arXiv subjects

Weijie Zheng

Publications and source records attributed to Weijie Zheng.

At least 19 recordsLinked to original sources

arXiv2026

CompKV: Compensation-Aware KV Selection for Long-Context LLM Inference

Despite their strong performance, large language models (LLMs) are bottlenecked by KV cache memory traffic during long-context inference. Sparse attention is widely used to accelerate LLM inference by computing exact attention over a selected subset of tokens. To recover the contribution of tokens excluded from exact attention, recent methods apply coarse-grained compensation to the omitted attention tail. However, existing methods typically select tokens based on attention mass and only then compensate for the unselected tokens. This decoupled design overlooks their interaction: selection should prioritize tokens that would leave the largest compensation error if omitted. To address this limitation, we introduce CompKV, the first compensation-aware sparse attention framework that divides tokens into blocks and explicitly optimizes selection for the downstream compensation mechanism. Our theoretical analysis shows that the residual left by block-level mean compensation is governed by both block attention mass and within-block logit variation. We approximate this residual using compact block-level statistics, yielding a deployable selection criterion. We further develop an efficient asynchronous implementation. Experiments on RULER and LongBench-Pro show that CompKV performs best among the evaluated sparse baselines while delivering up to a $6.85\times$ self-attention speedup over full attention.

cs.LG↗

arXiv2026

From Understanding Genetic Drift to a Smart-Restart Mechanism for Estimation-of-Distribution Algorithms

Estimation-of-distribution algorithms (EDAs) are optimization algorithms that learn a distribution on the search space from which good solutions can be sampled easily. A key parameter of most EDAs is the sample size (population size). If the population size is too small, the update of the probabilistic model builds on few samples, leading to the undesired effect of genetic drift. Too large population sizes avoid genetic drift, but slow down the process. Building on a recent quantitative analysis of how the population size leads to genetic drift, we design a smart-restart mechanism for EDAs. By stopping runs when the risk for genetic drift is high, it automatically runs the EDA in good parameter regimes. Via a mathematical runtime analysis, we prove a general performance guarantee for this smart-restart scheme. This in particular shows that in many situations where the optimal (problem-specific) parameter values are known, the restart scheme automatically finds these, leading to the asymptotically optimal performance. We also conduct an extensive experimental analysis. On four classic benchmark problems, we clearly observe the critical influence of the population size on the performance, and we find that the smart-restart scheme leads to a performance close to the one obtainable with optimal parameter values. Our results also show that previous theory-based suggestions for the optimal population size can be far from the optimal ones, leading to a performance clearly inferior to the one obtained via the smart-restart scheme. We also conduct experiments with PBIL (cross-entropy algorithm) on two combinatorial optimization problems from the literature, the max-cut problem and the bipartition problem. Again, we observe that the smart-restart mechanism finds much better values for the population size than those suggested in the literature, leading to a much better performance.

cs.NE↗

arXiv2026

Proven Advantage of Multiobjective Evolutionary Algorithms for Problems with Different Degrees of Conflict

The field of multiobjective evolutionary algorithms (MOEAs) often emphasizes its popularity for optimization problems with conflicting objectives. However, it is still theoretically unknown how MOEAs perform compared with typical approaches outside this field. This paper conducts such a systematic theoretical comparison on problem classes with different degrees of conflict. With OneMaxMin$_k$ depicting $k\in[0..n]$ degrees of conflict, we show the difficulties of two typical non-MOEA approaches, the scalarization (weighted-sum) and {the} $ε-$constraint approach. We prove that for any set of weights, the set of optima formed by {the} scalarization approach cannot cover its full Pareto front for $k>2$. Although constrained problems constructed from $ε-$constraint approach ensure the full coverage, general ways (via exterior or nonparameter penalty functions) to solve these constrained problems encounter difficulties. The nonparameter penalty function way cannot guarantee the full coverage, and the exterior way covers the Pareto front with expected $O(\max\{k,1\}n\ln n)$ number of function evaluations, but only with careful settings of $ε$ and $r$ ($r>1/(ε+1-\lceil ε\rceil)$). In contrast, MOEAs efficiently solve OneMaxMin$_k$ without careful designs. We prove the same expected runtime of $O(\max\{k,1\}n\ln n)$ for the (G)SEMO, MOEA/D, NSGA-II, and SMS-EMOA. Our brief discussions on a bi-objective LeadingOnes variant with different degrees of conflict show similar findings.

