arXiv subjects

Shubham Gupta

Publications and source records attributed to Shubham Gupta.

At least 19 recordsLinked to original sources

arXiv2026

Critical discrete Hardy inequalities in $L^p$

We establish ground-state representations and critical Hardy inequalities in the discrete $L^p$ setting. In particular, we construct critical Hardy weights for the discrete Dirichlet Laplacian on the half-line and the discrete fractional Laplacian on the integers for all $p\in(1,\infty)$. Our approach uses Sobolev--Bregman forms, for which the ground-state representations are exact identities and the corresponding Hardy weights are expressed through linear operators acting on powers of positive superharmonic functions.

math.CA↗

arXiv2026

On $\mathcal{B}^4$-almost periodicity for a class of arithmetical functions

In this paper, we establish the $\mathcal{B}^4$-almost periodicity in the sense of Besicovitch for a suitably normalized error term associated with a broad class of arithmetical functions introduced by Chandrasekharan and Narasimhan. This result significantly strengthens $\mathcal{B}^2$-almost periodicity previously investigated in the literature for related error terms. By deriving truncated Vorono\"{i}-type formulas, we demonstrate that the normalized error term lies in the Besicovitch space $B^4$. As a consequence, we deduce that the error term admits a limit probability distribution and establish an explicit formula for its mean fourth power moment.

math.NT↗

arXiv2026

Sharp asymptotics for higher-order Hardy constants on lattices

We study the optimal constants in higher-order Hardy inequalities on the lattice $\mathbb{Z}^d$. For each fixed $\ell \in \mathbb{N}$, we prove that the optimal constant $\mathcal{C}_\text{opt}^\ell(d)$ in $$ \sum_{n \in \mathbb{Z}^d} |\Delta^{\ell/2}u(n)|^2 \geq \mathcal{C}_\text{opt}^\ell(d)\sum_{n \in \mathbb{Z}^d} \frac{|u(n)|^2}{|n|^{2\ell}}. $$ satisfies $$ \lim_{d\rightarrow\infty}\frac{\mathcal{C}_\text{opt}^\ell(d)}{d^\ell} =2^\ell. $$ The proof is based on a Fourier reduction to a family of singular Hardy inequalities on the flat torus, involving the weight \[ \omega(x)^{-2\ell}, \qquad \omega(x)^2=\sum_{j=1}^d\sin^2\left(\frac{x_j}{2}\right), \] and zero average condition on admissible functions. We establish these torus inequalities by combining a ground state representation formula with a weighted integrated Bochner identity in an iterative scheme. The method yields explicit constants, defined recursively in the order $\ell$, and requires only the classical unweighted Poincar\'e inequality on the torus. The appearance of the limiting constant $2^\ell$ is particularly striking, as it suggests that, in the high dimensional regime, the optimizers are localized near the unit sphere $\{n\in\mathbb{Z}^d:|n|=1\}$ in $\mathbb{Z}^d$.

math.FA↗

arXiv2026

PiSAs: Benchmarking Contextual Integrity in Multi-User Agentic Systems

As LLM agents evolve from single-user assistants into shared organizational infrastructure, new privacy risks emerge: inappropriate information may not only be exposed through outputs for external recipients, but also internally across users through inter-agent messages, shared memory and agents. These data spillage risks are not captured by existing privacy benchmarks grounded in contextual integrity (CI) as they focus primarily on either single-user settings or interactions between independently owned agents. We introducePiSAs (Privacy in Shared Agentic systems), a benchmark for assessing unintentional leaks with dual CI annotations: whether an information is appropriate for the task, and which users may legitimately access it. This enables direct measurement of cross-user spillage across agentic system components and interfaces, such as outputs, inter-agent communication, and memory. PiSAsis system-agnostic and supports evaluation across different agent topologies and memory regimes. We find that, although system design improves CI compliance, results are bottlenecked by incorrect LLM judgment calls: even state-of-the-art models fail to reliably filter inappropriate content or restrict transmission to authorized users. Our findings underscore the need for privacy-preserving strategies, beyond those studied in this work.

