arXiv subjects

Anirban Dasgupta

Publications and source records attributed to Anirban Dasgupta.

At least 19 recordsLinked to original sources

arXiv2026

Probing Hairy Kerr Black Holes through Quasi-Periodic Oscillations I: A study based on the kinematic models

Black holes endowed with nontrivial scalar or matter fields, known as hairy black holes, possess additional parameters beyond mass, charge, and spin, leading to richer phenomenology. Constraining their parameter space is therefore essential, particularly in view of current electromagnetic and gravitational-wave observations. In this work, we study rotating hairy black hole solutions inspired by the gravitational decoupling method, which satisfy the Einstein field equations with a conserved energy-momentum tensor obeying the strong energy conditions. We explore in detail the horizon structure of such black holes and report for the first time certain unique features not observed in Kerr black holes. We examine how the hair parameters influence the fundamental frequencies governing particle motion in the hairy Kerr spacetime and compare these effects with the Kerr case. Since theoretical models of high-frequency quasi-periodic oscillations (HFQPOs) are directly linked to these fundamental frequencies, this provides a powerful observational probe of hairy black holes. By confronting several kinematic HFQPO models with observations from six black hole sources, we report that for most sources, the HFQPO data at the current level of precision cannot distinguish between the Kerr and hairy Kerr scenarios. However, based on agreement with previous spin estimates, our analysis provides a systematic framework to assess the relative suitability of different HFQPO models for each source. Notably, even with current observational precision, we find that both the Relativistic Precession Model and the Tidal Disruption Model appear unsuitable for the sources GRO J1655-40 and GRS 1915+105. The broader implications of these findings are discussed.

gr-qc↗

arXiv2026

'Si'multaneous 'S'patial-'T'emporal Message Passing for Dynamic Graph Representation Learning

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. \emph{Temporal-first} approaches build per-node temporal embeddings and only afterwards perform spatial aggregation, whereas \emph{Spatial-first} approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; concretely, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's \emph{past} trajectory. This paper introduces \textbf{SiST-GNN} (\textbf{Si}multaneous \textbf{S}patial-\textbf{T}emporal \textbf{GNN}), which fuses the two signals inside a single message-passing operation rather than chaining them. Concretely, at each snapshot we maintain a recurrent hidden state per node that summarises its history, pair it with the node's current feature vector, and treat the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. Our empirical study spans nine public baselines and fourteen model-dataset combinations, covering both fixed-split and live-update evaluation regimes. Across every public benchmark, SiST-GNN sets a new state of the art in link prediction task over the strongest prior method by $109$--$277\%$ in the fixed-split setting and by $68$--$194\%$ in the live-update setting. We additionally construct three dynamic node-classification tasks by discretising the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by $7$--$22\%$ and matches continuous-time (CTDG) methods that consume the raw events directly.

cs.LG↗

arXiv2026

Deterministic Coreset for Lp Subspace

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.

cs.DS↗

arXiv2026

FIT-GNN: Faster Inference Time for GNNs that 'FIT' in Memory Using Coarsening

Scalability of Graph Neural Networks (GNNs) remains a significant challenge. To tackle this, methods like coarsening, condensation, and computation trees are used to train on a smaller graph, resulting in faster computation. Nonetheless, prior research has not adequately addressed the computational costs during the inference phase. This paper presents a novel approach to improve the scalability of GNNs by reducing computational burden during the inference phase using graph coarsening. We demonstrate two different methods -- Extra Nodes and Cluster Nodes. Our study extends the application of graph coarsening for graph-level tasks, including graph classification and graph regression. We conduct extensive experiments on multiple benchmark datasets to evaluate the performance of our approach. Our results show that the proposed method achieves orders of magnitude improvements in single-node inference time compared to traditional approaches. Furthermore, it significantly reduces memory consumption for node and graph classification and regression tasks, enabling efficient training and inference on low-resource devices where conventional methods are impractical. Notably, these computational advantages are achieved while maintaining competitive performance relative to baseline models.

cs.LG↗

arXiv2025

Constraining the rotating Simpson-Visser spacetime from the observed quasi-periodic oscillations in black holes

