To understand double descent, we need to understand VC theory.

We analyze generalization performance of over-parameterized learning methods for classification, under VC-theoretical framework. Recently, practitioners in Deep Learning discovered 'double descent' phenomenon, when large networks can fit perfectly available training data, and at the same time, achieve good generalization for future (test) data. The current consensus view is that VC-theoretical results cannot account for good generalization performance of Deep Learning networks. In contrast, this paper shows that double descent can be explained by VC-theoretical concepts, such as VC-dimension and Structural Risk Minimization. We also present empirical results showing that double descent generalization curves can be accurately modeled using classical VC-generalization bounds. Proposed VC-theoretical analysis enables better understanding of generalization curves for data sets with different statistical characteristics, such as low vs high-dimensional data and noisy data. In addition, we analyze generalization performance of transfer learning using pre-trained Deep Learning networks.

Understanding Double Descent Using VC-Theoretical Framework.

In spite of many successful applications of deep learning (DL) networks, theoretical understanding of their generalization capabilities and limitations remains limited. We present analysis of generalization performance of DL networks for classification under VC-theoretical framework. In particular, we analyze the so-called "double descent" phenomenon, when large overparameterized networks can generalize well, even when they perfectly memorize all available training data. This appears to contradict conventional statistical view that optimal model complexity should reflect an optimal balance between underfitting and overfitting, i.e., the bias-variance trade-off. We present VC-theoretical explanation of double descent phenomenon, under classification setting. Our theoretical explanation is supported by empirical modeling of double descent curves, using analytic VC-bounds, for several learning methods, such as support vector machine (SVM), least squares (LS), and multilayer perceptron classifiers. The proposed VC-theoretical approach enables better understanding of overparameterized estimators during second descent.

Achieving near-perfect light absorption in atomically thin transition metal dichalcogenides through band nesting.

Near-perfect light absorbers (NPLAs), with absorbance, [Formula: see text], of at least 99%, have a wide range of applications ranging from energy and sensing devices to stealth technologies and secure communications. Previous work on NPLAs has mainly relied upon plasmonic structures or patterned metasurfaces, which require complex nanolithography, limiting their practical applications, particularly for large-area platforms. Here, we use the exceptional band nesting effect in TMDs, combined with a Salisbury screen geometry, to demonstrate NPLAs using only two or three uniform atomic layers of transition metal dichalcogenides (TMDs). The key innovation in our design, verified using theoretical calculations, is to stack monolayer TMDs in such a way as to minimize their interlayer coupling, thus preserving their strong band nesting properties. We experimentally demonstrate two feasible routes to controlling the interlayer coupling: twisted TMD bi-layers and TMD/buffer layer/TMD tri-layer heterostructures. Using these approaches, we demonstrate room-temperature values of [Formula: see text]=95% at λ=2.8 eV with theoretically predicted values as high as 99%. Moreover, the chemical variety of TMDs allows us to design NPLAs covering the entire visible range, paving the way for efficient atomically-thin optoelectronics.