arXiv subjects

Zixuan Xu

Publications and source records attributed to Zixuan Xu.

At least 19 recordsLinked to original sources

arXiv2026

Giant-exchange-driven Vectorial Control of a Minimal Topological Magnet in Eu3In2As4

The interplay between magnetism and band topology provides a route to controlling quantum states of matter, yet its realization in materials is often constrained by weak exchange coupling and complex electronic structures. Here, a giant exchange coupling is identified in the newly predicted topological magnet Eu3In2As4, giving rise to magnetization-dependent band shifts of up to 300 meV. Together with its intrinsically soft magnetic response, this strong cou-pling enables systematic tuning of topological phases by both the magnitude and orientation of applied magnetic fields. The magneto-topological phase diagram is mapped out in which an antiferromagnetic topological insulator ground state evolves, under modest fields, into a pro-posed intermediate 2/3-ferrimagnetic phase, and further into fully polarized ferromagnetic states predicted to host either Weyl or nodal-ring semimetals. Notably, the Weyl phase corresponds to a minimal model hosting a single pair of Weyl nodes. Quantum oscillations, anomalous Hall transport and magneto-infrared spectroscopy consistently reveal exchange-driven band recon-struction across these transitions. Rotation of the magnetization theoretically provides an effi-cient means to tune the momentum-space positions and separations of the Weyl nodes. These results establish Eu3In2As4 as a model system for exploring how strong exchange coupling can be used to control topological band structures with minimal complexity.

cond-mat.mtrl-sci↗

arXiv2026

Asymptotically sharp bounds for affine subspace statistics in $\mathbb F_2^n$

Given a subset $A \subseteq \mathbb F_2^n$, we can consider the distribution of the intersection size of $A$ with a uniformly random $d$-flat $F$. Motivated by the edge statistics problem and the hypercube statistics problem, the affine subspace statistics problem concerns the maximum of $\mathbb{P}[|F\cap A|=s]$ among $A \subseteq \mathbb F_2^n$ for any fixed $s\in\{1,\dots,2^d\}$ over a uniformly random $d$-flat $F$. We use $\lambda^*(d,s)$ to denote the limit of the maximum when $n$ goes to infinity. In this note, we prove tight bounds for $\lambda^*(d,s)$ in two different regimes. For $s=j2^k$ where $j$ is a positive odd integer, the best known lower bound construction achieving $\lambda^*(d,s)\ge 1-2^{-k}$ is due to taking $A$ as the union of $j$ parallel $(n-d+k)$-flats in $\mathbb F_2^n$. Our main result is a matching upper bound with an additive error term of $O(2^{-3k/2})$. We also study the case $s=1$, where we determine $\lambda^*(d,1)$ exactly. We show that the random construction where each point is included with probability $2^{-d}$ is optimal.

math.CO↗

arXiv2026

Understanding Perspectives of Patients, Caregivers and Clinicians towards Emerging Collaborative-decision Making Technologies

In pediatrics, patients, caregivers, and clinicians share responsibility for health decisions, but limited collaboration can undermine outcomes. We conducted a qualitative study examining decision-makers perceptions toward collaborative decision-making technologies, including interactive dashboards, VR simulators, and AI voice assistants. Findings reveal differences in user opinions across groups and indicate technology acceptance is linked to users trust of these technologies. Technology developers and researchers need to explore design and implementation strategies that build and facilitate trust or appropriate distrust between users and these novel technologies before these tools can effectively support collaborative decision-making.

cs.HC↗

arXiv2026

Vertex-minor universality of a random graph

Given a graph $G$ and a vertex $v\in V(G)$, a local complementation at $v$ on $G$ is an operation that replaces the induced graph on the neighborhood of $v$ by its complement. A graph $H$ is a vertex-minor if $H$ can be obtained from $G$ by a sequence of vertex deletions and local complementation. A graph is said to be $k$-vertex-minor universal if it contains every $k$-vertex graph on any $k$-subset of vertices as a vertex minor. Previously, Ascoli--Fredrickson--Fredrickson--McFarland--Post proved that with high probability $G(n,1/2)$ is $Ω(\sqrt{n})$-vertex-minor universal. Furthermore, they conjectured that with high probability $G(n,p)$ and $G(n,1-p)$ are $Ω(p\sqrt{n})$-vertex-minor universal for all $ω(1/\sqrt{n})\le p\le 1/2$. In this short note, we confirm this conjecture up to an extra logarithm factor and show that this is true with probability $1-2^{-Ω(p^2n)}$ if $Ω(\log n/\sqrt{n})\le p\le 1/2$. Together with a complementary result which applies to the regime where $1/\sqrt{n}\le p\le n^{-1/3}$ produced by an internal model at OpenAI, the conjecture is fully confirmed.