Regular black holes (BHs) which are singularity-free alternatives to the standard black hole paradigm in General Relativity (GR), offer effective models for probing the interface between classical and quantum gravity. They serve as promising candidates for exploring the nature of strong gravity and potential extensions of GR by providing testing grounds to understand how quantum corrections might manifest in astrophysical black holes. In the present work, we investigate the regular BH scenario described by the Simpson-Visser (SV) spacetime and explore its imprints on the high-frequency quasi-periodic oscillations (HFQPOs) observed in the black hole power spectrum. The Simpson-Visser spacetime represent the simplest, globally regular extensions of the Schwarzschild scenario, through the presence of a regularizing parameter. We explore the imprints of the regularizing parameter on the orbital and epicyclic frequencies associated with the motion of test particles in the rotating SV spacetime. Models aimed to explain the observed HFQPOs often invoke these fundamental frequencies and hence can potentially constrain the regularizing parameter from the available HFQPO data. We test eleven well-established HFQPO models against available observations from six black hole sources, obtaining spin constraints that, when compared with previous independent estimates, help identify the observationally favored models for each source. Based on the present data, we report that the observationally favored models cannot discriminate between the Kerr and the Simpson-Visser scenario. This when coupled with the large discrepancy in previous spin estimates of these sources, may plausibly indicate some deviation from GR in the strong gravity regime near BHs which requires further investigation.

gr-qc↗

arXiv2025

Local Fragments, Global Gains: Subgraph Counting using Graph Neural Networks

Subgraph counting is a fundamental task for analyzing structural patterns in graph-structured data, with important applications in domains such as computational biology and social network analysis, where recurring motifs reveal functional and organizational properties. In this paper, we propose localized versions of the Weisfeiler-Leman (WL) algorithms to improve both expressivity and computational efficiency for this task. We introduce Local $k$-WL, which we prove to be more expressive than $k$-WL and at most as expressive as $(k+1)$-WL, and provide a characterization of patterns whose subgraph and induced subgraph counts are invariant under Local $k$-WL equivalence. To enhance scalability, we present two variants -- Layer $k$-WL and Recursive $k$-WL -- that achieve greater time and space efficiency compared to applying $k$-WL on the entire graph. Additionally, we propose a novel fragmentation technique that decomposes complex subgraphs into simpler subpatterns, enabling the exact count of all induced subgraphs of size at most $4$ using only $1$-WL, with extensions possible for larger patterns when $k>1$. Building on these ideas, we develop a three-stage differentiable learning framework that combines subpattern counts to compute counts of more complex motifs, bridging combinatorial algorithm design with machine learning approaches. We also compare the expressive power of Local $k$-WL with existing GNN hierarchies and demonstrate that, under bounded time complexity, our methods are more expressive than prior approaches.

cs.LG↗

arXiv2025

Private Sketches for Linear Regression

Linear regression is frequently applied in a variety of domains, some of which might contain sensitive information. This necessitates that the application of these methods does not reveal private information. Differentially private (DP) linear regression methods, developed for this purpose, compute private estimates of the solution. These techniques typically involve computing a noisy version of the solution vector. Instead, we propose releasing private sketches of the datasets, which can then be used to compute an approximate solution to the regression problem. This is motivated by the \emph{sketch-and-solve} paradigm, where the regression problem is solved on a smaller sketch of the dataset instead of on the original problem space. The solution obtained on the sketch can also be shown to have good approximation guarantees to the original problem. Various sketching methods have been developed for improving the computational efficiency of linear regression problems under this paradigm. We adopt this paradigm for the purpose of releasing private sketches of the data. We construct differentially private sketches for the problems of least squares regression, as well as least absolute deviations regression. We show that the privacy constraints lead to sketched versions of regularized regression. We compute the bounds on the regularization parameter required for guaranteeing privacy. The availability of these private sketches facilitates the application of commonly available solvers for regression, without the risk of privacy leakage.

cs.LG↗

arXiv2025

Local Search-based Individually Fair Clustering with Outliers

In this paper, we present a local search-based algorithm for individually fair clustering in the presence of outliers. We consider the individual fairness definition proposed in Jung et al., which requires that each of the $n$ points in the dataset must have one of the $k$ centers within its $n/k$ nearest neighbors. However, if the dataset is known to contain outliers, the set of fair centers obtained under this definition might be suboptimal for non-outlier points. In order to address this issue, we propose a method that discards a set of points marked as outliers and computes the set of fair centers for the remaining non-outlier points. Our method utilizes a randomized variant of local search, which makes it scalable to large datasets. We also provide an approximation guarantee of our method as well as a bound on the number of outliers discarded. Additionally, we demonstrate our claims experimentally on a set of real-world datasets.

cs.DS↗

arXiv2025

Signatures of Einstein-Maxwell dilaton-axion gravity from the observed quasi-periodic oscillations in black holes

