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Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a quadratic behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency. 

We studied the dynamical behaviors of degenerate stochastic differential equations (SDEs). We selected an auxiliary Fisher information functional as the Lyapunov functional. Using generalized Fisher information, we conducted the Lyapunov exponential convergence analysis of degenerate SDEs. We derived the convergence rate condition by generalized Gamma calculus. Examples of the generalized Bochner’s formula are provided in the Heisenberg group, displacement group, and Martinet sub-Riemannian structure. We show that the generalized Bochner’s formula follows a generalized second-order calculus of Kullback–Leibler divergence in density space embedded with a sub-Riemannian-type optimal transport metric.

 

Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from quadratic to linear given the sufficiently many chains. However, such an innovation largely disappears in big data due to the limited chains and few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote non-reversibility and propose a few solutions to tackle the underlying bias caused by the geometric stopping time. Notably, in big data scenarios, we obtain a nearly linear communication cost based on the optimal window size. In addition, we also adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct approximation tasks for complex posteriors without much tuning costs.

 

Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from O(P 2) to O(P) given sufficient many P chains. However, such an innovation largely disappears in big data problems due to the limited chains and extremely few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote the non-reversibility and obtain an appealing communication cost O(P log P) based on the optimal window size. In addition, we also analyze the bias when we adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct large-scale uncertainty approximation tasks without much tuning costs. 

Abstract The discovery of two-dimensional (2D) ferromagnets and antiferromagnets with topologically nontrivial electronic band structures makes the study of the Nernst effect in 2D materials of great importance and interest. To measure the Nernst coefficient of 2D materials, the detection of the temperature gradient is crucial. Although the micro-fabricated metal wires provide a simple but accurate way for temperature detection, a linear-response assumption that the temperature gradient is a constant is still necessary and has been widely used to evaluate the temperature gradient. However, with the existence of substrates, this assumption cannot be precise. In this study, we clearly show that the temperature gradient strongly depends on the distance from the heater by both thermoelectric transport and thermoreflectance measurements. Fortunately, both measurements show that the temperature gradient can be well described by a linear function of the distance from the heater. This linearity is further confirmed by comparing the measured Nernst coefficient to the value calculated from the generalized Mott’s formula. Our results demonstrate a precise way to measure the Nernst coefficient of 2D materials and would be helpful for future studies. 

We propose an interacting contour stochastic gradient Langevin dynamics (IC-SGLD) sampler, an embarrassingly parallel multiple-chain contour stochastic gradient Langevin dynamics (CSGLD) sampler with efficient interactions. We show that ICSGLD can be theoretically more efficient than a single-chain CSGLD with an equivalent computational budget. We also present a novel random-field function, which facilitates the estimation of self-adapting parameters in big data and obtains free mode explorations. Empirically, we compare the proposed algorithm with popular benchmark methods for posterior sampling. The numerical results show a great potential of ICSGLD for large-scale uncertainty estimation tasks. 

The radiance of sky brightness differs principally with wavelength passband. Atmospheric scattering of sunlight causes the radiation in the near-infrared band. The Antarctic is a singular area of the planet, marked by an unparalleled climate and geographical conditions, including the coldest temperatures and driest climate on Earth, which leads it to be the best candidate site for observing in infrared bands. At present, there are still no measurements of night-sky brightness at DOME A. We have developed the Near-Infrared Sky Brightness Monitor (NISBM) in the J, H, and Ks bands for measurements at DOME A. The instruments were installed at DOME A in 2019 and early results of NIR sky brightness from 2019 January–April have been obtained. The variation of sky background brightness with solar elevation and scanning angle is analysed. The zenith sky flux intensity for the early night at DOME A in the J band is in the 600–1100 μJy arcsec−2 range, that in the H band is between 1100 and 2600 μJy arcsec−2, and that in the Ks band is in the range ∼200–900 μJy arcsec−2. This result shows that the sky brightness in J and H bands is close to that of Ali in China and Mauna Kea in the USA. The sky brightness in the Ks band is much better than that in Ali, China and Mauna Kea, USA. This shows that, from our early results, DOME A is a good site for astronomical observation in the Ks band.