arXiv subjects

Zixuan Xu

Publications and source records attributed to Zixuan Xu.

At least 37 records · Page 2Linked to original sources

arXiv2025

Testing Conditional Independence via Density Ratio Regression

This paper develops a conditional independence (CI) test from a conditional density ratio (CDR) for weakly dependent data. The main contribution is presenting a closed-form expression for the estimated conditional density ratio function with good finite-sample performance. The key idea is exploiting the linear sieve combined with the quadratic norm. Matsushita et al. (2022) exploited the linear sieve to estimate the unconditional density ratio. We must exploit the linear sieve twice to estimate the conditional density ratio. First, we estimate an unconditional density ratio with an unweighted sieve least-squares regression, as done in Matsushita et al. (2022), and then the conditional density ratio with a weighted sieve least-squares regression, where the weights are the estimated unconditional density ratio. The proposed test has several advantages over existing alternatives. First, the test statistic is invariant to the monotone transformation of the data distribution and has a closed-form expression that enhances computational speed and efficiency. Second, the conditional density ratio satisfies the moment restrictions. The estimated ratio satisfies the empirical analog of those moment restrictions. As a result, the estimated density ratio is unlikely to have extreme values. Third, the proposed test can detect all deviations from conditional independence at rates arbitrarily close to $n^{-1/2}$ , and the local power loss is independent of the data dimension. A small-scale simulation study indicates that the proposed test outperforms the alternatives in various dependence structures.

stat.ME↗

arXiv2025

New Separations and Reductions for Directed Preservers and Hopsets

We study distance preservers, hopsets, and shortcut sets in $n$-node, $m$-edge directed graphs, and show improved bounds and new reductions for various settings of these problems. Our first set of results is about exact and approximate distance preservers. We give the following bounds on the size of directed distance preservers with $p$ demand pairs: 1) $\tilde{O}(n^{5/6}p^{2/3} + n)$ edges for exact distance preservers in unweighted graphs; and 2) $Ω(n^{2/3}p^{2/3})$ edges for approximate distance preservers with any given finite stretch, in graphs with arbitrary aspect ratio. Additionally, we establish a new directed-to-undirected reduction for exact distance preservers. We show that if undirected distance preservers have size $O(n^λp^μ + n)$ for constants $λ, μ> 0$, then directed distance preservers have size $O\left( n^{\frac{1}{2-λ}}p^{\frac{1+μ-λ}{2-λ}} + n^{1/2}p + n\right).$ As a consequence of the reduction, if current upper bounds for undirected preservers can be improved for some $p \leq n$, then so can current upper bounds for directed preservers. Our second set of results is about directed hopsets and shortcut sets. For hopsets in directed graphs, we prove that the hopbound is: 1) $Ω(n^{2/9})$ for $O(m)$-size shortcut sets, improving the previous $Ω(n^{1/5})$ bound [Vassilevska Williams, Xu and Xu, SODA 2024]; 2) $Ω(n^{2/7})$ for $O(m)$-size exact hopsets in unweighted graphs, improving the previous $Ω(n^{1/4})$ bound [Bodwin and Hoppenworth, FOCS 2023]; and 3) $Ω(n^{1/2})$ for $O(n)$-size approximate hopsets with any given finite stretch, in graphs with arbitrary aspect ratio. This result establishes a separation between this setting and $O(n)$-size approximate hopsets for graphs with polynomial aspect ratio, which have hopbound $\widetilde{O}(n^{1/3})$ [Bernstein and Wein, SODA 2023].

cs.DS↗

arXiv2025

MetaSSC: Enhancing 3D Semantic Scene Completion for Autonomous Driving through Meta-Learning and Long-sequence Modeling

Semantic scene completion (SSC) is essential for achieving comprehensive perception in autonomous driving systems. However, existing SSC methods often overlook the high deployment costs in real-world applications. Traditional architectures, such as 3D Convolutional Neural Networks (3D CNNs) and self-attention mechanisms, face challenges in efficiently capturing long-range dependencies within 3D voxel grids, limiting their effectiveness. To address these issues, we introduce MetaSSC, a novel meta-learning-based framework for SSC that leverages deformable convolution, large-kernel attention, and the Mamba (D-LKA-M) model. Our approach begins with a voxel-based semantic segmentation (SS) pretraining task, aimed at exploring the semantics and geometry of incomplete regions while acquiring transferable meta-knowledge. Using simulated cooperative perception datasets, we supervise the perception training of a single vehicle using aggregated sensor data from multiple nearby connected autonomous vehicles (CAVs), generating richer and more comprehensive labels. This meta-knowledge is then adapted to the target domain through a dual-phase training strategy that does not add extra model parameters, enabling efficient deployment. To further enhance the model's capability in capturing long-sequence relationships within 3D voxel grids, we integrate Mamba blocks with deformable convolution and large-kernel attention into the backbone network. Extensive experiments demonstrate that MetaSSC achieves state-of-the-art performance, significantly outperforming competing models while also reducing deployment costs.

