arXiv research

Dropout increases the generalization of neural networks by expanding the weight space.

Let $φ\in C^\infty(\Complex^n)$ be a given real valued function. We assume that $\pr\ddbarφ$ is non-degenerate of constant signature $(n_-,n_+)$ on $\Complex^n$. When $q=n_-$, it is well-known that the Bergman kernel for $(0,q)$ forms with respect to the $k$-th weight $e^{-2kφ}$, $k>0$, admits a full asymptotic expansi…

The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.

We introduce an asymptotic small noise expansion, a so called vol-of-vol expansion, for potentially infinite dimensional and rough stochastic volatility models. Thereby we extend the scope of existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, …

A new test method improves goodness-of-fit tests for copulas.

New method recovers signals from compressed measurements using generative networks with contractive layers.

In this paper, we computed the first three coefficients of the asymptotic expansion of Zelditch. We also proved that in general, the $k$-th coefficient is a polynomial of the curvature and its derivative of weight $k$.

Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.

Proves conjecture linking WRT invariants and homological blocks for plumbed 3-manifolds.

The study of pseudo-Anosov maps with minimum expansion factor using train tracks.

Study integrates reliability constraints into generation planning models.

Conventional deep learning classifiers are static in the sense that they are trained on a predefined set of classes and learning to classify a novel class typically requires re-training. In this work, we address the problem of Low-Shot network expansion learning. We introduce a learning framework which enables expandin…

We compute the first four coefficients of the asymptotic off-diagonal expansion of the Bergman kernel for the N-th power of a positive line bundle on a compact Kaehler manifold, and we show that the coefficient b_1 of the N^{-1/2} term vanishes when we use a K-frame. We also show that all the coefficients of the expans…

Polyhomogeneous expansions for Calabi-Yau metrics near singularities.

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…

New method improves neural network performance by focusing on steep function regions.

The paper provides non-asymptotic Edgeworth expansions for neural network outputs.

Investment decisions shift earlier as patience decreases, with implications for pasting conditions.

We study the heat trace for both the drifting Laplacian as well as Schrödinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term) asymptotic expansion of the heat trace for small times as well as a suitable remainder…

We consider functions defined by deep neural networks as definable objects in an o-miminal expansion of the real field, and derive an almost linear (in the number of weights) bound on sample complexity of such networks.

A new Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.

The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan-Hartogs domain $Ω^{B^{d_0}}(μ)$ endowed with the canonical metric $g(μ)$, we obtain an explicit formula for the Bergman kernel of the weighted…

In his seminal paper, A. N. Varchenko precisely investigates the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase. He expresses the order of this term by means of the geometry of the Newton polyhedron of the phase. The purpose of this paper is to generalize and improve his re…

The paper studies invariant weighted Bergman metrics on domains.

Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the stochastic gradient descent algorithm and apply a pre-defined sensitivity to th…

Derives a series expansion for Asian option pricing with polynomial jump-diffusion moments.

Sparse random features improve accuracy in data-scarce settings.

Estimates hybrid dynamical systems with polynomial expansions and Markovian switching.

Efficiently trains deep Gaussian processes with sparse approximations.

Study Bergman kernels on Kähler orbifolds with specific properties.

Bayesian inference for wide neural networks using Edgeworth expansion.

We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the …

Large deviation principle for deep neural networks with ReLU activation.

We consider a compact CR manifold with a transversal CR locally free circle action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion. As a consequence, we establish an equivariant Kodaira em…

New method uses Ricci curvature for hypergraph clustering, outperforming existing techniques.

This work presents a new classifier that is specifically designed to be fully interpretable. This technique determines the probability of a class outcome, based directly on probability assignments measured from the training data. The accuracy of the predicted probability can be improved by measuring more probability es…

New sampling method for Heston model reduces complexity.

Develops tropical geometry for weighted Hurwitz numbers, generalizing previous results.

We consider an asymptotic expansion of Kashaev's invariant or the colored Jones function for the torus link T(2,2m). We shall give q-series identity related to these invariants, and show that the invariant is regarded as a limit of q being N-th root of unity of the Eichler integral of the modular form of weight 3/2.

Continual lifelong learning is essential to many applications. In this paper, we propose a simple but effective approach to continual deep learning. Our approach leverages the principles of deep model compression, critical weights selection, and progressive networks expansion. By enforcing their integration in an itera…

Deep multi-task learning benefits from low intrinsic dimensionality, leading to better generalization.

Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is also known as online quantile estimation. This area is relevant to the analysis …

In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In the second part we develop a Hamiltonian approach to the method of holographic re…

This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=κ_{t}\left(θ_{t}-V_{t}\right)dt+λ_{t}V_{t}dB_{t}$. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, e…

The study examines numerical aspects of Karhunen-Loève expansions for stochastic processes.

We use the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces $M_{g,s}^{disc}$ (discrete volumes), to express Gaussian means…

Expanding neural networks improves their learning from noisy data.

Rescaling expansiveness proven for k*-expansive vector fields.