We investigate Siamese networks for learning related embeddings for augmented
samples of molecular conformers. We find that a non-contrastive (positive-pair
only) auxiliary task aids in supervised training of Euclidean neural networks
(E3NNs) and increases manifold smoothness (MS) around point-cloud geometries.
We demonstrate this property for multiple drug-activity prediction tasks while
maintaining relevant performance metrics, and propose an extension of MS to
probabilistic and regression settings. We provide an analysis of representation
collapse, finding substantial effects of task-weighting, latent dimension, and
regularization. We expect the presented protocol to aid in the development of
reliable E3NNs from molecular conformers, even for small-data drug discovery
programs.

本研究探讨孪生网络用于学习与分子构象相关的嵌入式样本，并发现一种非对比式辅助任务可辅助监督学习和增加流形平滑度。我们在多项药物活性预测任务中展示了此属性，并提出将流形平滑度扩展到概率和回归设置。我们针对表征陷落进行了分析，发现任务加权、潜在维数和正则化等因素都有显著影响。我们期望提供的协议能帮助开发出可靠的 E3NNs 用于分子构象的小数据药物发现计划。

SupSiam：分子构象学习的非对比辅助损失

SupSiam: Non-contrastive Auxiliary Loss for Learning from Molecular  Conformers

We present e3nn, a generalized framework for creating E(3) equivariant
trainable functions, also known as Euclidean neural networks. e3nn naturally
operates on geometry and geometric tensors that describe systems in 3D and
transform predictably under a change of coordinate system. The core of e3nn are
equivariant operations such as the TensorProduct class or the spherical
harmonics functions that can be composed to create more complex modules such as
convolutions and attention mechanisms. These core operations of e3nn can be
used to efficiently articulate Tensor Field Networks, 3D Steerable CNNs,
Clebsch-Gordan Networks, SE(3) Transformers and other E(3) equivariant
networks.

e3nn 是一种通用的框架，用于创建 E (3) 可变换的可训练函数，操作对象为描述三维系统的几何和几何张量，并能运用核心的张量积类和球谐函数来构建复杂的模块，例如卷积和注意力机制，可用于高效地处理张量场网络，三维中的可定向卷积神经网络，Clebsch-Gordan Networks，SE (3) 变换和其他 E (3) 可变换网络。

e3nn：欧几里德神经网络

e3nn: Euclidean Neural Networks

Hyperbolic space can naturally embed hierarchies, unlike Euclidean space.
Hyperbolic Neural Networks (HNNs) exploit such representational power by
lifting Euclidean features into hyperbolic space for classification,
outperforming Euclidean neural networks (ENNs) on datasets with known semantic
hierarchies. However, HNNs underperform ENNs on standard benchmarks without
clear hierarchies, greatly restricting HNNs' applicability in practice.
Our key insight is that HNNs' poorer general classification performance
results from vanishing gradients during backpropagation, caused by their hybrid
architecture connecting Euclidean features to a hyperbolic classifier. We
propose an effective solution by simply clipping the Euclidean feature
magnitude while training HNNs.
Our experiments demonstrate that clipped HNNs become super-hyperbolic
classifiers: They are not only consistently better than HNNs which already
outperform ENNs on hierarchical data, but also on-par with ENNs on MNIST,
CIFAR10, CIFAR100 and ImageNet benchmarks, with better adversarial robustness
and out-of-distribution detection.

研究表明，超几何神经网络 (HNNs) 可以利用它将 Euclidean 空间嵌入到超半球中的表征能力实现更好的分类性能，但该架构连接 Euclidean 表征和超几何分类器存在着梯度消失的问题，本文提出一个简单的解决方法：在训练 HNNs 时裁剪 Euclidean 表征幅度，该方法在 MNIST，CIFAR10，CIFAR100 和 ImageNet 基准测试中不仅几乎可以取代 Euclidean 神经网络，而且在对抗性鲁棒性和超出分布检测方面表现更好.