arXiv:2605.16098v1 Announce Type: new Abstract: Federated learning (FL) is vulnerable to data poisoning attacks due to its distributed nature. Although recent GAN-based data poisoning methods have indicated the potential of using generative AI to generate seemingly legitimate poisoned data, the inherent consistency of GAN outputs can still reveal a sign of data poisoning. In this paper, we propose a diffusion-based data poisoning framework against FL systems, which leverages a Poisoning-Oriented Conditional Diffusion Model (PCDM) to enable fine-grained control over the local generation of poisoned data while ensuring both attack effectiveness and stealthiness. Our PCDM incorporates an adjustable poisoning vector within the global context to precisely control the generation of poisoned data, with theoretical guarantees on attack performance. Furthermore, it employs a novel jumping diffusion strategy for lightweight and efficient poisoned data generation. We conduct the most systematic and broad experimental evaluation for FL poisoning attacks against various defenses, including advanced Byzantine robust aggregation mechanisms, on four open datasets: MNIST, Fashion-MNIST, CIFAR-10, CIFAR-100, and a real-world wireless-specific dataset VRAI. Our results demonstrate that PCDM is less likely to exhibit statistical anomalies compared with the state-of-the-art methods while more effectively degrading global FL performance, which poses a significant risk to data security in FL.
Science Journals
arXiv:2605.15763v1 Announce Type: new Abstract: Current state-of-the-art Quality Estimation (QE) in machine translation relies on massive, proprietary LLMs, raising data privacy concerns. We demonstrate that smaller, open-source LLMs (<30B parameters) are a viable, cost-effective and privacy-preserving alternative. Using a single-pass prompting strategy, our models simultaneously generate quality scores, MQM error annotations, suggested error corrections, and full post-editions. Our analysis shows these models achieve highly competitive system-level correlations with human judgments that outperform traditional neural metrics, fine-tuned models, and human inter-annotator agreement, effectively approximating the capabilities of much larger proprietary LLMs.
arXiv:2605.16099v1 Announce Type: new Abstract: Federated Learning (FL) enables collaborative training across decentralized clients, but most methods assume aligned feature schemas, an assumption that rarely holds in tabular settings where clients observe only partially overlapping feature subsets. In these heterogeneous feature spaces, parameter-averaging methods (e.g., FedAvg) transfer little information across weakly overlapping or disjoint feature groups, limiting their effectiveness for federated imputation. To overcome this, we propose \textbf{FedHF-Impute}, a federated imputation framework that separates structural feature unavailability from conventional missingness and uses a shared global feature graph to propagate information across statistically related features through message passing. This enables indirect cross-client knowledge transfer, even when features are never jointly observed locally, while preserving standard federated communication. Under simulated partial schema overlap on the SECOM and AirQuality datasets, FedHF-Impute improves imputation accuracy (RMSE) over FL baselines by 26.9\%, and 8.4\% respectively, while achieving comparable performance on PhysioNET, with only a 0.3\% difference relative to the best baseline.
arXiv:2605.16102v1 Announce Type: new Abstract: Fractional boundary value problems are often used to model complex systems and processes characterized by memory effects and anomalous diffusion. In this paper, we consider fractional boundary value problems involving the Riesz-Caputo operator, which is particularly suited for modeling physical phenomena exhibiting symmetric diffusive effects. We provide an integral representation of the solution to prove existence and uniqueness of the fractional differential problem. We introduce a B-spline collocation method to approximate the solution of the problem and provide a convergence analysis, with both theoretical insights and numerical experiments.
