arXiv subjects
Publications and source records attributed to Jiaming Xu.
We prove uniform endpoint estimates, killed local limits, and conditioned-bridge invariance principles for triangular arrays of centered, aperiodic, integer-valued random walks with uniform exponential tails. The endpoint estimates cover all nonnegative heights, while the local limits treat positive diffusive and zero endpoints. The increment law may vary with the scaling parameter.
For every $β>0$, we establish multi-time soft-edge moment convergence for a class of Jack processes, including the Jack--Plancherel process, a discrete $β$-analogue of Dyson Brownian motion. The limiting moments admit an absolutely convergent expansion in terms of nonnegative Brownian bridges decorated by pairs of equal and opposite jumps. At equal times, we identify this limit with the joint Laplace statistics of the Airy$_β$ process for $β\geq1$. The same Brownian expansion yields an asymptotic $β$-topological expansion of the marginal $b$-conjecture and, at $β=2$, an explicit nonnegative formula for the Witten--Kontsevich intersection numbers.
We characterize central limit theorems for polynomial linear statistics of continuous $N$-particle systems on $\mathbb R$, in both the fixed-temperature regime $θ=β/2>0$ and the high-temperature regime $Nθ\toγ>0$. In each regime, we give necessary and sufficient conditions in terms of the coefficients of the logarithmic Bessel generating function, together with an explicit combinatorial formula for the limiting covariance. At fixed temperature, this formula recovers the classical second-order free moment--cumulant relation, up to the factor $1/θ$; at high temperature, it yields new second-order free $γ$-cumulants and their covariance relations. The proof combines moment extraction through Dunkl operators with a topological expansion of the logarithmic multivariate Bessel function indexed by ribbon graphs on surfaces. This expansion gives a topological interpretation of the free-cumulants: only genus zero contributes at fixed temperature, whereas arbitrarily high genera contribute at high temperature. As applications, we prove that $β$-addition preserves the CLT in both regimes and determine its limiting covariance from the input free cumulants, and establish a suitably rescaled transition from the high-temperature covariance to its fixed-temperature counterpart as $γ\to\infty$.
Speculative decoding has become a mainstream technique for accelerating large language model (LLM) inference by using a lightweight draft model to generate candidate tokens that are subsequently verified by the target model. However, agentic workloads introduce long and continuously evolving contexts and frequent multi-turn interactions. Under such workloads, we observe that existing draft models suffer from up to an 80% degradation in acceptance length, while maintaining their historical KV cache introduces substantial system overhead. In this paper, we identify the growing historical context as a common source of both problems and introduce DLite, a history-free speculative decoding framework for agentic AI. DLite directly reuses contextual hidden states from the target model and performs local speculative prediction without explicitly maintaining the historical context, transforming an increasingly complex modeling problem into local simple prediction problem. A lightweight sequential head further restores intra-block causal dependencies with low overhead. To effectively train this heterogeneous history-free architecture, we introduce a tailored two-stage training strategy. Experiments on general-purpose, long-context and agentic workloads show that DLite achieves 2-6 acceptance length and outperforms the state-of-the-art speculative decoding method, DSpark, up to 70%.
Training language agents on long-horizon interactive tasks is challenging because sparse terminal rewards provide weak credit signals for intermediate actions. Existing group-based methods either assign a shared trajectory-level advantage or estimate step-level advantages from state groups, which may conflate the current action with subsequent decisions. We propose Prefix Tree Group Policy Optimization (PTGPO), a critic-free method that constructs prefix trees over trajectory suffixes within anchor-state groups. PTGPO assigns each tree edge a credit given by the difference between its child and parent empirical mean returns, capturing the conditional return change revealed by each additional action. These prefix-tree credits provide fine-grained learning signals without requiring a critic or additional rollouts. Experiments on interactive benchmarks ALFWorld, WebShop and Sokoban show that PTGPO consistently improves over RL baselines, demonstrating its effectiveness.
We study the random geometric graph formed by connecting $n$ independent uniform points on $\mathbb S^{d-1}$ whenever their inner product exceeds a threshold chosen to give edge density $p$. We establish the conjectured dimensionality threshold for indistinguishability from the Erdös-Rényi graph $G(n,p)$ throughout the sparse regime with polynomially growing average degree. Specifically, for every fixed $δ>0$, if $p\to0$, $p\ge n^{-1+δ}$, and $d\gg (np\log(1/p))^3$, then the Kullback-Leibler (KL) divergence between the two distributions vanishes. Our proof builds on the posterior analysis framework introduced in previous work of the authors, combining a truncated second moment analysis with Fourier and spherical harmonic expansions. As in prior works, we reduce the KL bound to controlling a truncated $χ^2$-divergence $Δ$ for the neighborhood of the last vertex conditional on the graph induced by the preceding vertices. We then bound $Δ$ using a Fourier expansion of the conditional likelihood ratio for this neighborhood, where the high-frequency contribution is made negligible by truncation to a typical-degree event, while a spherical harmonic expansion approximates the low-frequency contribution in terms of posterior moments of bounded-degree harmonic polynomials. The key observation is that these moments and $Δ$ satisfy a coupled system of cavity recurrences, yielding a self-bounding inequality that implies the desired KL bound.