cs.NE↗

arXiv2026

First Mathematical Runtime Analyses of Multi-Objective Evolutionary Algorithms for Multi-Valued Decision Variables

Problems defined on binary decision spaces have been intensively studied in the theory of multi-objective evolutionary algorithms (MOEAs). In contrast, no mathematical runtime analyses exist so far for MOEAs dealing with decision variables that take a finite number $r > 2$ of values, despite the prevalence of such problems in practice. In this work, we begin to fill this research gap. We analyze how the classic SEMO algorithm with unit-strength local mutation computes the Pareto front of an $r$-valued counterpart of the classic \oneminmax benchmark. For the expected number of function evaluations until the Pareto front is covered by the population of this MOEA, we prove an upper bound of $O(n^2 r^2 \log n)$ and a near-tight lower bound of $Ω(n^2 r (r + \log n))$. We can close the small remaining gap between these two bounds by considering a variant of the algorithm that accepts only strictly better solutions; for this variant, we show an upper bound of $O(n^2 r (r + \log n))$, matching our lower bound (which also holds for this variant). Our results suggest that classic MOEAs encounter no significant additional difficulties when dealing with multi-valued decision variables. However, significantly more advanced tools may be required to obtain tight bounds for algorithms with more complex population dynamics.

cs.NE↗

arXiv2026

UniM: A Unified Any-to-Any Interleaved Multimodal Benchmark

In real-world multimodal applications, systems usually need to comprehend arbitrarily combined and interleaved multimodal inputs from users, while also generating outputs in any interleaved multimedia form. This capability defines the goal of any-to-any interleaved multimodal learning under a unified paradigm of understanding and generation, posing new challenges and opportunities for advancing Multimodal Large Language Models (MLLMs). To foster and benchmark this capability, this paper introduces the UniM benchmark, the first Unified Any-to-Any Interleaved Multimodal dataset. UniM contains 31K high-quality instances across 30 domains and 7 representative modalities: text, image, audio, video, document, code, and 3D, each requiring multiple intertwined reasoning and generation capabilities. We further introduce the UniM Evaluation Suite, which assesses models along three dimensions: Semantic Correctness & Generation Quality, Response Structure Integrity, and Interleaved Coherence. In addition, we propose UniMA, an agentic baseline model equipped with traceable reasoning for structured interleaved generation. Comprehensive experiments demonstrate the difficulty of UniM and highlight key challenges and directions for advancing unified any-to-any multimodal intelligence. The project page is https://any2any-mllm.github.io/unim.

cs.CV↗

arXiv2025

Runtime Analysis of the SMS-EMOA for Many-Objective Optimization

This paper conducts the first rigorous runtime analysis of the SMS-EMOA for many-objective optimization. To this aim, we first propose a many-objective counterpart of the bi-objective OJZJ benchmark. We prove that SMS-EMOA computes the full Pareto front of this benchmark in an expected number of $O(μM n^k)$ iterations, where $n$ denotes the problem size (length of the bit-string representation), $k$ the gap size (a difficulty parameter of the problem), $M=(2n/m-2k+3)^{m/2}$ the size of the Pareto front, and $μ$ the population size (at least the same size as the largest incomparable set). This result together with the existing negative result for the original NSGA-II shows that, in principle, the general approach of the NSGA-II is suitable for many-objective optimization, but the crowding distance as tie-breaker has deficiencies. We obtain three additional insights on the SMS-EMOA. Different from a recent result for the bi-objective \ojzj benchmark, a recently proposed stochastic population update often does not help for its many-objective counterpart. It at most results in a speed-up by a factor of order $2^{k} / μ$, which is $Θ(1)$ for large $m$, such as $m>k$. On the positive side, we prove that heavy-tailed mutation irrespective of the number $m$ of objectives results in a speed-up of order $k^{0.5+k-β}/e^k$. Finally, we conduct the first runtime analyses of the SMS-EMOA on the classic OMM and LOTZ and show that the SMS-EMOA has a performance comparable to the GSEMO and the NSGA-II. Our main technical insight, a general condition ensuring that the SMS-EMOA does not lose Pareto-optimal objective values, promises to be useful also in other runtime analyses of this algorithm.