arXiv:2605.15204v1 Announce Type: new Abstract: Multi-agent orchestration frameworks such as LangChain, LangGraph, and CrewAI route tasks through graph-based pipelines but do not enforce the stage constraints that govern real business processes. We present SDOF, a framework that treats multi-agent execution as a constrained state machine. SDOF operates through two primary defensive layers, implemented by three components: (1) an Online-RLHF Specialized Intent Router trained via Generative Reward Modeling (GRPO) and (2) a StateAwareDispatcher with GoalStage finite-automaton checks and precondition/postcondition SkillRegistry validation for auditable execution control. On a recruitment system backed by the Beisen iTalent platform (6000+ enterprises), 185 expert-curated scenarios trigger 1671 live API calls. Our GSPO-aligned 7B Intent Router achieves higher joint accuracy than zero-shot GPT-4o on this FSM-constrained adversarial routing benchmark (80.9% versus 48.9%). In end-to-end execution, SDOF reaches 86.5% task completion (95% confidence interval 80.8 to 90.7) and blocks all 22 operations in the injection, illegal HR subset. Under a broader message-level blocking audit, SDOF attains precision 100% and recall 88%, expert agreement kappa=0.94. A separate evaluation on 960 SGD-derived dialogues spanning 8 service domains surfaces 201 stage-order conflicts under our FSM mapping, 41 of which arise in the normal split. This arXiv version reports the current validated scope; extended multi-seed training comparisons and deeper workflow evaluations will be released in a subsequent update.
arXiv:2601.13039v2 Announce Type: replace Abstract: In this work, we study projection-based model order reduction (MOR) for switched linear systems (SLS) in control form, where the projection matrices are obtained from the solutions of generalized Lyapunov equations (GLEs). We investigate how numerical inaccuracies in solving the GLEs propagate through the MOR process and impact the accuracy and reliability of the resulting reduced-order model. This highlights the importance of accounting for such inaccuracies, motivating the introduction of a novel error bound to quantify and control the error in the approximation of the GLE solution. Moreover, classical balanced truncation error estimates for SLS are neither theoretically sound nor practically applicable, as they rely on restrictive assumptions requiring several linear matrix inequalities (LMIs) to be satisfied exactly by numerically computed GLE solutions. To address these limitations, we propose a new MOR framework for SLS, termed piecewise balanced reduction (PBR). The approach is based on solving multiple GLEs and constructing projection matrices that are piecewise constant in time. By extending the standard balanced truncation error bound for SLS, we show that the PBR framework effectively controls errors arising from inexact LMI satisfaction. In addition, the proposed error bound captures the influence of the piecewise constant in time projection matrices. Altogether, this makes the PBR approach applicable to a broad and flexible class of switched linear systems. Numerical experiments are presented to support the theoretical results.
arXiv:2605.15962v1 Announce Type: new Abstract: Website Fingerprinting (WFP) has traditionally focused on inferring which website a user visits from encrypted traffic metadata such as packet sizes and timing. In this paper, we identify and quantify a new privacy risk in modern web settings: an adversary can infer a user's persona using only packet-length and inter-arrival-time sequences. To study this risk at scale, we build an LLM-driven multi-agent browsing framework that enforces controllable persona constraints while a computer-use agent interacts with real websites and collects corresponding encrypted traffic traces. We formalize persona fingerprinting under both closed-set and open-world settings and further evaluate whether persona information is already embedded in representations learned by existing WFP models and can be amplified at low cost. Across 10 modern websites and 15 personas (plus an open-world class), persona inference achieves about 84% accuracy on mixed-site traffic; moreover, a lightweight multi-task objective can boost persona accuracy to around 80% while retaining strong site classification performance (about 93% baseline). Our results show that, on modern websites, encrypted traffic metadata can leak not only which site a user visits, but also how they browse and who is browsing.
