Training deep neural networks (DNNs) from noisy labels is an important and
challenging task. However, most existing approaches focus on the corrupted
labels and ignore the importance of inherent data structure. To bridge the gap
between noisy labels and data, inspired by the concept of potential energy in
physics, we propose a novel Potential Energy based Mixture Model (PEMM) for
noise-labels learning. We innovate a distance-based classifier with the
potential energy regularization on its class centers. Embedding our proposed
classifier with existing deep learning backbones, we can have robust networks
with better feature representations. They can preserve intrinsic structures
from the data, resulting in a superior noisy tolerance. We conducted extensive
experiments to analyze the efficiency of our proposed model on several
real-world datasets. Quantitative results show that it can achieve
state-of-the-art performance.

基于潜在能量的混合模型（PEMM）用于噪声标签学习，通过将深度学习骨干与我们提出的分类器相结合，可以得到具有更好特征表示和优越噪声容忍性的鲁棒网络。

基于势能的噪声标记学习混合模型

Potential Energy based Mixture Model for Noisy Label Learning

The dynamical formulation of the optimal transport can be extended through
various choices of the underlying geometry ($\textit{kinetic energy}$), and the
regularization of density paths ($\textit{potential energy}$). These
combinations yield different variational problems ($\textit{Lagrangians}$),
encompassing many variations of the optimal transport problem such as the
Schr\"odinger bridge, unbalanced optimal transport, and optimal transport with
physical constraints, among others. In general, the optimal density path is
unknown, and solving these variational problems can be computationally
challenging. Leveraging the dual formulation of the Lagrangians, we propose a
novel deep learning based framework approaching all of these problems from a
unified perspective. Our method does not require simulating or backpropagating
through the trajectories of the learned dynamics, and does not need access to
optimal couplings. We showcase the versatility of the proposed framework by
outperforming previous approaches for the single-cell trajectory inference,
where incorporating prior knowledge into the dynamics is crucial for correct
predictions.

通过动态形式化的最优输运，结合底层几何学（动能）选择和密度路径（势能）的正则化，构造了多种变分问题（Lagrangians），包括 Schrödinger 桥、非平衡最优输运和具有物理约束的最优输运等。采用双重 Lagrangians 的对偶形式提出了一种新颖的基于深度学习的统一框架，无需模拟或反向传播经过学习动力学的轨迹，并且不需要访问最优耦合。通过在单细胞轨迹推断中融入先验知识，展示了所提框架的多功能性能，从而在正确预测方面优于先前方法。

求解 Wasserstein 拉格朗日流的计算框架

A Computational Framework for Solving Wasserstein Lagrangian Flows

The development of accurate and transferable machine learning (ML) potentials
for predicting molecular energetics is a challenging task. The process of data
generation to train such ML potentials is a task neither well understood nor
researched in detail. In this work, we present a fully automated approach for
the generation of datasets with the intent of training universal ML potentials.
It is based on the concept of active learning (AL) via Query by Committee
(QBC), which uses the disagreement between an ensemble of ML potentials to
infer the reliability of the ensemble's prediction. QBC allows the presented AL
algorithm to automatically sample regions of chemical space where the ML
potential fails to accurately predict the potential energy. AL improves the
overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test
cases by mitigating human biases in deciding what new training data to use. AL
also reduces the training set size to a fraction of the data required when
using naive random sampling techniques. To provide validation of our AL
approach we develop the COMP6 benchmark (publicly available on GitHub), which
contains a diverse set of organic molecules. Through the AL process, it is
shown that the AL-based potentials perform as well as the ANI-1 potential on
COMP6 with only 10% of the data, and vastly outperforms ANI-1 with 25% the
amount of data. Finally, we show that our proposed AL technique develops a
universal ANI potential (ANI-1x) that provides accurate energy and force
predictions on the entire COMP6 benchmark. This universal ML potential achieves
a level of accuracy on par with the best ML potentials for single molecule or
materials, while remaining applicable to the general class of organic molecules
comprised of the elements CHNO.

我们基于主动学习算法，提出了一种全自动方法，用于生成分子能量的数据集，能够支持深度学习算法 ANI 在含有 CHNO 的有机分子的所有情况下实现精确的能量和力预测。

简洁即美：主动学习中的化学空间采样

Less is more: sampling chemical space with active learning

We study configurations of points on the unit sphere that minimize potential
energy for a broad class of potential functions (viewed as functions of the
squared Euclidean distance between points). Call a configuration sharp if there
are m distances between distinct points in it and it is a spherical
(2m-1)-design. We prove that every sharp configuration minimizes potential
energy for all completely monotonic potential functions. Examples include the
minimal vectors of the E_8 and Leech lattices. We also prove the same result
for the vertices of the 600-cell, which do not form a sharp configuration. For
most known cases, we prove that they are the unique global minima for energy,
as long as the potential function is strictly completely monotonic. For certain
potential functions, some of these configurations were previously analyzed by
Yudin, Kolushov, and Andreev; we build on their techniques. We also generalize
our results to other compact two-point homogeneous spaces, and we conclude with
an extension to Euclidean space.

研究了在单位球面上，通过一定的构造方法得到的具有球形设计的尖锐配置对于大部分势函数都是全局极小值，这些势函数包括 E8 和 Leech 格子的最小向量。