arXiv subjects
Publications and source records attributed to Gaurav Kumar.
In this article, we introduce a refinement of the method of Heap and Soundararajan to obtain lower bounds for the $2k$-th moment of a broad class of $L$-functions for all real $k\ge 0$. In particular, our method circumvents the need to estimate the twisted moments of $L$-functions.
Let $G$ be a group. The commuting graph $\zeta(G, V)$ of a group $G$ has a vertex set $V\subseteq G,$ two vertices are connected with an edge if the corresponding elements commute in $G.$ In this article, we study the commuting graphs for the non-abelian $p$-groups of order $p^n$ with center size $p^{n-2}.$ We study detour distance, metric dimension, resolving polynomials, and the spectral properties for these graphs.
Large Language Models such as GPT-4o and GPT-5 achieve strong zero-shot performance on biomedical claim verification, but cost and opacity limit scalable use. We fine-tune three small LLMs: Phi-3-mini (3.8B), Qwen2.5-3B, and Mistral-7B, via QLoRA on SciFact and HealthVer, providing the first study of QLoRA models against GPT-4o and fine-tuned BioLinkBERT encoders. Mistral-7B QLoRA surpasses both GPT-4o and GPT-5 (up to 12% F1 gain) at a fractional cost using just 1,008 training examples. We conduct extensive in-domain and cross-domain evaluation: models trained on SciFact tested on HealthVer and vice versa, at matched sizes to isolate dataset structure from data quantity. We identify a previously unreported structural artifact in SciFact that inflates in-domain scores, and show through bidirectional out-of-domain evaluation that training on structurally sound data enables robust cross-domain transfer. We plan to release all code and adapter checkpoints.
Multilingual fact verification requires evidence that is both relevant and sufficiently complete for reliable factuality prediction. However, existing systems often rely on search snippets, sentence-level evidence, or locally segmented passages, which can miss decisive context and produce fragmented evidence. To overcome these limitations, we propose SEEK, a Semantic Evidence Extraction with an adaptive chunKing framework that constructs coherent evidence chunks from full fact-checking articles by identifying semantic topic transitions and preserving local verification context. The constructed chunks are encoded using a multilingual encoder and then multilingual LLMs are finetuned using LoRA adapter for veracity prediction. Experiments on X-FACT and RU22Fact show that SEEK improves macro-f1 by up to 10% over semantic chunking, 19% over sentence chunking, and 20% over search-snippet baselines. Evidence completeness and significance analyses further show that SEEK preserves richer verification context and enables more reliable multilingual fact-checking.
The widespread use of clickbait headlines, crafted to mislead and maximize engagement, poses a significant challenge to online credibility. These headlines employ sensationalism, misleading claims, and vague language, underscoring the need for effective detection to ensure trustworthy digital content. The paper introduces, ClickGuard: a trustworthy adaptive fusion framework for clickbait detection. It combines BERT embeddings and structural features using a Syntactic-Semantic Adaptive Fusion Block (SSAFB) for dynamic integration. The framework incorporates a hybrid CNN-BiLSTM to capture patterns and dependencies. The model achieved 96.93% testing accuracy, outperforming state-of-the-art approaches. The model's trustworthiness is evaluated using LIME and Permutation Feature Importance (PFI) for interpretability and perturbation analysis. These methods assess the model's robustness and sensitivity to feature changes by measuring the average prediction variation. Ablation studies validated the SSAFB's effectiveness in optimizing feature fusion. The model demonstrated robust performance across diverse datasets, providing a scalable, reliable solution for enhancing online content credibility by addressing syntactic-semantic modelling challenges. Code of the work is available at: https://github.com/palindromeRice/ClickBait_Detection_Architecture
Applying large, proprietary API-based language models to text-to-SQL tasks poses a significant industry challenge: reliance on massive, schema-heavy prompts results in prohibitive per-token API costs and high latency, hindering scalable production deployment. We present a specialized, self-hosted 8B-parameter model designed for a conversational bot in CriQ, a sister app to Dream11, India's largest fantasy sports platform with over 250 million users, that answers user queries about cricket statistics. Our novel two-phase supervised fine-tuning approach enables the model to internalize the entire database schema, eliminating the need for long-context prompts. This reduces input tokens by over 99%, from a 17k-token baseline to fewer than 100, and replaces costly external API calls with efficient local inference. The resulting system achieves 98.4% execution success and 92.5% semantic accuracy, substantially outperforming a prompt-engineered baseline using Google's Gemini Flash 2.0 (95.6% execution, 89.4% semantic accuracy). These results demonstrate a practical path toward high-precision, low-latency text-to-SQL applications using domain-specialized, self-hosted language models in large-scale production environments.
