arXiv subjects

Pankaj Singh

Publications and source records attributed to Pankaj Singh.

13 recordsLinked to original sources

arXiv2026

Torsors of Generalized del Pezzo Tori and Brauer Groups

Using cohomological Mackey functors, we give an explicit Brauer group classification of torsors under tori of generalized del Pezzo varieties. This identifies the image of Lamarche's Brauer invariants and extends the Brauer-theoretic description in Blunk's classification of degree-six del Pezzo surfaces. We also determine which finite field extensions can appear in other Brauer group presentations of these torsors. The same tori act on Losev-Manin spaces, so the computation applies to these toric varieties as well.

math.AG↗

arXiv2025

Intent Aware Context Retrieval for Multi-Turn Agricultural Question Answering

Indian farmers often lack timely, accessible, and language-friendly agricultural advice, especially in rural areas with low literacy. To address this gap in accessibility, this paper presents a novel AI-powered agricultural chatbot, Krishi Sathi, designed to support Indian farmers by providing personalized, easy-to-understand answers to their queries through both text and speech. The system's intelligence stems from an IFT model, subsequently refined through fine-tuning on Indian agricultural knowledge across three curated datasets. Unlike traditional chatbots that respond to one-off questions, Krishi Sathi follows a structured, multi-turn conversation flow to gradually collect the necessary details from the farmer, ensuring the query is fully understood before generating a response. Once the intent and context are extracted, the system performs Retrieval-Augmented Generation (RAG) by first fetching information from a curated agricultural database and then generating a tailored response using the IFT model. The chatbot supports both English and Hindi languages, with speech input and output features (via ASR and TTS) to make it accessible for users with low literacy or limited digital skills. This work demonstrates how combining intent-driven dialogue flows, instruction-tuned models, and retrieval-based generation can improve the quality and accessibility of digital agricultural support in India. This approach yielded strong results, with the system achieving a query response accuracy of 97.53%, 91.35% contextual relevance and personalization, and a query completion rate of 97.53%. The average response time remained under 6 seconds, ensuring timely support for users across both English and Hindi interactions.

cs.CL↗

arXiv2025

PARAM-1 BharatGen 2.9B Model

Large Language Models (LLMs) have emerged as powerful general-purpose reasoning systems, yet their development remains dominated by English-centric data, architectures, and optimization paradigms. This exclusionary design results in structural under-representation of linguistically diverse regions such as India, where over 20 official languages and 100+ dialects coexist alongside phenomena like code-switching and diglossia. We introduce PARAM-1, a 2.9B parameter decoder-only, text-only language model trained from scratch with an explicit architectural and linguistic focus on Indian diversity. PARAM-1 is trained on a bilingual dataset consisting of only Hindi and English, constructed with a strong focus on fact-rich, high-quality content. It is guided by three core principles: equitable representation of Indic languages through a 25% corpus allocation; tokenization fairness via a SentencePiece tokenizer adapted to Indian morphological structures; and culturally aligned evaluation benchmarks across IndicQA, code-mixed reasoning, and socio-linguistic robustness tasks. By embedding diversity at the pretraining level-rather than deferring it to post-hoc alignment-PARAM-1 offers a design-first blueprint for equitable foundation modeling. Our results demonstrate that it serves as both a competent general-purpose model and a robust baseline for India-centric applications.

cs.CL↗

arXiv2025

Classifying torsors of tori with Brauer groups

Using Mackey functors, we provide a general framework for classifying torsors of algebraic tori in terms of Brauer groups of finite field extensions of the base field. This generalizes Blunk's description of the tori associated to del Pezzo surfaces of degree 6 to all retract rational tori, essentially the largest class for which this is possible.

math.AG↗

arXiv2024

On the weak Lefschetz property for ideals generated by powers of general linear forms

We provide a description of initial ideals for almost complete intersections generated by powers of general linear forms and prove that WLP in a fixed degree $d$ holds when the number of variables $n$ is sufficiently large compared to $d$. In particular, we show that if $n\geq 3d-2$ then WLP holds for the ideal generated by squares at the degree $d$ spot and for $n\ge \frac{3d-3}{2}$ WLP holds for ideal generated by cubes at the degree $d$ spot. Finally, we prove that WLP fails for the ideal generated by squares when $n< 3d -2$ at the $d$th spot by finding an explicit element in the kernel of the multiplication by a general linear form. This shows that our bound on $n$ is sharp in the case of the squares.