cs.NE↗

arXiv2025

Scalable Speed-ups for the SMS-EMOA from a Simple Aging Strategy

Different from single-objective evolutionary algorithms, where non-elitism is an established concept, multi-objective evolutionary algorithms almost always select the next population in a greedy fashion. In the only notable exception, Bian, Zhou, Li, and Qian (IJCAI 2023) proposed a stochastic selection mechanism for the SMS-EMOA and proved that it can speed up computing the Pareto front of the bi-objective jump benchmark with problem size $n$ and gap parameter $k$ by a factor of $\max\{1,2^{k/4}/n\}$. While this constitutes the first proven speed-up from non-elitist selection, suggesting a very interesting research direction, it has to be noted that a true speed-up only occurs for $k \ge 4\log_2(n)$, where the runtime is super-polynomial, and that the advantage reduces for larger numbers of objectives as shown in a later work. In this work, we propose a different non-elitist selection mechanism based on aging, which exempts individuals younger than a certain age from a possible removal. This remedies the two shortcomings of stochastic selection: We prove a speed-up by a factor of $\max\{1,Θ(k)^{k-1}\}$, regardless of the number of objectives. In particular, a positive speed-up can already be observed for constant $k$, the only setting for which polynomial runtimes can be witnessed. Overall, this result supports the use of non-elitist selection schemes, but suggests that aging-based mechanisms can be considerably more powerful than stochastic selection mechanisms.

cs.NE↗

arXiv2025

The First Theoretical Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm III (NSGA-III)

This work conducts a first theoretical analysis studying how well the NSGA-III approximates the Pareto front when the population size $N$ is less than the Pareto front size. We show that when $N$ is at least the number $N_r$ of reference points, then the approximation quality, measured by the maximum empty interval (MEI) indicator, on the OneMinMax benchmark is such that there is no empty interval longer than $\lceil\frac{(5-2\sqrt2)n}{N_r-1}\rceil$. This bound is independent of $N$, which suggests that further increasing the population size does not increase the quality of approximation when $N_r$ is fixed. This is a notable difference to the NSGA-II with sequential survival selection, where increasing the population size improves the quality of the approximations. We also prove two results indicating approximation difficulties when $N<N_r$. These theoretical results suggest that the best setting to approximate the Pareto front is $N_r=N$. In our experiments, we observe that with this setting the NSGA-III computes optimal approximations, very different from the NSGA-II, for which optimal approximations have not been observed so far.

cs.NE↗

arXiv2025

Towards Million-Scale Adversarial Robustness Evaluation With Stronger Individual Attacks

As deep learning models are increasingly deployed in safety-critical applications, evaluating their vulnerabilities to adversarial perturbations is essential for ensuring their reliability and trustworthiness. Over the past decade, a large number of white-box adversarial robustness evaluation methods (i.e., attacks) have been proposed, ranging from single-step to multi-step methods and from individual to ensemble methods. Despite these advances, challenges remain in conducting meaningful and comprehensive robustness evaluations, particularly when it comes to large-scale testing and ensuring evaluations reflect real-world adversarial risks. In this work, we focus on image classification models and propose a novel individual attack method, Probability Margin Attack (PMA), which defines the adversarial margin in the probability space rather than the logits space. We analyze the relationship between PMA and existing cross-entropy or logits-margin-based attacks, and show that PMA can outperform the current state-of-the-art individual methods. Building on PMA, we propose two types of ensemble attacks that balance effectiveness and efficiency. Furthermore, we create a million-scale dataset, CC1M, derived from the existing CC3M dataset, and use it to conduct the first million-scale white-box adversarial robustness evaluation of adversarially-trained ImageNet models. Our findings provide valuable insights into the robustness gaps between individual versus ensemble attacks and small-scale versus million-scale evaluations.

