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hessian-based-analysis.pdf

 hessian-based-analysis.pdf

11/11にDLHacksで発表した内容です。
GIthubにソースコードもUPしています。
https://github.com/mtkwT/Hessian-based-analysis-tensorflow

motokawa tetsuya

November 11, 2019
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  1. ΞδΣϯμ w ࿦จ֓ཁ w എܠ w ϔοηߦྻ w )FTTJBOCBTFE"OBMZTJTͱ͸ w

    TIBSQNJOJNVNWTqBUNJOJNVN w ࣮ݧ w ࣮ݧઃఆ w ࣮૷ w ߟ࡯ 4
  2. ϔοηߦྻ w ଛࣦؔ਺ʹ͓͚Δೋ֊ඍ෼શମͰߏ੒͞ΕΔߦྻ w ݻ༗஋ͷූ߸ɾେ͖͞ʹΑͬͯہॴೋ࣍ۙࣅͨ͠ͱ͖ͷܗঢ়͕Θ͔Δ w χϡʔϥϧωοτͰ͸ޯ഑ಉ༷ ޡࠩٯ఻೻๏ͰٻΊΔ͜ͱ͕Մೳʢ13.-ষʣ 8 ݻ༗஋͕શͯਖ਼ɿۃখ஋

    ݻ༗஋͕શͯෛɿۃେ஋ ݻ༗஋ʹਖ਼ෛͲͪΒ΋͋ΔɿҌ఺ ݻ༗஋ʹؚ͕·ΕΔɿ൑அෆೳʢϓϥτʔʁʣ IUUQXXXUIPUIDIJMESFODPNDIBQUFSCDGGFG
  3. )FTTJBOCBTFE"OBMZTJTͱ͸ w χϡʔϥϧωοτʹ͓͚ΔֶशͷڍಈΛϔοηߦྻͷݻ༗஋Λ༻͍ͯ෼ੳ͢Δख๏ w ݹ͘͸-V$VO ʹΑͬͯݴٴ w 9 ֶशޙͷଛࣦؔ਺ʹ͓͚Δϔοηߦྻͷݻ༗஋෼෍ ʢ)FTTJBOTQFDUSVNʣ

    ΄ͱΜͲͷݻ༗஋͸ʹ͍ۙ஋ΛऔΔ͕ɼҰ෦ͷඇৗʹେ͖ͳ ݻ༗஋͕ଘࡏ͢Δ ֶशޙͷύϥϝʔλۭؒͰ͸ɼ΄ͱΜͲͷ࣍ݩͰฏୱͳ஍ܗɼ গ਺ͷ࣍ݩ͕ٸफ़ʹۂ͕͍ͬͯΔ IUUQZBOOMFDVODPNFYECQVCMJTQEGMFDVOCQEG
  4. :BP ͷओு • sharp minimumΑΓ΋flat minimumͷํ͕൚Խੑೳ͕ߴ͍ʢHochreiter+ 1997ʣ • 11 ϔοηߦྻͷݻ༗஋͕খ͍͞

    όοναΠζ͕খ͍࣌͞ʹ౸ୡ ϔοηߦྻͷݻ༗஋͕େ͖͍ όοναΠζ͕େ͖͍࣌ʹ౸ୡ
  5. ࣮ݧઃఆ w σʔληοτ$*'"3 w Ϟσϧ࿦จ಺ͷ$ w ࿦จͷ࣮ݧೖྗʹؔ͢Δϔοηߦྻͷݻ༗஋෼ੳ w ࠓճͷ࣮ݧॏΈʹؔ͢Δϔοηߦྻͷݻ༗஋෼ੳ w

    શͯͷॏΈύϥϝʔλʹؔ͢Δϔοηߦྻ͸ڊେ w ͦ͜Ͱࠓճ͸࠷ऴ૚ͷॏΈʹؔ͢ΔϔοηߦྻͷΈར༻ʢޡࠩٯ఻೻๏ͷܭࢉ͕࠷΋ܰྔʣ w όοναΠζ   Ͱ࣮ݧ w .PNFOUVN4(%MS NPNFOUVN FQPDI 13
  6. ࣮ݧઃఆʢ:BP ʣ 14 1 2 i-1 i k-1 k ɾɾɾ

    X Y ଛࣦؔ਺ ೖྗͰͷ ϔοηߦྻ ݻ༗஋ ɾɾɾ ɾɾɾ
  7. ࣮ݧઃఆʢࠓճʣ 15 1 2 i-1 i k-1 k ɾɾɾ X

    Y ଛࣦؔ਺ ࠷ऴ૚Ͱͷ ϔοηߦྻ ݻ༗஋ ɾɾɾ ɾɾɾ
  8. ؔ࿈࿦จϦετ w )PDISFJUFS 'MBUNJOJNB /FVSBM$PNQVUBUJPO  IUUQ XXXCJPJOGKLVBUQVCMJDBUJPOTPMEFSQEG w -V$VO

    &⒏DJFOU#BDLQSPQ /FVSBMOFUXPSLT5SJDLTPGUIFUSBEF   IUUQZBOOMFDVODPNFYECQVCMJTQEGMFDVOCQEG w ,FTLBS 0O-BSHF#BUDI5SBJOJOHGPS%FFQ-FBSOJOH(FOFSBMJ[BUJPO(BQ BOE4IBSQ.JOJNB  *$-3 IUUQTBSYJWPSHBCT w 4BHVO &NQJSJDBM"OBMZTJTPGUIF)FTTJBOPG0WFS1BSBNFUSJ[FE/FVSBM /FUXPSLT  *$-3 IUUQTBSYJWPSHBCT 24