cs.CV↗

arXiv2025

Unexpected large electrostatic gating by pyroelectric charge accumulation

Pyroelectricity refers to the accumulation of charges due to changes in the spontaneous polarization of ferroelectric materials when subjected to temperature variations. Typically, these pyroelectric charges are considered unstable and dissipate quickly through interactions with the external environment. Consequently, the pyroelectric effect has been largely overlooked in ferroelectric field-effect transistors. In this work, we leverage the van der Waals interface of hBN to achieve a substantial and long-term electrostatic gating effect in graphene devices via the pyroelectric properties of a ferroelectric LiNbO3 substrate. Upon cooling, the polarization change in LiNbO3 induces high doping concentrations up to 1013 cm-2 in the adjacent graphene. Through a combination of transport measurements and non-contact techniques, we demonstrate that the pyroelectric charge accumulation, as well as its enhancement in electric fields, are responsible for this unexpectedly high doping level. Our findings introduce a novel mechanism for voltage-free electrostatic gating control with long retention.

cond-mat.mtrl-sci↗

arXiv2025

Broadband photoresponse enhancement by band engineering in Sb-doped MnBi2Te4

Topological materials have attracted considerable attention for their potential in broadband and fast photoresponse, particularly in the infrared regime. However, the high carrier concentration in these systems often leads to rapid recombination of photogenerated carriers, limiting the photoresponsivity. Here, we demonstrate that Sb doping in MnBi2Te4 effectively reduces carrier concentration and suppresses electron-hole recombination, thereby significantly improving the optoelectronic performance across the visible to mid-infrared spectra. The optimally doped Mn(Bi0.82Sb0.18)2Te4 photodetector achieves a responsivity of 3.02 mA W-1 with a response time of 18.5 μs at 1550 nm, and 0.795 mA W-1 with a response time of 9.0 μs at 4 μm. These values represent nearly two orders of magnitude improvement compared to undoped MnBi2Te4. Our results highlight band engineering as an effective strategy to enhance the infrared performance of topological material-based photodetectors, opening new avenues for high-sensitivity infrared detection.

cond-mat.mtrl-sci↗

arXiv2024

On off-diagonal $F$-Ramsey numbers

A graph is $(t_1, t_2)$-Ramsey if any red-blue coloring of its edges contains either a red copy of $K_{t_1}$ or a blue copy of $K_{t_2}$. The size Ramsey number is the minimum number of edges contained in a $(t_1,t_2)$-Ramsey graph. Generalizing the notion of size Ramsey numbers, the $F$-Ramsey number $r_F(t_1, t_2)$ is defined to be the minimum number of copies of $F$ in a $(t_1,t_2)$-Ramsey graph. It is easy to see that $r_{K_s}(t_1,t_2)\le \binom{r(t_1,t_2)}{s}$. Recently, Fox, Tidor, and Zhang showed that equality holds in this bound when $s=3$ and $t_1=t_2$, i.e. $r_{K_3}(t,t) = \binom{r(t,t)}{3}$. They further conjectured that $r_{K_s}(t,t)=\binom{r(t,t)}{s}$ for all $s\le t$, in response to a question of Spiro. In this work, we study the off-diagonal variant of this conjecture: is it true that $r_{K_s}(t_1,t_2)=\binom{r(t_1,t_2)}{s}$ whenever $s\le \max(t_1,t_2)$? Harnessing the constructions used in the recent breakthrough work of Mattheus and Verstraëte on the asymptotics of $r(4,t)$, we show that when $t_1$ is $3$ or $4$, the above equality holds up to a lower order term in the exponent.

math.CO↗

arXiv2024

Constraints on freeze-in dark matter from Lyman-$α$ forest and 21-cm signal : single-field models

We report new Lyman-$α$ and 21-cm constraints on freeze-in dark matter (FIDM) which injects energy into the intergalactic medium either through annihilation or decay to photon(s) or electron-positron pair. With respect to Lyman-$α$ we fix the baseline ionization history using low redshift data about astrophysical reionization, whereas for 21-cm signal we adopt the baseline values of 21-cm power spectrum through a standard modeling of star formation developed so far. Using the latest numerical tools, we show that (i) for sterile neutrino FIDM, current Lyman-$α$ data and future sensitivity of SKA-low (1000 hrs) on the 21-cm power spectra excludes the FIDM mass up to $1.8\times 10^{-3}$ GeV at 95$\%$ CL and $5.46\times 10^{-4}$ GeV, respectively, and (ii) for millicharged FIDM, current Lyman-$α$ data only excludes the millicharge down to $10^{-8}$ within the FIDM mass range of $10^{-3}-1$ GeV at 95$\%$ CL, suggesting that the surviving parameter space of millicharged FIDM is still intact.

