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Rong Chen

Publications and source records attributed to Rong Chen.

At least 19 recordsLinked to original sources

Tree-partitions of graphs with bounded tree-depth

Wood~ recently showed that every graph $G$ of pathwidth $h$ and $\Delta(G)\ge1$ admits a $T$-partition of width at most $4(h+1)^2\Delta(G)$ for some tree $T$ with $pw(T)\leq2h+1$. In this paper, we establish an analogous result for tree-depth, which is a stronger parameter than pathwidth. We prove that every connected graph with tree-depth $h$ admits a $T$-partition of width at most $\mathrm{max}\{1, (4h-10)\Delta(G)+1\}$ for some tree $T$ with $\operatorname{rad}(T)\leq h-1$.

math.CO

A Riemannian Factor Model for Manifold-Valued Time Series

We propose a Riemannian factor model (RFM), a novel framework for analyzing potentially high-dimensional time series data observed on Riemannian manifolds. Such time series are encountered in various applications, including economics, finance, medical imaging, and genomics and microbiome research. The proposed model is geometry-aware and accounts for the inherent nonlinearity in the data. In a high-dimensional asymptotic regime, where the manifold dimension is allowed to diverge with the sample size $n$, we establish convergence rates for the estimated loading space. In particular, under short-memory and strong factor conditions, we obtain a dimension-free $n^{-1/2}$ rate, which matches the convergence rate of the high-dimensional linear factor model. Finite-sample performance of the proposed RFM is demonstrated with simulated time series on the Bures--Wasserstein manifolds and products of spheres, as well as an application to monthly realized covariances of selected U.S. stock returns---modeled as time series in the Bures--Wasserstein manifold, where the RFM provides demonstrably interpretable factors and yields competitive predictive performance.

stat.ME

SMetric: Rethink LLM Scheduling for Serving Agents with Balanced Session-centric Scheduling

LLM scheduling is critical to serving, yet it remains unclear how well existing designs fit agentic serving--with LLM requests issued by agents instead of humans. This shifts the workload in two ways: (1) agents act only on complete responses, making the cluster's tokens per second (TPS) the primary goal and relaxing--not eliminating--per-token latency requirements; and (2) requests share much of their KV\$-reuse exceeds 80% of request tokens in a production trace from BAILIAN, versus 54-62% in chat. This paper first contributes a systematic study of request scheduling for agents on two real-world traces. We find that to increase KV\$ reuse, existing schedulers overly prioritize routing requests to instances caching their KV\$, overloading a few while leaving the rest idle, capping TPS. We thus present two key insights: (1) load balance need not sacrifice all KV\$ reuse, thanks to the global-tier KV\$ store and (2) by utilizing the workload's intra-session locality, balancing a small fraction of requests--the first request in each agent session--suffices to balance the cluster without sacrificing most KV\$ reuse on local instances. SMETRIC realizes these insights with balanced session-centric scheduling: it routes each session's first request purely for load balance and its follow-up requests in a cache-aware manner, preserving load balance and local reuse while keeping demand on the global tier low. Using the session turn information as the scheduling metric is deliberate: it is derived efficiently and accurately from the user inputs alone, so the scheduler stays clean and stateless. SMETRIC improves cluster TPS by 10-16% under prefill-decode colocation with a global store and prefill TPS by 2-34% under disaggregation over state-of-the-art schedulers, also with a better per-token latency.

cs.DC

Two-colored generalized Frobenius partitions and minimal-excludant sums over bipartitions

Let $\cpsi_{2,a}(n)$ denote the number of $(2,a)$-colored Frobenius partitions of weight $n$, where the two rows have prescribed length difference. We study the two cases $a=0$ and $a=1$ and connect them with minimal-excludant statistics on bipartitions. Let $\sigma\mex_2(n)$ be the sum of the Lin--Liu bipartition minimal excludants over all bipartitions of $n$, and let $E_2(n)$ be the number of bipartitions whose two component minimal excludants are equal. For all $n\geq 0$, we give a combinatorial proof of \[ \cpsi_{2,0}(n)=2\sigma\mex_2(n) \qquad\text{and}\qquad \cpsi_{2,1}(n)=2\sigma\mex_2(n)-E_2(n). \] These identities give direct combinatorial interpretations of two-colored Frobenius partition functions in terms of bipartition minimal-excludant sums.

