arXiv:2607.15841v1 Announce Type: cross
Abstract: This article is devoted to the inverse source problem of uniquely determining a measure-valued source from sparse boundary measurements. The measurements considered consist of flux observations over a time interval at two distinct points on the boundary of the domain. The main objective of this work is to extend the existing literature on inverse source problems from sparse boundary measurements, which has so far been limited to point sources or L2 sources, to the identification of a general class of Radon measures. Our approach combines several analytical tools, including regularity properties, boundary representations, and the time analyticity of solutions to the diffusion equation with singular sources. Our theoretical analysis is complemented by a numerical study of the problem. In particular, we investigate the reconstruction of point sources and of a source supported on a curve, and present numerical experiments illustrating the recovery of such sources from sparse boundary flux measurements.
Science Journals
arXiv:2607.15853v1 Announce Type: cross
Abstract: Maximal quantum leakage quantifies privacy against adversaries with arbitrary intentions. In this work, we prove that computing this leakage is equivalent to minimum-error quantum state discrimination with equal priors. This establishes a computable operational interpretation, addressing the previous difficulty in computing maximal quantum leakage. We further analyze the impact of collective measurements on multiple copies of a state, demonstrating that leakage increases monotonically with the number of copies, which leads to explicitly characterizing the maximal leakage in the asymptotic limit. Extending this framework to quantum channels, we develop an iterative algorithm for the jointly designing of input states and measurements. Numerical examples involving collective measurements and the maximal channel leakage demonstrate our theoretical findings.
arXiv:2607.15881v1 Announce Type: cross
Abstract: We study the class $\#\mathsf{L}$ of functions counting accepting paths of non-deterministic log-space Turing machines and construct methods to prove containment in $\#\mathsf{L}$. We prove that a large number of classical combinatorial and number theoretic functions belong to this class: classical functions from enumerative combinatorics (multinomial coefficients, Catalan numbers, linear extensions of trees, Stirling numbers, etc), algebraic combinatorics (number of standard Young tableaux, etc), discrete geometry, number theoretic functions, representation theoretic multiplicities in a large class of cases. We show that $\mathrm{GL}_2$-plethysm coefficients of bounded length outer partition can be counted by log$^2$-space polytime verifiers. We pose numerous questions and conjectures on $\#\mathsf{L}$ containment and its generalizations, that suggest venues for conditionally disproving $\#\mathsf{P}$-completeness. While studying which combinatorial functions are in $\#\mathsf{P}$ provides a formal way of (dis)proving the existence of combinatorial interpretations, the lower class $\#\mathsf{L}$ serves as an analogue for functions computable in polynomial time.
arXiv:2607.15884v1 Announce Type: cross
Abstract: This work presents a game-theoretic framework for interpretable hyperparameter-objective interaction analysis rather than proposing a new optimization algorithm. In the proposed framework, Shapley Effects are employed for global sensitivity analysis, while Pareto front sets are utilized to identify effective hyperparameter configurations and support early-stage model evaluation. The resulting analysis reveals which players (hyperparameters) are most influential with respect to different objectives in a given game (application). Consequently, the proposed framework provides interpretable insights into objective-aware hyperparameter interactions, enabling practitioners to guide subsequent optimization, reduce the search space, and perform early-stage model evaluation. The effectiveness of the proposed framework is demonstrated using three distinct neural network architectures across different problem domains under multi-objective settings.
arXiv:2607.15695v1 Announce Type: new
Abstract: Iterating the Dyson equation with the static part of the self-energy leads to a concise and possibly improved expression of the one-body reduced density matrix from any self-energy approximation. Here we apply the procedure to Hedin's $GW$ approximation. The non-iterated $GW$ based density matrix was already known to yield accurate density matrices for molecular systems. We show that the Dyson-equation-based procedure is equivalent to the so-called variational Z-vector approach applied to the Random-Phase approximation energy functional, but only in the case of a Hartree-Fock mean-field starting point. When a generalized Kohn-Sham scheme is employed instead, the two approaches differ. By comparing the density matrix for a benchmark set of 34 small molecules to coupled-cluster reference values, we conclude that the iterated Dyson equation indeed produces improved density matrices for molecular systems. Interestingly, we observe that the excitation rank of the reference coupled-cluster matters much and that the inclusion of triple excitations (CCSDT) quantitatively changes the conclusions of the benchmark as compared to single and double excitations coupled-cluster (CCSD).