arXiv:2605.15750v1 Announce Type: new Abstract: The rapid expansion of electric vehicles (EVs) necessitates scalable and efficient fast charging station (FCS) infrastructure. These stations often operate in oversubscribed configurations where the total port rating exceeds a station-level cap reflecting infrastructure limits, grid constraints or market setpoints. In such settings, ensuring fairness in real-time power allocation is essential to prevent user bias and secure equitable access to limited resources while maximizing infrastructure utilization. This task is further complicated by state-of-charge dependent EV power limits defined by charge curves, for which accurate data is often unavailable. This paper introduces two fairness-guaranteed online power allocation policies: FAIR-OPAP-C for conventional FCSs with continuously adjustable power delivery, and FAIR-OPAP-M for modular FCSs composed of discrete assignable power modules. Unlike existing methods, these algorithms require no prior knowledge of charge curves, utilizing only instantaneous power requests available via standard protocols. We formalize fairness with a unified framework encompassing envy-freeness, Pareto efficiency, and proportionality, and establish theoretical guarantees for both algorithms. The algorithms rely on lightweight operations, achieving near-linear and logarithmic scalability for the conventional and modular cases, respectively. Comprehensive evaluations show the proposed methods achieve superior performance across various metrics among seven benchmarks from EV charging and fair division literature. Furthermore, they are orders of magnitude faster than optimization-based approaches, with runtimes below 1 ms for up to 300 EVs, validating their suitability for real-time deployment on hardware-constrained edge devices.
arXiv:2605.15737v1 Announce Type: new Abstract: Machine unlearning has reached a critical bottleneck. As traditional weight-space interventions focus primarily on erasing targeted concepts, they often fail to prevent the unintended suppression of other significant representations. This leads to substantial collateral damage, with essential knowledge being forgotten, because these methods lack formal mathematical guarantees for the preservation of neutral concepts. To avoid degradation, they are frequently forced into conservative updates. We propose BARRIER (Bounded Activation Regions for Robust Information Erasure), a paradigm-shifting framework that shifts the locus of intervention from static model weights to the dynamic geometry of hidden-layer activations. Unlike existing methods, BARRIER employs Interval Arithmetic (IA) on SVD-based projections of the activation space to encapsulate the specific target region within a bounding hypercube. By driving unlearning updates exclusively within this forget interval and mathematically bounding the model response on the complement, we ensure rigorous protection of the retain distribution. This geometric construction transforms the preservation of knowledge from an empirical heuristic into a formal optimization target with a probabilistic tail bound on functional drift. Crucially, this stability permits highly aggressive unlearning updates within the forget region. Empirical evaluations demonstrate that BARRIER matches state-of-the-art trade-offs across classifiers and diffusion models, maximizing targeted concept erasure while safeguarding the integrity of all other representations. Our code is available at https://github.com/OneAndZero24/BARRIER.
arXiv:2601.02079v2 Announce Type: replace Abstract: The paper \cite{M0} studied, for a \emph{complex} linear ordinary differential equation $y^\prime(t)=Ay(t)$, the long-time propagation to the solution $y(t)$ of a perturbation of the initial value. By measuring the perturbations with relative errors, this paper introduced a directional pointwise condition number, defined for a specific initial value and for a specific direction of perturbation of this initial value, and a pointwise condition number, defined for a specific initial value and the worst-case scenario for the direction of perturbation. The asymptotic (long-time) behaviors of these two condition numbers were determined. The present paper analyzes such asymptotic behaviors in depth, for a \emph{real} linear ordinary differential equation in a generic case.
arXiv:2605.15959v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) are powerful surrogates for differential equations but are notoriously difficult to train due to spectral bias, stiffness, and poor accuracy on high-frequency or multiscale solutions. Adversarial training based on generative adversarial networks (GANs) has recently gained surprisingly strong empirical results in improving training, but the underlying mechanisms remain elusive. To this end, we propose a new analysis framework for adversarially trained PINNs, based on the key observation of how the discriminator in GANs can influence the training dynamics of PINNs. The framework first provides a much needed theoretical grounding to why and when adversarial training is effective in PINNs, then presents a unified analysis of GANs variants in such training, and finally leads to a new, practical, efficient training algorithm for PINNs. Empirical results demonstrate that our method can significantly reduce the pathology of PINNs training, thereby providing better models with superior performances, often several magnitudes more accurate than alternative methods.