cs.LG↗

arXiv2025

Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives

The theoretical understanding of MOEAs is lagging far behind their success in practice. In particular, previous theory work considers mostly easy problems that are composed of unimodal objectives. As a first step towards a deeper understanding of how evolutionary algorithms solve multimodal multiobjective problems, we propose the OJZJ problem, a bi-objective problem composed of two objectives isomorphic to the classic jump function benchmark. We prove that SEMO with probability one does not compute the full Pareto front, regardless of the runtime. In contrast, for all problem sizes $n$ and all jump sizes ${k \in [4..\frac n2 - 1]}$, the global SEMO (GSEMO) covers the Pareto front in an expected number of $Θ((n-2k)n^{k})$ iterations. For $k = o(n)$, we also show the tighter bound $\frac 32 e n^{k+1} \pm o(n^{k+1})$, which might be the first runtime bound for an MOEA that is tight apart from lower-order terms. We also combine the GSEMO with two approaches that showed advantages in single-objective multimodal problems. When using the GSEMO with a heavy-tailed mutation operator, the expected runtime improves by a factor of at least $k^{Ω(k)}$. When adapting the recent stagnation-detection strategy of Rajabi and Witt (2022) to the GSEMO, the expected runtime also improves by a factor of at least $k^{Ω(k)}$ and surpasses the heavy-tailed GSEMO by a small polynomial factor in $k$. Via an experimental analysis, we show that these asymptotic differences are visible already for small problem sizes: A factor-$5$ speed-up from heavy-tailed mutation and a factor-$10$ speed-up from stagnation detection can be observed already for jump size~$4$ and problem sizes between $10$ and $50$. Overall, our results show that the ideas recently developed to aid single-objective evolutionary algorithms to cope with local optima can be effectively employed also in multiobjective optimization.

cs.NE↗

arXiv2024

A Crowding Distance That Provably Solves the Difficulties of the NSGA-II in Many-Objective Optimization

Recent theoretical works have shown that the NSGA-II can have enormous difficulties to solve problems with more than two objectives. In contrast, algorithms like the NSGA-III or SMS-EMOA, differing from the NSGA-II only in the secondary selection criterion, provably perform well in these situations. To remedy this shortcoming of the NSGA-II, but at the same time keep the advantages of the widely accepted crowding distance, we use the insights of these previous work to define a variant of the crowding distance, called truthful crowding distance. Different from the classic crowding distance, it has for any number of objectives the desirable property that a small crowding distance value indicates that some other solution has a similar objective vector. Building on this property, we conduct mathematical runtime analyses for the NSGA-II with truthful crowding distance. We show that this algorithm can solve the many-objective versions of the OneMinMax, COCZ, LOTZ, and OJZJ$_k$ problems in the same (polynomial) asymptotic runtimes as the NSGA-III and the SMS-EMOA. This contrasts the exponential lower bounds previously shown for the classic NSGA-II. For the bi-objective versions of these problems, our NSGA-II has a similar performance as the classic NSGA-II, gaining however from smaller admissible population sizes. For the bi-objective OneMinMax problem, we also observe a (minimally) better performance in approximating the Pareto front. These results suggest that our truthful version of the NSGA-II has the same good performance as the classic NSGA-II in two objectives, but can resolve the drastic problems in more than two objectives.

cs.NE↗

arXiv2024

Downstream Transfer Attack: Adversarial Attacks on Downstream Models with Pre-trained Vision Transformers