cs.MA↗

arXiv2026

Enhancing Audio Captioning with Auxiliary AudioSet Semantics

Automatic Audio Captioning (AAC) seeks to generate natural language descriptions of complex acoustic scenes, bridging auditory perception and language understanding. However, word-selection indeterminacy and increasing reliance on large-scale sequence-to-sequence or LLM-based models limit practical deployment. We propose a resource-efficient AAC framework that explicitly grounds caption generation in auxiliary AudioSet semantics. Frame-level acoustic representations extracted using a ConvNeXt encoder are augmented with top-$K$ predicted AudioSet keywords, providing structured contextual cues for decoding. A compact six-layer BART-style decoder conditions on this joint acoustic-semantic representation, enabling caption generation without LLM-scale decoding. The proposed design balances semantic grounding and computational efficiency within a compact architecture. Evaluations on Clotho V2 and AudioCaps confirm competitive caption quality under practical deployment constraints.

eess.AS↗

arXiv2026

HeartBeatAI: An Interpretable and Robust Deep Learning Framework for Multi-Label ECG Arrhythmia Detection

While Deep Learning (DL) enhances automated electrocardiogram (ECG) analysis, clinical deployment is hindered by class imbalance and the generalization gap. This paper presents HeartBeatAI, a deep learning framework combining domain generalization, multi-scale feature aggregation, and clinical explainability for robust 12-lead ECG classification. Moving beyond image-based paradigms, HeartBeatAI integrates a Squeeze-and-Excitation (SE) ResNet to isolate diagnostic leads alongside a Multi-Layer Concentration Pipeline to capture macro-rhythm and micro-morphological anomalies. To mitigate domain shift, the framework employs MixStyle regularization and Label Smoothing. Rigorous benchmarking across four large-scale datasets using intra-source and Leave-One-Domain-Out (LODO) protocols demonstrates high performance (98% Macro F1-score) under intra-source conditions. However, LODO evaluations reveal significant degradation in detecting rare anomalies, highlighting a persistent challenge in cross-institutional deployment.

cs.AI↗

arXiv2026

Shared Representation Learning for Reference-Guided Targeted Sound Detection

Human listeners exhibit the remarkable ability to segregate a desired sound from complex acoustic scenes through selective auditory attention, motivating the study of Targeted Sound Detection (TSD). The task requires detecting and localizing a target sound in a mixture when a reference audio of that sound is provided. Prior approaches, rely on generating a sound-discriminative conditional embedding vector for the reference and pairing it with a mixture encoder, jointly optimized with a multi-task learning approach. In this work, we propose a unified encoder architecture that processes both the reference and mixture audio within a shared representation space, promoting stronger alignment while reducing architectural complexity. This design choice not only simplifies the overall framework but also enhances generalization to unseen classes. Following the multi-task training paradigm, our method achieves substantial improvements over prior approaches, surpassing existing methods and establishing a new state-of-the-art benchmark for targeted sound detection, with a segment-level F1 score of 83.15% and an overall accuracy of 95.17% on the URBAN-SED dataset.

eess.AS↗

arXiv2025

Joint Multimodal Contrastive Learning for Robust Spoken Term Detection and Keyword Spotting

Acoustic Word Embeddings (AWEs) improve the efficiency of speech retrieval tasks such as Spoken Term Detection (STD) and Keyword Spotting (KWS). However, existing approaches suffer from limitations, including unimodal supervision, disjoint optimization of audio-audio and audio-text alignment, and the need for task-specific models. To address these shortcomings, we propose a joint multimodal contrastive learning framework that unifies both acoustic and cross-modal supervision in a shared embedding space. Our approach simultaneously optimizes: (i) audio-text contrastive learning, inspired by the CLAP loss, to align audio and text representations and (ii) audio-audio contrastive learning, via Deep Word Discrimination (DWD) loss, to enhance intra-class compactness and inter-class separation. The proposed method outperforms existing AWE baselines on word discrimination task while flexibly supporting both STD and KWS. To our knowledge, this is the first comprehensive approach of its kind.

