L2

Images are important tools in various sciences. Despite the development of photo-taking tools, creating clear and image without noise remains challenging in practice. In particular, Poisson noise has an effect on medical and astronomical images, and reduces their quality. Additionally, blur is another factor that has an effect on image quality. The problem of image restoration becomes very complicated when we have no information about the Point Spread Function (PSF). These types of problems are known as blind case. However, in some images, such as some astronomical images, the type of PSF can be specified, and these types of problems are known as nonblind problems. Total Variation (TV) is a widely used method for solving such inverse problems, where the selection of the penalty function is the most critical factor that affects the method's performance. In this paper, to improve edge preservation, we employ a reweighted $\ell_1$-regularization of the fractional order derivative. Furthermore, we propose a nonblind and blind image deblurring approach under Poisson noise using the Minimax Concave Penalty (MCP), which is a continuous, sparsity promoting, and nearly unbiased regularizer. This formulation leads to a nonconvex optimization model. To solve the proposed model, we introduce an efficient numerical algorithm based on the Alternating Direction Method of Multipliers (ADMM) and provide an analysis of its convergence. Finally, the effectiveness of the proposed algorithm are demonstrated through extensive experiments on various images.

We prove a depth hierarchy for ReLU neural networks in which every additional ReLU layer can save exponentially many neurons. For all $k\geq2$, we construct a globally $[0,1]$-valued, $1$-Lipschitz function realized by a depth-$(k+1)$ network of width $\mathcal{O}(d^4)$, whereas any depth-$k$ network with unrestricted weights and width at most $\frac{2^d}{2d(k-1)}$ has squared $L_2$ error at least $1/24$ under an absolutely continuous distribution supported at exponential distance from the origin. To the best of our knowledge, this is the first exponential hierarchy across all adjacent fixed depths, and the first exponential separation for ReLU networks between two fixed depths whose shallower network has depth at least $3$. The lower bound also immediately yields the corresponding hierarchy for exact computation. Moreover, the case $k=2$ gives a compactly supported separation between depths $3$ and $2$ with unrestricted shallow-network weights, answering a question raised by Safran, Eldan, and Shamir (2019). The distribution used in our construction nevertheless has all its mass at exponential radius, placing the hierarchy outside the regularity regime in which such a separation would imply major threshold-circuit lower bounds. We also prove an exact separation for a more regular target, which is globally $[0,1]$-valued and $\mathcal{O}(\sqrt d)$-Lipschitz and maps the unit hypercube onto $[0,1]$. It is computed by a polynomial-width depth-$4$ network, whereas any depth-$3$ network agreeing with it on the unit hypercube requires exponentially many first-layer neurons, even with unrestricted weights.

Text-to-image (T2I) generation has achieved remarkable progress in recent years. However, existing research has largely focused on English-only settings, leaving cross-lingual performance gaps and language-specific effects insufficiently explored. To fill this gap, we introduce LingT2I, a benchmark covering 10 widely used languages with 33K prompts, designed to evaluate cross-lingual effects in both content generation and text rendering. Building on this benchmark, we conduct a comprehensive cross-lingual analysis, uncovering linguistic inequality and language-dependent trade-offs across evaluation dimensions. Beyond quantitative evaluation, we further reveal a range of language-dependent generation patterns, highlighting how linguistic factors and their corresponding cultural contexts systematically impact model outputs. Our benchmark and analysis provide a foundation for studying cross-lingual behavior in T2I generation and facilitate the development of more robust and inclusive models. Code and dataset are available at https://github.com/RISys-Lab/LingT2I.