math.AC↗

arXiv2022

Multilingual CheckList: Generation and Evaluation

Multilingual evaluation benchmarks usually contain limited high-resource languages and do not test models for specific linguistic capabilities. CheckList is a template-based evaluation approach that tests models for specific capabilities. The CheckList template creation process requires native speakers, posing a challenge in scaling to hundreds of languages. In this work, we explore multiple approaches to generate Multilingual CheckLists. We device an algorithm - Template Extraction Algorithm (TEA) for automatically extracting target language CheckList templates from machine translated instances of a source language templates. We compare the TEA CheckLists with CheckLists created with different levels of human intervention. We further introduce metrics along the dimensions of cost, diversity, utility, and correctness to compare the CheckLists. We thoroughly analyze different approaches to creating CheckLists in Hindi. Furthermore, we experiment with 9 more different languages. We find that TEA followed by human verification is ideal for scaling Checklist-based evaluation to multiple languages while TEA gives a good estimates of model performance.

cs.CL↗

arXiv2022

VL4Pose: Active Learning Through Out-Of-Distribution Detection For Pose Estimation

Advances in computing have enabled widespread access to pose estimation, creating new sources of data streams. Unlike mock set-ups for data collection, tapping into these data streams through on-device active learning allows us to directly sample from the real world to improve the spread of the training distribution. However, on-device computing power is limited, implying that any candidate active learning algorithm should have a low compute footprint while also being reliable. Although multiple algorithms cater to pose estimation, they either use extensive compute to power state-of-the-art results or are not competitive in low-resource settings. We address this limitation with VL4Pose (Visual Likelihood For Pose Estimation), a first principles approach for active learning through out-of-distribution detection. We begin with a simple premise: pose estimators often predict incoherent poses for out-of-distribution samples. Hence, can we identify a distribution of poses the model has been trained on, to identify incoherent poses the model is unsure of? Our solution involves modelling the pose through a simple parametric Bayesian network trained via maximum likelihood estimation. Therefore, poses incurring a low likelihood within our framework are out-of-distribution samples making them suitable candidates for annotation. We also observe two useful side-outcomes: VL4Pose in-principle yields better uncertainty estimates by unifying joint and pose level ambiguity, as well as the unintentional but welcome ability of VL4Pose to perform pose refinement in limited scenarios. We perform qualitative and quantitative experiments on three datasets: MPII, LSP and ICVL, spanning human and hand pose estimation. Finally, we note that VL4Pose is simple, computationally inexpensive and competitive, making it suitable for challenging tasks such as on-device active learning.

cs.CV↗

arXiv2021

RDD-Eclat: Approaches to Parallelize Eclat Algorithm on Spark RDD Framework (Extended Version)

Frequent itemset mining (FIM) is a highly computational and data intensive algorithm. Therefore, parallel and distributed FIM algorithms have been designed to process large volume of data in a reduced time. Recently, a number of FIM algorithms have been designed on Hadoop MapReduce, a distributed big data processing framework. But, due to heavy disk I/O, MapReduce is found to be inefficient for the highly iterative FIM algorithms. Therefore, Spark, a more efficient distributed data processing framework, has been developed with in-memory computation and resilient distributed dataset (RDD) features to support the iterative algorithms. On this framework, Apriori and FP-Growth based FIM algorithms have been designed on the Spark RDD framework, but Eclat-based algorithm has not been explored yet. In this paper, RDD-Eclat, a parallel Eclat algorithm on the Spark RDD framework is proposed with its five variants. The proposed algorithms are evaluated on the various benchmark datasets, and the experimental results show that RDD-Eclat outperforms the Spark-based Apriori by many times. Also, the experimental results show the scalability of the proposed algorithms on increasing the number of cores and size of the dataset.

cs.DC↗

arXiv2019

RDD-Eclat: Approaches to Parallelize Eclat Algorithm on Spark RDD Framework

Initially, a number of frequent itemset mining (FIM) algorithms have been designed on the Hadoop MapReduce, a distributed big data processing framework. But, due to heavy disk I/O, MapReduce is found to be inefficient for such highly iterative algorithms. Therefore, Spark, a more efficient distributed data processing framework, has been developed with in-memory computation and resilient distributed dataset (RDD) features to support the iterative algorithms. On the Spark RDD framework, Apriori and FP-Growth based FIM algorithms have been designed, but Eclat-based algorithm has not been explored yet. In this paper, RDD-Eclat, a parallel Eclat algorithm on the Spark RDD framework is proposed with its five variants. The proposed algorithms are evaluated on the various benchmark datasets, which shows that RDD-Eclat outperforms the Spark-based Apriori by many times. Also, the experimental results show the scalability of the proposed algorithms on increasing the number of cores and size of the dataset.

