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of 72
pro vyhledávání: '"Belius, David"'
This paper conducts a comprehensive study of the learning curves of kernel ridge regression (KRR) under minimal assumptions. Our contributions are three-fold: 1) we analyze the role of key properties of the kernel, such as its spectral eigen-decay, t
Externí odkaz:
http://arxiv.org/abs/2410.17796
We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in the over-parameterized regime for a fixed input dimension. For kernels w
Externí odkaz:
http://arxiv.org/abs/2402.01297
Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a pre-trained d
Externí odkaz:
http://arxiv.org/abs/2310.00987
Autor:
Belius, David, Fröber, Leon
The Sherrington-Kirkpatrick Hamiltonian is a random quadratic function on the high-dimensional sphere. This article studies the ground state (i.e. maximum) of this Hamiltonian with external field, or more generally with a non-linear "spike" term. We
Externí odkaz:
http://arxiv.org/abs/2307.14836
Spin glass models involving multiple replicas with constrained overlaps have been studied in [FPV92; PT07; Pan18a]. For the spherical versions of these models [Ko19; Ko20] showed that the limiting free energy is given by a Parisi type minimization. I
Externí odkaz:
http://arxiv.org/abs/2304.04031
When can the input of a ReLU neural network be inferred from its output? In other words, when is the network injective? We consider a single layer, $x \mapsto \mathrm{ReLU}(Wx)$, with a random Gaussian $m \times n$ matrix $W$, in a high-dimensional s
Externí odkaz:
http://arxiv.org/abs/2302.14112
Autor:
Belius, David, Schmidt, Marius A.
We study the number of local maxima with given radial derivative of spherical mixed $p$-spin models and prove that the second moment matches the square of the first moment on exponential scale for arbitrary mixtures and any radial derivative. This is
Externí odkaz:
http://arxiv.org/abs/2207.14361
Autor:
Belius, David, Schmidt, Marius A.
We solve the Thouless-Anderson-Palmer (TAP) variational principle associated to the spherical pure $p$-spin mean field spin glass Hamiltonian and present a detailed phase diagram. In the high temperature phase the maximum of variational principle is
Externí odkaz:
http://arxiv.org/abs/2207.02821
Autor:
Belius, David
This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed $p$-spin
Externí odkaz:
http://arxiv.org/abs/2204.00681
Autor:
Banerjee, Debapratim, Belius, David
We prove the convergence in distribution of the fluctuations of the free energy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing $2$-spin component at high enough temperature. The limit is Gaussian, and the fluctuations are seen
Externí odkaz:
http://arxiv.org/abs/2108.03109