With the advancement of vision transformers (ViTs) and self-supervised learning (SSL) techniques, pre-trained large ViTs have become the new foundation models for computer vision applications. However, studies have shown that, like convolutional neural networks (CNNs), ViTs are also susceptible to adversarial attacks, where subtle perturbations in the input can fool the model into making false predictions. This paper studies the transferability of such an adversarial vulnerability from a pre-trained ViT model to downstream tasks. We focus on \emph{sample-wise} transfer attacks and propose a novel attack method termed \emph{Downstream Transfer Attack (DTA)}. For a given test image, DTA leverages a pre-trained ViT model to craft the adversarial example and then applies the adversarial example to attack a fine-tuned version of the model on a downstream dataset. During the attack, DTA identifies and exploits the most vulnerable layers of the pre-trained model guided by a cosine similarity loss to craft highly transferable attacks. Through extensive experiments with pre-trained ViTs by 3 distinct pre-training methods, 3 fine-tuning schemes, and across 10 diverse downstream datasets, we show that DTA achieves an average attack success rate (ASR) exceeding 90\%, surpassing existing methods by a huge margin. When used with adversarial training, the adversarial examples generated by our DTA can significantly improve the model's robustness to different downstream transfer attacks.

cs.CV↗

arXiv2023

Choosing the Right Algorithm With Hints From Complexity Theory

Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm in a certain broad class of black-box optimizers can give fruitful indications in which direction to search for good established optimization heuristics. We demonstrate this approach on the recently proposed DLB benchmark, for which the only known results are $O(n^3)$ runtimes for several classic evolutionary algorithms and an $O(n^2 \log n)$ runtime for an estimation-of-distribution algorithm. Our finding that the unary unbiased black-box complexity is only $O(n^2)$ suggests the Metropolis algorithm as an interesting candidate and we prove that it solves the DLB problem in quadratic time. Since we also prove that better runtimes cannot be obtained in the class of unary unbiased algorithms, we shift our attention to algorithms that use the information of more parents to generate new solutions. An artificial algorithm of this type having an $O(n \log n)$ runtime leads to the result that the significance-based compact genetic algorithm (sig-cGA) can solve the DLB problem also in time $O(n \log n)$ with high probability. Our experiments show a remarkably good performance of the Metropolis algorithm, clearly the best of all algorithms regarded for reasonable problem sizes.

cs.NE↗

arXiv2023

Sharp Bounds for Genetic Drift in Estimation of Distribution Algorithms

Estimation of Distribution Algorithms (EDAs) are one branch of Evolutionary Algorithms (EAs) in the broad sense that they evolve a probabilistic model instead of a population. Many existing algorithms fall into this category. Analogous to genetic drift in EAs, EDAs also encounter the phenomenon that updates of the probabilistic model not justified by the fitness move the sampling frequencies to the boundary values. This can result in a considerable performance loss. This paper proves the first sharp estimates of the boundary hitting time of the sampling frequency of a neutral bit for several univariate EDAs. For the UMDA that selects $μ$ best individuals from $λ$ offspring each generation, we prove that the expected first iteration when the frequency of the neutral bit leaves the middle range $[\tfrac 14, \tfrac 34]$ and the expected first time it is absorbed in 0 or 1 are both $Θ(μ)$. The corresponding hitting times are $Θ(K^2)$ for the cGA with hypothetical population size $K$. This paper further proves that for PBIL with parameters $μ$, $λ$, and $ρ$, in an expected number of $Θ(μ/ρ^2)$ iterations the sampling frequency of a neutral bit leaves the interval $[Θ(ρ/μ),1-Θ(ρ/μ)]$ and then always the same value is sampled for this bit, that is, the frequency approaches the corresponding boundary value with maximum speed. For the lower bounds implicit in these statements, we also show exponential tail bounds. If a bit is not neutral, but neutral or has a preference for ones, then the lower bounds on the times to reach a low frequency value still hold. An analogous statement holds for bits that are neutral or prefer the value zero.