Inspired by non-equilibrium thermodynamics, diffusion models have achieved state-of-the-art performance in generative modeling. However, their iterative sampling nature results in high inference latency. While recent distillation techniques accelerate sampling, they discard intermediate trajectory steps. This sparse supervision leads to a loss of structural information and introduces significant discretization errors. To mitigate this, we propose B-DENSE, a novel framework that leverages multi-branch trajectory alignment. We modify the student architecture to output $K$-fold expanded channels, where each subset corresponds to a specific branch representing a discrete intermediate step in the teacher's trajectory. By training these branches to simultaneously map to the entire sequence of the teacher's target timesteps, we enforce dense intermediate trajectory alignment. Consequently, the student model learns to navigate the solution space from the earliest stages of training, demonstrating superior image generation quality compared to baseline distillation frameworks.
Large Language Models (LLMs) often struggle with complex multi-step planning tasks, showing high rates of constraint violations and inconsistent solutions. Existing strategies such as Chain-of-Thought and ReAct rely on implicit state tracking and lack an explicit problem representation. Inspired by classical AI planning, we propose Model-First Reasoning (MFR), a two-phase paradigm in which the LLM first constructs an explicit model of the problem, defining entities, state variables, actions, and constraints, before generating a solution plan. Across multiple planning domains, including medical scheduling, route planning, resource allocation, logic puzzles, and procedural synthesis, MFR reduces constraint violations and improves solution quality compared to Chain-of-Thought and ReAct. Ablation studies show that the explicit modeling phase is critical for these gains. Our results suggest that many LLM planning failures stem from representational deficiencies rather than reasoning limitations, highlighting explicit modeling as a key component for robust and interpretable AI agents. All prompts, evaluation procedures, and task datasets are documented to facilitate reproducibility.
Real-world complex systems are often better modeled as hypergraphs, where edges represent group interactions involving multiple entities. Understanding and quantifying homophily (similarity-driven association) in such networks is essential for analyzing community formation and information flow. We propose a hyperedge-centric framework to quantify homophily in hypergraphs. Each interaction is represented as a hyperedge, and its interaction perplexity measures the effective number of distinct attributes it contains. Comparing this observed perplexity with a degree-preserving random baseline defines the diversity gap, which quantifies how diverse an interaction is than expected by chance. The global homophily score for a network, called Perplexity-Homophily Index, is computed by averaging the normalized diversity gap across all hyperedges. Experiments on synthetic and real-world datasets show that the proposed index captures the full distribution of homophily and reveals how homophilic and heterophilic tendencies vary with interaction size in hypergraphs.
Upcycling pre-trained dense models into sparse Mixture-of-Experts (MoEs) efficiently increases model capacity but often suffers from poor expert specialization due to naive weight replication. Our analysis reveals that upcycled MoEs, even with conventional regularization, exhibit low-confidence, weakly differentiated routing, hindering performance. We introduce Dirichlet-Prior Shaping Loss (DPSL), a novel router regularization technique that directly shapes routing probability distributions by matching expert assignments to a target Dirichlet prior. DPSL offers fine-grained control over expert balance and specialization, and enables encoding of inductive biases such as encouraging experts to focus on specific modalities or tasks, without requiring manual intervention; notably, DPSL is a general tool applicable to any module that outputs categorical probability distributions, extending its utility beyond MoE training. Experiments on upcycled MoE vision-language models (with Qwen2, Phi3, Llama3.2 LLM backbones) show DPSL consistently outperforms upcycling strategies and regularization techniques across standard vision-language benchmarks, addressing the critical issue of poor specialization and fostering more adaptive, higher-performing models.
The challenge of translating vast, multimodal biological data into predictive and mechanistic understanding of cellular function is a central theme in modern biology. Virtual cells, or digital cellular twins, have emerged as a critical paradigm to meet this challenge by creating integrative computational models of cellular processes. This review synthesizes the evolution and current state of the virtual cell, from foundational mechanistic frameworks like the Virtual Cell that employ deterministic and stochastic simulations to the recent transformative impact of artificial intelligence and foundation models. We examine the core technological pillars required to build these models, including the integration of various data types, such as single-cell and spatial omics, the spectrum of modeling approaches, and the bioengineering principles that connect simulation to application. We further discuss key applications, frameworks for model benchmarking and validation, and the significant hurdles that remain, including computational scalability, parameter inference, and ethical considerations, which provides a roadmap for development of predictive virtual cells that promise to revolutionize biomedical research and clinical practice.
Homophily, the tendency of individuals to connect with others who share similar attributes, is a defining feature of social networks. Understanding how groups interact, both within and across, is crucial for uncovering the dynamics of network evolution and the emergence of structural inequalities in these network. This tutorial offers a comprehensive overview of homophily, covering its various definitions, key properties, and the limitations of widely used metrics. Extending beyond traditional pairwise interactions, we will discuss homophily in higher-order network structures such as hypergraphs and simplicial complexes. We will further discuss network generating models capable of producing different types of homophilic networks with tunable levels of homophily and highlight their relevance in real-world contexts. The tutorial concludes with a discussion of open challenges, emerging directions, and opportunities for further research in this area.