Automatic speaking assessment systems are increasingly deployed in high-stakes settings to mark second language (L2) learners' speaking tests, making it critical to show that their scores depend on speaking proficiency rather than irrelevant speaker attributes such as first language (L1) or age. Transformer-based foundation models have improved the accuracy of these L2 speaking graders, but their black-box representations make fairness and interpretability analysis more difficult. Building on prior work that used Concept Activation Vectors (CAVs) to detect bias towards unwanted attributes (`concepts') in feature-based graders, we extend CAV-based analysis to two neural speaking assessment systems: a text-based BERT grader and a speech-and-text multimodal grader based on Whisper. CAVs represent human-interpretable concepts as directions in a model's activation space, allowing us to distinguish between whether a concept is encoded in a model's internal representations and whether it influences the predicted score, the latter quantified using a gradient-based sensitivity metric. Since CAVs rely on linear separability, which is less likely in complex neural embedding spaces, we also investigate whether sparse autoencoders (SAEs) provide cleaner concept directions by learning CAVs in a sparse latent space and mapping them back to activation space. Our analysis shows that concept recoverability depends strongly on the representation and architecture being probed, rather than on the concept alone. Sensitivity to concepts is also architecture-dependent. SAEs make concepts more linearly recoverable, but attenuate the original activation-space sensitivity, especially in low-dimensional layers. These findings highlight the need to distinguish concept recoverability from concept influence when auditing bias in speaking assessment systems.

Large language models (LLMs) increasingly evaluate human writing in high-stakes domains such as hiring and academic assessment, putting non-native speakers at particular risk. Drawing on the language attitudes framework, we compared human and LLM evaluations of parallel L1- and L2-written Japanese emails on three dimensions: fluency, status, and solidarity. Japanese raters rated L2 texts significantly lower on all three dimensions, with a fluency gap roughly twice the size of the status and solidarity gaps. Six LLM judges reproduced the direction of this bias, and five reproduced its ordering across dimensions. The models diverged from humans in two ways: all understated the solidarity gap, the most socially grounded dimension, and all differentiated among learner L1 backgrounds where humans did not. LLM judges thus reproduce native speakers' language attitudes in a structured yet attenuated form, and the language attitudes framework offers a ready-made yardstick for auditing them beyond English.

Text-to-image (T2I) workflows are increasingly deployed on serverless platforms because users often compose customized workflows and invoke them intermittently. Existing platforms typically deploy each workflow as an opaque GPU function, provisioning, placing, and scaling all constituent models in the workflow together. This monolithic design obscures workflow structure, inflates scaling overhead, forces users to manage low-level GPU coordination, and limits fine-grained fairness in multi-tenant clusters. In this paper, we present ServerlessT2I, a serverless-native system that decomposes a T2I workflow into loosely coupled model functions that can be independently managed and scheduled. By explicitly managing individual model execution, ServerlessT2I enables per-model scaling, declarative workflow composition, transparent GPU-resident communication, and fairness-aware scheduling. To make this decomposition efficient, ServerlessT2I harvests slack GPU memory left idle by compute-bound T2I inference to build a data plane that reduces model loading and data communication overheads. \sys{} further introduces a fair scheduler for multi-tenant serving. Using production traces, ServerlessT2I sustains up to 2$\times$ higher request rates than existing T2I workflow serving systems with the same GPU budget; for a fixed request rate, it saves up to 3$\times$ GPU resources while satisfying service level objectives (SLOs).

Scaled dot product attention conflates directional alignment and vector magnitude, limiting its effectiveness as a similarity metric in Transformer models. We introduce L1 augmented attention, a simple and computationally parallelizable modification that subtracts a learned, head specific L1 distance between queries and keys from the dot product score. This hybrid similarity captures complementary geometric information. Dot product rewards directional alignment, while L1 penalizes coordinate deviations. To reduce the cost of L1 computation, we project queries and keys into low dimensional subspaces whose parameters specialize to preserve informative L1 structure. Evaluated on WikiText 2 using a compact transformer, L1 augmented attention achieves up to a 14.5% reduction in perplexity over the original transformer baseline and outperforms an RBF L2 kernel. Analysis of norm variance and learned L1 weights reveals distinct geometric roles across layers and strong head level specialization. These results demonstrate that enriching attention with L1 geometry provides a principled and effective improvement to similarity computation in modern language models, with practical benefits for both accuracy and parallel efficiency.

