Linghai Liu

Linghai Liu, Sinho Chewi

We propose an algorithm to sample from composite log-concave distributions over $\mathbb{R}^d$, i.e., densities of the form $π\propto e^{-f-g}$, assuming access to gradient evaluations of $f$ and a restricted Gaussian oracle (RGO) for $g$. The latter requirement means that we can easily sample from the density $\text{RGO}_{g,h,y}(x) \propto \exp(-g(x) -\frac{1}{2h}||y-x||^2)$, which is the sampling analogue of the proximal operator for $g$. If $f + g$ is $α$-strongly convex and $f$ is $β$-smooth, our sampler achieves $\varepsilon$ error in total variation distance in $\widetilde{\mathcal O}(κ\sqrt d \log^4(1/\varepsilon))$ iterations where $κ:= β/α$, which matches prior state-of-the-art results for the case $g=0$. We further extend our results to cases where (1) $π$ is non-log-concave but satisfies a Poincaré or log-Sobolev inequality, and (2) $f$ is non-smooth but Lipschitz.

Mingchao Jiang, Yin Cheng, Linghai Liu

The development of online high-definition maps is significant since they provide real-time, accurate, and updatable geographic information for location-based applications, such as autonomous driving and intelligent transportation, thus improving the performance and reliability of these applications. Previous works, such as VectorMapNet and MapTR, show that direct model generation of vectorized HD maps is a promising solution. However, these methods did not take into account the usage of global semantic information to improve map construction accuracy. To address this limitation, we propose a segmentation-guided structured model (MapSeg) for online HD map construction. Specifically, we added a UV segmentation module (USM) and a BEV segmentation module (BSM) based on the MapTR structure, enabling the model to better capture the semantic information.

Linghai Liu, Shuaicheng Tong, Lisa Zhao

Recent efforts in applying implicit networks to solve inverse problems in imaging have achieved competitive or even superior results when compared to feedforward networks. These implicit networks only require constant memory during backpropagation, regardless of the number of layers. However, they are not necessarily easy to train. Gradient calculations are computationally expensive because they require backpropagating through a fixed point. In particular, this process requires solving a large linear system whose size is determined by the number of features in the fixed point iteration. This paper explores a recently proposed method, Jacobian-free Backpropagation (JFB), a backpropagation scheme that circumvents such calculation, in the context of image deblurring problems. Our results show that JFB is comparable against fine-tuned optimization schemes, state-of-the-art (SOTA) feedforward networks, and existing implicit networks at a reduced computational cost.