math.CO↗

arXiv2026

Even-degeneracy of a random graph

A graph is even-degenerate if one can iteratively remove a vertex of even degree at each step until at most one edge remains. Recently, Janzer and Yip showed that the Erdős--Renyi random graph $G(n,1/2)$ is even-degenerate with high probability, and asked whether an analogous result holds for any general $G(n,p)$. In this paper, we answer this question for any constant $p\in (0,1)$ in affirmation by proving that $G(n,p)$ is even-degenerate with high probability.

math.CO↗

arXiv2026

A GPU-Accelerated Framework for Multi-Attribute Range Filtered Approximate Nearest Neighbor Search

Range-filtered approximate nearest neighbor search (RFANNS) is increasingly critical for modern vector databases. However, existing solutions suffer from severe index inflation and construction overhead. Furthermore, they rely exclusively on CPUs for the heavy indexing and query processing, significantly restricting the throughput due to the limited memory bandwidth and parallelism. In this paper, we present Garfield, a GPU-accelerated framework for multi-attribute range filtered ANNS that overcomes these bottlenecks through designing a lightweight index structure and hardware-aware execution pipeline. Garfield introduces the GMG index, which partitions data into cells and builds local graph indexes. It guarantees linear storage and indexing overhead by adding a constant number of cross-cell edges. For queries, Garfield utilizes a cluster-guided ordering strategy that reorders query-relevant cells, enabling a highly efficient cell-by-cell traversal on the GPU that aggressively reuses candidates as entry points across cells. To handle datasets exceeding GPU memory, Garfield features a cell-oriented out-of-core pipeline. It dynamically schedules cells to minimize the number of active queries per batch and overlaps GPU computation with CPU-to-GPU index streaming. Extensive evaluations demonstrate that Garfield reduces index size by 4.4x, while delivering 119.8x higher throughput than state-of-the-art RFANNS methods.

cs.DB↗

arXiv2026

Affine Subspace Statistics in the Hypercube

We study the intersection statistics of affine subspaces in the hypercube $\mathbb{F}_2^n$, motivated by recent work of Alon, Axenovich, and Goldwasser on the intersection statistics of axis-aligned subcubes of an $n$-dimensional cube. Let $d\ge 1$ and $0\le s\le 2^d$ be nonnegative integers. For a subset $A\subseteq \mathbb{F}_2^n$ where $n\ge d$, define $λ^*(n,d,s,A)$ to be the fraction of affine $d$-flats in $\mathbb{F}_2^n$ that intersect $A$ at exactly $s$ points. Let $λ^*(n,d,s) = \max_{A\subseteq \mathbb{F}_2^n}λ^*(n,d,s,A)$ and let $λ^*(d,s) = \lim_{n\to \infty}λ^*(n,d,s)$. We show that when $s = j\cdot 2^k$ with $j$ odd and $k\ge 1$, we have $λ^*(d,s)\to 1-Θ(2^{-k})$ as $d\to \infty$. This implies that $λ^*(d,s)$ is controlled up to constant factors by the $2$-adic valuation of $s$ when $s$ is even. When $s$ is odd, we show that $λ^*(d,s)\le \frac{1}{2}$ in contrast to the behavior of axis-aligned subcube statistics. We also present several upper and lower bounds for certain specific values of $s$.

math.CO↗

arXiv2026

Co-designing for the Triad: Design Considerations for Collaborative Decision-Making Technologies in Pediatric Chronic Care

In pediatric chronic care, the triadic relationship among patients, caregivers, and healthcare providers introduces unique challenges for youth in managing their conditions. Diverging values, roles, and asymmetrical situational awareness across decision-maker groups often hinder collaboration and affect health outcomes, highlighting the need to support collaborative decision-making. We conducted co-design workshops with 6 youth with chronic kidney disease, 6 caregivers, and 7 healthcare providers to explore how digital technologies can be designed to support collaborative decision-making. Findings identify barriers across all levels of situational awareness, ranging from individual cognitive and emotional constraints, misaligned mental models, to relational conflicts regarding care goals. We propose design implications that support continuous decision-making practice, align mental models, balance caregiver support and youth autonomy development, and surface potential care challenges. This work advances the design of collaborative decision-making technologies that promote shared understanding and empower families in pediatric chronic care.