High-fidelity reconstruction of dynamic urban environments is a cornerstone of autonomous driving simulation and large-scale world modeling. While 3D Gaussian Splatting (3DGS) has established a new standard for real-time rendering, its reliance on expensive per-scene optimization limits scalability. Conversely, recent feedforward methods that infer Gaussian parameters offer faster speed but face fundamental bottlenecks: they are memory-prohibitive at high resolutions and struggle to fuse dense multi-view observations consistently. This paper presents L2D2-GS, a unified framework that reformulates generalizable reconstruction not as a one-shot regression, but as a robust iterative process of optimization and densification. To resolve the ambiguity of supervision in primitive generation, we propose a self-supervised densification policy that derives explicit reward signals from global reconstruction gains to guide local densification. Furthermore, we mitigate irreversible early-stage artifacts through a geometric regularization mechanism, utilizing reparameterization to constrain the optimization manifold and prevent convergence to poor local optima. Extensive experiments on the PandaSet and Waymo datasets demonstrate that our method achieves state-of-the-art reconstruction fidelity and strong zero-shot generalization, while using fewer primitives than competing baselines.

Constrained single-objective numerical optimization requires a careful balance among feasibility, objective convergence, and computational efficiency under a fixed function-evaluation budget. This paper proposes DE-2LS, a late-stage, locally search-enhanced variant of differential evolution built on the RDEx framework. The proposed method preserves the original RDEx components, including mutation and crossover operators, success-history adaptation, archive mechanism, population-size reduction, and $ε$-based constraint handling. A lightweight coordinate-pattern local search is added as a guarded polishing component around the current best solution. It is activated only in the late stage of the run, uses a small evaluation budget, and accepts candidates through a feasibility-aware comparison rule. Ablation results show that the finalized DE-2LS configuration achieves the best U-score among all tested variants, confirming that controlled late-stage refinement is more effective than aggressive or premature local search. In the direct comparison with RDEx, DE-2LS achieves a 5.58% gain in U-score. In the four-algorithm comparison, DE-2LS obtains the highest overall U-score of 80968 and the best total rank of 48 among RDEx, CL-SRDE, and UDE-III. These results indicate that DE-2LS improves the exploitation capability of the RDEx-based search framework while preserving its speed advantage under the combined speed-accuracy scoring criterion. The source code of DE-2LS is available at https://github.com/ChauhanDikshit?tab=repositories.

Unconstrained single-objective numerical optimization requires a careful balance among global exploration, late-stage exploitation, and function-evaluation efficiency. This paper presents DE-2LS, a late-stage, local-search-enhanced differential evolution framework built on RDEx for unconstrained single-objective optimization with variable bounds. The proposed method preserves the original RDEx evolutionary search engine and introduces two conservative refinements: a smoothed exploitation-biased branch-rate update in the late search stage and a guarded coordinate-pattern local-search that serves as a budget-aware refinement mechanism. Since the considered setting is unconstrained apart from variable bounds, all selection and local-search acceptance decisions are based solely on objective values. To determine the final algorithm configuration, we conduct a staged ablation study by testing multiple settings of the EB-rate smoothing mechanism, the initial EB-rate, the standard-branch Gaussian sampling scale, the selection-pressure parameters, and the local-search coefficients. The final configuration is selected using a U-score-based evaluation that jointly reflects solution quality and convergence speed. Experimental results show that DE-2LS consistently improves the original RDEx in direct head-to-head comparison. In particular, DE-2LS increases the U-score from $33602.0$ to $37448.0$, corresponding to an improvement of $11.45\%$. Moreover, compared with several competitive and IEEE CEC-winning algorithms, DE-2LS achieves the best overall U-score of $178966.5$, outperforming the others by $34.43\%$. These results show that a carefully designed late-stage local-search strategy can improve both convergence speed and the final objective quality of the algorithm. The source code of DE-2LS is available at https://github.com/ChauhanDikshit?tab=repositories.

Large language models are increasingly deployed for written pronunciation feedback in second-language (L2) English learning, under the assumption that their diagnoses are grounded in the supplied speech evidence rather than in priors from pretraining. This assumption is tested on 1,800 L2-Arctic utterances spanning six L1 backgrounds, three audio-capable LLMs, four pronunciation dimensions, and five evidence conditions ranging from a text-only baseline to numeric acoustic features and raw audio. Each (utterance x model x condition x dimension) cell is scored on three metrics: Rating Accuracy (RA) against gold labels, Evidence Coherence (EC) assessing internal consistency without ground truth, and Grounded Correctness (GC) evaluated against gold evidence. Results show three findings across models. First, rating accuracy and grounded reasoning decouple: 39.6% of judged cells contain internally coherent reasoning that supports a wrong rating, against only 15.8% where the reasoning supports a correct rating. Second, phoneme-level feedback converges to a fixed inventory of L2-English difficulty phones that recurs across all six L1 backgrounds and all evidence conditions. Third, acoustic evidence improves the rating only when the supplied feature directly probes the target dimension: textualised F0 range raises pitch-variation grounding from (0.18-0.19) to (0.45-0.62) across all three models, while stress and phoneme correctness, which require target-to-realisation alignment, remain ungrounded. The same audio waveform without textualised F0 values does not reproduce this improvement. These findings indicate that current general-purpose LLMs are more reliable as verbalisers of externally computed pronunciation evidence than as standalone diagnostic engines.