arXiv:2607.15902v1 Announce Type: cross
Abstract: We investigate the ultrametric organization of energy landscapes defined on sparse random Erd\H{o}s--R\'enyi graphs. Each graph vertex is assigned a random free energy from a uniform distribution over an interval of width $\Delta F$, and the kinetics are modeled by a Markov process with Kramers transition rates. Using spectral decomposition of the rate matrix, we construct a kinetic Mahalanobis metric between basins of attraction. Computational experiments for graphs with $V=5000$ vertices and $E=5000$ edges show that the degree of nontrivial ultrametricity increases monotonically from $\approx42\%$ for $\Delta F=10$ kJ/mol to $\approx96\%$ for $\Delta F=1000$ kJ/mol. We prove a limit theorem: as $\Delta F\to\infty$, the logarithmic asymptotics of this metric converge pointwise to the classical single-linkage ultrametric. For finite $\Delta F$, corrections from suboptimal paths are exponentially suppressed with increasing $\Delta F$, so that the metric becomes asymptotically ultrametric. Our results suggest that ultrametricity is a universal property of sparse, locally tree-like networks with rugged energy landscapes in the limit of large energy spreads.
arXiv:2607.15698v1 Announce Type: new
Abstract: We propose and evaluate three hierarchical ensemble setups for zebrafish phenotype classification from embryo images. In all setups, stage 1 uses a single four-class classifier to assign images to one of the exclusive phenotypes: Normal, Chorion, Dead, or Other. Images classified as Other are then processed in stage 2, where the ensemble design differs across setups: a single multi-label classifier, two specialized multi-label classifiers, or an ensemble of binary classifiers. We compare these setups using three backbone architectures: ResNet18, ViT, and ConvNeXt. Overall, ConvNeXt achieves the best performance across setups, while the specialized hierarchical ensemble in setup 2 provides the best balance in terms of F1-score. The results show that the proposed specialised hierarchical ensembles are effective for zebrafish phenotype recognition, and suggest that ConvNeXt is particularly useful backbone model.
arXiv:2607.15975v1 Announce Type: cross
Abstract: Collective migration of epithelial monolayers emerges from the interplay between mechanical interactions and biochemical signalling. Here, we present a phenomenological mechanobiological framework linking cell-scale orientational interactions to tissue-scale mechanics. We distinguish reversible and irreversible head-on and glancing collisions, showing that reversible interactions store orientational mechanical energy while preserving collision geometry, whereas irreversible interactions dissipate energy and alter cell orientation. The balance between energy storage and dissipation governs collective migration, mechanical feedback, and density-dependent processes including cell jamming and live cell extrusion. These interactions regulate cell elasticity, contractility, and adhesion, thereby modifying epithelial surface tension and the effective viscoelastic response of the monolayer. We quantify these effects using orientational interaction potentials, an effective second virial coefficient, and dimensionless measures of stored and dissipated orientational energy. The relative contribution of these mechanisms increases with cell packing density, becoming dominant near the jamming transition. This framework provides a constitutive interpretation connecting collision-induced orientation dynamics with emergent epithelial rheology and suggests how density-dependent interaction regimes shape collective migration and tissue viscoelasticity.
arXiv:2607.16178v1 Announce Type: cross
Abstract: In many applications of matching, the point clouds to be matched are not merely unstructured sets of points but rather samples from distributions with an intrinsic cluster structure. In such cases, as individual points are often interchangeable within a coherent region, finding a robust region-to-region alignment is more desirable than establishing a precise point-to-point correspondence. To this end, we propose a novel approach for cluster-aware matching based on Laplacian Optimal Transport (LapOT). The key idea is to regularize the optimal transport problem with quadratic Laplacian terms constructed from similarity graphs of the point clouds, which encourages the optimal coupling to respect the cluster structure of both point sets. We also introduce Refined Simultaneous Clustering (RSC), a method that leverages the cluster-aware coupling obtained from LapOT to produce consistent partitions across the point sets, which can overcome the limitations of independent clustering and yield more stable and interpretable results. We demonstrate the effectiveness of our approach through theoretical analysis and empirical experiments, showing that LapOT indeed produces cluster-aware matching that leads to more consistent and meaningful alignments between point clouds.
