We present CosmoPower-JAX, a JAX-based implementation of the CosmoPower
framework, which accelerates cosmological inference by building neural
emulators of cosmological power spectra. We show how, using the automatic
differentiation, batch evaluation and just-in-time compilation features of JAX,
and running the inference pipeline on graphics processing units (GPUs),
parameter estimation can be accelerated by orders of magnitude with advanced
gradient-based sampling techniques. These can be used to efficiently explore
high-dimensional parameter spaces, such as those needed for the analysis of
next-generation cosmological surveys. We showcase the accuracy and
computational efficiency of CosmoPower-JAX on two simulated Stage IV
configurations. We first consider a single survey performing a cosmic shear
analysis totalling 37 model parameters. We validate the contours derived with
CosmoPower-JAX and a Hamiltonian Monte Carlo sampler against those derived with
a nested sampler and without emulators, obtaining a speed-up factor of
$\mathcal{O}(10^3)$. We then consider a combination of three Stage IV surveys,
each performing a joint cosmic shear and galaxy clustering (3x2pt) analysis,
for a total of 157 model parameters. Even with such a high-dimensional
parameter space, CosmoPower-JAX provides converged posterior contours in 3
days, as opposed to the estimated 6 years required by standard methods.
CosmoPower-JAX is fully written in Python, and we make it publicly available to
help the cosmological community meet the accuracy requirements set by
next-generation surveys.

CosmoPower-JAX 是一种用于 - cosmological inferece - 的 JAX 实现。通过构建 - cosmological power spectra - 的神经仿真器，使用 JAX 的自动分化、批量评估和及时编译功能，并在 GPU 上运行推断管道，使用先进的基于梯度的采样技术加速参数估计数个数量级。

高维贝叶斯推断与可微宇宙学模拟器 ——CosmoPower-JAX

CosmoPower-JAX: high-dimensional Bayesian inference with differentiable  cosmological emulators

Bayesian optimization (BO) is a popular approach to optimize
expensive-to-evaluate black-box functions. A significant challenge in BO is to
scale to high-dimensional parameter spaces while retaining sample efficiency. A
solution considered in existing literature is to embed the high-dimensional
space in a lower-dimensional manifold, often via a random linear embedding. In
this paper, we identify several crucial issues and misconceptions about the use
of linear embeddings for BO. We study the properties of linear embeddings from
the literature and show that some of the design choices in current approaches
adversely impact their performance. We show empirically that properly
addressing these issues significantly improves the efficacy of linear
embeddings for BO on a range of problems, including learning a gait policy for
robot locomotion.

本文通过对现有线性嵌入的文献进行研究后，识别出其中的一些关键问题和误解，并在解决这些问题的基础上，极大地提高了利用线性嵌入进行 Bayesian 优化的效能，包括机器人运动中学习步态策略等方面。

高维贝叶斯优化中线性嵌入的重新审视

Re-Examining Linear Embeddings for High-Dimensional Bayesian  Optimization

Large scale dynamical systems (e.g. many nonlinear coupled differential
equations) can often be summarized in terms of only a few state variables (a
few equations), a trait that reduces complexity and facilitates exploration of
behavioral aspects of otherwise intractable models. High model dimensionality
and complexity makes symbolic, pen--and--paper model reduction tedious and
impractical, a difficulty addressed by recently developed frameworks that
computerize reduction. Symbolic work has the benefit, however, of identifying
both reduced state variables and parameter combinations that matter most
(effective parameters, "inputs"); whereas current computational reduction
schemes leave the parameter reduction aspect mostly unaddressed. As the
interest in mapping out and optimizing complex input--output relations keeps
growing, it becomes clear that combating the curse of dimensionality also
requires efficient schemes for input space exploration and reduction. Here, we
explore systematic, data-driven parameter reduction by means of effective
parameter identification, starting from current nonlinear manifold-learning
techniques enabling state space reduction. Our approach aspires to extend the
data-driven determination of effective state variables with the data-driven
discovery of effective model parameters, and thus to accelerate the exploration
of high-dimensional parameter spaces associated with complex models.

本研究探索了一种通过有效参数识别的数据驱动参数缩减方法，从目前的非线性流形学习技术开始，以实现对与复杂模型相关的高维参数空间的高效探索。

参数降维的流形学习

Manifold learning for parameter reduction

Gradient-based meta-learning techniques are both widely applicable and
proficient at solving challenging few-shot learning and fast adaptation
problems. However, they have practical difficulties when operating on
high-dimensional parameter spaces in extreme low-data regimes. We show that it
is possible to bypass these limitations by learning a data-dependent latent
generative representation of model parameters, and performing gradient-based
meta-learning in this low-dimensional latent space. The resulting approach,
latent embedding optimization (LEO), decouples the gradient-based adaptation
procedure from the underlying high-dimensional space of model parameters. Our
evaluation shows that LEO can achieve state-of-the-art performance on the
competitive miniImageNet and tieredImageNet few-shot classification tasks.
Further analysis indicates LEO is able to capture uncertainty in the data, and
can perform adaptation more effectively by optimizing in latent space.

本文提出了一种称为 Latent Embedding Optimization (LEO) 的方法，通过学习基于数据的潜在生成表示和在低维潜在空间中进行梯度元学习，以解决基于梯度的元学习在高维参数空间中的实际困难。实验结果表明，LEO 在 miniImageNet 和 tieredImageNet 几个少样本学习任务上表现优异，并能够更有效地执行调整，同时也能捕捉数据中的不确定性。