arXiv:2605.09869v2 Announce Type: replace Abstract: Zero-shot object navigation has advanced rapidly with open-vocabulary detectors, image--text models, and language-guided exploration. However, even after current methods detect a plausible target hypothesis, the agent may still oscillate between exploration and pursuit, or abandon the object near success. We identify this failure mode as an action consistency gap: semantic evidence is repeatedly reinterpreted at each step without persistent commitment across the episode. We introduce ConsistNav, a training-free zero-shot ObjectNav framework built around a semantic executive composed of three coordinated modules: Finite-State Executive Controller stages target pursuit through guarded semantic phases; Persistent Candidate Memory accumulates cross-frame target evidence into stable object hypotheses; and Stability-Aware Action Control suppresses rotational stagnation, ineffective pursuit, and unverified stopping. This design changes neither the detector nor the low-level planner; instead, it controls when semantic evidence should influence navigation and when it should be suppressed or revisited. We conduct extensive experiments on HM3D and MP3D, where ConsistNav achieves state-of-the-art results among compared zero-shot ObjectNav methods and improves SR by 11.4% and SPL by 7.9% over the controlled baseline on MP3D. Ablation studies and real-world deployment experiments further demonstrate the effectiveness and robustness of the proposed executive mechanism.
arXiv:2603.14764v4 Announce Type: replace Abstract: Geometric data augmentation is widely used in segmentation workflows, but polygon annotations are often assumed to remain valid after transformation. This assumption can fail in structured domains such as architectural floorplan analysis, where a region may contain an interior void encoded as part of a single ordered polygon chain. Cropping or clipping can remove bridge vertices in this chain, causing one semantic region to split into disconnected components. We propose a lightweight topology-preserving augmentation strategy that repairs missing adjacency relations in index space while preserving the original vertex order. The method adds minimal overhead and can be integrated into existing preprocessing workflows. Experiments show that the proposed approach achieves near-perfect Cyclic Adjacency Preservation (CAP) across common geometric transformations and improves annotation consistency in polygon-based segmentation.
arXiv:2603.09650v2 Announce Type: replace Abstract: Toroidal topologies and helicity are pervasive in nature and hold basic importance in scientific research. In particular, the interplay between these features gives rise to fascinating toroidal helical electromagnetic excitations. Here, we present a theoretical framework and experimental realization to introduce a family of toroidal helical pulses, exploring the intersection of the helicity and propagating toroidal modes. For this purpose, we propose a configuration combining a coaxial horn emitter and an equiangular spiral grating to directly generate such single-cycle pulses. In addition to their inherent non-transverse toroidal topology and space-time nonseparability, such pulses also possess controllable helicity. This work gives rise to a helical version of propagating toroidal electrodynamics, thereby paving the way for advanced applications, such as nontrivial light-matter interactions and data transfer.
arXiv:2605.16107v1 Announce Type: new Abstract: Machine-generated texts (MGTs) pose risks such as disinformation and phishing, underscoring the need for reliable detection. Metric-based methods, which extract statistically distinguishable features of MGTs, are often more practical than complex model-based methods that are prone to overfitting. Given their diverse designs, we first place representative metric-based methods within a unified framework, enabling a clear assessment of their advantages and limitations. Our analysis identifies a core challenge across these methods: the token-level detection score is easily biased by the inherent randomness of the MGTs generation process. Then, we theoretically derive the multi-hop transitions of the token-level detection score and explore their local and global relations. Based on these findings, we propose a multi-level contextual token relation modeling framework for MGT detection. Specifically, for local relations, we model them through a lightweight Markov-informed calibration module that refines token-level evidence before aggregation. For global relations, we introduce a rule-support reasoning module that uses explicit logical rules derived from contextual score statistics. Finally, we combine the local calibrated score and the global rule-support reasoning signal in a joint multi-level inference framework. Extensive experiments show broad and substantial improvements across various real-world scenarios, including cross-LLM and cross-domain settings, with low computational overhead.