arXiv:2012.13132v2 Announce Type: replace
Abstract: Persistent homology (PH), a key tool in topological data analysis (TDA), captures global topological features of digital images through \emph{topological filtrations}. Alternatively, mathematical morphology (MM), rooted in set theory and lattice theory, provides operations such as opening and closing to modify local geometric structures in digital images. This motivates incorporating local geometric information into a PH framework via morphological filtrations, yielding an MM-based PH framework. However, the validity of such filtrations depends on the absorption property of MM operations, which may fail for arbitrary structuring elements, the components defining MM operators. To address this issue, we introduce shift inclusion as a sufficient condition for ensuring absorption, provide a formal proof, and demonstrate its utility in pore-structure analysis, highlighting the synergy between MM and PH for image and scientific data analysis.
arXiv:2404.16741v3 Announce Type: replace
Abstract: A crucial challenge arising in the design of large-scale logistical networks is to optimize parcel sortation for routing. We study this problem under the recent graph-theoretic formalization of Van Dyk, Klause, Koenemann and Megow (IPCO 2024). The problem asks - given an input digraph D (the fulfillment network) together with a set of commodities represented as source-sink tuples - for a minimum-outdegree subgraph H of the transitive closure of D that contains a source-sink route for each of the commodities. Given the underlying motivation, we study two variants of the problem which differ in whether the routes for the commodities are assumed to be given, or can be chosen arbitrarily.
We perform a thorough parameterized analysis of the complexity of both problems. Our results concentrate on three fundamental parameterizations of the problem: (1) When attempting to parameterize by the target outdegree of H, we show that the problems are paraNP-hard even in highly restricted cases; (2) When parameterizing by the number of commodities, we utilize Ramsey-type arguments and color-coding techniques to obtain parameterized algorithms for both problems; (3) When parameterizing by the structure of D, we establish fixed-parameter tractability for both problems w.r.t. treewidth, maximum degree and the maximum routing length. We combine this with lower bounds which show that omitting any of the three parameters results in paraNP-hardness.
arXiv:2406.01514v5 Announce Type: replace
Abstract: We introduce a training-free safety enhancement method for aligning large language models (LLMs) without the need for supervised fine-tuning or reinforcement learning from human feedback. Our main idea is to provide a robust plug-and-play approach to prevent shadow alignment when models are adapted to downstream tasks. Specifically, we leverage knowledge distillation to extract alignment signals from well-aligned LLMs and inject them into shadow-aligned models via model fusion, enabling plug-and-play alignment correction. In our methodology, we employ delta debugging to identify the critical components of knowledge necessary for effective distillation. On the harmful question dataset, our method significantly enhances the average defense success rate by approximately 14.42%, reaching as high as 51.39% across 17 influenced LLMs, without compromising performance. Our code is available at https://github.com/NWULIST/DAPA.
arXiv:2409.10897v3 Announce Type: replace
Abstract: The increasing adoption of neural networks in learning-augmented systems highlights the growing need for model safety and robustness, especially in safety-critical domains. While recent advances in neural network verification offer formal guarantees on worst-case behavior, existing approaches require users to manually define model specifications, an error-prone, incomplete, and time-consuming process. In this paper, we present AutoSpec, the first comprehensive framework for automatically generating and evaluating neural network specifications for learning-augmented systems. AutoSpec introduces a tree-based algorithm that adaptively partitions the input space to generate specification sets aligned with model behavior, as well as a statistical certification framework that provides rigorous accuracy guarantees for each specification. We also propose a principled evaluation framework that defines interpretable metrics for specification accuracy and coverage, establishing a benchmark for future research. Experiments across four diverse applications show that AutoSpec outperforms both manually defined specifications and existing baseline algorithms, improving the F1 score by up to 53% over human-defined specifications and 73% over the strongest baseline.
arXiv:2410.21214v4 Announce Type: replace
Abstract: People increasingly use digital platforms to exchange resources in accordance with some policies stating what resources users offer and what they require in return. In this paper, we propose a formal model of these environments, focussing on how users' policies are defined and enforced, so ensuring that malicious users cannot take advantage of honest ones. To that end, we introduce the declarative policy language MuAC and equip it with a formal semantics. To determine if a resource exchange is fair, i.e., if it respects the MuAC policies in force, we introduce the non-standard logic MuACL that combines non-linear, linear and contractual aspects, and prove it decidable. Notably, the operator for contractual implication of MuACL is not expressible in linear logic. We define a semantics preserving compilation of MuAC policies into MuACL, thus establishing that exchange fairness is reduced to finding a proof in MuACL. Finally, we show how this approach can be put to work on a blockchain to exchange non-fungible tokens.
