搜索结果：Conquer

Divide and Conquer (D&C) is a widely used algorithmic strategy for symmetric eigenvalue decomposition. Its natural parallelism makes D&C attractive on modern multicore CPUs and GPUs, but existing eigenvalue-only routines often default to QR-based methods because conventional D&C still materializes or replays large transformation matrices during the conquer phase. This paper proposes a boundary-row D&C algorithm for eigenvalue-only computation. The key observation is that the conquer phase only needs selected boundary rows/columns rather than the full accumulated eigenvector matrix. By propagating these boundary rows directly through the recursion, the proposed algorithm reduces the memory requirement from quadratic to linear space while also eliminating unnecessary matrix-vector work in the conventional lazy-replay formulation. We provide the algorithm, its time and space complexity analysis, correctness and stability arguments, optimized CPU and GPU implementations, and an evaluation against QR and D&C routines in standard numerical libraries.

Diffusion-based large language models (dLLMs) have shown promising performance across various reasoning tasks, establishing themselves as an alternative to autoregressive large language models (LLMs). Unlike autoregressive LLMs that generate one token per step based on all previous tokens, dLLMs theoretically enable parallel generation of multiple tokens at each decoding step. However, recent dLLMs still favor one-token-per-step generation in practice, as directly decoding multiple masked tokens often leads to degraded generation quality and stability. This reveals a substantial gap between the theoretical parallelism and practical performance of dLLMs. To bridge this gap, we introduce an adaptive parallel decoding approach, namely DiCo, which features a three-phase divide-and-conquer paradigm to unleash the inherent parallelism of dLLMs. During the Divide phase, DiCo first explores the input masked sequence and identifies masked tokens as seed tokens, which are then expanded to construct a set of local clusters. During the Conquer phase, DiCo performs parallel decoding across different local clusters constructed in the Divide phase. The divide-and-conquer process repeatedly altern

Quantum generative models based on instantaneous quantum polynomial (IQP) circuits show great promise in learning complex distributions while maintaining classical trainability. However, current implementations suffer from two key limitations: lack of controllability over generated outputs and severe generation bias towards certain expected patterns. We present a Controllable Quantum Generative Framework, ConQuER, which addresses both challenges through a modular circuit architecture. ConQuER embeds a lightweight controller circuit that can be directly combined with pre-trained IQP circuits to precisely control the output distribution without full retraining. Leveraging the advantages of IQP, our scheme enables precise control over properties such as the Hamming Weight distribution with minimal parameter and gate overhead. In addition, inspired by the controller design, we extend this modular approach through data-driven optimization to embed implicit control paths in the underlying IQP architecture, significantly reducing generation bias on structured datasets. ConQuER retains efficient classical training properties and high scalability. We experimentally validate ConQuER on multi

We introduce a quantum algorithm design paradigm called combine and conquer, which is a quantum version of the "marriage-before-conquest" technique of Kirkpatrick and Seidel. In a quantum combine-and-conquer algorithm, one performs the essential computation of the combine step of a quantum divide-and-conquer algorithm prior to the conquer step while avoiding recursion. This model is better suited for the quantum setting, due to its non-recursive nature. We show the utility of this approach by providing quantum algorithms for 2D maxima set and convex hull problems for sorted point sets running in $\tilde{O}(\sqrt{nh})$ time, w.h.p., where $h$ is the size of the output.

In this work, we present Transitive Reinforcement Learning (TRL), a new value learning algorithm based on a divide-and-conquer paradigm. TRL is designed for offline goal-conditioned reinforcement learning (GCRL) problems, where the aim is to find a policy that can reach any state from any other state in the smallest number of steps. TRL converts a triangle inequality structure present in GCRL into a practical divide-and-conquer value update rule. This has several advantages compared to alternative value learning paradigms. Compared to temporal difference (TD) methods, TRL suffers less from bias accumulation, as in principle it only requires $O(\log T)$ recursions (as opposed to $O(T)$ in TD learning) to handle a length-$T$ trajectory. Unlike Monte Carlo methods, TRL suffers less from high variance as it performs dynamic programming. Experimentally, we show that TRL achieves the best performance in highly challenging, long-horizon benchmark tasks compared to previous offline GCRL algorithms.