arXiv:2605.15958v1 Announce Type: new Abstract: Energy system models are increasingly dependent on representative climate input. Yet, a fundamental mismatch persists between the hundreds of simulated years often used in climate science and the handful of years that computationally demanding power system models can process. Current practice, including ENTSO-E's European Resource Adequacy Assessment, relies on climate year selections that have not been validated against explicit representativeness criteria. This risks biased investment decisions and blind spots for plausible weather conditions. This study proposes simulated annealing as an optimisation method for selecting representative subsets of complete climate years from large climate ensembles. Representativeness is quantified using the seasonal sliced Wasserstein distance, a metric from optimal transport theory that captures representativeness on marginal distributions, inter-variable correlations, and seasonal structure simultaneously. We evaluate simulated annealing against the alternative methods random search, filtered random search, and K-Medoids clustering across three test cases spanning the Netherlands and Europe, using 180 climate years from the Pan-European Climate Database as a reference. Simulated annealing consistently produces the most representative subsets and outperforms all compared methods. Simulated annealing achieves an effective sample size four to five times the actual subset size. The resulting subsets are roughly 2.5--3.5 times more representative than current ENTSO-E practice. The method is application-agnostic and its output can serve as a validated climate data input to any subsequent (energy) impact study.
arXiv:2512.24366v2 Announce Type: replace Abstract: Text-based explainable recommendation aims to generate natural-language explanations that justify item recommendations, to improve user trust and system transparency. Although recent advances leverage LLMs to produce fluent outputs, a critical question remains underexplored: are these explanations factually consistent with the available evidence? We introduce a comprehensive framework for evaluating the factual consistency of text-based explainable recommenders. We design a prompting-based pipeline that uses LLMs to extract atomic explanatory statements from reviews, thereby constructing a ground truth that isolates and focuses on their factual content. Applying this pipeline to five categories from the Amazon Reviews dataset, we create augmented benchmarks for fine-grained evaluation of explanation quality. We further propose statement-level alignment metrics that combine LLM- and NLI-based approaches to assess both factual consistency and relevance of generated explanations. Across extensive experiments on six state-of-the-art explainable recommendation models, we uncover a critical gap: while models achieve high semantic similarity scores (BERTScore F1: 0.81-0.90), all our factuality metrics reveal alarmingly low performance (LLM-based statement-level precision: 4.38%-32.88%). These findings underscore the need for factuality-aware evaluation in explainable recommendation and provide a foundation for developing more trustworthy explanation systems.
arXiv:2605.15253v1 Announce Type: new Abstract: Machine learning research increasingly bifurcates into two disconnected modes: benchmark-driven engineering that prioritizes metrics over understanding, and idealized theory that often fails to transfer to modern systems. In this position paper, we argue that the field focuses too heavily on these endpoints, neglecting the central scientific object: the idea. We propose an Ideas First framework in which ideas are valued for the behavioral signatures they predict in modern models, and these signatures are tested through tailored experiments designed to detect the relevant patterns rather than to win leaderboards. This shift not only bridges the gap between theory and practice but also promotes equity by removing the "complexity premium," enabling rigorous scientific contributions from researchers with modest computational, financial, and human resources. Ultimately, we advocate for a research culture centered on ideas, treating benchmarks and theorems as instruments for testing mechanistic hypotheses rather than as ends in themselves.
arXiv:2605.12253v2 Announce Type: replace-cross Abstract: An \emph{outer-string representation} of a graph $G$ is an intersection representation of $G$ where vertices are represented by curves (strings) inside the unit disk and each curve has exactly one endpoint on the boundary of the unit disk (the anchor of the curve). Additionally, if each two curves are allowed to cross at most once, we call this an \emph{outer-$1$-string representation} of $G$. If we impose a cyclic ordering on the vertices of $G$ and require the cyclic order of the anchors to respect this cyclic order, such a representation is called a \emph{constrained outer-string representation}. In this paper, we present two results about graphs admitting outer-string representations. Firstly, we show that for a bipartite graph $G$ (and, more generally, for any $\{C_3,C_5\}$-free graph $G$) with a given cyclic order of vertices, we can decide in polynomial time whether $G$ admits a constrained outer-string representation. Our algorithm follows from a characterization by a single forbidden configuration, similar to that of Biedl et al. [GD 2024] for chordal graphs. Secondly, we answer an open question from the same authors and show that determining whether a given graph admits an outer-1-string representation is NP-hard. More generally, we show that it is NP-hard to determine if a given graph $G$ admits an outer-$k$-string representation for any fixed $k\ge1$.