hep-ph↗

arXiv2024

Lyman-$α$ limit on axion-like cold dark matter

Using low redshift data on astrophysical reionization, we report new Lyman-$α$ limit on axion-like particle (ALP) as cold dark matter in ALP mass range of $m_{a}\sim 30-1000$ eV. Compared to the Leo T and soft-X ray bound, this limit is so far the most stringent in the ALP mass range of $m_{a}\sim 375-425$ eV and complementary in the ALP mass range otherwise. Combing these limits, we show new exclusion limits on $m_a$ for the ALP DM from either misalignment or freeze-in mechanism.

hep-ph↗

arXiv2024

Additive Spanner Lower Bounds with Optimal Inner Graph Structure

We construct $n$-node graphs on which any $O(n)$-size spanner has additive error at least $+Ω(n^{3/17})$, improving on the previous best lower bound of $Ω(n^{1/7})$ [Bodwin-Hoppenworth FOCS '22]. Our construction completes the first two steps of a particular three-step research program, introduced in prior work and overviewed here, aimed at producing tight bounds for the problem by aligning aspects of the upper and lower bound constructions. More specifically, we develop techniques that enable the use of inner graphs in the lower bound framework whose technical properties are provably tight with the corresponding assumptions made in the upper bounds. As an additional application of our techniques, we improve the corresponding lower bound for $O(n)$-size additive emulators to $+Ω(n^{1/14})$.

cs.DS↗

arXiv2023

Gravitational freeze-in dark matter from Higgs Preheating

Gravitational freeze-in is a mechanism to explain the observed dark matter relic density if dark matter neither couples to inflation nor to standard model sector. In this work, we study gravitational freeze-in dark matter production during Higgs preheating based on non-perturbative resonance. Using reliable lattice method to handle this non-perturbative process, we show that tachyonic resonance is prohibited by strong back reaction due to Higgs self interaction needed to keep the positivity of potential during preheating, and parameter resonance is viable by tuning the Higgs self-interaction coupling to be small enough in ultraviolet energy scale. We then derive the dark matter relic density under the context of Higgs preheating, and uncover a new dark matter parameter space with dark matter mass larger than inflaton mass, which arises from out-of-equilium Higgs annihilation. Finally, we briefly remark the open question of testing gravitational dark matter.

hep-ph↗

arXiv2023

New Bounds for Matrix Multiplication: from Alpha to Omega

The main contribution of this paper is a new improved variant of the laser method for designing matrix multiplication algorithms. Building upon the recent techniques of [Duan, Wu, Zhou, FOCS 2023], the new method introduces several new ingredients that not only yield an improved bound on the matrix multiplication exponent $ω$, but also improve the known bounds on rectangular matrix multiplication by [Le Gall and Urrutia, SODA 2018]. In particular, the new bound on $ω$ is $ω\le 2.371552$ (improved from $ω\le 2.371866$). For the dual matrix multiplication exponent $α$ defined as the largest $α$ for which $ω(1,α,1)=2$, we obtain the improvement $α\ge 0.321334$ (improved from $α\ge 0.31389$). Similar improvements are obtained for various other exponents for multiplying rectangular matrices.

