LSTM ࠁ׮ ੜೞח ੉ਬח? • BERT ҳઑо ޙ੢੄ ਫ਼੤੸ੋ ҳઑܳ ؊ Generalization ਸ ੜ ೮ӝ ٸޙ

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#FUUFS"MJHONFOU#FUUFS(FOFSBMJ[BUJPO "MHPSJUINJD"MJHONFOU • Generalization ਸ ੜ ޅೞח ݽ؛਷ য۰਍ ޙઁܳ ೟णೞӝ য۰਑ • ࣘغѱ ݈ೞ੗ݶ ݽ؛੄ ࠂ੟بী ٮۄ Ӓ ޙઁܳ ಽ “ल”੉ ࠁੋ׮ח Ѫ • п ޙઁী ؀ೠ ࢿמ

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#FUUFS"MJHONFOU#FUUFS(FOFSBMJ[BUJPO "MHPSJUINJD"MJHONFOU • Generalization ਸ ੜ ޅೞח ݽ؛਷ য۰਍ ޙઁܳ ೟णೞӝ য۰਑ • ࣘغѱ ݈ೞ੗ݶ ݽ؛੄ ࠂ੟بী ٮۄ Ӓ ޙઁܳ ಽ “ल”੉ ࠁੋ׮ח Ѫ • Monster Trainer (Path Searching) ޙઁী ؀ೠ п ݽ؛੄ ࢿמ

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$PODMVTJPO

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$PODMVTJPO $PODMVTJPO • যڃ न҃ݎ ݽ؛ਸ ഝਊ೧ࢲ যڃ ޙઁী ؀೧ࢲ ಽ ٸ • Ӓ ݽ؛੄ ҳઑо ޙઁ੄ ࢲࢎ ҳઑܳ ನҚೡ ࣻ ੓যঠ ೣ • ݅ড Ӓۧ૑ ঋ׮ݶ ই઱ ݆਷ ࢠ೒੉ ೙ਃೣ = ݽ؛੉ ޙઁܳ ੌ߈ചೡ ࣻ হ਺ • ࠂ੟ೠ ݽ؛੉ ԙ ੜ ಽ૑ח ঋ૑݅, рױೠ ݽ؛਷ ಽӝ য۰਑ • ਋ܻীѱ ઱ח दࢎ • औѱ ߓ਍ ݽ؛, рױೠ ഋక۽ ҳࢿػ ݽ؛੉ ঱য੄ ޷ޑೣਸ ੜ աఋյ ࣻ ੓ਸө? • അ੤੄ BERT ҳઑח ցޖ ࠂ੟ೠ Ѫ੉ ইקө?