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Minghui Hu

Publications and source records attributed to Minghui Hu.

21 records · Page 2Linked to original sources

Global Context with Discrete Diffusion in Vector Quantised Modelling for Image Generation

The integration of Vector Quantised Variational AutoEncoder (VQ-VAE) with autoregressive models as generation part has yielded high-quality results on image generation. However, the autoregressive models will strictly follow the progressive scanning order during the sampling phase. This leads the existing VQ series models to hardly escape the trap of lacking global information. Denoising Diffusion Probabilistic Models (DDPM) in the continuous domain have shown a capability to capture the global context, while generating high-quality images. In the discrete state space, some works have demonstrated the potential to perform text generation and low resolution image generation. We show that with the help of a content-rich discrete visual codebook from VQ-VAE, the discrete diffusion model can also generate high fidelity images with global context, which compensates for the deficiency of the classical autoregressive model along pixel space. Meanwhile, the integration of the discrete VAE with the diffusion model resolves the drawback of conventional autoregressive models being oversized, and the diffusion model which demands excessive time in the sampling process when generating images. It is found that the quality of the generated images is heavily dependent on the discrete visual codebook. Extensive experiments demonstrate that the proposed Vector Quantised Discrete Diffusion Model (VQ-DDM) is able to achieve comparable performance to top-tier methods with low complexity. It also demonstrates outstanding advantages over other vectors quantised with autoregressive models in terms of image inpainting tasks without additional training.

cs.CV↗

Extraordinary-log surface phase transition in the three-dimensional $XY$ model

Universality is a pillar of modern critical phenomena. The standard scenario is that the two-point correlation algebraically decreases with the distance $r$ as $g(r) \sim r^{2-d-η}$, with $d$ the spatial dimension and $η$ the anomalous dimension. Very recently, a logarithmic universality was proposed to describe the extraordinary surface transition of O($N$) system. In this logarithmic universality, $g(r)$ decays in a power of logarithmic distance as $g(r) \sim ({\rm ln}r)^{-\hatη}$, dramatically different from the standard scenario. We explore the three-dimensional $XY$ model by Monte Carlo simulations, and provide strong evidence for the emergence of logarithmic universality. Moreover, we propose that the finite-size scaling of $g(r,L)$ has a two-distance behavior: simultaneously containing a large-distance plateau whose height decays logarithmically with $L$ as $g(L) \sim ({\rm ln}L)^{-\hatη'}$ as well as the $r$-dependent term $g(r) \sim ({\rm ln}r)^{-\hatη}$, with ${\hatη'} \approx {\hatη}-1$. The critical exponent $\hatη'$, characterizing the height of the plateau, obeys the scaling relation $\hatη'=(N-1)/(2πα)$ with the RG parameter $α$ of helicity modulus. Our picture can also explain the recent numerical results of a Heisenberg system. The advances on logarithmic universality significantly expand our understanding of critical universality.

cond-mat.stat-mech↗

History-dependent percolation in two dimensions

We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various generations on periodic square lattices up to side length $L=4096$. From finite-size scaling, we find that the model undergoes a continuous phase transition, which, for any finite number of generations, falls into the universality of standard 2D percolation. At the limit of infinite generation, we determine the correlation-length exponent $1/ν=0.828(5)$ and the fractal dimension $d_{\rm f}=1.864\,4(7)$, which are not equal to $1/ν=3/4$ and $d_{\rm f}=91/48$ for 2D percolation. Hence, the transition in the infinite-generation limit falls outside the standard percolation universality and differs from the discontinuous transition of history-dependent percolation on random networks. Further, a crossover phenomenon is observed between the two universalities in infinite and finite generations.

cond-mat.stat-mech↗