cs.NE↗

arXiv2023

Mathematical Runtime Analysis for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for the NSGA-II so far. In this work, we show that mathematical runtime analyses are feasible also for the NSGA-II. As particular results, we prove that with a population size four times larger than the size of the Pareto front, the NSGA-II with two classic mutation operators and four different ways to select the parents satisfies the same asymptotic runtime guarantees as the SEMO and GSEMO algorithms on the basic OneMinMax and LeadingOnesTrailingZeros benchmarks. However, if the population size is only equal to the size of the Pareto front, then the NSGA-II cannot efficiently compute the full Pareto front: for an exponential number of iterations, the population will always miss a constant fraction of the Pareto front. Our experiments confirm the above findings.

cs.NE↗

arXiv2023

Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

Recent theoretical works have shown that the NSGA-II efficiently computes the full Pareto front when the population size is large enough. In this work, we study how well it approximates the Pareto front when the population size is smaller. For the OneMinMax benchmark, we point out situations in which the parents and offspring cover well the Pareto front, but the next population has large gaps on the Pareto front. Our mathematical proofs suggest as reason for this undesirable behavior that the NSGA-II in the selection stage computes the crowding distance once and then removes individuals with smallest crowding distance without considering that a removal increases the crowding distance of some individuals. We then analyze two variants not prone to this problem. For the NSGA-II that updates the crowding distance after each removal (Kukkonen and Deb (2006)) and the steady-state NSGA-II (Nebro and Durillo (2009)), we prove that the gaps in the Pareto front are never more than a small constant factor larger than the theoretical minimum. This is the first mathematical work on the approximation ability of the NSGA-II and the first runtime analysis for the steady-state NSGA-II. Experiments also show the superior approximation ability of the two NSGA-II variants.

cs.NE↗

arXiv2023

Runtime Analysis for the NSGA-II: Proving, Quantifying, and Explaining the Inefficiency For Many Objectives

The NSGA-II is one of the most prominent algorithms to solve multi-objective optimization problems. Despite numerous successful applications, several studies have shown that the NSGA-II is less effective for larger numbers of objectives. In this work, we use mathematical runtime analyses to rigorously demonstrate and quantify this phenomenon. We show that even on the simple $m$-objective generalization of the discrete OneMinMax benchmark, where every solution is Pareto optimal, the NSGA-II also with large population sizes cannot compute the full Pareto front (objective vectors of all Pareto optima) in sub-exponential time when the number of objectives is at least three. The reason for this unexpected behavior lies in the fact that in the computation of the crowding distance, the different objectives are regarded independently. This is not a problem for two objectives, where any sorting of a pair-wise incomparable set of solutions according to one objective is also such a sorting according to the other objective (in the inverse order).

cs.NE↗

arXiv2023

Theoretical Analyses of Evolutionary Algorithms on Time-Linkage OneMax with General Weights

Evolutionary computation has shown its superiority in dynamic optimization, but for the (dynamic) time-linkage problems, some theoretical studies have revealed the possible weakness of evolutionary computation. Since the theoretically analyzed time-linkage problem only considers the influence of an extremely strong negative time-linkage effect, it remains unclear whether the weakness also appears in problems with more general time-linkage effects. Besides, understanding in depth the relationship between time-linkage effect and algorithmic features is important to build up our knowledge of what algorithmic features are good at what kinds of problems. In this paper, we analyze the general time-linkage effect and consider the time-linkage OneMax with general weights whose absolute values reflect the strength and whose sign reflects the positive or negative influence. We prove that except for some small and positive time-linkage effects (that is, for weights $0$ and $1$), randomized local search (RLS) and (1+1)EA cannot converge to the global optimum with a positive probability. More precisely, for the negative time-linkage effect (for negative weights), both algorithms cannot efficiently reach the global optimum and the probability of failing to converge to the global optimum is at least $1-o(1)$. For the not so small positive time-linkage effect (positive weights greater than $1$), such a probability is at most $c+o(1)$ where $c$ is a constant strictly less than $1$.

cs.NE↗