AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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We study the non-parametric estimation of the roughness of a path from discretely sampled observations. Our approach is based on the concept of normalized power variation of a path. The estimator identifies a variation index by comparing coarse increments with local sums of fine increments. We prove pathwise consistenc...
Probability-flow ordinary differential equations (PF-ODEs) are widely used as deterministic samplers for score-based diffusion models. Their usual justification is that the Fokker--Planck equation of a diffusion can be rewritten as a continuity equation driven by the score function of the forward diffusion. This identi...
The probability-flow ordinary differential equation (PF-ODE) associated with a diffusion process is widely used in score-based generative modeling as a deterministic sampler that reproduces the marginal distributions of the diffusion. The validity of this marginal-matching property depends on the well-posedness of an o...
We develop an intrinsic calculus for smooth functions of paths of arbitrarily low regularity on smooth manifolds. The regularity of paths is defined in terms of a $p$-th variation tensor along a sequence of partitions, for an arbitrary integer $p$; this tensor is constructed as a local symmetric tensor measure along th...
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