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Zhiqi Chen

Zhiqi Chen appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.DGmath-phmath.MPmath.RAArtificial IntelligenceComputer VisionMachine Learningmath.GRmath.RT

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Published work

18 published item(s)

preprint2026arXiv

What Matters in Practical Learned Image Compression

One of the major differentiators unlocked by learned codecs relative to their hard-coded traditional counterparts is their ability to be optimized directly to appeal to the human visual system. Despite this potential, a perceptual yet practical image codec is yet to be proposed. In this work, we aim to close this gap. We conduct a comprehensive study of the key modeling choices that govern the design of a practical learned image codec, jointly optimized for perceptual quality and runtime -- including within the ablations several novel techniques. We then perform performance-aware neural architecture search over millions of backbone configurations to identify models that achieve the target on-device runtime while maximizing compression performance as captured by perceptual metrics. We combine the various optimizations to construct a new codec that achieves a significantly improved tradeoff between speed and perceptual quality. Based on rigorous subjective user studies, it provides 2.3-3x bitrate savings against AV1, AV2, VVC, ECM and JPEG-AI, and 20-40% bitrate savings against the best learned codec alternatives. At the same time, on an iPhone 17 Pro Max, it encodes 12MP images as fast as 230ms, and decodes them in 150ms -- faster than most top ML-based codecs run on a V100 GPU.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Weakly Symmetric Pseudo-Riemannian Nilmanifolds

In an earlier paper we developed the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derived the classification from the cases where $G$ is compact. As a consequence we obtained the classification of semisimple weakly symmetric manifolds of Lorentz signature $(n-1,1)$ and trans--lorentzian signature $(n-2,2)$. Here we work out the classification of weakly symmetric pseudo--riemannian nilmanifolds $G/H$ from the classification for the case $G = N\rtimes H$ with $H$ compact and $N$ nilpotent. It turns out that there is a plethora of new examples that merit further study. Starting with that riemannian case, we see just when a given involutive automorphism of $H$ extends to an involutive automorphism of $G$, and we show that any two such extensions result in isometric pseudo--riemannian nilmanifolds. The results are tabulated in the last two sections of the paper.

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preprint2016arXiv

An analogue of the Kostant criterion for quadratic Lie superalgebras

Let $\mathfrak{r}$ be a finite dimensional complex Lie superalgebra with a non-degenerate super-symmetric invariant bilinear form, let $\mathfrak{p}$ be a finite dimensional complex super vector space with a non-degenerate super-symmetric bilinear form, and let $ν: \mathfrak{r}\rightarrow\mathfrak{osp}(\mathfrak{p})$ be a Lie superalgebra homomorphism. In this paper, we give a necessary and sufficient condition for $\mathfrak{r}\oplus\mathfrak{p}$ to be a quadratic Lie superalgebra. The criterion obtained is an analogue of a constancy condition given by Kostant in the Lie algebra setting. As an application, we prove an analogue of the Parthasarathy's formula for the square of the Dirac operator attached to a pair of quadratic Lie superalgebras.

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preprint2016arXiv

Conformal vector fields on Lie groups

In this paper, we investigated the behavior of left-invariant conformal vector fields on Lie groups with left-invariant pseudo-Riemannian metrics. First of all, we prove that conformal vector fields on pseudo-Riemannian unimodular Lie groups are Killing. Then we obtain a necessary condition for a pseudo-Rimennian non-unimodular Lie group admitting a non-Killing conformal vector field. Finally, we give examples of non-Killing conformal vector fields and Yamabe solitons on non-unimodular Lorentzian Lie groups based on the above study.

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preprint2015arXiv

Non-trivial $m$-quasi-Einstein metrics on quadratic Lie groups

We call a metric $m$-quasi-Einstein if $Ric_X^m$ (a modification of the $m$-Bakry-Emery Ricci tensor in terms of a suitable vector field $X$) is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which contains Ricci solitons. In this paper, we focus on left-invariant vector fields and left-invariant Riemannian metrics on quadratic Lie groups. First we prove that any left-invariant vector field $X$ such that the left-invariant Riemannian metric on a quadratic Lie group is $m$-quasi-Einstein is a Killing field. Then we construct infinitely many non-trivial $m$-quasi-Einstein metrics on solvable quadratic Lie groups $G(n)$ for $m$ finite.

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preprint2014arXiv

Non-trivial $m$-quasi-Einstein metrics on simple Lie groups

We call a metric $m$-quasi-Einstein if $Ric_X^m$, which replaces a gradient of a smooth function $f$ by a vector field $X$ in $m$-Bakry-Emery Ricci tensor, is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which contains Ricci solitons. In this paper, we focus on left-invariant metrics on simple Lie groups. First, we prove that $X$ is a left-invariant Killing vector field if the metric on a compact simple Lie group is $m$-quasi-Einstein. Then we show that every compact simple Lie group admits non-trivial $m$-quasi-Einstein metrics except $SU(3)$, $E_8$ and $G_2$, and most of them admit infinitely many metrics. Naturally, the study on $m$-quasi-Einstein metrics can be extended to pseudo-Riemannian case. And we prove that every compact simple Lie group admits non-trivial $m$-quasi-Einstein Lorentzian metrics and most of them admit infinitely many metrics. Finally, we prove that some non-compact simple Lie groups admit infinitely many non-trivial $m$-quasi-Einstein Lorentzian metrics.

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preprint2013arXiv

Left-symmetric algebroids

In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie algebroid. We construct left-symmetric algebroids from $\mathcal O$-operators on Lie algebroids. We study phase spaces of Lie algebroids in terms of left-symmetric algebroids. Representations of left-symmetric algebroids are studied in detail. At last, we study deformations of left-symmetric algebroids, which could be controlled by the second cohomology class in the deformation cohomology.

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preprint2012arXiv

The decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness

In this paper, we discuss the decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness. In fact, it is a decomposition of a Lie group into totally geodesic sub-manifolds which is different from the De Rham decomposition on a Lie group. As an application, we give a decomposition of a Lie group with a left invariant pseudo-Riemannian Einstein metric, and prove that the decomposition is unique up to the order of the parts in the decomposition.

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preprint2011arXiv

Pseudo-Riemannian Weakly Symmetric Manifolds

There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit property, weak symmetries, and the structure of the nilradical of the isometry group. Also, we give a number of examples of weakly symmetric pseudo-Riemannian manifolds, some mirroring the Riemannian case and some indicating the problems in extending Riemannian results to weakly symmetric pseudo-Riemannian spaces.

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