cs.DS↗

arXiv2023

Improved Roundtrip Spanners, Emulators, and Directed Girth Approximation

Roundtrip spanners are the analog of spanners in directed graphs, where the roundtrip metric is used as a notion of distance. Recent works have shown existential results of roundtrip spanners nearly matching the undirected case, but the time complexity for constructing roundtrip spanners is still widely open. This paper focuses on developing fast algorithms for roundtrip spanners and related problems. For any $n$-vertex directed graph $G$ with $m$ edges (with non-negative edge weights), our results are as follows: - 3-roundtrip spanner faster than APSP: We give an $\tilde{O}(m\sqrt{n})$-time algorithm that constructs a roundtrip spanner of stretch $3$ and optimal size $O(n^{3/2})$. Previous constructions of roundtrip spanners of the same size either required $Ω(nm)$ time [Roditty, Thorup, Zwick SODA'02; Cen, Duan, Gu ICALP'20], or had worse stretch $4$ [Chechik and Lifshitz SODA'21]. - Optimal roundtrip emulator in dense graphs: For integer $k\ge 3$, we give an $O(kn^2\log n)$-time algorithm that constructs a roundtrip \emph{emulator} of stretch $(2k-1)$ and size $O(kn^{1+1/k})$, which is optimal for constant $k$ under Erdős' girth conjecture. Previous work of [Thorup and Zwick STOC'01] implied a roundtrip emulator of the same size and stretch, but it required $Ω(nm)$ construction time. Our improved running time is near-optimal for dense graphs. - Faster girth approximation in sparse graphs: We give an $\tilde{O}(mn^{1/3})$-time algorithm that $4$-approximates the girth of a directed graph. This can be compared with the previous $2$-approximation algorithm in $\tilde{O}(n^2, m\sqrt{n})$ time by [Chechik and Lifshitz SODA'21]. In sparse graphs, our algorithm achieves better running time at the cost of a larger approximation ratio.

cs.DS↗

arXiv2023

Simpler and Higher Lower Bounds for Shortcut Sets

We provide a variety of lower bounds for the well-known shortcut set problem: how much can one decrease the diameter of a directed graph on $n$ vertices and $m$ edges by adding $O(n)$ or $O(m)$ of shortcuts from the transitive closure of the graph. Our results are based on a vast simplification of the recent construction of Bodwin and Hoppenworth [FOCS 2023] which was used to show an $\widetildeΩ(n^{1/4})$ lower bound for the $O(n)$-sized shortcut set problem. We highlight that our simplification completely removes the use of the convex sets by Bárány and Larman [Math. Ann. 1998] used in all previous lower bound constructions. Our simplification also removes the need for randomness and further removes some log factors. This allows us to generalize the construction to higher dimensions, which in turn can be used to show the following results. For $O(m)$-sized shortcut sets, we show an $Ω(n^{1/5})$ lower bound, improving on the previous best $Ω(n^{1/8})$ lower bound. For all $\varepsilon > 0$, we show that there exists a $δ> 0$ such that there are $n$-vertex $O(n)$-edge graphs $G$ where adding any shortcut set of size $O(n^{2-\varepsilon})$ keeps the diameter of $G$ at $Ω(n^δ)$. This improves the sparsity of the constructed graph compared to a known similar result by Hesse [SODA 2003]. We also consider the sourcewise setting for shortcut sets: given a graph $G=(V,E)$, a set $S\subseteq V$, how much can we decrease the sourcewise diameter of $G$, $\max_{(s, v) \in S \times V, \text{dist}(s, v) < \infty} \text{dist}(s,v)$ by adding a set of edges $H$ from the transitive closure of $G$? We show that for any integer $d \ge 2$, there exists a graph $G=(V, E)$ on $n$ vertices and $S \subseteq V$ with $|S| = \widetildeΘ(n^{3/(d+3)})$, such that when adding $O(n)$ or $O(m)$ shortcuts, the sourcewise diameter is $\widetildeΩ(|S|^{1/3})$.

cs.DS↗

arXiv2023

Essential covers of the hypercube require many hyperplanes

We prove a new lower bound for the almost 20 year old problem of determining the smallest possible size of an essential cover of the $n$-dimensional hypercube $\{\pm 1\}^n$, i.e. the smallest possible size of a collection of hyperplanes that forms a minimal cover of $\{\pm 1\}^n$ and such that furthermore every variable appears with a non-zero coefficient in at least one of the hyperplane equations. We show that such an essential cover must consist of at least $10^{-2}\cdot n^{2/3}/(\log n)^{2/3}$ hyperplanes, improving previous lower bounds of Linial-Radhakrishnan, of Yehuda-Yehudayoff and of Araujo-Balogh-Mattos.

math.CO↗

arXiv2023

Better Lower Bounds for Shortcut Sets and Additive Spanners via an Improved Alternation Product

We obtain improved lower bounds for additive spanners, additive emulators, and diameter-reducing shortcut sets. Spanners and emulators are sparse graphs that approximately preserve the distances of a given graph. A shortcut set is a set of edges that when added to a directed graph, decreases its diameter. The previous best known lower bounds for these three structures are given by Huang and Pettie [SWAT 2018]. For $O(n)$-sized spanners, we improve the lower bound on the additive stretch from $Ω(n^{1/11})$ to $Ω(n^{2/21})$. For $O(n)$-sized emulators, we improve the lower bound on the additive stretch from $Ω(n^{1/18})$ to $Ω(n^{1/16})$. For $O(m)$-sized shortcut sets, we improve the lower bound on the graph diameter from $Ω(n^{1/11})$ to $Ω(n^{1/8})$. Our key technical contribution, which is the basis of all of our bounds, is an improvement of a graph product known as an alternation product.