arXiv:2607.15284v1 Announce Type: new
Abstract: While recommendation systems enable users to find articles of interest, they can also create ``filter bubbles'' by presenting content that reinforces users' pre-existing beliefs. Users are often unaware that the system placed them in a filter bubble and, even when aware, they often lack direct control over it. To address these issues, we first design a political news recommendation system augmented with an enhanced interface that exposes the political and topical interests the system inferred from user behavior. This allows the user to adjust the recommendation system to receive more articles on a particular topic or presenting a particular political stance. We then conduct a user study to compare our system to a traditional interface and found that the transparent approach helped users realize that they were in a filter bubble. Additionally, the enhanced system led to less extreme news for most users but also allowed others to move the system to more extremes. Similarly, while many users moved the system from extreme liberal/conservative to the center, this came at the expense of reducing political diversity of the articles shown. These findings suggest that, while the proposed system increased awareness of the filter bubbles, it had heterogeneous effects on news consumption depending on user preferences.
arXiv:2607.15285v1 Announce Type: new
Abstract: Multimodal video systems often expose clip-level scores while hiding the local temporal failure that makes a video inconsistent. We formulate video-audio consistency as finite-trace modal monitoring over synchronized visual, audio, and subtitle/OCR atoms. A formula library specifies speech-speaker agreement, audio-visual event agreement, subtitle-video agreement, scene continuity, and edit-induced temporal shock. A certificate records the trace hash, formula identifier, verdict, violating indices, defect score, first counterexample window, execution engine, and certificate hash. The certificate is not a proof that a detector is correct; it is a reproducible witness that the finite-trace checker can independently reconstruct once the atom trace is fixed. The artifact decodes real MP4 video, extracts CLIP visual atoms, extracts AST audio atoms, runs dense counterfactual perturbation sweeps, emits CSV traces and JSON certificates, and renders manuscript figures from those files.
arXiv:2411.11380v3 Announce Type: replace
Abstract: To safeguard sensitive user data, web developers typically rely on implicit access-control policies, which they implement using access checks and query filters. This ad hoc approach is error-prone as these scattered checks and filters are easy to misplace or misspecify, and the lack of an explicit policy precludes external access-control enforcement. More critically, it is difficult for humans to discern what policy is embedded in application code (i.e., what data the application may access) -- an issue that worsens as development teams evolve.
This paper tackles policy extraction: the task of extracting the access-control policy embedded in an application by summarizing its data queries. An extracted policy, once vetted for errors, can stand alone as a specification for the application's data access, and can be enforced to ensure compliance as code changes over time. We introduce Ote, a policy extractor for Ruby on Rails web applications. Ote uses concolic execution to explore execution paths through the application, generating traces of SQL queries and conditions that trigger them. It then merges and simplifies these traces into a final policy that aligns with the observed behaviors. We applied Ote to three real-world applications and compared extracted policies to handwritten ones, revealing several errors in the latter.
arXiv:2607.15364v1 Announce Type: new
Abstract: Social media companies have shifted away from human fact-checkers and instead have embedded conversational Large Language Models (LLM) on their platforms. LLM chatbots differ from human fact-checkers in many ways that may shape user responses to corrections. Of particular interest in this study is that LLM chatbots can be ideologically configured via the content emphasized in their responses, the sources cited, and the configured persona. Using data from two within-subjects experiments (n=705), this paper investigates the effectiveness of fact checking information from ideologically configured LLM chatbots. We find that LLM fact-checkers significantly shift trust in true and false political news headlines, even when the chatbot is politically incongruent with the user. The perceived political congruency between the participant and the bot matters only when headlines are politically distant. That is, trust in correctly labeled true headlines increases less when politically distant chatbots check distant headlines and increases more when moderate chatbots check distant headlines. The perceived political congruency of LLM chatbots did not impact their effectiveness at decreasing trust in false headlines. Unfortunately, LLM fact-checkers also significantly change trust in news when they are wrong or provide inconclusive answers. Our results demonstrate both the potential for LLMs to correct false information at scale but also their potential to taint the truth at scale.
