Related papers: Equivariant Hamiltonian Flows
We present a new probabilistic model of compact commutative Lie groups that produces invariant-equivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that…
Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…
Geometric quantum machine learning uses the symmetries inherent in data to design tailored machine learning tasks with reduced search space dimension. The field has been well-studied recently in an effort to avoid barren plateau issues…
We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an…
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to…
In this study, we introduce a method for learning group (known or unknown) equivariant functions by learning the associated quadratic form $x^T A x$ corresponding to the group from the data. Certain groups, known as orthogonal groups,…
We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
Current density modeling approaches suffer from at least one of the following shortcomings: expensive training, slow inference, approximate likelihood, mode collapse or architectural constraints like bijective mappings. We propose a simple…
This paper establishes a unified framework integrating geometric flows with deep learning through three fundamental innovations. First, we propose a thermodynamically coupled Ricci flow that dynamically adapts parameter space geometry to…
Computing the marginal likelihood (also called the Bayesian model evidence) is an important task in Bayesian model selection, providing a principled quantitative way to compare models. The learned harmonic mean estimator solves the…
This work presents DCFlow, a novel unsupervised cross-modal flow estimation framework that integrates a decoupled optimization strategy and a cross-modal consistency constraint. Unlike previous approaches that implicitly learn flow…
Generative models are a promising tool to address the sampling problem in multi-body and condensed-matter systems in the framework of statistical mechanics. In this work, we show that normalizing flows can be used to learn a transformation…
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…
Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…
Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and…
The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…
Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the…
Inspired by constraints from physical law, equivariant machine learning restricts the learning to a hypothesis class where all the functions are equivariant with respect to some group action. Irreducible representations or invariant theory…
We study reductions of the Hamiltonian flows restricted to their invariant submanifolds. As examples, we consider partial Lagrange-Routh reductions of the natural mechanical systems such as geodesic flows on compact Lie groups and…