math.CO

A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture

In this paper, we prove a generalization of a conjecture of Amdeberhan, Andrews, and Ballantine on double Lambert series. Motivated by a question raised by Cui, Kumar, and Singh concerning the existence of a generalization of this conjecture, we establish an identity in which the coefficients are given by the generalized divisor function $\sigma_k(n)$. As a special case, our result includes the original conjecture.

math.NT

Transformation Formulae and Applications for Double Lambert Series

In this paper, we study a class of double Lambert series and establish several identities and transformation relations for them. These formulae provide useful tools for reducing certain double Lambert series to single Lambert series. As applications, we derive identities related to recent conjectures of Andrews, Dixit, Schultz, and Yee, and of Amdeberhan, Andrews, and Ballantine. We also propose a new proof of a result of Amdeberhan, Andrews, and Ballantine.

math.NT

On tree decompositions whose trees are subgraphs

Fix $k \in \mathbb{N}$ and let $G$ be a connected graph with treewidth at most $k$. We say that $xy \notin E(G)$ is a {\em $k$-ghost-edge} of $G$ if for every tree decomposition $(T, \cB)$ of $G$ with width at most $k$, both $x$ and $y$ are contained in a bag of $(T, \cB)$. Moreover, if $G$ does not contain any $k$-ghost-edges, then $G$ is {\em $k$-ghost-free}. Hickingbotham proposed a conjecture that every connected $k$-ghost-free graph $G$ has a tree decomposition $(T, \cB)$ with width at most $k$ such that $T$ is a subgraph of $G$. In this paper, we prove that Hickingbotham's conjecture is false for all $k\geq3$.

math.CO

Simple is Better: Multiplication May Be All You Need for LLM Request Scheduling

High-quality LLM request scheduling requires meeting two key objectives: ensuring the routed instance has KVCache to accelerate request execution, and ensuring that the workload is balanced across instances. Achieving both objectives is challenging because pursuing one may compromise the other. Current approaches use various combinators (e.g., linear combinations) to compute a scheduling score that combines indicators for the two objectives. These approaches are complex: they either require significant workload-specific hyperparameter tuning or model-hardware-aware simulator development, yet could still lead to suboptimal performance. In this paper, we show that using a simple multiplication of two carefully chosen indicators: one KVCache-aware (new prefill tokens if routed to an instance) and one load-balancing-aware (current batch size of the instance), as the scheduling score (LMETRIC) can achieve both objectives simultaneously without any hyperparameter tuning. The key idea is that the simply multiplied score considers both objectives in a manner similar to a linear combination, but the original hyperparameters cancel out during comparison, so no tuning is needed to find the best parameters. The two indicators are chosen based on our analysis of LLM characteristics. Our extensive experiments show that this simple approach can reduce TTFT by 92% and 39%, and TPOT by 24% and 51%, compared to vLLM-v1 and an in-production scheduler on real-world workloads covering chatbots and coding agents. We also derive the mathematical conditions under which multiplication may fail, and find that such conditions are extremely rare in practice and can be detected (and mitigated) beforehand. LMETRIC has been deployed in production and canary release confirms its effectiveness

cs.DC

Efficient Vector Search in the Wild: One Model for Multi-K Queries

Learned top-K search is a promising approach for serving vector queries with both high accuracy and performance. However, current models trained for a specific K value fail to generalize to real-world multi-K queries: they suffer from accuracy degradation (for larger Ks) and performance loss (for smaller Ks). Training the model to generalize on different Ks requires orders of magnitude more preprocessing time and is not suitable for serving vector queries in the wild. We present OMEGA, a K-generalizable learned top-K search method that simultaneously achieves high accuracy, high performance, and low preprocessing cost for multi-K vector queries. The key idea is that a base model properly trained on K=1 with our trajectory-based features can be used to accurately predict larger Ks with a dynamic refinement procedure and smaller Ks with minimal performance loss. To make our refinements efficient, we further leverage the statistical properties of top-K searches to reduce excessive model invocations. Extensive evaluations on multiple public and production datasets show that, under the same preprocessing budgets, OMEGA achieves 6-33% lower average latency compared to state-of-the-art learned search methods, while all systems achieve the same recall target. With only 16-30% of the preprocessing time, OMEGA attains 1.01-1.28x of the optimal average latency of these baselines.