cs.HC↗

arXiv2026

Uniform Set Systems with Uniform Witnesses

Frankl--Pach and Erdős conjectured that any $(d+1)$-uniform set family $\mathcal{F}\subseteq \binom{[n]}{d+1}$ with VC-dimension at most $d$ has size at most $\binom{n-1}{d}$ when $n$ is sufficiently large. Ahlswede and Khachatrian showed that the conjecture is false by giving a counterexample of size $\binom{n-1}{d}+\binom{n-4}{d-2}$. For a set family $\mathcal{F}\subseteq \binom{[n]}{d+1}$, the condition that its VC-dimension is at most $d$ can be reformulated as follows: for any $F\in\mathcal{F}$, there exists a set $B_F\subseteq F$ such that $F\cap F'\neq B_F$ for all $F'\in\mathcal{F}$. In this direction, the first author, Xu, Yip, and Zhang conjectured that the bound $\binom{n-1}{d}$ holds if we further assume that $|B_F|=s$ for every $F\in \mathcal{F}$ and for some fixed $0\leq s\leq d$. The case $s=0$ is exactly the Erdős--Ko--Rado theorem, and the cases $s\in \{1,d\}$ were proved in the paper by the first author, Xu, Yip, and Zhang. In this short note, we show that the conjecture holds when $s\leq d/2$, and the maximal constructions are stars. Moreover, we construct non-star set families of size $\binom{n-1}{d}$ satisfying the condition for $d/2<s\leq d-1$, which suggests that the problem is substantially different in these cases.

math.CO↗

arXiv2026

Nondegenerate hyperplane covers of the hypercube

We consider collections of hyperplanes in $\mathbb{R}^n$ covering all vertices of the $n$-dimensional hypercube $\{0,1\}^n$, which satisfy the following nondegeneracy condition: For every $v\in \{0,1\}^n$ and every $i=1,\dots,n$, we demand that there is a hyperplane $H$ in the collection with $v\in H$ such that the variable $x_i$ appears with a non-zero coefficient in the hyperplane equation describing $H$. We prove that every collection $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ covering $\{0,1\}^n$ with this nondegeneracy condition must have size $|\mathcal{H}|\ge n/2$. This bound is tight up to constant factors. It generalizes a recent result concerning the intensively studied skew covers problem, which asks about the minimum possible size of a hyperplane cover of $\{0,1\}^n$ in which all variables appear with non-zero coefficients in all hyperplane equations. As an application of our result, we also obtain an essentially tight bound for an old problem about collections of hyperplanes slicing all edges of the $n$-dimensional hypercube, in the case where all of the hyperplanes have bounded integer coefficients.

math.CO↗

arXiv2026

SaFeR-ToolKit: Structured Reasoning via Virtual Tool Calling for Multimodal Safety

Vision-language models remain susceptible to multimodal jailbreaks and over-refusal because safety hinges on both visual evidence and user intent, while many alignment pipelines supervise only the final response. To address this, we present SaFeR-ToolKit, which formalizes safety decision-making as a checkable protocol. Concretely, a planner specifies a persona, a Perception $\to$ Reasoning $\to$ Decision tool set, and a constrained transition graph, while a responder outputs a typed key-value tool trace before the final answer. To make the protocol reliably followed in practice, we train a single policy with a three-stage curriculum (SFT $\to$ DPO $\to$ GRPO), where GRPO directly supervises tool usage beyond answer-level feedback. Our contributions are two-fold: I. Dataset. The first tool-based safety reasoning dataset, comprising 31,654 examples (SFT 6k, DPO 18.6k, GRPO 6k) plus 1k held-out evaluation. II. Experiments. On Qwen2.5-VL, SaFeR-ToolKit significantly improves Safety/Helpfulness/Reasoning Rigor on 3B (29.39/45.04/4.98 $\to$ 84.40/71.13/78.87) and 7B (53.21/52.92/19.26 $\to$ 86.34/80.79/85.34), while preserving general capabilities (3B: 58.67 $\to$ 59.21; 7B: 66.39 $\to$ 66.81). Codes are available at https://github.com/Duebassx/SaFeR_ToolKit.

cs.LG↗

arXiv2025

Defect Engineering for Stabilizing Magnetic and Topological Properties in Mn(Bi1-xSbx)2Te4

