arXiv subjects

Himanshu Kumar

Publications and source records attributed to Himanshu Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Generalized tri-circular projections on some vector-valued spaces of analytic functions

In this paper, we characterize generalized tri-circular projections on the following three vector-valued spaces of analytic functions on the open unit disk $\mathbb{D}$: the Hardy space $H^p(\mathcal{K})$ for a complex separable Hilbert space $\mathcal{K}$ and $1 \le p < \infty,p \neq 2$; the space $H^\infty(E)$ of $E$-valued bounded analytic functions for a Banach space $E$ with trivial multiplier algebra; and the little Bloch spaces $\mathcal{B}_0(\mathbb{D}, E)$ and $\mathcal{B}_{\ast}(\mathbb{D}, E)$, for $E$ smooth, strictly convex, and reflexive.

math.FA↗

arXiv2026

Beyond the Vacuum: Combinatorial Strategy Selection for Competitor-Aware Generative Engine Optimization

Generative Engine Optimization (GEO) has emerged as a novel paradigm for transforming content to increase visibility in Large Language Model (LLM) responses. Traditional GEO methods, however, select rewriting strategies in isolation, ignoring a critical externality: as adoption of content optimization grows, optimal strategies for rewriting content change. We formalize GEO as a competitor-aware strategy selection problem and propose a two-phase pipeline to solve it: (1) We use Bayesian Optimization of Combinatorial Structures (BOCS) to efficiently search the space of rewriting strategies, (2) We generate preference pairs and grounded reasoning traces from the BOCS black-box observations to fine-tune a language model to analyze a document corpus and propose optimal rewriting strategy combinations. We achieve state-of-the-art performance across several impression metrics over existing agentic and single-heuristic methods on both geo-bench and our synthetically augmented competitive dataset geo-bench_comp. Our method also transfers to multiple out-of-distribution datasets, proving effective across domains, queries, and document types.

cs.IR↗

arXiv2026

Workspace Topology as an Attack Vector in Agentic Coding Assistants

Agentic coding assistants are finding widespread use, not just in new code development but in quickly ingesting and leveraging third-party code. This opens up a risk of malicious code being ingested as these coding tools operate with broad filesystem access inside developer workspaces. In this paper, we extensively study the impact of different dimensions of a novel attack surface we term workspace topology -- defined via directory depth, codebase modularity, in-file injection position and context framing -- on the attack success rate of adversarial prompt injection attempts. We perform an empirical study of indirect prompt injection (IPI) across a diverse set of open-source repositories spanning 10 languages and 6 engineering domains, evaluating three IPI entry points against open-weight models operating open source code harnesses. We find that workspace topology measurably affects IPI success. Specifically, changes in codebase modularity can significantly alter the Attack Success Rate (ASR), with highly modular environments demonstrating significantly lower attack success rates. Furthermore, context framing and introduction of security-cues in the workspace can also alter the ASR. Our findings offer practical value for the evaluation and security testing of coding agents across diverse settings, while underscoring the importance of an uncontaminated testing environment to obtain reliable results and conclusions.

cs.CR↗

arXiv2026

Generalized tri-circular projections on some spaces of analytic functions

In this paper, we obtain the structure of a class of contractive projections, known as generalized tri-circular projections, on some functional Banach spaces on the open unit disk $\mathbb{D}$, which includes Hardy, Bergman and Bloch spaces. We then consider the space $S^p_{\mathcal{K}}$ of $\mathcal{K}$-valued analytic functions on $\mathbb{D}$ such that $f' \in H^p(\mathcal{K})$ and give complete description of generalized tri-circular projections on this space. Here, $\mathcal{K}$ is a complex separable Hilbert space, and $H^p(\mathcal{K})$ denotes the Hardy space of $\mathcal{K}$-valued analytic functions on $\mathbb{D}$.

math.FA↗

arXiv2026

On Nonlinear Idempotents and Metric Projections in Normed Spaces

Let $X$ be a normed linear space. A map $P: X \rightarrow X$ is called idempotent if $P^2 = P$. In this paper, we introduce some new classes of idempotent maps (linearity is not assumed) on $X$ and study their properties. A well-known example of an idempotent map is the metric projection $P_K$ onto a Chebyshev subset $K$ of $X$. We provide some necessary conditions for the map $I- P_K$ to be idempotent, where $I$ denotes the identity operator on $X$.

math.FA↗

arXiv2026

Generalized idempotents on the space of analytic functions with bounded derivatives

