Related papers: Rieoptax: Riemannian Optimization in JAX
Differentiable simulators are an emerging concept with applications in several fields, from reinforcement learning to optimal control. Their distinguishing feature is the ability to calculate analytic gradients with respect to the input…
Automatic differentiation (AD) frameworks such as JAX and PyTorch have enabled gradient-based optimization for a wide range of scientific fields. Yet, many "hard" primitives in these libraries such as thresholding, Boolean logic, discrete…
Riemannian meta-optimization provides a promising approach to solving non-linear constrained optimization problems, which trains neural networks as optimizers to perform optimization on Riemannian manifolds. However, existing Riemannian…
Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the symplecticity constraint. As this constraint nicely forms a…
Among numerical libraries capable of computing gradient descent optimization, JAX stands out by offering more features, accelerated by an intermediate representation known as Jaxpr language. However, editing the Jaxpr code is not directly…
In robot control, planning, and learning, there is a need for rigid-body dynamics libraries that are highly performant, easy to use, and compatible with CPUs and accelerators. While existing libraries often excel at either low-latency CPU…
A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the…
TorchOptics is an open-source Python library for differentiable Fourier optics simulations, developed using PyTorch to enable GPU-accelerated tensor computations and automatic differentiation. It provides a comprehensive framework for…
Although Deep Learning (DL) has achieved success in complex Artificial Intelligence (AI) tasks, it suffers from various notorious problems (e.g., feature redundancy, and vanishing or exploding gradients), since updating parameters in…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
Epithelial tissues dynamically reshape through local mechanical interactions among cells, a process well captured by vertex models. Yet their many tunable parameters make inference and optimization challenging, motivating computational…
This paper proposes a novel general framework of Riemannian conjugate gradient methods, that is, conjugate gradient methods on Riemannian manifolds. The conjugate gradient methods are important first-order optimization algorithms both in…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel…
Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
OpenReservoirComputing (ORC) is a Python library for reservoir computing (RC) written in JAX (Bradbury et al. 2018) and Equinox (Kidger and Garcia 2021). JAX is a Python library for high-performance numerical computing that enables…
In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently using modern computational frameworks that mix symbolic…