The inference efficiency of Multimodal Large Language Models (MLLMs) is severely constrained by massive visual token sequences induced by high-resolution inputs, with computational cost scaling quadratically. Existing approaches primarily focus on downstream token compression, while overlooking a fundamental upstream inefficiency: input resolution is treated as a static, task-agnostic hyperparameter. We propose Task-Conditioned Resolution Routing (TCRR), which formulates visual compression as a task-conditioned decision and employs a lightweight cross-modal router that conditions backbone visual representations on textual semantics via feature-wise modulation and cross-attention to predict the minimal sufficient compression level per query. To support this, we curate a dataset of 500k samples across 12 task categories, labeled via a teacher-oracle pipeline to approximate Pareto-optimal compression scales. Extensive experiments across diverse architectures show that TCRR achieves a superior efficiency frontier, specifically reducing visual FLOPs by 40.9% and latency by 53.7% on Qwen3-VL-8B while preserving competitive performance. Further analysis of scaling behavior confirms that dynamically routing visual compression enables optimal resource allocation without modifying the MLLM backbone.
The problems of designing sparse networks arise frequently in resource allocation and operations research. In production systems, for example, sparse process flexibility designs are used to handle uncertain demand effectively: the goal is to construct the sparsest bipartite graph between supply and demand that still achieves an expected fulfilled demand comparable to that of a fully flexible system. In middle-mile transportation, sparse delivery-route subgraphs that sustain large matchings after random node deletions help reduce delivery costs; here, the goal is to design the sparsest graph whose maximum matching size remains comparable to that of the fully connected graph under node deletions. The design of sparse networks has been studied extensively, with state-of-the-art results providing order-wise optimal designs for both bipartite and unipartite networks (Chen et al., 2015; Feng et al., 2024). However, identifying designs that achieve the sharp theoretical limit -- where the average degree asymptotically matches the lower bound of any graph to achieve a given loss level, has remained open. In this paper, we prove that the random regular graph achieves this sharp optimal condition in both bipartite and unipartite settings. Numerical experiments further validate this optimality. Our results highlight a practical guideline for sparse flexibility networks: designs that combine degree regularity with dispersed edge placement can achieve optimal performance under uncertainty.
Multimodal large language models (MLLMs) have substantially advanced mobile agents, yet proactive mobile assistance remains challenging because agents must decide when to intervene before determining how to assist. Existing systems often implement these two decisions within a unified MLLM-based pipeline, leading to goal misalignment between conservative intervention filtering and comprehensive assistance generation, as well as redundant inference when the agent should remain silent. To address these limitations, we propose the Pre-Reasoning Perception Framework (PRPF), a two-stage framework built on perceiving before reasoning. PRPF introduces a lightweight Multimodal Proactive Perceptor (MPP) for intervention gating and context compression, and activates the Proactive Agent Reasoner (PAR) only when intervention is warranted. Experiments on the ProactiveMobile benchmark show that PRPF substantially reduces false trigger rates (FTR) while improving success rates (SR) and inference efficiency over the ProactiveMobile baseline.
We introduce and study the perturbed $β$-corners process, a deformation of the classical $β$-corners process. The latter is a probability measure on interlacing arrays of real numbers that, for the classical values $β=1,2,4$, describes the joint distribution of eigenvalues of principal submatrices of a Gaussian random matrix with the corresponding GOE/GUE/GSE symmetry. For classical $β$, the perturbed process arises from adding a deterministic diagonal matrix $A=diag(a_1,...,a_N)$ to a GOE/GUE/GSE matrix. The eigenvalues of the resulting random matrix depend symmetrically on $a_1,...,a_N$, but this symmetry does not extend to the whole corners process. We extend the construction to all $β>0$ via multivariate Bessel functions, and analyze the crystallization ($β\to\infty$) of the resulting interlacing array, proving a law of large numbers and a central limit theorem in two regimes. For fixed perturbation, the eigenvalue repulsion dominates, and the array crystallizes on the same lattice of polynomial-derivative roots, with the same discrete Gaussian free field fluctuations, as in the unperturbed case treated by Gorin and Marcus (arXiv:1706.07393). New phenomena appear in the second regime, where the $a_i$'s grow linearly in $β$. Then the external source competes with the repulsion at leading order. Here the array freezes on a deformed lattice characterized by a coupled system of optimality equations. The fluctuations are governed by the same discrete Gaussian free field, now attached to the deformed lattice. The deformed lattice equations decouple in the special case of a single spike in the last coordinate. Then the deformed lattice is obtained explicitly by applying one shifted derivative $D_c f = f' + cf$ followed by iterated ordinary derivatives.