Let $X$ be a complex normed space. A map $P: X \rightarrow X$ is called idempotent if $P^2 = P$. A collection $\mathcal{C} = \{P_1, P_2\}$ of nonzero distinct orthogonal ($P_1P_2 = P_2P_1 = 0$) idempotent maps on $X$ is said to be a family of generalized bi-circular idempotents if there exist distinct unit modulus complex numbers $\lambda_1, \lambda_2$ such that $P_1 + P_2 = I$ (identity operator on $X$) and $\lambda_1P_1 + \lambda_2P_2$ is a surjective isometry on $X$. This generalizes the notion of generalized bi-circular projections on Banach spaces introduced by Fo\v{s}ner, Ili\v{s}evi\'{c} and Li \cite{MDC} to nonlinear maps. In this paper, we describe the structure of generalized bi-circular idempotents over the space of analytic functions on the open unit disk with bounded derivatives.

math.FA↗

arXiv2026

Continual Segmentation under Joint Nonstationarity

Evolving data streams induce joint nonstationarity in continual semantic segmentation, where semantic classes, input distributions, and supervision availability change simultaneously over time. This setting reflects practical structured prediction systems, yet remains largely unexplored in prior continual learning work, which typically studies these factors in isolation. We formalize continual segmentation under coupled class, domain, and label shifts and investigate learning in heterogeneous dense prediction environments with limited annotations and abundant unlabeled data. To address instability and overfitting arising from few-shot supervision under distribution drift, we introduce gradient-adaptive stabilization, a parameter-wise regularization mechanism implemented via gradient-scaled stochastic perturbations that promotes a principled stability-plasticity tradeoff. We further leverage unlabeled data through semi-supervised learning and introduce prototype anchored supervision that validates pseudo-labels via joint confidence and prototype consistency. Together, these mechanisms enable learning under joint nonstationarity in continual segmentation. Extensive empirical evaluation across class-incremental, domain-incremental, and few-shot regimes demonstrates consistent improvements over prior methods in heterogeneous structured prediction settings. Our results expose fundamental failure modes of existing continual segmentation approaches and provide insight into learning robust dense predictors in dynamically evolving environments.

cs.CV↗

arXiv2026

Scene Representation using 360{\deg} Saliency Graph and its Application in Vision-based Indoor Navigation

A Scene, represented visually using different formats such as RGB-D, LiDAR scan, keypoints, rectangular, spherical, multi-views, etc., contains information implicitly embedded relevant to applications such as scene indexing, vision-based navigation. Thus, these representations may not be efficient for such applications. This paper proposes a novel 360{\deg} saliency graph representation of the scenes. This rich representation explicitly encodes the relevant visual, contextual, semantic, and geometric information of the scene as nodes, edges, edge weights, and angular position in the 360{\deg} graph. Also, this representation is robust against scene view change and addresses challenges of indoor environments such as varied illumination, occlusions, and shadows as in the case of existing traditional methods. We have utilized this rich and efficient representation for vision-based navigation and compared it with existing navigation methods using 360{\deg} scenes. However, these existing methods suffer from limitations of poor scene representation, lacking scene-specific information. This work utilizes the proposed representation first to localize the query scene in the given topological map, and then facilitate 2D navigation by estimating the next required movement directions towards the target destination in the topological map by using the embedded geometric information in the 360{\deg} saliency graph. Experimental results demonstrate the efficacy of the proposed 360{\deg} saliency graph representation in enhancing both scene localization and vision-based indoor navigation.

cs.CV↗

arXiv2026

ART: Adaptive Reasoning Trees for Explainable Claim Verification

Large Language Models (LLMs) are powerful candidates for complex decision-making, leveraging vast encoded knowledge and remarkable zero-shot abilities. However, their adoption in high-stakes environments is hindered by their opacity; their outputs lack faithful explanations and cannot be effectively contested to correct errors, undermining trustworthiness. In this paper, we propose ART (Adaptive Reasoning Trees), a hierarchical method for claim verification. The process begins with a root claim, which branches into supporting and attacking child arguments. An argument's strength is determined bottom-up via a pairwise tournament of its children, adjudicated by a judge LLM, allowing a final, transparent and contestable verdict to be systematically derived which is missing in methods like Chain-of-Thought (CoT). We empirically validate ART on multiple datasets, analyzing different argument generators and comparison strategies. Our findings show that ART's structured reasoning outperforms strong baselines, establishing a new benchmark for explainable claim verification which is more reliable and ensures clarity in the overall decision making step.

