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zfso.TT General p spin model Hulot the centered Gaussian with yN - PDF document

Jan 24, 2023 •453 likes •514 views

Sherrington Kirkpatrick model Hn Ily R 6 Wo Wn GOEIN HN 161 21 j W La G 1Gt o N 10,1 Gigi N centered Hw 16 Gaussian process oey yw ELHnldthd D zfso.TT General p spin model Hulot the centered Gaussian with yN EE l I ELHnlolH.de f

  1. Sherrington Kirkpatrick model Hn Ily R 6 Wo Wn GOEIN HN 161 21 j W La G 1Gt o N 10,1 Gigi N centered Hw 16 Gaussian process oey yw ELHnldthd D zfso.TT General p spin model Hulot the centered Gaussian with yN EE l I ELHnlolH.de f Ngc Hz Zzz CEXk Sk 347 3 G oak LW Halo Ez 7 Wk indep gaussian tensors 112 how convex many local minima Hnl 6 maximize subj to o c LI lb Q solve this approx in poly time can we NH 5 S EL 11 14N st input Output zz N 2 N n HN lo Ci e Ancoats p n max g

  2. IN H feet yN this Is possible V E o V E If not C 70 Exact optimization PCH.vlo hst 21 mgxth.to Upper bd Refutation st c IR ALG w 4 mix Halo ALG W P 7 Halo 2 ALG W E HE m no algorithm can do Worst Unless P NP case ab Ao b 07 3 cmf Parisi's formula Typical value o nondecr So'HHdt soo Lt V 2K 0,1 l 54H 20lt.xl HHG.ro lt xlTT zollt.xl o Io Dx IR 016 7 1 1 lo i EHIdHH N3t I fo't g lHHtIdt Rr Igloo vt mix Hnk The OPT v info Pcr OPTN firm is strictly convex Pcr The igf par ft EU at unique achieved 8 EU

  3. Interpretation of I Gibbs Consider measure Nb L Zyp EP Mwp o o LILY 4 e mix Halo b Se Halo Unit Se E Cf E Mw p 02 Iw o Mw p Mw p Hid V ko law of Pp N N N soo o D on Up Pp w CEO t line t Pip structure of r on 6,1 I No overlap gap strictly incr r Fct ta EEo at Il Overlap gap e srctntl rlt.is Htt rct is t if Ceo t strictly increasing for te lo g constant above ko 1197 of'Ese left stts a

  4. ft 0,9 1 E Algorithms rico D Rao L 113 rll w.co sottEl9D Jo 3 rfttodtJ 3 htt Htt 3 Htt non deer fittlott soo f L Z U r n f L U non dear Then HE PCH is achieved of alg Assume Thin fifth with linear complexity St Pif Hulot infzRH t 1 Rmt Pan signaler in L Pcr intfift an.t fact higfsinuf I hear opt no overlap gap Le m If then in.fi crl iyfuPC8 OPT g linear time 1g no gap TE te of If Greoltry N 70 sit ACH Isa's 4 e mix HNK 21 a no overlapgap For SK Conj no poly time 21g V E If overlap gap Conjecture

  5. P Unless NP AMP algo Construct Proof Sk W f try xt it ftp.t.sfs.icxi I x zt ftG 7 zt zt In Czt o t E o 8 7 8 I I 8 20 st evolution drift SDE choose coefficients of SDE opt solving a stock opt contr infzPL'T B E Exit z Nco 8 Id x

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