We show that the lower edge of the appropriately scaled size $n$ Laguerre beta-ensemble with parameter $a=a_n$ converges to the $\operatorname{Airy}_β$ process as $n\to \infty$ when $a_n\to \infty$ and $\tfrac{a_n}{n}\to 0$. This completes the picture of the possible edge scaling limits of the Laguerre beta-ensemble with a fixed $β>0$. When $a_n\gg (\log \log n)^3$ our proof establishes operator level convergence of the inverse of the scaled Dumitriu-Edelman tridiagonal matrix to the inverse of the stochastic Airy operator. Our methods allow us to prove similar operator level limits for the known soft edge scaling limits of the Laguerre and Gaussian beta-ensembles. For $a_n\le (\log n)^{1/2}$ we give a different argument that relies on coupling and a result of Dumaz-Li-Valko for the transition between the hard and soft edge limits of the Laguerre beta-ensemble.
Suppose we observe two sets of $n$ Gaussian vectors in $\mathbb{R}^d$, with the promise that, after applying a permutation of $[n]$ and a rotation of $\mathbb{R}^d$, the two sets are $ρ$-correlated. The Procrustes matching problem asks us to recover the unknown permutation of $[n]$ that aligns the two sets. The problem is well-studied in the low-dimensional regime $d=O(\log n)$, but the high-dimensional regime $d\gg \log n$ has remained largely uncharted: prior matching guarantees require nearly perfect correlation $ρ=1-o(1)$, even for information-theoretic recovery. Our main result is a polynomial-time algorithm for exact recovery at constant correlation. The algorithm works by computing and comparing weighted counts of a specially chosen family of ``wide'' trees. So long as $d\ge \mathrm{polylog}(n)$, the algorithm succeeds with high probability for any $ρ^2>\sqrtα$, where $α\approx 0.338$ is Otter's tree-counting constant. We complement this algorithmic result with an improved information-theoretic guarantee, showing that exact recovery is possible when $ρ^2 \gtrsim \max\{\log n/d,\sqrt{\log n/n}\}$. We also carry out a low-degree advantage calculation, which suggests that the condition $ρ^2 > \sqrtα$ is necessary for any tree-counting algorithm.
We revisit the classical broken sample problem: Two samples of i.i.d.\ data points ${\mathbf{X}}=\{X_{1},\ldots , X_{n}\}$ and ${\mathbf{Y}}=\{Y_{1},\ldots ,Y_{m}\}$ are observed without correspondence with $m\leq n$. Under the null hypothesis, ${\mathbf{X}}$ and ${\mathbf{Y}}$ are independent. Under the alternative hypothesis, ${\mathbf{Y}}$ is correlated with a random subsample of ${\mathbf{X}}$, in the sense that $(X_{π(i)},Y_{i})$'s are drawn independently from some bivariate distribution for some latent injection $π:[m] \to [n]$. Originally introduced by DeGroot, Feder, and Goel to model matching records in census data, this problem has recently gained renewed interest due to its applications in data de-anonymization, data integration, and target tracking. Despite extensive research over the past decades, determining the precise detection threshold has remained an open problem even for equal sample sizes ($m=n$). Assuming $m$ and $n$ grow proportionally, we show that the sharp threshold is given by a spectral and an $L_{2}$ condition of the likelihood ratio operator, resolving a conjecture of Bai and Hsing in the positive. These results are extended to high dimensions and settle the sharp detection thresholds for Gaussian and Bernoulli models.
Generative models have shown promising results for speech enhancement (SE), but they often rely on multi-step inference, limiting low-latency deployment. We propose SB-RF, a one-step generative framework that integrates Rectified Flow (RF) with Schrödinger Bridge (SB) theory. During training, SB-RF samples intermediate states from an SB time marginal and trains a conditional velocity field with the RF velocity-matching objective. At inference, SB-RF starts from the noisy observation and applies a single Euler update. Experiments show that SB-RF achieves competitive performance among generative methods on the VoiceBank-DEMAND benchmark. To further assess performance beyond this standard setting, we evaluate SB-RF on a simulated low signal-to-noise ratio test set using an expanded training dataset. Under these conditions, SB-RF achieves superior performance over the compared baselines, supporting its potential for real-world applications.
