arXiv subjects

Yuchen Mao

Publications and source records attributed to Yuchen Mao.

29 records · Page 2Linked to original sources

arXiv2025

A Nearly Quadratic-Time FPTAS for Knapsack

We investigate the classic Knapsack problem and propose a fully polynomial-time approximation scheme (FPTAS) that runs in $\widetilde{O}(n + (1/\varepsilon)^2)$ time. This improves upon the $\widetilde{O}(n + (1/\varepsilon)^{11/5})$-time algorithm by Deng, Jin, and Mao [\textit{Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms, 2023}]. Our algorithm is the best possible (up to a polylogarithmic factor) conditioned on the conjecture that $(\min, +)$-convolution has no truly subquadratic-time algorithm, since this conjecture implies that Knapsack has no $O((n + 1/\varepsilon)^{2-δ})$-time FPTAS for any constant $δ> 0$.

cs.DS↗

arXiv2024

SeLoRA: Self-Expanding Low-Rank Adaptation of Latent Diffusion Model for Medical Image Synthesis

The persistent challenge of medical image synthesis posed by the scarcity of annotated data and the need to synthesize `missing modalities' for multi-modal analysis, underscored the imperative development of effective synthesis methods. Recently, the combination of Low-Rank Adaptation (LoRA) with latent diffusion models (LDMs) has emerged as a viable approach for efficiently adapting pre-trained large language models, in the medical field. However, the direct application of LoRA assumes uniform ranking across all linear layers, overlooking the significance of different weight matrices, and leading to sub-optimal outcomes. Prior works on LoRA prioritize the reduction of trainable parameters, and there exists an opportunity to further tailor this adaptation process to the intricate demands of medical image synthesis. In response, we present SeLoRA, a Self-Expanding Low-Rank Adaptation Module, that dynamically expands its ranking across layers during training, strategically placing additional ranks on crucial layers, to allow the model to elevate synthesis quality where it matters most. The proposed method not only enables LDMs to fine-tune on medical data efficiently but also empowers the model to achieve improved image quality with minimal ranking. The code of our SeLoRA method is publicly available on https://anonymous.4open.science/r/SeLoRA-980D .

cs.CV↗

arXiv2024

Spider2-V: How Far Are Multimodal Agents From Automating Data Science and Engineering Workflows?

Data science and engineering workflows often span multiple stages, from warehousing to orchestration, using tools like BigQuery, dbt, and Airbyte. As vision language models (VLMs) advance in multimodal understanding and code generation, VLM-based agents could potentially automate these workflows by generating SQL queries, Python code, and GUI operations. This automation can improve the productivity of experts while democratizing access to large-scale data analysis. In this paper, we introduce Spider2-V, the first multimodal agent benchmark focusing on professional data science and engineering workflows, featuring 494 real-world tasks in authentic computer environments and incorporating 20 enterprise-level professional applications. These tasks, derived from real-world use cases, evaluate the ability of a multimodal agent to perform data-related tasks by writing code and managing the GUI in enterprise data software systems. To balance realistic simulation with evaluation simplicity, we devote significant effort to developing automatic configurations for task setup and carefully crafting evaluation metrics for each task. Furthermore, we supplement multimodal agents with comprehensive documents of these enterprise data software systems. Our empirical evaluation reveals that existing state-of-the-art LLM/VLM-based agents do not reliably automate full data workflows (14.0% success). Even with step-by-step guidance, these agents still underperform in tasks that require fine-grained, knowledge-intensive GUI actions (16.2%) and involve remote cloud-hosted workspaces (10.6%). We hope that Spider2-V paves the way for autonomous multimodal agents to transform the automation of data science and engineering workflow. Our code and data are available at https://spider2-v.github.io.

cs.AI↗

arXiv2024

Approximating Partition in Near-Linear Time

We propose an $\widetilde{O}(n + 1/\eps)$-time FPTAS (Fully Polynomial-Time Approximation Scheme) for the classical Partition problem. This is the best possible (up to a polylogarithmic factor) assuming SETH (Strong Exponential Time Hypothesis) [Abboud, Bringmann, Hermelin, and Shabtay'22]. Prior to our work, the best known FPTAS for Partition runs in $\widetilde{O}(n + 1/\eps^{5/4})$ time [Deng, Jin and Mao'23, Wu and Chen'22]. Our result is obtained by solving a more general problem of weakly approximating Subset Sum.

cs.DS↗

arXiv2023

Faster Algorithms for Bounded Knapsack and Bounded Subset Sum Via Fine-Grained Proximity Results