The convex Latent Optimal Partition (LOP)-l2/l1 approach enables block-sparse signal recovery with unknown partitions but relies on manual hyperparameter tuning. Additionally, numerical instability in differentiating its proximal operator prevents its automatic parameter tuning via Deep Unfolding (DU). To address these limitations, we propose two architectures: a stable framework utilizing implicit differentiation and a flexible variant leveraging Deep Weight Factorization (DWF). The DWF-based approach also supports nonconvex smooth data fidelity terms. Numerical experiments demonstrate that DU-LOP-l2/l1 yields competitive performance and high resilience against impulsive noise.

Recent work has sought to understand Large Language Models (LLMs) reasoning, yet a principled, model-intrinsic signal that captures its layer-wise reasoning dynamics remains underexplored. We bridge this gap by demonstrating that the l2 norm of hidden states serves as an endogenous signal of the model's reasoning intensity. Using Sparse Autoencoders (SAEs) as a diagnostic probe, we observe that LLMs' internal reasoning is marked by a sharp increase in reasoning feature activations concentrated in late layers. Motivated by this pattern, we establish a formal link between reasoning intensity and the model's latent geometry and theoretically prove that the l2 norm of hidden states bounds the activation strength of SAE reasoning features. Empirical correlation analysis and causal interventions further validate the l2 norm as a faithful indicator, where heightened norms consistently correspond to critical reasoning steps. We then introduce three test-time scaling techniques guided by l2 norms: (i) Adaptive Layer-wise Reasoning Recursion, (ii) Endogenous Reasoning State Steering, and (iii) l2-guided Response Selection, which requires no additional training or data and is compatible with advanced inference engines. Experiments across model architectures and benchmarks show that l2-norm-based techniques significantly improve reasoning performance, offering a principled yet simple lens to perceive and control LLM latent reasoning dynamics. Our code is available at https://github.com/zjy1298/The-Tell-Tale-Norm.

Korean grammatical error correction (K-GEC) presents a structural mismatch between word-based evaluation and the morpheme-level locus of many learner errors. Postpositions and verbal endings are bound to lexical hosts, but they encode grammatical relations that must be represented in correction and evaluation. This paper refines word-based grammatical error annotation for L2 Korean by addressing three connected problems in existing resources: surface target realization, Korean-specific edit annotation, and single-reference evaluation. We reconstruct target sentences from the National Institute of Korean Language (NIKL) L2 corpus under morphologically constrained realization rules and convert its morpheme-level annotations into word-level \texttt{m2} edits. We then define a Korean ERRANT-style annotation scheme that preserves the MRU core while distinguishing functional morpheme errors, spelling errors, word boundary errors, and word order errors. We also augment the KoLLA corpus with an additional reference correction, yielding a multi-reference evaluation setting for Korean GEC. Empirical validation shows that the refined NIKL targets yield lower perplexity, the converted \texttt{m2} files achieve higher agreement with source-target edit representations, and the refined resources improve KoBART-based correction under the same model setting. Multi-reference KoLLA evaluation further reduces the penalty imposed on valid corrections that diverge from a single reference, especially for neural and prompted GEC systems. These results show that Korean GEC evaluation depends not only on correction models, but also on reference data and edit annotations that reflect Korean morphology, spacing, and correction variability.

