Self-Paced Learning: an Implicit Regularization Perspective

Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by minimizer function. Existing methods usually pursue this by artificially designing the explicit form of SPL regularizer. In this paper, we focus on the minimizer function, and study a group of new regularizer, named self-paced implicit regularizer that is deduced from robust loss function. Based on the convex conjugacy theory, the minimizer function for self-paced implicit regularizer can be directly learned from the latent loss function, while the analytic form of the regularizer can be even known. A general framework (named SPL-IR) for SPL is developed accordingly. We demonstrate that the learning procedure of SPL-IR is associated with latent robust loss functions, thus can provide some theoretical inspirations for its working mechanism. We further analyze the relation between SPL-IR and half-quadratic optimization. Finally, we implement SPL-IR to both supervised and unsupervised tasks, and experimental results corroborate our ideas and demonstrate the correctness and effectiveness of implicit regularizers.Comment: 12 pages, 3 figure

44-choosability of planar graphs with 44-cycles far apart via the Combinatorial Nullstellensatz

By a well-known theorem of Thomassen and a planar graph depicted by Voigt, we know that every planar graph is $5$-choosable, and the bound is tight. In 1999, Lam, Xu and Liu reduced $5$ to $4$ on $C_4$-free planar graphs. In the paper, by applying the famous Combinatorial Nullstellensatz, we design an effective algorithm to deal with list coloring problems. At the same time, we prove that a planar graph $G$ is $4$-choosable if any two $4$-cycles having distance at least $5$ in $G$, which extends the result of Lam et al

Ultrathin Acoustic Parity-Time Symmetric Metasurface Cloak

Invisibility or unhearability cloaks have beenmade possible by using metamaterials enabling light or sound to flow around obstacle without the trace of reflections or shadows. Metamaterials are known for being flexible building units that can mimic a host of unusual and extreme material responses, which are essential when engineering artificial material properties to realize a coordinate transforming cloak. Bending and stretching the coordinate grid in space require stringent material parameters; therefore, small inaccuracies and inevitablematerial losses become sources for unwanted scattering that are decremental to the desired effect.These obstacles further limit the possibility of achieving a robust concealment of sizeable objects from either radar or sonar detection. By using an elaborate arrangement of gain and lossy acousticmedia respecting parity-time symmetry, we built a one-way unhearability cloak able to hide objects seven times larger than the acoustic wavelength. Generally speaking, our approach has no limits in terms of working frequency, shape, or size, specifically though we demonstrate how, in principle, an object of the size of a human can be hidden from audible sound