cs.DS↗

arXiv2023

Freeze-in Dark Matter via Lepton Portal: Hubble Tension and Stellar Cooling

We propose a new freeze-in dark matter candidate which feebly couples to the standard model charged leptons. The feeble interactions allow it (i) to freeze-in from the Standard Model thermal bath with its relic density being either a fraction or the entirety of the observed dark matter density and (ii) to radiatively decay to two photons in the dark matter mass ranges of order keV scale with lifetime larger than the age of Universe. These features make this model a realistic realization of dark matter with late-time decay to reduce Hubble tension. We show the best-fit value of H_{0}=68.31(69.34) km s^{-1}Mpc^{-1} in light of Planck 2018+BAO(+LSS)+Pantheon data sets. We then use stellar cooling data to place constraints on the parameter space favored by the Hubble tension. While the universal coupling scenario is excluded, the hierarchical coupling scenario can be tested by future observations of white dwarfs after a careful look into photon inverse decay, Primakoff and Bremsstrahlung emission of the dark matter in various stellar systems. The viable parameter space may be linked to anomalies in future X-ray telescopes.

hep-ph↗

arXiv2023

Faster Detours in Undirected Graphs

The $k$-Detour problem is a basic path-finding problem: given a graph $G$ on $n$ vertices, with specified nodes $s$ and $t$, and a positive integer $k$, the goal is to determine if $G$ has an $st$-path of length exactly $\text{dist}(s, t) + k$, where $\text{dist}(s, t)$ is the length of a shortest path from $s$ to $t$. The $k$-Detour problem is NP-hard when $k$ is part of the input, so researchers have sought efficient parameterized algorithms for this task, running in $f(k)\text{poly}(n)$ time, for $f$ as slow-growing as possible. We present faster algorithms for $k$-Detour in undirected graphs, running in $1.853^k \text{poly}(n)$ randomized and $4.082^k \text{poly}(n)$ deterministic time. The previous fastest algorithms for this problem took $2.746^k \text{poly}(n)$ randomized and $6.523^k \text{poly}(n)$ deterministic time [Bezáková-Curticapean-Dell-Fomin, ICALP 2017]. Our algorithms use the fact that detecting a path of a given length in an undirected graph is easier if we are promised that the path belongs to what we call a "bipartitioned" subgraph, where the nodes are split into two parts and the path must satisfy constraints on those parts. Previously, this idea was used to obtain the fastest known algorithm for finding paths of length $k$ in undirected graphs [Björklund-Husfeldt-Kaski-Koivisto, JCSS 2017]. Our work has direct implications for the $k$-Longest Detour problem: in this problem, we are given the same input as in $k$-Detour, but are now tasked with determining if $G$ has an $st$-path of length at least $\text{dist}(s, t) + k.$ Our results for k-Detour imply that we can solve $k$-Longest Detour in $3.432^k \text{poly}(n)$ randomized and $16.661^k \text{poly}(n)$ deterministic time. The previous fastest algorithms for this problem took $7.539^k \text{poly}(n)$ randomized and $42.549^k \text{poly}(n)$ deterministic time [Fomin et al., STACS 2022].

cs.DS↗

arXiv2023

Correlative Preference Transfer with Hierarchical Hypergraph Network for Multi-Domain Recommendation

Advanced recommender systems usually involve multiple domains (such as scenarios or categories) for various marketing strategies, and users interact with them to satisfy diverse demands. The goal of multi-domain recommendation (MDR) is to improve the recommendation performance of all domains simultaneously. Conventional graph neural network based methods usually deal with each domain separately, or train a shared model to serve all domains. The former fails to leverage users' cross-domain behaviors, making the behavior sparseness issue a great obstacle. The latter learns shared user representation with respect to all domains, which neglects users' domain-specific preferences. In this paper we propose $\mathsf{H^3Trans}$, a hierarchical hypergraph network based correlative preference transfer framework for MDR, which represents multi-domain user-item interactions into a unified graph to help preference transfer. $\mathsf{H^3Trans}$ incorporates two hyperedge-based modules, namely dynamic item transfer (Hyper-I) and adaptive user aggregation (Hyper-U). Hyper-I extracts correlative information from multi-domain user-item feedbacks for eliminating domain discrepancy of item representations. Hyper-U aggregates users' scattered preferences in multiple domains and further exploits the high-order (not only pair-wise) connections to improve user representations. Experiments on both public and production datasets verify the superiority of $\mathsf{H^3Trans}$ for MDR.

cs.IR↗