Adapting large language models (LLMs) for personalized recommendation requires aligning their general-purpose capabilities with user-specific preferences while effectively leveraging both behavioral and semantic signals. Existing approaches typically integrate these signals at either the input level (e.g., injecting behavioral embeddings into the token space) or the output level (e.g., contrastive alignment of separate encoders), suffering from distribution gaps or lack of end-to-end task supervision. In this work, we introduce L2Rec, which unifies behavioral and semantic understanding at the parameter level of LLMs. Our key insight is that the same set of Transformer parameters can serve as a shared medium for both views: by applying view-specific, personalized low-rank perturbations via a Dual-view Personalized Mixture-of-Experts (DPMoE) mechanism, L2Rec enables a single LLM backbone to produce complementary behavioral and semantic adaptations for each user with minimal representation-level misalignment. An adaptive cross-view fusion module further integrates the dual-view outputs into a unified user preference. Experiments on four datasets show that L2Rec consistently outperforms state-of-the-art baselines, and online A/B testing on a large-scale industrial platform validates significant improvements in key engagement metrics.

Graph fraud detection has long depended on Graph Neural Networks (GNNs) to propagate and aggregate information across relational data. A critical obstacle in practice, however, is that fraudsters frequently disguise themselves by forging numerous connections with benign users, causing fraud signals to be progressively diluted during neighborhood aggregation and undermining detection reliability. While recent efforts have used Large Language Models (LLMs) to provide rich semantic cues for fraud detection, the underlying intent behind suspicious connections remains insufficiently explored. Compounding this issue, the scarcity of annotated fraud samples makes it difficult to train detectors that remain robust under heavy camouflage. To address these gaps, we propose L2IR, an LLM-driven Latent Intent Revealing framework for graph fraud detection. By uncovering latent intent from both user behaviors and suspicious connections, L2IR extracts intent-aware representations from raw behavioral traces and reasons about the true purpose behind individual connections, effectively distinguishing supportive links from misleading ones. It further incorporates adaptive self-training to enhance robustness under limited supervision. Evaluations on two real-world datasets characterized by pervasive camouflage demonstrate that L2IR surpasses strong baselines and can function as a plug-in enhancement for a range of GNN-based detectors, improving AUPRC by up to 8.27%.

We study fixed-cardinality maximization of the inverse-matrix Solow--Polasky diversity, equivalently finite metric magnitude for the exponential kernel, on one-dimensional and ordered metric sets. The analysis starts from the known finite-line gap formula for the exponential kernel, which writes the excess inverse-matrix diversity as a sum of functions of consecutive gaps. Building on this formula, the main interval theorem proves that, for every $k\geq 2$, the unique maximizing $k$-point subset of $[0,1]$ is the equally spaced set. Thus the objective selects a uniform gap representation on the real line. A converse kernel proposition shows that, among normalized non-increasing distance kernels, requiring the corresponding adjacent-gap additive structure forces the exponential family. Further results transfer the interval theorem to ordered $\ell_1$ (L1, or Manhattan) curves by isometry: the maximizing sets are uniform in accumulated $\ell_1$ length. As a consequence, monotone biobjective Pareto fronts admit Solow--Polasky optimal finite approximations that are uniformly spaced in accumulated objective-space change, a natural representation when all parts of a continuous front should be covered. Examples, including a dense connected front and a finite disconnected ZDT3 front, illustrate how the continuous uniform-gap result appears on discrete candidate sets. Solow-Polasky diversity; diversity measures; finite metric magnitude; L1 distance; uniform spacing; Pareto-front approximation; multiobjective optimization; fixed-cardinality subset selection

The integration of Generative AI (GenAI) into language learning offers second language (L2) writers powerful tools for text optimization. However, pursuing native-like fluency often sacrifices sociopragmatic diversity. Investigating "pragmatic flattening" - the systematic erasure of culturally preferred politeness and authorial stance - this study conducts a comparative analysis of argumentative essays by Chinese B2-level university students from the ICNALE corpus. The original texts were polished via the APIs of four leading Large Language Models at a zero-temperature setting for reproducibility. Findings reveal a nuanced "dimensional divergence" within the Semantic Preservation Paradox. While models corrected lexicogrammatical errors and retained propositional meaning, sociopragmatic interventions were bifurcated. In the interactive dimension, all models showed a drastic collapse of dialogic engagement markers, turning negotiated discourse into monologic assertions. Conversely, in the epistemic stance dimension, models showed architecture-based variability: some aggressively scrubbed epistemic markers, while others reinforced tentative hedging as decontextualized algorithmic caution. This confirms that while GenAI enhances accuracy, it systematically overwrites L2 writers' unique rhetorical identities into a homogenized Anglo-American paradigm. We argue that future instruction must move beyond error correction, advocating for Critical AI Literacy to empower multilingual writers to use GenAI for linguistic enhancement while safeguarding sociopragmatic diversity and rhetorical agency.

