<latexit 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Needed for <latexit 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gradient descent <latexit 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! problem with ReLu! <latexit sha1_base64="fx+HffkAoo+Y8HF+nawz9WhLq4g=">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</latexit> ! = ei·: Fourier features ) translation invariant kernels. <latexit sha1_base64="wWydWg5M93YZwdc1onAt6ESmkYE=">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</latexit> For vt 2 V, ||vt ||1 + ||Dvt ||1 + ||D2vt ||1 6 ||vt ||V <latexit 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Condition 1: regularity. <latexit 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Example: Mattern kernel ehaviour of GD in the training of RKHS-NODE. In the following, we show how one can enforce he hypothesis of Theorem 2 to be verified and prove two global convergence results. The first one elies on suitably choosing matrices A and B in order to satisfy Eq. (15) and applies in the case f infinite width, i.e. with residual layers in a universal RKHS. The second result recovers global onvergence in a finite width regime, relying on a high number r of Random Fourier Features. or the sake of readability we only consider here the case where V belongs to a restricted class of KHSs and refer to Appendix D for more general results and complete proofs. For some positive arameter ⌫ > 0 we consider the Matérn kernel k defined in [57]: 8r 2 R +, k(r) = 21 ⌫ (⌫) p 2⌫ 2⇡ r ! ⌫ K ⌫ ⇣p 2⌫ 2⇡ r ⌘ , (17) where is the Gamma function and K ⌫ is the modified Bessel function of the second kind. Equiva- ently, k can be defined by its frequency distribution over Rq as: 8x 2 Rq, k(kxk) = Z Rq eıhx,!iµq (!)d! with µq (!) = Cq,⌫ (1 + k!k2 2⌫ ) ( q 2 +⌫) (18) nd Cq,⌫ a normalizing constant. For every q 1, such a function is known to define a structure f vector-valued RKHS Vq over Rq corresponding to the Sobolev space H⌫+q/2(Rq, Rq) [52, 57]. he associated kernel is given for every z, z0 2 Rq by: Kq (z, z0) = k(kz z0k) Id q . Note that is important for this RKHS to depend on the ambient dimension q. In particular the Sobolev pace Hs(Rq, Rq) is a RKHS if and only if it has regularity s > q/2. Assuming ⌫ > 2, µq further dmits up to 4 finite order moment implying that k is four times differentiable at 0 [28]. Then Vq atisfies Assumption 1 with some constant depending only on ⌫ and given by Property 4: = p k(0) + p k00(0) + q k(4)(0) = 1 + r ⌫ ⌫ 1 + s 3⌫2 (⌫ 1)(⌫ 2). (19) <latexit 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ˆ k(!) / (1 + ||!||2/⌫) (d/2+⌫) <latexit sha1_base64="2xV+w5agszY16YT/aWJPdJuKehg=">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</latexit> V = H⌫ (Sobolev) <latexit sha1_base64="74mWKZWxPGMDwJqADej242G+u3o=">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</latexit> Proposition: <latexit sha1_base64="5TTBalfein0utJCxvg4yERu5TQo=">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</latexit> x x0 <latexit 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⌫ = 1: Gaussian. <latexit 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x x0 <latexit 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(⌫ > 2) <latexit sha1_base64="hKoF5FFj1XhZNvs94WTqL+GTghw=">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</latexit> ⌫ = 0: Laplacian.
problem (even for linear networks) Open Problems! <latexit 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<latexit 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Training inner weights: <latexit 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RKHS <latexit 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Banach space <latexit 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(Barron) <latexit 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✓in <latexit 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✓out