We present a pose adaptive few-shot learning procedure and a two-stage data
interpolation regularization, termed Pose Adaptive Dual Mixup (PADMix), for
single-image 3D reconstruction. While augmentations via interpolating
feature-label pairs are effective in classification tasks, they fall short in
shape predictions potentially due to inconsistencies between interpolated
products of two images and volumes when rendering viewpoints are unknown.
PADMix targets this issue with two sets of mixup procedures performed
sequentially. We first perform an input mixup which, combined with a pose
adaptive learning procedure, is helpful in learning 2D feature extraction and
pose adaptive latent encoding. The stagewise training allows us to build upon
the pose invariant representations to perform a follow-up latent mixup under
one-to-one correspondences between features and ground-truth volumes. PADMix
significantly outperforms previous literature on few-shot settings over the
ShapeNet dataset and sets new benchmarks on the more challenging real-world
Pix3D dataset.

本文提出了一种姿态自适应的 few-shot 学习方法以及两阶段数据插值规则，称为姿态自适应双混合（PADMix），用于单幅图像的 3D 重建，并在 ShapeNet 数据集上实现了显著优于先前文献的结果，并在更具挑战性的实际数据集 Pix3D 上创新了最好的表现。

针对少样本单视角三维重建的姿态自适应双 Mixup

Pose Adaptive Dual Mixup for Few-Shot Single-View 3D Reconstruction

Classically, data interpolation with a parametrized model class is possible
as long as the number of parameters is larger than the number of equations to
be satisfied. A puzzling phenomenon in deep learning is that models are trained
with many more parameters than what this classical theory would suggest. We
propose a partial theoretical explanation for this phenomenon. We prove that
for a broad class of data distributions and model classes, overparametrization
is necessary if one wants to interpolate the data smoothly. Namely we show that
smooth interpolation requires $d$ times more parameters than mere
interpolation, where $d$ is the ambient data dimension. We prove this universal
law of robustness for any smoothly parametrized function class with polynomial
size weights, and any covariate distribution verifying isoperimetry. In the
case of two-layers neural networks and Gaussian covariates, this law was
conjectured in prior work by Bubeck, Li and Nagaraj. We also give an
interpretation of our result as an improved generalization bound for model
classes consisting of smooth functions.

本文研究通过参数化模型类进行数据插值的现象与深度学习中使用数量远高于方程数的参数进行拟合训练的关系，证明了平滑插值需要的参数数量是简单插值的 $d$ 倍， 并将结果解释为改进的模型泛化边界。

通过等周性得出的强韧普适定律

A Universal Law of Robustness via Isoperimetry

The over-parameterized models attract much attention in the era of data
science and deep learning. It is empirically observed that although these
models, e.g. deep neural networks, over-fit the training data, they can still
achieve small testing error, and sometimes even {\em outperform} traditional
algorithms which are designed to avoid over-fitting. The major goal of this
work is to sharply quantify the benefit of data interpolation in the context of
nearest neighbors (NN) algorithm. Specifically, we consider a class of
interpolated weighting schemes and then carefully characterize their asymptotic
performances. Our analysis reveals a U-shaped performance curve with respect to
the level of data interpolation, and proves that a mild degree of data
interpolation {\em strictly} improves the prediction accuracy and statistical
stability over those of the (un-interpolated) optimal $k$NN algorithm. This
theoretically justifies (predicts) the existence of the second U-shaped curve
in the recently discovered double descent phenomenon. Note that our goal in
this study is not to promote the use of interpolated-NN method, but to obtain
theoretical insights on data interpolation inspired by the aforementioned
phenomenon.

本研究通过研究最近邻算法的类等权重方案，量化了数据内插法的好处，并证明了数据内插法可以在最佳 kNN 算法的基础上具有更好的预测精度和统计稳定性，在解释二次下降现象方面提供了理论依据。