Related papers: Learning Polynomial Problems with $SL(2,\mathbb{R}…

Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…

We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques…

Data augmentation is a powerful mechanism in equivariant machine learning, encouraging symmetry by training networks to produce consistent outputs under transformed inputs. Yet, effective augmentation typically requires the underlying…

We study separable plus quadratic (SPQ) polynomials, i.e., polynomials that are the sum of univariate polynomials in different variables and a quadratic polynomial. Motivated by the fact that nonnegative separable and nonnegative quadratic…

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and…

Processing spatial data is a key component in many learning tasks for autonomous driving such as motion forecasting, multi-agent simulation, and planning. Prior works have demonstrated the value in using SE(2) invariant network…

Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…

Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…

Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation,…

Machine learning and deep learning have revolutionized computational physics, particularly the simulation of complex systems. Equivariance is essential for simulating physical systems because it imposes a strong inductive bias on the…

A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…

In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…

We propose learnable polyphase sampling (LPS), a pair of learnable down/upsampling layers that enable truly shift-invariant and equivariant convolutional networks. LPS can be trained end-to-end from data and generalizes existing handcrafted…

Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models.…

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…

A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…

We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…

Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples…