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Xia Liao

Publications and source records attributed to Xia Liao.

17 recordsLinked to original sources

DeCoRAG: Cognitive Decoupling and Semantic-Aware Cropping for Complex Document Understanding

Advancing multimodal retrieval-augmented generation (RAG) for complex document understanding presents a formidable dual dilemma of accuracy and efficiency, particularly in graph RAG. Processing structurally sparse yet visually dense layouts, such as extracting a tiny data marker from a financial chart, often incurs computationally prohibitive token overhead while still triggering catastrophic hallucination. However, multimodal Graph RAG pipelines rely on graph-construction stages that assume Vision-Language Models (VLMs) can resolve sparse semantics within high-density layouts. We challenge this assumption, revealing that forcing VLMs to localize visual evidence, interpret semantics, and extract relations triggers a "Visual Attention Sink," a mechanism driving catastrophic semantic loss, while full-page processing incurs massive computational overhead. Controlled interventions verify that this failure is boundary-driven rather than content-specific and that semantic anchoring mitigates it. To fundamentally correct this flawed paradigm, we introduce DeCoRAG, a multimodal Graph RAG pipeline that shifts knowledge processing from coupled visual-semantic reasoning to "Cognitive Decoupling." Rather than passively processing raw pixels, its graph-construction stage establishes a macroscopic Semantic Anchor to neutralize the attention sink. This anchor subsequently drives our Region-Aware Pruning and Cropping (RAP-Crop) mechanism, shifting the reasoning space from dense, noisy backgrounds to purified, intent-driven semantic clusters. The resulting graph supports hybrid retrieval and answer generation. Across complex document benchmarks, DeCoRAG improves the semantic pass rate by up to 12.5 percentage points over the strongest baseline and generalizes to DocVQA. RAP-Crop reduces offline graph-construction prompt tokens by 40.8% without sacrificing end-to-end accuracy.

cs.IR

Microlocal indices and Chern Classes of Foliations

In this paper, we study how global index formulas arise in the theory of one-dimensional holomorphic foliation from the microlocal point of view. We give short proofs and generalizations to a few exisiting index formulas concerning Schwartz, GSV and logarithmic indices.

math.AG

A Syzygy Rank Characterization of Strongly Euler Homogeneity for Projective Hypersurfaces

In this paper we give a characterization of strongly Euler homogeneous singular points on a reduced complex projective hypersurface $D=V(f)\subset \PP^n$ using the Jacobian syzygies of $f$. The characterization compares the ranks of the first syzygy matrices of the global Jacobian ideal $J_f$ and its quotient $J_f/(f)$. When $D$ has only isolated singularities, our characterization refines a recent result of Andrade-Beorchia-Dimca-Mir\'{o}-Roig. We also prove a generalization of this characterization to smooth projective toric varieties.

math.AG

TrEnv-X: Transparently Share Serverless Execution Environments Across Different Functions and Nodes

Serverless computing is renowned for its computation elasticity, yet its full potential is often constrained by the requirement for functions to operate within local and dedicated background environments, resulting in limited memory elasticity. To address this limitation, this paper introduces TrEnv-X, a co-designed integration of the serverless platform with the operating system and CXL/RDMA-based remote memory pools. TrEnv-X's core innovations are repurposable sandboxes, which can be shared across different functions to decrease the associated creation overhead, and OS-level memory templates, which enable rapid state restoration from CXL/RDMA-based remote memory pools. To further demonstrate TrEnv-X's versatility, we generalize its design from traditional containers for microVM-based agent workloads and introduce new optimizations, including browser sharing and a page cache bypassing mechanism. Our evaluation shows that TrEnv-X achieves up to 7x reduction in P99 latency and 48% memory savings for container-based functions. When applied to LLM agents, it reduces the P99 latency by up to 58% and memory usage by 61% compared to state-of-the-art systems like E2B.

