Related papers: Learning Broken Symmetries with Approximate Invari…

Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…

Deep semi-supervised learning has been widely implemented in the real-world due to the rapid development of deep learning. Recently, attention has shifted to the approaches such as Mean-Teacher to penalize the inconsistency between two…

Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was…

Exploiting symmetry inherent in data can significantly improve the sample efficiency of a learning procedure and the generalization of learned models. When data clearly reveals underlying symmetry, leveraging this symmetry can naturally…

The immense computational cost of simulating turbulence has motivated the use of machine learning approaches for super-resolving turbulent flows. A central challenge is ensuring that learned models respect physical symmetries, such as…

In this paper, we studied two identically-trained neural networks (i.e. networks with the same architecture, trained on the same dataset using the same algorithm, but with different initialization) and found that their outputs discrepancy…

Providing invariances in a given learning task conveys a key inductive bias that can lead to sample-efficient learning and good generalisation, if correctly specified. However, the ideal invariances for many problems of interest are often…

Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using…

Spontaneous symmetry breaking in statistical mechanics primarily occurs during phase transitions at the thermodynamic limit where the Hamiltonian preserves inversion symmetry, yet the low-temperature free energy exhibits reduced symmetry.…

Learning dynamics is essential for model-based control and Reinforcement Learning in engineering systems, such as robotics and power systems. However, limited system measurements, such as those from low-resolution sensors, demand…

The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…

Geometric regularity, which leverages data symmetry, has been successfully incorporated into deep learning architectures such as CNNs, RNNs, GNNs, and Transformers. While this concept has been widely applied in robotics to address the curse…

In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…

Many practical anomalies are not merely rare inputs, but violations of semantic constraints: objects co-occur in structured ways, actions imply preconditions, and events satisfy temporal or relational regularities. We study anomaly…

What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…

Understanding the geometry of neural network loss landscapes is a central question in deep learning, with implications for generalization and optimization. A striking phenomenon is linear mode connectivity (LMC), where independently trained…

Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a…

Labeling a training set is often expensive and susceptible to errors, making the design of robust loss functions for label noise an important problem. The symmetry condition provides theoretical guarantees for robustness to such noise. In…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…