String-inspired models are often believed to provide an interesting framework for quantum gravity and force unification with promising prospects to resolve issues like dark matter and dark energy which cannot be satisfactorily incorporated within the framework of general relativity (GR). The goal of the present work is to investigate the role of the Einstein-Maxwell dilaton-axion (EMDA) gravity arising in the low energy effective action of the heterotic string theory in explaining astrophysical observations, in particular, the high-frequency quasi-periodic oscillations (HFQPOs) observed in the power spectrum of black holes. EMDA gravity has interesting cosmological implications and hence it is worthwhile to explore the footprints of such a theory in available astrophysical observations. This requires one to study the stationary, axi-symmetric black hole solution in EMDA gravity, which corresponds to the Kerr-Sen spacetime. Such black holes are endowed with a dilatonic charge while the rotation is sourced from the axionic field. We investigate the orbital and epicyclic frequencies of matter rotating in the Kerr-Sen spacetime and consider eleven well-studied QPO models in this work. We compare the model dependent QPO frequencies with the available observations of five BH sources, namely, XTE J1550-564, GRS 1915+105, H 143+322, GRO J1655-40 and Sgr A*. Our analysis provides constrains on the spins of the aforesaid black holes which when compared with previous estimates enables us to understand the observationally favored QPO models for each of these sources. Further, from the current data the EMDA scenario cannot be ruled out in favor of general relativity. We comment on the implications and limitations of our finding and how the present constrains compare with the existing literature.

gr-qc↗

arXiv2024

Linear Programming based Approximation to Individually Fair k-Clustering with Outliers

Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair $k$-means clustering algorithm for datasets that contain outliers. That is, given $n$ points and $k$ centers, we want that for each point which is not an outlier, there must be a center within the $\frac{n}{k}$ nearest neighbours of the given point. While a few of the recent works have looked into individually fair clustering, this is the first work that explores this problem in the presence of outliers for $k$-means clustering. For this purpose, we define and solve a linear program (LP) that helps us identify the outliers. We exclude these outliers from the dataset and apply a rounding algorithm that computes the $k$ centers, such that the fairness constraint of the remaining points is satisfied. We also provide theoretical guarantees that our method leads to a guaranteed approximation of the fair radius as well as the clustering cost. We also demonstrate our techniques empirically on real-world datasets.

cs.LG↗

arXiv2023

Simple Weak Coresets for Non-Decomposable Classification Measures

While coresets have been growing in terms of their application, barring few exceptions, they have mostly been limited to unsupervised settings. We consider supervised classification problems, and non-decomposable evaluation measures in such settings. We show that stratified uniform sampling based coresets have excellent empirical performance that are backed by theoretical guarantees too. We focus on the F1 score and Matthews Correlation Coefficient, two widely used non-decomposable objective functions that are nontrivial to optimize for and show that uniform coresets attain a lower bound for coreset size, and have good empirical performance, comparable with ``smarter'' coreset construction strategies.

cs.LG↗

arXiv2023

A Novel Pipeline for Improving Optical Character Recognition through Post-processing Using Natural Language Processing

Optical Character Recognition (OCR) technology finds applications in digitizing books and unstructured documents, along with applications in other domains such as mobility statistics, law enforcement, traffic, security systems, etc. The state-of-the-art methods work well with the OCR with printed text on license plates, shop names, etc. However, applications such as printed textbooks and handwritten texts have limited accuracy with existing techniques. The reason may be attributed to similar-looking characters and variations in handwritten characters. Since these issues are challenging to address with OCR technologies exclusively, we propose a post-processing approach using Natural Language Processing (NLP) tools. This work presents an end-to-end pipeline that first performs OCR on the handwritten or printed text and then improves its accuracy using NLP.

cs.CV↗

arXiv2021

Random projections in gravitational-wave searches from compact binaries II: efficient reconstruction of the detection statistic

Low-latency gravitational wave search pipelines such as GstLAL take advantage of low-rank factorization of the template matrix via singular value decomposition (SVD). With unprecedented improvements in detector bandwidth and sensitivity in advanced-LIGO and Virgo detectors, one expects several orders of magnitude increase in the size of template banks. This poses a formidable computational challenge in factorizing huge template matrices. Previously, [in Kulkarni et al. [6]], we introduced the idea of random projection (RP)-based matrix factorization as a computationally viable alternative to SVD, applicable for large template banks. This follow-up paper demonstrates the application of a block-wise randomized matrix factorization (RMF) algorithm for computing low-rank factorizations at a preset average fractional loss of SNR. This new scheme is shown to be more efficient in the context of the LLOID framework of the GstLAL search pipeline. Further, it is well-known that for huge template banks, the total computational cost of the search is dominated by reconstructing the detection statistic compared to that of filtering the data. However, optimizing the reconstruction cost has not been addressed satisfactorily so far in the available literature. We show that it is possible to approximately reconstruct the time-series of the matched-filter detection statistic at a fraction of the total cost using the matching pursuit algorithm. Combining the two algorithms presented in this paper can handle online searches involving large template banks more efficiently. We have analyzed the total computational cost in detail and offer various tips for optimally applying the RMF scheme in different parts of the parameter space. The algorithms presented in this paper are designed in a suitable manner that can be efficiently implemented over a distributed computing architecture.