A random geometric graph (RGG) is generated by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the unit sphere in $\mathbb{R}^d$, and then connecting each pair $(i,j)$ if $\langle x_i,x_j\rangle$ exceeds some threshold $τ$. We study the sharp detection threshold -- the largest dimension at which the RGG can be statistically distinguished from the Erdős--Rényi graph with the same edge density $p$. This threshold is conjectured to be $d \asymp (nh(p))^3$, where $h(p)=p \log \frac{1}{p} + (1-p) \log \frac{1}{1-p}$ is the binary entropy function. Previous works proved this conjecture for dense graphs with constant $p$ and, up to polylogarithmic factors, very sparse graphs with $p=Θ(1/n)$. In this paper, we prove that detection is impossible when $d\gg (nh(p))^3$ and $d\ge (1+ε) n$ for any constant $ε>0$, thereby resolving the conjecture in the regime $p\gtrsim n^{-2/3}/\log n$ and improving upon the state of the art in the regime $1/n \ll p \ll n^{-2/3}/\log n$. The key to our proof is a sharp analysis of the posterior distribution of the latent points given the observed graph, obtained through an information-theoretic comparison argument combined with strong log-concavity.
Robust state estimation and mapping in long-term, large-scale, and highly dynamic environments remains a key challenge in robotics. Existing LiDAR-Inertial-Visual Odometry (LIVO) systems achieve strong local accuracy but suffer from accumulated drift over long distances and may fail in geometrically degraded or textureless scenes. Meanwhile, GNSS-aided fusion frameworks often rely on LiDAR or visual odometry for state prediction and outlier rejection, making them vulnerable when odometry degenerates. To address these limitations, we propose a tightly coupled LiDAR-Inertial-Visual-GNSS fusion framework based on an Error-State Iterated Kalman Filter. An online spatiotemporal alignment module using Dynamic Time Warping is introduced for highly dynamic conditions. To better exploit GNSS precision, we develop observation models based on Doppler shifts and fixed-anchor Time-Differenced Carrier Phase, providing millimeter-level relative constraints without augmenting historical anchor states. We further design a degeneracy-aware dual-mode outlier rejection strategy that switches between LIVO-prior-guided rejection and GNSS-aided recovery according to the LIVO degeneracy level. Experiments on the public M3DGR dataset and a custom 20~m/s fixed-wing UAV dataset demonstrate that our system reduces accumulated drift and map ghosting, outperforming state-of-the-art methods in accuracy and robustness.
Gaussian Splatting has enabled real-time neural rendering, yet existing LiDAR-inertial-visual (LIV) Gaussian mapping pipelines remain fragile under illumination changes and texture-deficient scenes due to their reliance on RGB photometric cues. We present LIT-GS, a LiDAR-inertial-thermal Gaussian Splatting framework that injects LiDAR-derived plane geometry as an explicit constraint in both pose/structure refinement and Gaussian optimization. Specifically, we exploit LIV visual map points as confidence-aware cross-modal anchors to establish reliable thermal-LiDAR associations, and incorporate weighted LiDAR point-to-plane residuals into bundle adjustment to jointly refine camera poses and 3D points under weak thermal supervision. Building on the refined structure, we further introduce a LiDAR-plane-regularized differentiable splatting objective that constrains rendered 3D points to align with locally observed planes, mitigating surface thickening and structural drift in low-contrast thermal imagery. Experiments on proprietary sequences and public datasets demonstrate that LIT-GS consistently improves geometric accuracy and rendering quality over state-of-the-art LIV-based Gaussian Splatting baselines, particularly in challenging lighting conditions.
This paper studies the problem of inferring a $k$-factor, specifically a spanning $k$-regular graph, planted within an Erdos-Renyi random graph $G(n,λ/n)$. We show that as the average degree $λ$ surpasses the critical threshold of $1/k$, the inference problem undergoes a transition from almost exact recovery to partial recovery. Moreover, as $λ$ tends to infinity, the accuracy of recovery diminishes to zero. In addition, we characterize the recovery accuracy of a linear-time iterative pruning algorithm and show that it achieves almost exact recovery when $λ< 1/k$. A key component of our analysis is a two-step cycle construction: we first build trees through local neighborhood exploration and then connect them by sprinkling using reserved edges. Interestingly, for proving impossibility of almost exact recovery, we construct $Θ(n)$ many small trees of size $Θ(1)$, whereas for establishing the algorithmic lower bound, a single large tree of size $Θ(\sqrt{n\log n})$ suffices.