Quizzes play a crucial role in education by reinforcing students' understanding of key concepts and encouraging self-directed exploration. However, compiling high-quality quizzes can be challenging and require deep expertise and insight into specific subject matter. Although LLMs have greatly enhanced the efficiency of quiz generation, concerns remain regarding the quality of these AI-generated quizzes and their educational impact on students. To address these issues, we introduce ConQuer, a concept-based quiz generation framework that leverages external knowledge sources. We employ comprehensive evaluation dimensions to assess the quality of the generated quizzes, using LLMs as judges. Our experiment results demonstrate a 4.8% improvement in evaluation scores and a 77.52% win rate in pairwise comparisons against baseline quiz sets. Ablation studies further underscore the effectiveness of each component in our framework. Code available at https://github.com/sofyc/ConQuer.

Tracking surgical modifications based on endoscopic videos is technically feasible and of great clinical advantages; however, it still remains challenging. This report presents a modular pipeline to divide and conquer the clinical challenges in the process. The pipeline integrates frame selection, depth estimation, and 3D reconstruction components, allowing for flexibility and adaptability in incorporating new methods. Recent advancements, including the integration of Depth-Anything V2 and EndoDAC for depth estimation, as well as improvements in the Iterative Closest Point (ICP) alignment process, are detailed. Experiments conducted on the Hamlyn dataset demonstrate the effectiveness of the integrated methods. System capability and limitations are both discussed.

Large language models (LLMs) have shown impressive performance in reasoning benchmarks with the emergence of Chain-of-Thought (CoT), particularly in multi-choice question (MCQ). However, current works equally resolve questions regardless of the problem-solving difficulty, leading to an excessive focus on simple items while insufficient attention on intricate ones. To address this challenge, we propose a simple yet effective strategy, Divide and Conquer Reasoning (DCR), to enhance the reasoning capability of LLMs for MCQs, as inspired by human beings using heuristics to first categorize tasks and then handle them separately. In particular, we first categorize questions into two subsets based on confidence score ($\mathcal{CS}$), which is estimated by statistical frequency of generated answers. Subsequently, we propose Filter Choices based Reasoning (FCR) to improve model performance on MCQs with low ($\mathcal{CS}$). Our experiments demonstrate that the proposed strategy only costs 85% of SOTA, while still achieves average accuracy improvement of 1.56% across nine datasets including arithmetic, commonsense, and logic reasoning tasks. The code is at \url{https://github.com/AiMijie/Di

In modern software development, vulnerability detection is crucial due to the inevitability of bugs and vulnerabilities in complex software systems. Effective detection and elimination of these vulnerabilities during the testing phase are essential. Current methods, such as fuzzing, are widely used for this purpose. While fuzzing is efficient in identifying a broad range of bugs and vulnerabilities by using random mutations or generations, it does not guarantee correctness or absence of vulnerabilities. Therefore, non-random methods are preferable for ensuring the safety and security of critical infrastructure and control systems. This paper presents a vulnerability detection approach based on symbolic execution and control flow graph analysis to identify various types of software weaknesses. Our approach employs a divide-and-conquer algorithm to eliminate irrelevant program information, thus accelerating the process and enabling the analysis of larger programs compared to traditional symbolic execution and model checking methods.

We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure in mind, while abstracting quantum parts into subgraphs with simple boundaries as needed. As an example, we show how to combine a \emph{switching network} with arbitrary quantum subroutines, to compute a composed function. As another application, we give a time-efficient implementation of quantum Divide \& Conquer when the sub-problems are combined via a Boolean formula. We use this to quadratically speed up Savitch's algorithm for directed $st$-connectivity.

Video anomaly detection is a complex task, and the principle of "divide and conquer" is often regarded as an effective approach to tackling intricate issues. It's noteworthy that recent methods in video anomaly detection have revealed the application of the divide and conquer philosophy (albeit with distinct perspectives from traditional usage), yielding impressive outcomes. This paper systematically reviews these literatures from six dimensions, aiming to enhance the use of the divide and conquer strategy in video anomaly detection. Furthermore, based on the insights gained from this review, a novel approach is presented, which integrates human skeletal frameworks with video data analysis techniques. This method achieves state-of-the-art performance on the ShanghaiTech dataset, surpassing all existing advanced methods.

Reinforcement learning (RL) often faces the challenges of uninformed search problems where the agent should explore without access to the domain knowledge such as characteristics of the environment or external rewards. To tackle these challenges, this work proposes a new approach for curriculum RL called Diversify for Disagreement & Conquer (D2C). Unlike previous curriculum learning methods, D2C requires only a few examples of desired outcomes and works in any environment, regardless of its geometry or the distribution of the desired outcome examples. The proposed method performs diversification of the goal-conditional classifiers to identify similarities between visited and desired outcome states and ensures that the classifiers disagree on states from out-of-distribution, which enables quantifying the unexplored region and designing an arbitrary goal-conditioned intrinsic reward signal in a simple and intuitive way. The proposed method then employs bipartite matching to define a curriculum learning objective that produces a sequence of well-adjusted intermediate goals, which enable the agent to automatically explore and conquer the unexplored region. We present experimental r

We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms are amenable to quantum speedup and apply these theorems to an array of problems involving strings, integers, and geometric objects. They include LONGEST DISTINCT SUBSTRING, KLEE'S COVERAGE, several optimization problems on stock transactions, and k-INCREASING SUBSEQUENCE. For most of these results, our quantum time upper bound matches the quantum query lower bound for the problem, up to polylogarithmic factors.

