What neural networks learn depends fundamentally on the geometry of the
underlying loss function. We study how different regularizers affect the
geometry of this function. One of the most basic geometric properties of a
smooth function is whether it is Morse or not. For nonlinear deep neural
networks, the unregularized loss function $L$ is typically not Morse. We
consider several different regularizers, including weight decay, and study for
which regularizers the regularized function $L_\epsilon$ becomes Morse.

神经网络学习的关键取决于损失函数的几何形态，我们通过研究不同的正则化方法对函数的几何形态的影响，发现在非线性深度神经网络中，正则化前的损失函数通常不是莫尔斯函数；我们考虑了几种不同的正则化方法，包括权重衰减，研究发现哪些正则化方法可以使得正则化后的函数成为莫尔斯函数。

正则化对损失函数的几何影响

How regularization affects the geometry of loss functions

Integrating high-level semantically correlated contents and low-level
anatomical features is of central importance in medical image segmentation.
Towards this end, recent deep learning-based medical segmentation methods have
shown great promise in better modeling such information. However, convolution
operators for medical segmentation typically operate on regular grids, which
inherently blur the high-frequency regions, i.e., boundary regions. In this
work, we propose MORSE, a generic implicit neural rendering framework designed
at an anatomical level to assist learning in medical image segmentation. Our
method is motivated by the fact that implicit neural representation has been
shown to be more effective in fitting complex signals and solving computer
graphics problems than discrete grid-based representation. The core of our
approach is to formulate medical image segmentation as a rendering problem in
an end-to-end manner. Specifically, we continuously align the coarse
segmentation prediction with the ambiguous coordinate-based point
representations and aggregate these features to adaptively refine the boundary
region. To parallelly optimize multi-scale pixel-level features, we leverage
the idea from Mixture-of-Expert (MoE) to design and train our MORSE with a
stochastic gating mechanism. Our experiments demonstrate that MORSE can work
well with different medical segmentation backbones, consistently achieving
competitive performance improvements in both 2D and 3D supervised medical
segmentation methods. We also theoretically analyze the superiority of MORSE.

本文提出了一种名为 MORSE 的通用隐式神经渲染框架，以医学图像分割为例，通过多尺度像素级特征的并行优化和自适应细化边界区域的特征聚合，相比基于网格的曲卡尔卷积能更好地整合在高水平的语义相关内容和低水平的解剖特征，从而在 2D 和 3D 监督医学分割方法中持续取得了有竞争力的性能提升。

随机专家医学图像分割的隐式解剖渲染

Implicit Anatomical Rendering for Medical Image Segmentation with  Stochastic Experts

We introduce Morse, a recurrent encoder-decoder model that produces
morphological analyses of each word in a sentence. The encoder turns the
relevant information about the word and its context into a fixed size vector
representation and the decoder generates the sequence of characters for the
lemma followed by a sequence of individual morphological features. We show that
generating morphological features individually rather than as a combined tag
allows the model to handle rare or unseen tags and outperform whole-tag models.
In addition, generating morphological features as a sequence rather than e.g.\
an unordered set allows our model to produce an arbitrary number of features
that represent multiple inflectional groups in morphologically complex
languages. We obtain state-of-the art results in nine languages of different
morphological complexity under low-resource, high-resource and transfer
learning settings. We also introduce TrMor2018, a new high accuracy Turkish
morphology dataset. Our Morse implementation and the TrMor2018 dataset are
available online to support future research\footnote{See
\url{this https URL} for a Morse implementation in
Julia/Knet \cite{knet2016mlsys} and \url{this https URL}
for the new Turkish dataset.}.

本文介绍 Morse，一种循环编码器解码器模型，用于生成语句中每个单词的形态分析。该模型可生成单独的形态特征，表现出色且能处理少见标签和各种复杂语言。