cs.DC

Logrithmic Versions of Ginzburg's Sharp Operation for Free Divisors

Let $M$ be a complex manifold, $D\subset M$ a free divisor and $U=M\setminus D$ its complement. In this paper we study the characteristic cycle $\textup{CC}(\gamma\cdot \ind_U)$ of the restriction of a constructible function $\gamma$ on $U$. We globalise Ginzburg's local sharp construction and introduce the log transversality condition, which is a new transversality condition about the relative position of $\gamma$ and $D$. We prove that the log transversality condition is satisfied if either $D$ is normal crossing and $\gamma$ is arbitrary, or $D$ is holonomic strongly Euler homogheneous and $\gamma$ is non-characteristic. Under the log transversality assumption we establish a logarithmic pullback formula for $\textup{CC}(\gamma\cdot \ind_U)$. Mixing Ginzburg's sharp construction with the logarithmic pullback, we obtain a double restriction formula for the Chern-Schwartz-MacPherson class $c_*(\gamma\cdot \ind_{D\cup V})$ where $V$ is any reduced hypersurface in $M$. Applications of our results include the non-negativity of Euler characteristics of effective constructible functions, and CSM classes of hypersurfaces in the open manifold $\mathbb{P}^n\setminus D$ when $D$ is a linear free divisor or a free hyperplane arrangement.

math.AG

Efficient Graph-Based Approximate Nearest Neighbor Search Achieving: Low Latency Without Throughput Loss

The increase in the dimensionality of neural embedding models has enhanced the accuracy of semantic search capabilities but also amplified the computational demands for Approximate Nearest Neighbor Searches (ANNS). This complexity poses significant challenges in online and interactive services, where query latency is a critical performance metric. Traditional graph-based ANNS methods, while effective for managing large datasets, often experience substantial throughput reductions when scaled for intra-query parallelism to minimize latency. This reduction is largely due to inherent inefficiencies in the conventional fork-join parallelism model. To address this problem, we introduce AverSearch, a novel parallel graph-based ANNS framework that overcomes these limitations through a fully asynchronous architecture. Unlike existing frameworks that struggle with balancing latency and throughput, AverSearch utilizes a dynamic workload balancing mechanism that supports continuous, dependency-free processing. This approach not only minimizes latency by eliminating unnecessary synchronization and redundant vertex processing but also maintains high throughput levels. Our evaluations across various datasets, including both traditional benchmarks and modern large-scale model generated datasets, show that AverSearch consistently outperforms current state-of-the-art systems. It achieves up to 2.1-8.9 times higher throughput at comparable latency levels across different datasets and reduces minimum latency by 1.5 to 1.9 times.

cs.DC

Xorbits: Automating Operator Tiling for Distributed Data Science

Data science pipelines commonly utilize dataframe and array operations for tasks such as data preprocessing, analysis, and machine learning. The most popular tools for these tasks are pandas and NumPy. However, these tools are limited to executing on a single node, making them unsuitable for processing large-scale data. Several systems have attempted to distribute data science applications to clusters while maintaining interfaces similar to single-node libraries, enabling data scientists to scale their workloads without significant effort. However, existing systems often struggle with processing large datasets due to Out-of-Memory (OOM) problems caused by poor data partitioning. To overcome these challenges, we develop Xorbits, a high-performance, scalable data science framework specifically designed to distribute data science workloads across clusters while retaining familiar APIs. The key differentiator of Xorbits is its ability to dynamically switch between graph construction and graph execution. Xorbits has been successfully deployed in production environments with up to 5k CPU cores. Its applications span various domains, including user behavior analysis and recommendation systems in the e-commerce sector, as well as credit assessment and risk management in the finance industry. Users can easily scale their data science workloads by simply changing the import line of their pandas and NumPy code. Our experiments demonstrate that Xorbits can effectively process very large datasets without encountering OOM or data-skewing problems. Over the fastest state-of-the-art solutions, Xorbits achieves an impressive 2.66* speedup on average. In terms of API coverage, Xorbits attains a compatibility rate of 96.7%, surpassing the fastest framework by an impressive margin of 60 percentage points. Xorbits is available at https://github.com/xorbitsai/xorbits.

cs.DC

A parallel structured divide-and-conquer algorithm for symmetric tridiagonal eigenvalue problems

In this paper, a parallel structured divide-and-conquer (PSDC) eigensolver is proposed for symmetric tridiagonal matrices based on ScaLAPACK and a parallel structured matrix multiplication algorithm, called PSMMA. Computing the eigenvectors via matrix-matrix multiplications is the most computationally expensive part of the divide-and-conquer algorithm, and one of the matrices involved in such multiplications is a rank-structured Cauchy-like matrix. By exploiting this particular property, PSMMA constructs the local matrices by using generators of Cauchy-like matrices without any communication, and further reduces the computation costs by using a structured low-rank approximation algorithm. Thus, both the communication and computation costs are reduced. Experimental results show that both PSMMA and PSDC are highly scalable and scale to 4096 processes at least. PSDC has better scalability than PHDC that was proposed in [J. Comput. Appl. Math. 344 (2018) 512--520] and only scaled to 300 processes for the same matrices. Comparing with \texttt{PDSTEDC} in ScaLAPACK, PSDC is always faster and achieves $1.4$x--$1.6$x speedup for some matrices with few deflations. PSDC is also comparable with ELPA, with PSDC being faster than ELPA when using few processes and a little slower when using many processes.