arXiv:2605.15951v1 Announce Type: new Abstract: Finetuning Large Vision-Language Models with reinforcement learning has emerged as a promising approach to enhance their capability in object-level grounding. However, existing methods, mainly based on GRPO, assign rewards at the response level. Such sparse reward, often criterion-induced, leads to minimal learning signals when all candidate responses fail in challenging scenarios. In this work, we propose a group-revision optimisation paradigm that enhances learning on hard cases. It begins with a sampled initial response and generates a set of revised candidates to explore improved grounding outcomes. Inspired by reward shaping, we introduce a consolidation process that quantifies each candidate's improvement over the initial attempt and converts it into informative shaping signals. These signals are used to both refine the reward and modulate the advantage, amplifying the influence of high-quality revisions. Our method achieves consistent gains across referring and reasoning segmentation, REC, and counting benchmarks compared with prior GRPO-based models. Our code is available at https://github.com/yyliu01/GroupRevision.
arXiv:2605.15950v1 Announce Type: new Abstract: This work extends the generalized nearest neighbor decoding (GNND), originally developed as a receiver architecture for memoryless channels, to a vectorized GNND (Vec-GNND) suitable for in-block memory (IBM) channels. Leveraging the generalized mutual information (GMI) as an operational lower bound on the mismatch capacity, an analytical characterization of the optimal Vec-GNND is obtained for general IBM channels with Gaussian codebooks. The formalism further provides closed-form optimality conditions and achievable GMIs for restricted variants of the receiver architecture. Furthermore, we formulate a GMI-based joint design viewpoint for Gaussian codebook covariance and decoding metrics. Since the metric optimization admits a closed-form solution for each fixed covariance, the joint design is reduced to an input-covariance optimization problem; for the diagonal covariance family, we derive first-order self-consistent optimality conditions. Numerical evaluations on block noncoherent additive white Gaussian noise channels and phase noise channels demonstrate consistent performance gains over conventional scaling-based baselines, highlighting the substantial advantages and potential relevance of the proposed Vec-GNND in realistic communication scenarios.
arXiv:2605.15935v1 Announce Type: new Abstract: Plasma shape control in tokamaks requires a real-time controller that tracks dynamically changing shape targets while tolerating diagnostic failures. Classical approaches decompose the problem into equilibrium reconstruction followed by a linear controller, and assume a fixed, fully operational sensor set. We present a reinforcement learning agent that addresses both limitations simultaneously. The agent is trained in NSFsim, a high-fidelity tokamak simulator configured for DIII-D, on a curated dataset of 120 experimental plasma shapes. The shape targets are resampled as random step changes every 0.25 s, exposing the agent to diverse transitions across the full shape envelope. At test time the agent zero-shot tracks dynamic shape sequences; on a held-out static configuration in simulation it achieves a mean shape error of 2.01 cm, and dynamic trajectory following is demonstrated qualitatively in simulation and on the physical device. Diagnostic dropout randomly masks 30% of magnetic sensors per episode, yielding a single policy robust to arbitrary sensor subsets without backup controllers or mode-switching logic. An asymmetric actor-critic architecture with privileged equilibrium information improves value estimation under partial observability; an auxiliary shape reconstruction head on the actor enables end-to-end shape reconstruction from raw diagnostics and serves as an interpretability tool for policy analysis. The policy transfers to experimental DIII-D shots, where it directly commands the coil actuators on two dynamic shape maneuvers, and to the independent GSevolve simulator.
