arXiv subjects

Bohan Zhou

Publications and source records attributed to Bohan Zhou.

25 records · Page 2Linked to original sources

arXiv2024

Connections between Bressan's Mixing Conjecture, the Branched Optimal Transport and Combinatorial Optimization

We investigate the 1D version of the notable Bressan's mixing conjecture, and introduce various formulation in the classical optimal transport setting, the branched optimal transport setting and a combinatorial optimization. In the discrete case of the combinatorial problem, we prove the number of admissible solutions is on the Catalan number. Our investigation sheds light on the intricate relationship between mixing problem in the fluid dynamics and many other popular fields, leaving many interesting open questions in both theoretical and practical applications across disciplines.

math.OC↗

arXiv2023

Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs

In this paper, we address the numerical solution to the multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including image processing, density functional theory and machine learning, but yet lacks efficient and exact numerical methods. The popular entropy-regularized method may suffer numerical instability and blurring issues. Inspired by the back-and-forth method introduced by Jacobs and Léger, we investigate MMOT problems with pairwise costs. First, such problems have a graphical representation and we prove equivalent MMOT problems that have a tree representation. Second, we introduce a noval algorithm to solve MMOT on a rooted tree, by gradient based method on the dual formulation. Last, we obtain accurate solutions which can be used for the regularization-free applications.

math.OC↗

arXiv2023

Learning from Visual Observation via Offline Pretrained State-to-Go Transformer

Learning from visual observation (LfVO), aiming at recovering policies from only visual observation data, is promising yet a challenging problem. Existing LfVO approaches either only adopt inefficient online learning schemes or require additional task-specific information like goal states, making them not suited for open-ended tasks. To address these issues, we propose a two-stage framework for learning from visual observation. In the first stage, we introduce and pretrain State-to-Go (STG) Transformer offline to predict and differentiate latent transitions of demonstrations. Subsequently, in the second stage, the STG Transformer provides intrinsic rewards for downstream reinforcement learning tasks where an agent learns merely from intrinsic rewards. Empirical results on Atari and Minecraft show that our proposed method outperforms baselines and in some tasks even achieves performance comparable to the policy learned from environmental rewards. These results shed light on the potential of utilizing video-only data to solve difficult visual reinforcement learning tasks rather than relying on complete offline datasets containing states, actions, and rewards. The project's website and code can be found at https://sites.google.com/view/stgtransformer.

cs.LG↗

arXiv2022

A note on equivalences between various mixing scales

In this note, we provide with a simple example to show a defect in the definition of the geometric mixing scale, and then introduce an improved scale, called as the strong geometric mixing scale. The main theorem in this note is the equivalence between geometric mixing scale, strong geometric mixing scale and functional mixing scale, in the sense of weak convergences.

math.DS↗

arXiv2022

Micromachining & FBG fabrication using point by point technique utilizing femto-second laser

Fiber bragg gratings (FBG) has wide variety of applications in sensor and laser devices. In this work, we have fabricated FBG using point by point (PbP) technique utilizing fs laser. FBGs spectral characteristics were explored through the variation of grating length, fiber holder position, laser power and coated layer. Fs FBG is fabricated on small mode field diameter fiber which shows enhancement of transmission depth to 2.5 dB. The center wavelength shift is observed from 1520 nm to 1568 nm with the change in translational stage speed. The fs FBGs can be utilized in high pressure sensing, high temperature sensing and hazardous environment monitoring purposes.

physics.optics↗

arXiv2021

Distilling Neuron Spike with High Temperature in Reinforcement Learning Agents

Spiking neural network (SNN), compared with depth neural network (DNN), has faster processing speed, lower energy consumption and more biological interpretability, which is expected to approach Strong AI. Reinforcement learning is similar to learning in biology. It is of great significance to study the combination of SNN and RL. We propose the reinforcement learning method of spike distillation network (SDN) with STBP. This method uses distillation to effectively avoid the weakness of STBP, which can achieve SOTA performance in classification, and can obtain a smaller, faster convergence and lower power consumption SNN reinforcement learning model. Experiments show that our method can converge faster than traditional SNN reinforcement learning and DNN reinforcement learning methods, about 1000 epochs faster, and obtain SNN 200 times smaller than DNN. We also deploy SDN to the PKU nc64c chip, which proves that SDN has lower power consumption than DNN, and the power consumption of SDN is more than 600 times lower than DNN on large-scale devices. SDN provides a new way of SNN reinforcement learning, and can achieve SOTA performance, which proves the possibility of further development of SNN reinforcement learning.

cs.NE↗

arXiv2020

The existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains

In this article, we consider the (double) minimization problem $$\min\left\{P(E;Ω)+λW_p(E,F):~E\subseteqΩ,~F\subseteq \mathbb{R}^d,~\lvert E\cap F\rvert=0,~ \lvert E\rvert=\lvert F\rvert=1\right\},$$ where $p\geqslant 1$, $Ω$ is a (possibly unbounded) domain in $\mathbb{R}^d$, $P(E;Ω)$ denotes the relative perimeter of $E$ in $Ω$ and $W_p$ denotes the $p$-Wasserstein distance. When $Ω$ is unbounded and $d\geqslant 3$, it is an open problem proposed by Buttazzo, Carlier and Laborde in the paper ON THE WASSERSTEIN DISTANCE BETWEEN MUTUALLY SINGULAR MEASURES. We prove the existence of minimizers to this problem when $\frac{1}{p}+\frac{2}{d}>1$, $Ω=\mathbb{R}^d$ and $λ$ is sufficiently small.

math.CA↗