cs.DB

Deformation mechanisms and compressive response of NbTaTiZr alloy via machine learning potentials

Refractory multi-principal element alloys (MPEAs) are key research focus for excellent high-temp properties and engineering potential. Deformation mechanisms/mechanical behaviors of quaternary NbTaTiZr MPEA under high strain rates/extreme temps remain unclear. We built a variable-composition ML potential for NbTaTiZr, combined with MD simulations to study effects of crystal orientation, strain rate, temp, composition on compressive mechanics. NbTaTiZr shows structural/mechanical anisotropy in compression [111] max yield strength, [110] min (prone to twinning), [100] via local disorder/dislocation slip (dominant 1/2<111> dislocations). At 10^10 s^-1, yield strength rises sharply, disordered structures increase; high strain rates suppress dislocations to promote disordering. Retains high strength at 2100 K. Higher Nb/Ta boosts yield strength, Ti/Zr reduce it. Reveals MPEA mechanical anisotropy and strain-rate-dependent disordering, guiding high-performance refractory alloy design.

cond-mat.mtrl-sci

PRECTR-V2:Unified Relevance-CTR Framework with Cross-User Preference Mining, Exposure Bias Correction, and LLM-Distilled Encoder Optimization

In search systems, effectively coordinating the two core objectives of search relevance matching and click-through rate (CTR) prediction is crucial for discovering users' interests and enhancing platform revenue. In our prior work PRECTR, we proposed a unified framework to integrate these two subtasks,thereby eliminating their inconsistency and leading to mutual benefit.However, our previous work still faces three main challenges. First, low-active users and new users have limited search behavioral data, making it difficult to achieve effective personalized relevance preference modeling. Second, training data for ranking models predominantly come from high-relevance exposures, creating a distribution mismatch with the broader candidate space in coarse-ranking, leading to generalization bias. Third, due to the latency constraint, the original model employs an Emb+MLP architecture with a frozen BERT encoder, which prevents joint optimization and creates misalignment between representation learning and CTR fine-tuning. To solve these issues, we further reinforce our method and propose PRECTR-V2. Specifically, we mitigate the low-activity users' sparse behavior problem by mining global relevance preferences under the specific query, which facilitates effective personalized relevance modeling for cold-start scenarios. Subsequently, we construct hard negative samples through embedding noise injection and relevance label reconstruction, and optimize their relative ranking against positive samples via pairwise loss, thereby correcting exposure bias. Finally, we pretrain a lightweight transformer-based encoder via knowledge distillation from LLM and SFT on the text relevance classification task. This encoder replaces the frozen BERT module, enabling better adaptation to CTR fine-tuning and advancing beyond the traditional Emb+MLP paradigm.

cs.IR

A counterexample to Hickingbotham's conjecture about $k$-ghost-edges

Fix $k\in \mathbb{N}$ and let $G$ be a connected graph with $tw(G)\leq k$. We say that $xy\in E(G^c)$ is a {\em $k$-ghost-edge} of $G$ if for every tree decomposition $(T,\cB)$ of $G$ with width at most $k$, the set $\{x,y\}$ is contained in a bag of $(T,\cB)$. Although a $k$-ghost-edge of $G$ is not an edge of $G$, but it behaves like real edges with respect to tree decomposition of $G$ with width at most $k$. For any graph $G$ with treewidth $k$ and $xy\in E(G^c)$, when there are at least $k+1$ internally vertex disjoint $(x,y)$-paths, Hickingbotham proved that $xy$ is a $k$-ghost-edge of $G$; while when there are at most $k$ internally vertex disjoint $(x,y)$-paths, he conjectured that it is not a $k$-ghost-edge of $G$. In this paper, we prove that this conjecture is wrong.

math.CO

Towards Fully-fledged GPU Multitasking via Proactive Memory Scheduling

The limited HBM capacity has become the primary bottleneck for hosting an increasing number of larger-scale GPU tasks. While demand paging extends capacity via host DRAM, it incurs up to 78x slowdown due to the massive working sets and poor locality of GPU workloads. We observe, however, that GPU memory access patterns are inherently predictable via kernel launch arguments and their asynchronous execution nature. Leveraging this, we propose MSched, an OS-level scheduler that extends GPU context switching to include proactive working set preparation, thereby coalescing fragmented, eventual, and expensive page faults into a single efficient migration. MSched employs a template-based approach to predict working sets with near-perfect accuracy and proposes a co-design between task scheduler and memory manager to enforce a globally optimal page placement policy. Evaluation demonstrates that MSched outperforms demand paging by up to 11.05x for scientific and deep learning workloads, and 57.88x for LLM under memory oversubscription.