arXiv:2605.15254v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN training still suffers from high-dimensional non-convex loss landscapes, imbalanced multiobjective constraints, and ineffective information propagation. Existing curriculum learning and causality-guided strategies improve training stability, but mainly focus on temporal or parametric progression, lacking explicit treatment of spatial information propagation and inter-region consistency. Moreover, they are not directly applicable to boundary value problems (BVPs) with strong spatial coupling. To address this issue, we propose a spatially correlated curriculum learning framework for PINNs. To the best of our knowledge, this is the first work to address PINN training difficulties from the perspective of spatial coupling among subregions. First, spatial causal weights guide information from near-boundary regions inward, reducing optimization failures and spurious convergence. Second, a low-frequency information bridge enforces pseudo-label-based consistency across spatially separated regions, suppressing global low-frequency drift. Third, a region-adaptive reweighting strategy adjusts subregion losses to reduce local residuals and recover high-frequency details. Experiments on PDE benchmarks show that, under comparable computational cost, the proposed method alleviates training failures and improves solution accuracy. The code is available at https://github.com/pigofmomo/CurriculumLearningPINN.
arXiv:2601.00361v3 Announce Type: replace Abstract: We introduce the first iterative algorithm for constructing a $\varepsilon$-coreset that guarantees deterministic $\ell_p$ subspace embedding for any $p \in [1,\infty)$ and any $\varepsilon > 0$. For a given full rank matrix $\mathbf{X} \in \mathbb{R}^{n \times d}$ where $n \gg d$, $\mathbf{X}' \in \mathbb{R}^{m \times d}$ is an $(\varepsilon,\ell_p)$-subspace embedding of $\mathbf{X}$, if for every $\mathbf{q} \in \mathbb{R}^d$, $(1-\varepsilon)\|\mathbf{Xq}\|_{p}^{p} \leq \|\mathbf{X'q}\|_{p}^{p} \leq (1+\varepsilon)\|\mathbf{Xq}\|_{p}^{p}$. Specifically, in this paper, $\mathbf{X}'$ is a weighted subset of rows of $\mathbf{X}$ which is commonly known in the literature as a coreset. In every iteration, the algorithm ensures that the loss on the maintained set is upper and lower bounded by the loss on the original dataset with appropriate scalings. So, unlike typical coreset guarantees, due to bounded loss, our coreset gives a deterministic guarantee for the $\ell_p$ subspace embedding. For an error parameter $\varepsilon$, our algorithm takes $O(\mathrm{poly}(n,d,\varepsilon^{-1}))$ time and returns a deterministic $\varepsilon$-coreset, for $\ell_p$ subspace embedding whose size is $O\left(\frac{d^{\max\{1,p/2\}}}{\varepsilon^{2}}\right)$. Here, we remove the $\log$ factors in the coreset size, which had been a long-standing open problem. Our coresets are optimal as they are tight with the lower bound. As an application, our coreset can also be used for approximately solving the $\ell_p$ regression problem in a deterministic manner.
arXiv:2603.05917v3 Announce Type: replace Abstract: Stock market prediction presents considerable challenges for investors, financial institutions, and policymakers operating in complex market environments characterized by noise, non-stationarity, and behavioral dynamics. Traditional forecasting methods, including fundamental analysis and technical indicators, often fail to capture the intricate patterns and cross-sectional dependencies inherent in financial markets. This paper presents an integrated framework combining a node transformer architecture with BERT-based sentiment analysis for stock price forecasting. The proposed model represents the stock market as a graph structure where individual stocks form nodes and edges capture relationships including sectoral affiliations, correlated price movements, and supply chain connections. A fine-tuned BERT model extracts sentiment information from social media posts and combines it with quantitative market features through attention-based fusion mechanisms. The node transformer processes historical market data while capturing both temporal evolution and cross-sectional dependencies among stocks. Experiments conducted on 20 S&P 500 stocks spanning January 1982 to March 2025 demonstrate that the integrated model achieves a mean absolute percentage error (MAPE) of 0.80% for one-day-ahead predictions, compared to 1.20% for ARIMA and 1.00% for LSTM. The inclusion of sentiment analysis reduces prediction error by 10% overall and 25% during earnings announcements, while the graph-based architecture contributes an additional 15% improvement by capturing inter-stock dependencies. Directional accuracy reaches 65% for one-day forecasts. Statistical validation through paired t-tests confirms the significance of these improvements (p < 0.05 for all comparisons). The model maintains lower error during high-volatility periods, achieving MAPE of 1.50% while baseline models range from 1.60% to 2.10%.