cs.AI↗

arXiv2026

Cavity-Driven Multispectral Gain for High-Sensitivity NV Center Magnetometers

We report a cavity-enabled solid-state magnetometer based on an NV ensemble coupled with a dielectric cavity, achieving 12 pT/$\sqrt{\rm{Hz}}$ sensitivity and a nearly threefold gain from multispectral features. The features originate from cavity-induced splitting of the NV hyperfine levels and leverages robust quantum coherence in the doubly dressed states of the system to achieve high sensitivity. We project simulated near-term sensitivities approaching 100 fT/$\sqrt{\rm{Hz}}$, close to the Johnson-Nyquist limit. Our results establish frequency multiplexing as a new operational paradigm, offering a robust and scalable quantum resource for metrology under ambient conditions.

quant-ph↗

arXiv2026

The Language of Bargaining: Linguistic Effects in LLM Negotiations

Negotiation is a core component of social intelligence, requiring agents to balance strategic reasoning, cooperation, and social norms. Recent work shows that LLMs can engage in multi-turn negotiation, yet nearly all evaluations occur exclusively in English. Using controlled multi-agent simulations across Ultimatum, Buy-Sell, and Resource Exchange games, we systematically isolate language effects across English and four Indic framings (Hindi, Punjabi, Gujarati, Marwadi) by holding game rules, model parameters, and incentives constant across all conditions. We find that language choice can shift outcomes more strongly than changing models, reversing proposer advantages and reallocating surplus. Crucially, effects are task-contingent: Indic languages reduce stability in distributive games yet induce richer exploration in integrative settings. Our results demonstrate that evaluating LLM negotiation solely in English yields incomplete and potentially misleading conclusions. These findings caution against English-only evaluation of LLMs and suggest that culturally-aware evaluation is essential for fair deployment.

cs.AI↗

arXiv2025

GRAID: Synthetic Data Generation with Geometric Constraints and Multi-Agentic Reflection for Harmful Content Detection

We address the problem of data scarcity in harmful text classification for guardrailing applications and introduce GRAID (Geometric and Reflective AI-Driven Data Augmentation), a novel pipeline that leverages Large Language Models (LLMs) for dataset augmentation. GRAID consists of two stages: (i) generation of geometrically controlled examples using a constrained LLM, and (ii) augmentation through a multi-agentic reflective process that promotes stylistic diversity and uncovers edge cases. This combination enables both reliable coverage of the input space and nuanced exploration of harmful content. Using two benchmark data sets, we demonstrate that augmenting a harmful text classification dataset with GRAID leads to significant improvements in downstream guardrail model performance.

cs.CL↗

arXiv2025

Barnsley-Navascu\'es fractal operators on Banach spaces on the Sierpi\'nski gasket

In this article, we define fractal operators motivated by the works of Barnsley and Navascu\'es on various function spaces such as energy space, Lebesgue space, and oscillation space on the well-known fractal domain Sierpi\'nski gasket. We further explore the properties of these operators from the perspectives of operator and approximation theory.

math.FA↗

arXiv2025

Enhancing Cache-Augmented Generation (CAG) with Adaptive Contextual Compression for Scalable Knowledge Integration

The rapid progress in large language models (LLMs) has paved the way for novel approaches in knowledge-intensive tasks. Among these, Cache-Augmented Generation (CAG) has emerged as a promising alternative to Retrieval-Augmented Generation (RAG). CAG minimizes retrieval latency and simplifies system design by preloading knowledge into the model's context. However, challenges persist in scaling CAG to accommodate large and dynamic knowledge bases effectively. This paper introduces Adaptive Contextual Compression (ACC), an innovative technique designed to dynamically compress and manage context inputs, enabling efficient utilization of the extended memory capabilities of modern LLMs. To further address the limitations of standalone CAG, we propose a Hybrid CAG-RAG Framework, which integrates selective retrieval to augment preloaded contexts in scenarios requiring additional information. Comprehensive evaluations on diverse datasets highlight the proposed methods' ability to enhance scalability, optimize efficiency, and improve multi-hop reasoning performance, offering practical solutions for real-world knowledge integration challenges.

cs.CL↗

arXiv2025

PNN: A Novel Progressive Neural Network for Fault Classification in Rotating Machinery under Small Dataset Constraint