We investigate pseudopolynomial-time algorithms for Bounded Knapsack and Bounded Subset Sum. Recent years have seen a growing interest in settling their fine-grained complexity with respect to various parameters. For Bounded Knapsack, the number of items $n$ and the maximum item weight $w_{\max}$ are two of the most natural parameters that have been studied extensively in the literature. The previous best running time in terms of $n$ and $w_{\max}$ is $O(n + w^3_{\max})$ [Polak, Rohwedder, Wegrzycki '21]. There is a conditional lower bound of $O((n + w_{\max})^{2-o(1)})$ based on $(\min,+)$-convolution hypothesis [Cygan, Mucha, Wegrzycki, Wlodarczyk '17]. We narrow the gap significantly by proposing a $\tilde{O}(n + w^{12/5}_{\max})$-time algorithm. Note that in the regime where $w_{\max} \approx n$, our algorithm runs in $\tilde{O}(n^{12/5})$ time, while all the previous algorithms require $Ω(n^3)$ time in the worst case. For Bounded Subset Sum, we give two algorithms running in $\tilde{O}(nw_{\max})$ and $\tilde{O}(n + w^{3/2}_{\max})$ time, respectively. These results match the currently best running time for 0-1 Subset Sum. Prior to our work, the best running times (in terms of $n$ and $w_{\max}$) for Bounded Subset Sum is $\tilde{O}(n + w^{5/3}_{\max})$ [Polak, Rohwedder, Wegrzycki '21] and $\tilde{O}(n + μ_{\max}^{1/2}w_{\max}^{3/2})$ [implied by Bringmann '19 and Bringmann, Wellnitz '21], where $μ_{\max}$ refers to the maximum multiplicity of item weights.

cs.DS↗

arXiv2023

Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties

We give new proofs of general relativistic initial data gluing results on unit-scale annuli based on explicit solution operators for the linearized constraint equation around the flat case with prescribed support properties. These results retrieve and optimize - in terms of positivity, regularity, size and/or spatial decay requirements - a number of known theorems concerning asymptotically flat initial data, including Kerr exterior gluing by Corvino-Schoen and Chruściel-Delay, interior gluing (or "fill-in") by Bieri-Chruściel, and obstruction-free gluing by Czimek-Rodnianski. In particular, our proof of the strengthened obstruction-free gluing theorem relies on purely spacelike techniques, rather than null gluing as in the original approach.

math.AP↗

arXiv2023

Localized initial data for Einstein equations

We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in Carlotto--Schoen [arXiv:1407.4766] to $\mathcal{O}(|x|^{-(d-2)})$ and a construction of nontrivial asymptotically flat initial data supported in a degenerate sector $\{(x',x_d)\in\mathbb{R}^d:|x'|\leq x_d^α\}$ for $\frac{3}{d+1}<α<1$.

math.AP↗

arXiv2019

Restricted Max-Min Allocation: Approximation and Integrality Gap

Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most $4$. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts have been devoted to designing an efficient algorithm whose approximation ratio can match this upper bound for the integrality gap. In ICALP 2018, we present a $(6 + δ)$-approximation algorithm where $δ$ can be any positive constant, and there is still a gap of roughly $2$. In this paper, we narrow the gap significantly by proposing a $(4+δ)$-approximation algorithm where $δ$ can be any positive constant. The approximation ratio is with respect to the optimal value of the configuration LP, and the running time is $\mathit{poly}(m,n)\cdot n^{\mathit{poly}(\frac{1}δ)}$ where $n$ is the number of players and $m$ is the number of resources. We also improve the upper bound for the integrality gap of the configuration LP to $3 + \frac{21}{26} \approx 3.808$.

cs.DS↗

arXiv2018

The diophantine exponent of the $\mathbb{Z}/q\mathbb{Z}$ points of $S^{d-2}\subset S^d$

Assume a polynomial-time algorithm for factoring integers, Conjecture~\ref{conj}, $d\geq 3,$ and $q$ and $p$ are prime numbers, where $p\leq q^A$ for some $A>0$. We develop a polynomial-time algorithm in $\log(q)$ that lifts every $\mathbb{Z}/q\mathbb{Z}$ point of $S^{d-2}\subset S^{d}$ to a $\mathbb{Z}[1/p]$ point of $S^d$ with the minimum height. We implement our algorithm for $d=3 \text{ and }4$. Based on our numerical results, we formulate a conjecture which can be checked in polynomial-time and gives the optimal bound on the diophantine exponent of the $\mathbb{Z}/q\mathbb{Z}$ points of $S^{d-2}\subset S^d$.

math.NT↗

arXiv2018

Restricted Max-Min Fair Allocation

The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current best algorithm for estimating the optimal value with the current best for constructing an allocation, there is quite a gap between the ratios that can be achieved in polynomial time: roughly 4 for estimation and roughly $6 + 2\sqrt{10}$ for construction. We propose an algorithm that constructs an allocation with value within a factor of $6 + δ$ from the optimum for any constant $δ> 0$. The running time is polynomial in the input size for any constant $δ$ chosen.

cs.DS↗

arXiv2018

Integrality Gap of the Configuration LP for the Restricted Max-Min Fair Allocation

The max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. Each player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted case, we have $v_{pr}\in \{v_r, 0\}$. That is, a resource $r$ is worth value $v_r$ for the players who desire it and value 0 for the other players. In this paper, we consider the configuration LP, a linear programming relaxation for the restricted problem. The integrality gap of the configuration LP is at least $2$. Asadpour, Feige, and Saberi proved an upper bound of $4$. We improve the upper bound to $23/6$ using the dual of the configuration LP. Since the configuration LP can be solved to any desired accuracy $δ$ in polynomial time, our result leads to a polynomial-time algorithm which estimates the optimal value within a factor of $23/6+δ$.

cs.DS↗