gr-qc↗

arXiv2021

Statistical Measures For Defining Curriculum Scoring Function

Curriculum learning is a training strategy that sorts the training examples by some measure of their difficulty and gradually exposes them to the learner to improve the network performance. Motivated by our insights from implicit curriculum ordering, we first introduce a simple curriculum learning strategy that uses statistical measures such as standard deviation and entropy values to score the difficulty of data points for real image classification tasks. We empirically show its improvements in performance with convolutional and fully-connected neural networks on multiple real image datasets. We also propose and study the performance of a dynamic curriculum learning algorithm. Our dynamic curriculum algorithm tries to reduce the distance between the network weight and an optimal weight at any training step by greedily sampling examples with gradients that are directed towards the optimal weight. Further, we use our algorithms to discuss why curriculum learning is helpful.

cs.LG↗

arXiv2020

Online Coresets for Clustering with Bregman Divergences

We present algorithms that create coresets in an online setting for clustering problems according to a wide subset of Bregman divergences. Notably, our coresets have a small additive error, similar in magnitude to the lightweight coresets Bachem et. al. 2018, and take update time $O(d)$ for every incoming point where $d$ is dimension of the point. Our first algorithm gives online coresets of size $\tilde{O}(\mbox{poly}(k,d,ε,μ))$ for $k$-clusterings according to any $μ$-similar Bregman divergence. We further extend this algorithm to show existence of a non-parametric coresets, where the coreset size is independent of $k$, the number of clusters, for the same subclass of Bregman divergences. Our non-parametric coresets are larger by a factor of $O(\log n)$ ($n$ is number of points) and have similar (small) additive guarantee. At the same time our coresets also function as lightweight coresets for non-parametric versions of the Bregman clustering like DP-Means. While these coresets provide additive error guarantees, they are also significantly smaller (scaling with $O(\log n)$ as opposed to $O(d^d)$ for points in $R^d$) than the (relative-error) coresets obtained in Bachem et. al. 2015 for DP-Means. While our non-parametric coresets are existential, we give an algorithmic version under certain assumptions.

cs.DS↗

arXiv2020

On Additive Approximate Submodularity

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function evaluation might not be exact. In this paper we study how close such approximately submodular functions are to truly submodular functions. We show that an approximately submodular function defined on a ground set of $n$ elements is $O(n^2)$ pointwise-close to a submodular function. This result also provides an algorithmic tool that can be used to adapt existing submodular optimization algorithms to approximately submodular functions. To complement, we show an $Ω(\sqrt{n})$ lower bound on the distance to submodularity. These results stand in contrast to the case of approximate modularity, where the distance to modularity is a constant, and approximate convexity, where the distance to convexity is logarithmic.

cs.DS↗

arXiv2020

Efficient Hierarchical Clustering for Classification and Anomaly Detection

We address the problem of large scale real-time classification of content posted on social networks, along with the need to rapidly identify novel spam types. Obtaining manual labels for user-generated content using editorial labeling and taxonomy development lags compared to the rate at which new content type needs to be classified. We propose a class of hierarchical clustering algorithms that can be used both for efficient and scalable real-time multiclass classification as well as in detecting new anomalies in user-generated content. Our methods have low query time, linear space usage, and come with theoretical guarantees with respect to a specific hierarchical clustering cost function (Dasgupta, 2016). We compare our solutions against a range of classification techniques and demonstrate excellent empirical performance.

cs.DS↗

arXiv2020

Scalable Estimation of Epidemic Thresholds via Node Sampling

Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by the ongoing Covid-19 pandemic. It is therefore of great practical relevance to investigate the network trans-mission of contagious diseases from the perspective of statistical inference. An important and widely studied boundary condition for contagion processes over networks is the so-called epidemic threshold. The epidemic threshold plays a key role in determining whether a pathogen introduced into a social contact network will cause an epidemic or die out. In this paper, we investigate epidemic thresholds from the perspective of statistical network inference. We identify two major challenges that are caused by high computational and sampling complexity of the epidemic threshold. We develop two statistically accurate and computationally efficient approximation techniques to address these issues under the Chung-Lu modeling framework. The second approximation, which is based on random walk sampling, further enjoys the advantage of requiring data on a vanishingly small fraction of nodes. We establish theoretical guarantees for both methods and demonstrate their empirical superiority.

cs.SI↗