Misinformation on the web increasingly appears in multimodal forms, combining text, images, and OCR-rendered content in ways that amplify harm to public trust and vulnerable communities. While prior fact-checking systems often rely on unimodal signals or shallow fusion strategies, modern misinformation campaigns operate across modalities and require models that can reason over subtle cross-modal inconsistencies in a transparent and responsible manner. We introduce MultiCheck, a lightweight and interpretable framework for multimodal fact verification that jointly analyzes textual, visual, and OCR evidence. At its core, MultiCheck employs a relational fusion module based on element-wise difference and product operations, allowing for explicit cross-modal interaction modeling with minimal computational overhead. A contrastive alignment objective further helps the model distinguish between supporting and refuting evidence while maintaining a small memory and energy footprint, making it suitable for low-resource deployment. Evaluated on the Factify-2 (5-class) and Mocheg (3-class) benchmarks, MultiCheck achieves huge performance improvement and remains robust under noisy OCR and missing modality conditions. Its efficiency, transparency, and real-world robustness make it well-suited for journalists, civil society organisations, and web integrity efforts working to build a safer and more trustworthy web.
We study the generating function of the excess number of Rogers-Ramanujan partitions with odd rank over those with even rank, and, using combinatorial and analytical techniques, show that this generating function is closely connected with an interesting class of restricted partitions, namely, partitions into distinct parts where the number of parts is not a part. We derive arithmetic properties of the number of such partitions and conjecture an interesting mod $4$ congruence. Generalizations of most of these results in a parameter $\ell$ are also obtained.
A new sums-of-tails identity involving two parameters $b$ and $d$ is obtained and is used to derive more results of similar type. One of Ramanujan's sums-of-tails identities from the Lost Notebook is shown to be a special case of our result. In the course of deriving Ramanujan's identity, we obtain a new result of combinatorial significance. Two new representations for an infinite series associated to a mock theta function are derived. Also, we give an application of an identity of Andrews and Onofri.
Preclinical sleep research remains constrained by labor intensive, manual vigilance state classification and inter rater variability, limiting throughput and reproducibility. This study presents an automated framework developed by Team Neural Prognosticators to classify electroencephalogram (EEG) recordings of small rodents into three critical vigilance states paradoxical sleep (REM), slow wave sleep (SWS), and wakefulness. The system integrates advanced signal processing with machine learning, leveraging engineered features from both time and frequency domains, including spectral power across canonical EEG bands (delta to gamma), temporal dynamics via Maximum-Minimum Distance, and cross-frequency coupling metrics. These features capture distinct neurophysiological signatures such as high frequency desynchronization during wakefulness, delta oscillations in SWS, and REM specific bursts. Validated during the 2024 Big Data Health Science Case Competition (University of South Carolina Big Data Health Science Center, 2024), our XGBoost model achieved 91.5% overall accuracy, 86.8% precision, 81.2% recall, and an F1 score of 83.5%, outperforming all baseline methods. Our approach represents a critical advancement in automated sleep state classification and a valuable tool for accelerating discoveries in sleep science and the development of targeted interventions for chronic sleep disorders. As a publicly available code (BDHSC) resource is set to contribute significantly to advancements.
Image to image translation is an active area of research in the field of computer vision, enabling the generation of new images with different styles, textures, or resolutions while preserving their characteristic properties. Recent architectures leverage Generative Adversarial Networks (GANs) to transform input images from one domain to another. In this work, we focus on the study of both paired and unpaired image translation across multiple image domains. For the paired task, we used a conditional GAN model, and for the unpaired task, we trained it using cycle consistency loss. We experimented with different types of loss functions, multiple Patch-GAN sizes, and model architectures. New quantitative metrics - precision, recall, and FID score - were used for analysis. In addition, a qualitative study of the results of different experiments was conducted.
Automated fact-checking has been a challenging task for the research community. Prior work has explored various strategies, such as end-to-end training, retrieval-augmented generation, and prompt engineering, to build robust fact-checking systems. However, their accuracy has not been high enough for real-world deployment. We, on the other hand, propose a new learning paradigm, where evidence classification and entailed justifications made by generative language models (GLMs) are used to train encoder-only language models (ELMs). We conducted a rigorous set of experiments, comparing our approach with recent works along with various prompting and fine-tuning strategies. Additionally, we performed ablation studies, error analysis, quality analysis of model explanations, and a domain generalisation study to provide a comprehensive understanding of our approach.