Query reformulation is a key mechanism to alleviate the linguistic chasm of query in ad-hoc retrieval. Among various solutions, query reduction effectively removes extraneous terms and specifies concise user intent from long queries. However, it is challenging to capture hidden and diverse user intent. This paper proposes Contextualized Query Reduction (ConQueR) using a pre-trained language model (PLM). Specifically, it reduces verbose queries with two different views: core term extraction and sub-query selection. One extracts core terms from an original query at the term level, and the other determines whether a sub-query is a suitable reduction for the original query at the sequence level. Since they operate at different levels of granularity and complement each other, they are finally aggregated in an ensemble manner. We evaluate the reduction quality of ConQueR on real-world search logs collected from a commercial web search engine. It achieves up to 8.45% gains in exact match scores over the best competing model.

MD4 and MD5 are fundamental cryptographic hash functions proposed in the early 1990s. MD4 consists of 48 steps and produces a 128-bit hash given a message of arbitrary finite size. MD5 is a more secure 64-step extension of MD4. Both MD4 and MD5 are vulnerable to practical collision attacks, yet it is still not realistic to invert them, i.e., to find a message given a hash. In 2007, the 39-step version of MD4 was inverted by reducing to SAT and applying a CDCL solver along with the so-called Dobbertin's constraints. As for MD5, in 2012 its 28-step version was inverted via a CDCL solver for one specified hash without adding any extra constraints. In this study, Cube-and-Conquer (a combination of CDCL and lookahead) is applied to invert step-reduced versions of MD4 and MD5. For this purpose, two algorithms are proposed. The first one generates inverse problems for MD4 by gradually modifying the Dobbertin's constraints. The second algorithm tries the cubing phase of Cube-and-Conquer with different cutoff thresholds to find the one with the minimum runtime estimate of the conquer phase. This algorithm operates in two modes: (i) estimating the hardness of a given propositional Boolean fo

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of divide-and-conquer estimators in the scenario that the target function does not necessarily reside in the underlying RKHS. As a decomposition-based scalable approach, the divide-and-conquer estimators of functional linear regression can substantially reduce the algorithmic complexities in time and memory. We develop an integral operator approach to establish sharp finite sample upper bounds for prediction with divide-and-conquer estimators under various regularity conditions of explanatory variables and target function. We also prove the asymptotic optimality of the derived rates by building the mini-max lower bounds. Finally, we consider the convergence of noiseless estimators and show that the rates can be arbitrarily fast under mild conditions.

Recent work introduced the cube-and-conquer technique to solve hard SAT instances. It partitions the search space into cubes using a lookahead solver. Each cube is tackled by a conflict-driven clause learning (CDCL) solver. Crucial for strong performance is the cutoff heuristic that decides when to switch from lookahead to CDCL. Yet, this offline heuristic is far from ideal. In this paper, we present a novel hybrid solver that applies the cube and conquer steps simultaneously. A lookahead and a CDCL solver work together on each cube, while communication is restricted to synchronization. Our concurrent cube-and-conquer solver can solve many instances faster than pure lookahead, pure CDCL and offline cube-and-conquer, and can abort early in favor of a pure CDCL search if an instance is not suitable for cube-and-conquer techniques.

Given a rectangle $R$ with area $A$ and a set of areas $L=\{A_1,...,A_n\}$ with $\sum_{i=1}^n A_i = A$, we consider the problem of partitioning $R$ into $n$ sub-regions $R_1,...,R_n$ with areas $A_1,...,A_n$ in a way that the total perimeter of all sub-regions is minimized. The goal is to create square-like sub-regions, which are often more desired. We propose an efficient $1.203$--approximation algorithm for this problem based on a divide and conquer scheme that runs in $\mathcal{O}(n^2)$ time. For the special case when the aspect ratios of all rectangles are bounded from above by 3, the approximation factor is $2/\sqrt{3} \leq 1.1548$. We also present a modified version of out algorithm as a heuristic that achieves better average and best run times.