What makes a word difficult to learn, and how does the difficulty depend on the learner's native language? We computationally model vocabulary difficulty for English learners whose first language is Spanish, German, or Chinese with gradient-boosted models trained on features related to a word's familiarity (e.g., frequency), meaning, surface form, and cross-linguistic transfer. Using Shapley values, we determine the importance of each feature group. Word familiarity is the dominant feature group shared by all three languages. However, predictions for Spanish- and German-speaking learners rely additionally on orthographic transfer. This transfer mechanism is unavailable to Chinese learners, whose difficulty is shaped by a combination of familiarity and surface features alone. Our models provide interpretable, L1-tailored difficulty estimates that can be used to design vocabulary curricula.

We propose a simplified human-in-the-loop workflow for second language (L2) Korean morphosyntactic annotation by leveraging agreement between two domain-adapted parsers. We first evaluate whether parser agreement can serve as a proxy for annotation correctness by comparing it with independent human judgments. The results show strong correspondence between parser and human judgments, supporting the feasibility of semi-automatic L2-Korean UD annotation. Further analysis demonstrates that parser disagreements cluster in linguistically predictable domains such as grammatical-relation distinctions and clause-boundary ambiguity. While many disagreement cases are tractable for iterative model refinement, others reflect deeper representational challenges inherent in parsing and tagging L2-Korean corpora.

This paper presents the development and validation of an eye-tracking dataset designed to investigate how second-language (L2) learners process idiomatic expressions. While native speakers often rely on direct retrieval of figurative meanings, L2 speakers frequently adopt a literal-first approach, which incurs measurable cognitive costs. This resource captures these costs through ocular metrics recorded from Portuguese L1 speakers of English across all CEFR proficiency levels (A1-C2). Although the study uses entry-level 60 Hz hardware (Tobii Pro Spark), we demonstrate that this sampling rate provides sufficient data density to detect macro-cognitive events such as fixations and regressions in reading. Preliminary analysis validates the dataset by revealing a strong inverse correlation between language proficiency and regressive eye movements. Integrated into the MIA (Modeling Idiomaticity in Human and Artificial Language Processing) initiative, this dataset serves as a cognitively grounded benchmark for evaluating both human processing models and the alignment of large language models with human-like figurative understanding.

Multi Armed Bandit (MAB) algorithms are a cornerstone of reinforcement learning and have been studied both theoretically and numerically. One of the most commonly used implementation uses a softmax mapping to prescribe the optimal policy and served as the foundation for downstream algorithms, including REINFORCE. Distinct from vanilla approaches, we consider here the L2 regularized softmax policy gradient where a quadratic term is subtracted from the mean reward. Previous studies exploiting convexity failed to identify a suitable theoretical framework to analyze its convergence when the regularization parameter vanishes. We prove here theoretical convergence results and confirm empirically that this regime makes the L2 regularization numerically advantageous on standard benchmarks.

The development of 3D scanning technology has enabled the acquisition of massive point cloud models with diverse structures and large scales, thereby presenting significant challenges in point cloud processing. Fast neighboring points search is one of the most common problems, which is frequently used in model reconstruction, classification, retrieval and feature visualization. Hash function is well known for its high-speed and accurate performance in searching high-dimensional data, which is also the core of the proposed 2L-LSH. Specifically, the 2L-LSH algorithm adopts a two-step hash function strategy, in which the popular step divides the bounding box of the point cloud model and the second step constructs a generalized table-based data structure. The proposed 2L-LSH offers a highly efficient and accurate solution for fast neighboring points search in large-scale 3D point cloud models, making it a promising technique for various applications in the field. The proposed algorithm is compared with the well-known methods including Kd-tree and Octree; the obtained results demonstrated that the proposed method outperforms Kd-tree and Octree in terms of speed, i.e. the time consumption of kNN search can be 51.111% and 94.159% lower than Kd-tree and Octree, respectively. And the RN search time can be 54.519% and 41.840% lower than Kd-tree and Octree, respectively.