cs.OS

Large longitudinal and anomalous transverse Magneto-thermoelectric effect in kagome antiferromagnet FeGe

Topological Kagome magnets, characterized by nontrivial electronic band structures featuring flat band, Dirac cone and van Hove singularities, provide a new avenue for the realization of thermoelectric devices. Unlike the conventional longitudinal Seebeck effect, transverse thermoelectric (TE) effects like the Nernst effect have attracted growing interest due to their unique transverse geometry and potential advantages. Here, we report the observation of a significant transverse thermoelectric conductivity alpha A_zx of 15 A K-1m-1 at low temperatures, together with a pronounced anomalous Nernst effect in the Kagome antiferromagnet FeGe, which exhibits a charge density wave inside the antiferromagnetic (AFM) state. This value is the highest record among known AFM materials. Furthermore, the thermopower at 14 T increases by 102-104% around the canted-AFM (CAFM) transition temperature, Tcant, comparable to that of the well-known AFM thermoelectric materials. These effects are attributed to large Berry curvature arising from the non-collinear spin texture in FeGe, highlighting its potential for enhancing thermoelectric performance and its candidacy for magneto-TE applications in Kagome antiferromagnetic materials.

cond-mat.mtrl-sci

Threshold Tensor Factor Model in CP Form

This paper proposes a new Threshold Tensor Factor Model in Canonical Polyadic (CP) form for tensor time series. By integrating a thresholding autoregressive structure for the latent factor process into the tensor factor model in CP form, the model captures regime-switching dynamics in the latent factor processes while retaining the parsimony and interpretability of low-rank tensor representations. We develop estimation procedures for the model and establish the theoretical properties of the resulting estimators. Numerical experiments and a real-data application illustrate the practical performance and usefulness of the proposed framework.

stat.ME

Fast LLM Post-training via Decoupled and Fastest-of-N Speculation

Rollout dominates the training time in large language model (LLM) post-training, where the trained model is used to generate tokens given a batch of prompts. This work, SpecActor, achieves fast rollout with speculative decoding that deploys a fast draft path to accelerate the unparallelizable generation, while the correctness is guaranteed by fast parallel verification of the outputs with the original model. SpecActor addresses two foundational challenges that hinder speculation efficiency: (1) a Decoupled speculation method that overcomes the computation inefficiency issue when executing speculative decoding with relative large per-worker batch size -- a common configuration in training but unfriendly to speculation, and (2) a Fastest-of-N speculation method that selects and combines different draft methods according to the rollout progress to approximate the optimal draft method even when the best one is unknown a priori. Extensive evaluations on production traces show that SpecActor accelerates mean rollout speed by 2.0--2.4x, with up to 2.7x speedup, over common post-training baselines. The results are consistent across both dense and MoE models and across different RL algorithms. Notably, SpecActor is 1.1--2.6x faster compared to vanilla speculative rollout in different traces. The accelerated rollout achieves 1.4--2.3x faster end-to-end training time.

cs.DC

Unbiased Platform-Level Causal Estimation for Search Systems: A Competitive Isolation PSM-DID Framework

Evaluating platform-level interventions in search-based two-sided marketplaces is fundamentally challenged by systemic effects such as spillovers and network interference. While widely used for causal inference, the PSM (Propensity Score Matching) - DID (Difference-in-Differences) framework remains susceptible to selection bias and cross-unit interference from unaccounted spillovers. In this paper, we introduced Competitive Isolation PSM-DID, a novel causal framework that integrates propensity score matching with competitive isolation to enable platform-level effect measurement (e.g., order volume, GMV) instead of item-level metrics in search systems. Our approach provides theoretically guaranteed unbiased estimation under mutual exclusion conditions, with an open dataset released to support reproducible research on marketplace interference (github.com/xxxx). Extensive experiments demonstrate significant reductions in interference effects and estimation variance compared to baseline methods. Successful deployment in a large-scale marketplace confirms the framework's practical utility for platform-level causal inference.

cs.AI

A generalization of the Mordell integral

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

math.NT