相关论文: LieGG: Studying Learned Lie Group Generators

The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases,…

In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

Human reasoning involves recognising common underlying principles across many examples. The by-products of such reasoning are invariants that capture patterns such as "if someone went somewhere then they are there", expressed using…

Empirical studies of the loss landscape of deep networks have revealed that many local minima are connected through low-loss valleys. Yet, little is known about the theoretical origin of such valleys. We present a general framework for…

Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…

Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines…

Following the growing success of generative neural networks in LHC simulations, the crucial question is how to control the networks and assign uncertainties to their event output. We show how Bayesian normalizing flow or invertible networks…

The performance of machine learning models is determined by the quality of their learned features. They should be invariant under irrelevant data variation but sensitive to task-relevant details. To visualize whether this is the case, we…

Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and…

We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded…

Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

In this paper we study the spontaneous development of symmetries in the early layers of a Convolutional Neural Network (CNN) during learning on natural images. Our architecture is built in such a way to mimic the early stages of biological…

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate…

Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincar\'{e} invariance, allow physical laws discovered in laboratories on Earth to be…

Parameter-space and function-space provide two different duality frames in which to study neural networks. We demonstrate that symmetries of network densities may be determined via dual computations of network correlation functions, even…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…