arXiv:2607.15389v1 Announce Type: new
Abstract: This work investigates a generalized Choquet-integral-based feature aggregation framework to improve anomaly detection in high-dimensional network traffic data. The approach combines adaptive weighting with incremental feature selection to address feature redundancy. Using Random Forest and XGBoost classifiers, we evaluate models trained with both raw and Choquet-aggregated features under varying feature subset sizes. The proposed aggregation achieves up to $7\%$ higher accuracy while reducing data volume by $77.5\%$ (from $214$~MB to $48$~MB), without degrading precision and recall. Results averaged over multiple stratified repetitions indicate that Choquet-based aggregation yields statistically significant gains ($p < 0.05$) in scenarios with limited feature availability, highlighting its suitability for real-time intrusion detection under bandwidth and feature-availability constraints.
arXiv:2607.15401v1 Announce Type: new
Abstract: High-quality, large-scale paired data is essential for training learning-based image deblurring models. However, synthetic blurry images generally lack realism, while real-world captured images require complex and inflexible camera systems. In this work, we propose GS-RealBlur, a data acquisition framework for real-world image deblurring, achieving both blur realism and acquisition flexibility. Specifically, we use a handheld camera to capture blurry images, and deploy a gimbal to densely capture sharp images of the same scene. We reconstruct the 3D representation of sharp images and calibrate the camera pose of each blurry frame within this 3D. The image rendered from this 3D according to the pose serves as the sharp counterpart. To better align the rendered image with the blurry image, we introduce a Blur-aware Pose Refinement (BPR) module that refines the pose using appearance consistency and centroid alignment constraints. Leveraging GS-RealBlur, we construct a high-quality and diverse dataset. Extensive experiments demonstrate that a deblurring model trained on our dataset achieves superior generalization performance across various real-world deblurring benchmarks, consistently outperforming models trained on existing synthetic and real-world datasets. The code and dataset will be made publicly available.
arXiv:2607.15407v1 Announce Type: new
Abstract: We introduce and study the multiple-choice matroid secretary problem, denoted $(J,\kappa)$-MSP. For rank-one matroids and $\kappa=\infty$, it reduces to the classical secretary problem with $J$ choices. Elements arrive in uniformly random order. Algorithms may keep a candidate pool $\mathrm{AUX}$ feasible in the $J$-fold union matroid $\mathcal{M}^{(J)}$ satisfying $|\mathrm{AUX}|\le \kappa\cdot\mathrm{rank}(\mathcal{M})$. Finally, one extracts the maximum-weight independent subset of $\mathrm{AUX}$ in $\mathcal{M}$. This model separates online storage from the final feasible solution. We study two multiple-choice implementations: multi-track algorithms (maintaining $J$ independent sets of $\mathcal{M}$) and union-based algorithms (maintaining the pool directly in $\mathcal{M}^{(J)}$).
Our main result is an exact optimal algorithm for transversal matroids in the uncapacitated $(J,\infty)$ setting. For fixed $J$, its probability-competitive ratio equals the optimal success probability of the classical $J$-choice secretary problem. Thus, rank-one instances are the worst case for the whole transversal class, and the optimal guarantee converges exponentially fast to $1$ as $J$ grows. We also analyze a simple single-threshold routing algorithm for capacitated transversal matroids with local capacities $b$ and global capacity $\kappa\cdot\mathrm{rank}(\mathcal{M})$. Its analysis provides explicit finite-parameter bounds and asymptotic formulas, showing how finite-rank loss caused by global capacity decays, and how $b$, $J$, and $\kappa$ interact. Finally, we instantiate the multi-track approach for $k$-column-sparse matroids (guarantee $1-O(e^{-J/(ke)})$) and the union-based approach for laminar matroids (guarantee $1-O(e^{-J/e})$).
arXiv:2607.15281v1 Announce Type: new
Abstract: Causal and intervention-based question answering is fundamental to advancing large language models (LLMs) toward reasoning beyond surface-level correlations and understanding underlying causal mechanisms. However, existing LLM-based methods often rely on implicit language-level reasoning, resulting in opaque causal assumptions, unverifiable reasoning paths, and fragile predictions under complex interventions, particularly in context-free settings. In this paper, we propose an explicit and auditable causal reasoning framework for context-free intervention-based question answering. Our method formulates causal inference as structured reasoning over an explicit causal graph through four modular stages, rather than implicit end-to-end prediction. A key innovation is a target-aware causal graph construction strategy that treats the target variable as a core constraint during graph expansion, effectively suppressing irrelevant variables, spurious causal relations, and reasoning noise. We further introduce a path-level causal evidence aggregation mechanism that combines multiple causal paths while modeling both reinforcing and counteracting effects, enabling robust decision-making beyond single-chain reasoning. Extensive experiments on three benchmarks demonstrate that our framework consistently outperforms existing LLM-based methods while providing interpretable and auditable causal reasoning traces.
