Given sparse depths and the corresponding RGB images, depth completion aims
at spatially propagating the sparse measurements throughout the whole image to
get a dense depth prediction. Despite the tremendous progress of
deep-learning-based depth completion methods, the locality of the convolutional
layer or graph model makes it hard for the network to model the long-range
relationship between pixels. While recent fully Transformer-based architecture
has reported encouraging results with the global receptive field, the
performance and efficiency gaps to the well-developed CNN models still exist
because of its deteriorative local feature details. This paper proposes a Joint
Convolutional Attention and Transformer block (JCAT), which deeply couples the
convolutional attention layer and Vision Transformer into one block, as the
basic unit to construct our depth completion model in a pyramidal structure.
This hybrid architecture naturally benefits both the local connectivity of
convolutions and the global context of the Transformer in one single model. As
a result, our CompletionFormer outperforms state-of-the-art CNNs-based methods
on the outdoor KITTI Depth Completion benchmark and indoor NYUv2 dataset,
achieving significantly higher efficiency (nearly 1/3 FLOPs) compared to pure
Transformer-based methods. Code is available at
https://github.com/youmi-zym/CompletionFormer.

本文提出了一个联合卷积注意力和 Transformer 块的深度完成模型，其在建筑物深度完成基准和室内 NYUv2 数据集上最新的 CNNs 方法实现较高的效率，相比之下，有效地降低了 1/3 FLOPs。

CompletionFormer：基于卷积和 Vision  Transformers 的深度完成

CompletionFormer: Depth Completion with Convolutions and Vision  Transformers

With the increasing interest in deeper understanding of the loss surface of
many non-convex deep models, this paper presents a unifying framework to
establish the local/global optima equivalence of the optimization problems
arising from training of such non-convex models. Using the local openness
property of the underlying training models, we provide simple sufficient
conditions under which any local optimum of the resulting optimization problem
is globally optimal. We first completely characterize the local openness of the
symmetric and non-symmetric matrix multiplication mapping in its range. Then we
use our characterization to: 1) provide a simple proof for the classical result
of Burer-Monteiro and extend it to non-continuous loss functions. 2) show that
every local optimum of two layer linear networks is globally optimal. Unlike
many existing results in the literature, our result requires no assumption on
the target data matrix Y, and input data matrix X. 3) Develop almost complete
characterization of the local/global optima equivalence of multi-layer linear
neural networks. We provide various counterexamples to show the necessity of
each of our assumptions. 4) Show global/local optima equivalence of non-linear
deep models having certain pyramidal structure. Unlike some existing works, our
result requires no assumption on the differentiability of the activation
functions and can go beyond "full-rank" cases.

该篇论文提出了一个统一框架，确定了训练非凸模型产生的优化问题的局部 / 全局最优等价性，讨论了线性神经网络和具有一定金字塔结构的非线性深层模型的局部 / 全局最优等价性，并提供了简单的充分条件。

学习深度模型：临界点和局部开放性

Learning Deep Models: Critical Points and Local Openness

While the optimization problem behind deep neural networks is highly
non-convex, it is frequently observed in practice that training deep networks
seems possible without getting stuck in suboptimal points. It has been argued
that this is the case as all local minima are close to being globally optimal.
We show that this is (almost) true, in fact almost all local minima are
globally optimal, for a fully connected network with squared loss and analytic
activation function given that the number of hidden units of one layer of the
network is larger than the number of training points and the network structure
from this layer on is pyramidal.

本文研究完全连接网络的优化问题，发现在具有金字塔结构、使用平方损失函数和分析激活函数的情况下，只要网络每层隐藏单元数大于训练点数，几乎所有的局部最小值都是全局最优解。