Fault detection in rotating machinery is a complex task, particularly in small and heterogeneous dataset scenarios. Variability in sensor placement, machinery configurations, and structural differences further increase the complexity of the problem. Conventional deep learning approaches often demand large, homogeneous datasets, limiting their applicability in data-scarce industrial environments. While transfer learning and few-shot learning have shown potential, however, they are often constrained by the need for extensive fault datasets. This research introduces a unified framework leveraging a novel progressive neural network (PNN) architecture designed to address these challenges. The PNN sequentially estimates the fixed-size refined features of the higher order with the help of all previously estimated features and appends them to the feature set. This fixed-size feature output at each layer controls the complexity of the PNN and makes it suitable for effective learning from small datasets. The framework's effectiveness is validated on eight datasets, including six open-source datasets, one in-house fault simulator, and one real-world industrial dataset. The PNN achieves state-of-the-art performance in fault detection across varying dataset sizes and machinery types, highlighting superior generalization and classification capabilities.

cs.LG↗

arXiv2025

NanoVLMs: How small can we go and still make coherent Vision Language Models?

Vision-Language Models (VLMs), such as GPT-4V and Llama 3.2 vision, have garnered significant research attention for their ability to leverage Large Language Models (LLMs) in multimodal tasks. However, their potential is constrained by inherent challenges, including proprietary restrictions, substantial computational demands, and limited accessibility. Smaller models, such as GIT and BLIP, exhibit marked limitations, often failing to generate coherent and consistent text beyond a few tokens, even with extensive training. This underscores a pivotal inquiry: how small can a VLM be and still produce fluent and consistent text? Drawing inspiration from the exceptional learning process of 3-4 year old children, who rely heavily on visual cues for understanding and communication, we introduce two novel datasets: ShortDesc (featuring concise image descriptions) and LongDesc (containing more detailed image descriptions). These datasets consist of image-text pairs where the text is restricted to the simple vocabulary and syntax typically used by young children, generated with a scaled-down model, GPT-4o. Using these datasets, we demonstrate that it is possible to train VLMs that are significantly smaller, up to 10 times smaller than state of the art(SOTA) small VLMs while maintaining architectural simplicity. To evaluate the outputs, we leverage GPT-4o to grade the text, as if stories written by students, on creativity, meaningfulness, and consistency, assigning scores out of 10. This method addresses limitations of standard benchmarks by accommodating unstructured outputs and providing a multidimensional evaluation of the model capabilities. Our findings contribute to the development of lightweight, accessible multimodal models for resource constrained environments.

cs.CV↗

arXiv2025

3rd Workshop on Maritime Computer Vision (MaCVi) 2025: Challenge Results

The 3rd Workshop on Maritime Computer Vision (MaCVi) 2025 addresses maritime computer vision for Unmanned Surface Vehicles (USV) and underwater. This report offers a comprehensive overview of the findings from the challenges. We provide both statistical and qualitative analyses, evaluating trends from over 700 submissions. All datasets, evaluation code, and the leaderboard are available to the public at https://macvi.org/workshop/macvi25.

cs.CV↗

arXiv2025

A Multimodal Dataset for Enhancing Industrial Task Monitoring and Engagement Prediction

Detecting and interpreting operator actions, engagement, and object interactions in dynamic industrial workflows remains a significant challenge in human-robot collaboration research, especially within complex, real-world environments. Traditional unimodal methods often fall short of capturing the intricacies of these unstructured industrial settings. To address this gap, we present a novel Multimodal Industrial Activity Monitoring (MIAM) dataset that captures realistic assembly and disassembly tasks, facilitating the evaluation of key meta-tasks such as action localization, object interaction, and engagement prediction. The dataset comprises multi-view RGB, depth, and Inertial Measurement Unit (IMU) data collected from 22 sessions, amounting to 290 minutes of untrimmed video, annotated in detail for task performance and operator behavior. Its distinctiveness lies in the integration of multiple data modalities and its emphasis on real-world, untrimmed industrial workflows-key for advancing research in human-robot collaboration and operator monitoring. Additionally, we propose a multimodal network that fuses RGB frames, IMU data, and skeleton sequences to predict engagement levels during industrial tasks. Our approach improves the accuracy of recognizing engagement states, providing a robust solution for monitoring operator performance in dynamic industrial environments. The dataset and code can be accessed from https://github.com/navalkishoremehta95/MIAM/.

cs.CV↗