arXiv:2607.15621v1 Announce Type: new
Abstract: Large language models bring instruction following and scene reasoning to end-to-end driving, but their inference latency collides with the control rate a vehicle requires. Existing closed-loop agents hide this gap by invoking the model on alternate simulation ticks and replaying the previous command in between, so half of all control outputs ignore the newest observations. We present a fast-slow architecture that removes this compromise. A frozen 7B vision-language backbone acts as the slow system, digesting navigation instructions and visual history at low frequency while exposing its per-layer key-value cache as a standing representation of the scene. A lightweight action expert acts as the fast system, attending to this cache and to the current camera frame at every simulation tick to regress waypoints in a single forward pass. Since the cache lags behind the world at deployment, we train the expert under randomized staleness, aligning training with asynchronous execution. On LangAuto-Short routes in CARLA, our system produces fresh control at every 50 ms simulation tick and lifts route completion from 37.0 to 94.0 over the frame-skipping baseline. A frame-skip ablation with the same expert separates the two factors at work: the expert raises the driving score on its own, while per-tick freshness raises completion from 82.1 to 94.0 and cuts red-light violations by a third. Trained on a single town, the expert transfers zero-shot to two unseen towns, holding 84-94% route completion where the baseline reaches 31-41%. It reduces open-loop waypoint error by nearly a factor of four compared to the backbone's own action head, at a per-tick model cost of 32 ms that is independent of history length on a single consumer GPU.
arXiv:2607.15283v1 Announce Type: new
Abstract: Biomedical question answering (QA) encompasses diverse question types, including yes/no, factoid, list, and summary questions, each requiring distinct forms of evidence and reasoning. However, most retrieval-augmented QA systems rely on a unified retrieval pipeline, regardless of the information needs of different question categories. This one-size-fits-all approach may limit the effectiveness of evidence acquisition and downstream answer generation. In this work, we propose an adaptive retrieval framework that selects retrieval and evidence aggregation strategies according to question type. The system combines query understanding, biomedical document retrieval, reranking, knowledge graph augmentation, document clustering, and large language model-based answer generation. For yes/no questions, it focuses on precise evidence retrieval; for factoid and list questions, it emphasizes entity-oriented retrieval and clustering; and for summary questions, it performs broader evidence collection and synthesis. We evaluate the proposed framework on the BioASQ benchmark and demonstrate that adaptive retrieval strategies improve evidence relevance and answer quality across multiple question types. Our results suggest that aligning retrieval mechanisms with question-specific information needs provides an effective direction for enhancing retrieval-augmented biomedical QA systems.
arXiv:2607.15412v1 Announce Type: new
Abstract: Multi-objective learning (MOL) aims to optimize multiple objectives simultaneously. The multi-gradient descent algorithm (MGDA) is a workhorse that iteratively updates along a common descent or conflict-avoidant (CA) direction across objectives. In stochastic settings, however, the vanilla stochastic MGDA method, SMG, lacks a fast convergence rate because mini-batch sampling introduces noise in the gradients. This causes bias in the update direction, which is controlled by the CA direction continuity. In this paper, we show that the CA direction is $1/2$-Holder continuous with respect to the Jacobian matrix, and the exponent $1/2$ cannot be improved in the worst case. This leads to a suboptimal convergence rate for vanilla stochastic MGDA in prior works. Nevertheless, under additional regularity conditions, we show this can be improved to Lipschitz continuity. Based on this insight, we propose a stochastic multi-objective regularity-aware (MoRe) method that exploits the Lipschitz continuity of the CA direction when the subproblem is regular, and switches to a fixed scalarization weight otherwise. Intuitively, the proposed algorithm employs CA direction update when the gradient conflict is large, and linear scalarization update otherwise. Theoretically, our method improves the convergence rate of SMG in the nonconvex setting from $\widetilde{\mathcal O}(T^{-1/4})$ to $\widetilde{\mathcal O}(T^{-1/2})$, where $\widetilde{\mathcal O}(\cdot)$ hides logarithmic factors. Meanwhile, we also establish the per-iterate conflict-avoidance guarantees. Empirically, experiments demonstrate its effectiveness in multi-task performance and verify convergence behavior consistent with the established theoretical rate.