cs.MS

An approach to Lagrangian specialisation through MacPherson's graph construction

Let $f: M \to N$ be a holomorphic map between two complex manifolds. Assume $f$ is flat and sans éclatement en codimension 0 (no blowup in codimension 0). We study the theory of Lagrangian specialisation for such $f$, and prove a González-Sprinberg type formula for the local Euler obstruction relative to $f$. With the help of this formula and MacPherson's graph construction for the vector bundle map $f^*T^*N \to T^*M$, we find the Lagrangian cycle of the Milnor number constructible function $μ$. As an application, we study the Chern class transformation of $μ$ when $f$ has finite contact type.

math.AG

On the explicit calculation of Hirzebruch-Milnor classes of hyperplane arrangements

The Hirzebruch-Milnor class is given by the difference between the homology Hirzebruch characteristic class and the virtual one. It is known that the Hirzebruch-Milnor class for a certain singular hypersurface can be calculated by using the Hodge spectrum of each stratum of singular locus. So far there is no explicit calculation of this invariant for any non-trivial examples, and we calculate this invariant by two different ways for low dimmensional hyperplane arrangements.

math.AG

Chern Classes of Logarithmic Derivations for Free Divisors with Jacobian Ideal of Linear Type

Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$, and $D$ be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along $D$ and compare it with the Chern-Schwartz-MacPherson class of the hypersurface complement. Our result establishes a conjecture by Aluffi raised in \cite{hyparr}.

math.AG

A cohomological interpretation of derivations on graded algebras

We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $D$. We obtain a generalized Euler sequence involving a sheaf on $X$ whose space of global sections consists of all homogeneous $k$-linear derivations of $A$ and a sheaf of logarithmic derivations on $X$.

math.AG

Chern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free Divisors

Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on $X$ with respect to $D$, and the Chern-Schwartz-MacPherson class of the complement of $D$ in $X$. Our result confirms a conjectural formula for these classes, at least after push-forward to projective space; it proves the full form of the conjecture for locally quasi-homogeneous free divisors in $\mathbb P^n$. The result generalizes several previously known results. For example, it recovers a formula of M. Mustata and H. Schenck for Chern classes for free hyperplane arrangements. Our main tools are Riemann-Roch and the logarithmic comparison theorem of Calderon-Moreno, Castro-Jimenez, Narvaez-Macarro, and David Mond. As a subproduct of the main argument, we also obtain a schematic Bertini statement for locally quasi-homogeneous divisors.

math.AG

K-theoretic defect in Chern class identity for a free divisor

Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$, and $D$ be a free divisor. We study the motivic Chern class of $D$ in the Grothendieck group of coherent sheaves $G_0(X)$, and another class defined by the sheaf of logarithmic differentials along $D$. We give explicit calculations of the difference of these two classes when: $D$ is a divisor on a nonsingular surface; $D$ is a hyperplane arrangement whose affine cone is free.

math.AG

Chern Classes of Logarithmic Vector Fields

Let $X$ be a nonsingular complex variety and $D$ a reduced effective divisor in $X$. In this paper we study the conditions under which the formula $c_{SM}(1_U)=c(\textup{Der}_X(-\log D))\cap [X]$ is true. We prove that this formula is equivalent to a Riemann-Roch type of formula. As a corollary, we show that over a surface, the formula is true if and only if the Milnor number equals the Tjurina number at each singularity of $D$. We also show the Rimann-Roch type of formula is true if the Jacobian scheme of $D$ is nonsingular or a complete intersection.

math.AG

Stable Birational Equivalence and Geometric Chevalley-Warning

We propose a 'geometric Chevalley-Warning' conjecture, that is a motivic extension of the Chevalley-Warning theorem in number theory. It is equivalent to a particular case of a recent conjecture of F. Brown and O.Schnetz. In this paper, we show the conjecture is true for linear hyperplane arrangements, quadratic and singular cubic hypersurfaces of any dimension, and cubic surfaces in $\Pbb^3$. The last section is devoted to verifying the conjecture for certain special kinds of hypersurfaces of any dimension. As a by-product, we obtain information on the Grothendieck classes of the affine 'Potts model' hypersurfaces considered in \cite{aluffimarcolli1}.

math.AG