cs.DC↗

arXiv2019

A Data Structure Perspective to the RDD-based Apriori Algorithm on Spark

During the recent years, a number of efficient and scalable frequent itemset mining algorithms for big data analytics have been proposed by many researchers. Initially, MapReduce-based frequent itemset mining algorithms on Hadoop cluster were proposed. Although, Hadoop has been developed as a cluster computing system for handling and processing big data, but the performance of Hadoop does not meet the expectation for the iterative algorithms of data mining, due to its high I/O, and writing and then reading intermediate results in the disk. Consequently, Spark has been developed as another cluster computing infrastructure which is much faster than Hadoop due to its in-memory computation. It is highly suitable for iterative algorithms and supports batch, interactive, iterative, and stream processing of data. Many frequent itemset mining algorithms have been re-designed on the Spark, and most of them are Apriori-based. All these Spark-based Apriori algorithms use Hash Tree as the underlying data structure. This paper investigates the efficiency of various data structures for the Spark-based Apriori. Although, the data structure perspective has been investigated previously, but for MapReduce-based Apriori, and it must be re-investigated in the distributed computing environment of Spark. The considered underlying data structures are Hash Tree, Trie, and Hash Table Trie. The experimental results on the benchmark datasets show that the performance of Spark-based Apriori with Trie and Hash Table Trie are almost similar but both perform many times better than Hash Tree in the distributed computing environment of Spark.

cs.DC↗

arXiv2019

Mining Association Rules in Various Computing Environments: A Survey

Association Rule Mining (ARM) is one of the well know and most researched technique of data mining. There are so many ARM algorithms have been designed that their counting is a large number. In this paper we have surveyed the various ARM algorithms in four computing environments. The considered computing environments are sequential computing, parallel and distributed computing, grid computing and cloud computing. With the emergence of new computing paradigm, ARM algorithms have been designed by many researchers to improve the efficiency by utilizing the new paradigm. This paper represents the journey of ARM algorithms started from sequential algorithms, and through parallel and distributed, and grid based algorithms to the current state-of-the-art, along with the motives for adopting new machinery.

cs.DC↗

arXiv2018

Learning From Less Data: Diversified Subset Selection and Active Learning in Image Classification Tasks

Supervised machine learning based state-of-the-art computer vision techniques are in general data hungry and pose the challenges of not having adequate computing resources and of high costs involved in human labeling efforts. Training data subset selection and active learning techniques have been proposed as possible solutions to these challenges respectively. A special class of subset selection functions naturally model notions of diversity, coverage and representation and they can be used to eliminate redundancy and thus lend themselves well for training data subset selection. They can also help improve the efficiency of active learning in further reducing human labeling efforts by selecting a subset of the examples obtained using the conventional uncertainty sampling based techniques. In this work we empirically demonstrate the effectiveness of two diversity models, namely the Facility-Location and Disparity-Min models for training-data subset selection and reducing labeling effort. We do this for a variety of computer vision tasks including Gender Recognition, Scene Recognition and Object Recognition. Our results show that subset selection done in the right way can add 2-3% in accuracy on existing baselines, particularly in the case of less training data. This allows the training of complex machine learning models (like Convolutional Neural Networks) with much less training data while incurring minimal performance loss.

cs.CV↗

arXiv2013

On d+id density wave and superconducting orderings in hole-doped cuprates

The Chiral d-density wave (CDDW) order, at the anti-ferromagnetic wave vector (pi,pi), is assumed to represent the pseudo-gap (PG) state of a hole-doped cuprate superconductor. The pairing interaction required for the PG phase corresponds to a repulsive interaction of Coulombic origin. The d-wave superconductivity (DSC), driven by an appropriate assumed attractive interaction, is discussed within the mean-field framework together with the CDDW ordering. The single-particle excitation spectrum in the CDDW and DSC state is characterized by the Bogolubov quasi-particle bands-a characteristic feature of SC state. The coupled gap equations are solved self-consistently together with the equation to determine the chemical potential. With the pinning of the van Hove-singularities close to the chemical potential, one is able to calculate the thermodynamic and transport properties of the under-doped cuprates in a consistent manner. The electronic specific heat displays non-Fermi liquid feature in the CDDW state. The CDDW and DSC are found to represent two competing orders as the former brings about a depletion of the spectral weight (and Raman response function density) available for pairing in the anti-nodal region of momentum space.This is not in agreement with a preformed pairing scenario and justifies the different structures we have assumed for the pseudo-gap and the superconducting gap. Furthermore, these gaps in the excitation spectrum do not merge into a single quadrature gap. It is also shown that the depletion of the spectral weight below Tc at energies larger than the gap amplitude occurs. This is an indication of the strong-coupling superconductivity in cuprates. The calculation of the ratio of the quasi-particle thermal conductivity and temperature in the superconductiong phase is found to be constant in the limit of near-zero quasi-particle scattering rate.

cond-mat.supr-con↗