MnBi2Te4 is a versatile platform for exploring diverse topological quantum states, yet its potential is hampered by intrinsic antisite defects. While Sb substitution has been employed to tune the Fermi level towards the charge neutral point, it exacerbates the formation of Mn-Sb antisite defects. Here, we address this challenge by combining first-principles calculations with strategic synthesis to systematically investigate and control antisite defects in Mn(Bi1-xSbx)2Te4. Our calculations reveal that increasing antisite defect density progressively destroys the field-forced magnetic Weyl state, eventually driving the system into a trivial magnetic insulator. Motivated by these findings, we develop an optimized chemical vapor transport method, yielding high-quality Mn(Bi1-xSbx)2Te4 crystals with significantly reduced antisite defect density. The emergence of strong Shubnikov-de Haas oscillations in the forced ferromagnetic state and a pronounced anomalous Hall effect near charge neutrality, with opposite signs for n- and p-type samples, confirms the type-II Weyl semimetal nature. These findings underscore the critical role of antisite defects in determining the magnetic and topological properties of Mn(Bi1-xSbx)2Te4 and establish defect engineering via optimized synthesis as a crucial strategy for realizing its exotic magnetic topological states.

cond-mat.mtrl-sci↗

arXiv2025

Improved lower bound for hypercube edge slicing

How many hyperplanes in $\mathbb{R}^n$ are needed in order to slice every edge of the $n$-dimensional hypercube with vertex set $\{\pm 1\}^n$? Here, we say that a hyperplane $H\subseteq \mathbb{R}^n$ slices an edge of the hypercube if it contains exactly one interior point of the edge. The problem of determining the minimum possible size of a collection of hyperplanes in $\mathbb{R}^n$, such that every edge of the hypercube is sliced by at least one of these hyperplanes, is more than 50 years old and has been studied by many researchers. We prove that, for sufficiently large $n$, at least $Ω(n^{13/19}\log^{-32/19}n)$ hyperplanes are needed, improving upon the best previous lower bound $Ω(n^{2/3}\log^{-4/3}n)$ due to Klein.

math.CO↗

arXiv2025

Interpreting the Hubble tension with a cascade decaying dark matter sector

Hubble tension can be alleviated by altering either early- or late-time $\Lambda$CDM. With only one of these effects introduced, early dark energy remains the only solution capable of reducing the tension to the $3\sigma$ level or below. In this work, we instead consider a modification of the dark matter sector that incorporates both the early- and late-time effects, with the goal of achieving the largest possible value of $H_0$ within this framework. As a realization of these two-fold effects, we study a cascade decaying dark matter model. By fitting the model to the latest datasets of Planck CMB+ DESI BAO+Pantheon (+SH0ES), we find that a 68$\%$ CL value of $H_{0}=68.76\pm0.35 (69.05^{+0.31}_{-0.27})$ km s$^{-1}$ Mpc$^{-1}$ with $\Delta \rm{AIC}=+22.0(18.4)$, and larger value of $H_0$ can be obtained by adjusting parameter priors but with a cost of significantly increased value of $\Delta \rm{AIC}$. These findings revise the earlier results on the tension level in the literature. For completeness, we show that the parameter regions favored by the cosmological datasets are compatible with complementary limits arising from the Big Bang Nucleosynthesis, neutrino flux, and structure formation.

astro-ph.CO↗

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

Large-Small Model Collaboration for Enhancing Edge-Deployed Small Models

Edge devices host domain-specific small language models (SLMs) with limited resources, while private clouds offer larger LLMs. We propose G-Boost, an adaptive edge-cloud framework that improves a deployed SLM's task performance without parameter updates. It formulates reasoning as a tree search, choosing at each step between SLM-only inference and SLM-LLM logit fusion---which transfers domain knowledge from the SLM's adapted version to the cloud LLM without exposing private data. A process reward model guides Monte Carlo tree search to select beneficial collaboration steps dynamically. The edge runs the SLM and search controller; the cloud hosts the LLM and reward model, exchanging only current context. Evaluated on GSM8K and MATH-500 with Qwen2.5 and LLaMA2, G-Boost outperforms the SLM alone, static fusion, and fine-tuned baselines, gaining up to 8.6 and 10.7 percentage points over MCTS and Proxy-Tuning, respectively. Results confirm that step-level, reward-guided dynamic collaboration enhances reasoning and domain utilization for deployed edge SLMs.

cs.CL↗

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↗