cs.SD↗

arXiv2025

Private Map-Secure Reduce: Infrastructure for Efficient AI Data Markets

The modern AI data economy centralizes power, limits innovation, and misallocates value by extracting data without control, privacy, or fair compensation. We introduce Private Map-Secure Reduce (PMSR), a network-native paradigm that transforms data economics from extractive to participatory through cryptographically enforced markets. Extending MapReduce to decentralized settings, PMSR enables computation to move to the data, ensuring verifiable privacy, efficient price discovery, and incentive alignment. Demonstrations include large-scale recommender audits, privacy-preserving LLM ensembling (87.5\% MMLU accuracy across six models), and distributed analytics over hundreds of nodes. PMSR establishes a scalable, equitable, and privacy-guaranteed foundation for the next generation of AI data markets.

cs.CR↗

arXiv2025

Data-driven learning of feedback maps for explicit robust predictive control: an approximation theoretic view

We establish an algorithm to learn feedback maps from data for a class of robust model predictive control (MPC) problems. The algorithm accounts for the approximation errors due to the learning directly at the synthesis stage, ensuring recursive feasibility by construction. The optimal control problem consists of a linear noisy dynamical system, a quadratic stage and quadratic terminal costs as the objective, and convex constraints on the state, control, and disturbance sequences; the control minimizes and the disturbance maximizes the objective. We proceed via two steps -- (a) Data generation: First, we reformulate the given minmax problem into a convex semi-infinite program and employ recently developed tools to solve it in an exact fashion on grid points of the state space to generate (state, action) data. (b) Learning approximate feedback maps: We employ a couple of approximation schemes that furnish tight approximations within preassigned uniform error bounds on the admissible state space to learn the unknown feedback policy. The stability of the closed-loop system under the approximate feedback policies is also guaranteed under a standard set of hypotheses. Two benchmark numerical examples are provided to illustrate the results.

math.OC↗

arXiv2025

Diophantine tuples and Integral Ideals of $\mathbb{Q}(\sqrt{d})$

Suppose $n$ is the fundamental discriminant associated with a quadratic extension of $\mathbb{Q}$. We show that for every Diophantine $m$-tuple $ \{t_1, t_2, \ldots, t_m\} $ with the property $ D(n) $, there exists integral ideals $ \mathfrak{t}_1, \mathfrak{t}_2, \ldots, \mathfrak{t}_m $ of $ \mathbb{Q}(\sqrt{n}) $ and $c\in \{1,2\}$ such that $ t_i= c\mathcal{N}(\mathfrak{t}_i) $ for $ i=1,2, \ldots, m $. Here, $ \mathcal{N}(\cdot) $ denotes the norm map from $\mathbb{Q}(\sqrt{n})$ to $\mathbb{Q}$. Moreover, we explicitly construct the above ideals for Diophantine pairs $\{a_1, a_2\}$ whenever $\gcd(a_1, a_2) = 1$.

math.NT↗

arXiv2025

LLM-based Contrastive Self-Supervised AMR Learning with Masked Graph Autoencoders for Fake News Detection

The proliferation of misinformation in the digital age has led to significant societal challenges. Existing approaches often struggle with capturing long-range dependencies, complex semantic relations, and the social dynamics influencing news dissemination. Furthermore, these methods require extensive labelled datasets, making their deployment resource-intensive. In this study, we propose a novel self-supervised misinformation detection framework that integrates both complex semantic relations using Abstract Meaning Representation (AMR) and news propagation dynamics. We introduce an LLM-based graph contrastive loss (LGCL) that utilizes negative anchor points generated by a Large Language Model (LLM) to enhance feature separability in a zero-shot manner. To incorporate social context, we employ a multi view graph masked autoencoder, which learns news propagation features from social context graph. By combining these semantic and propagation-based features, our approach effectively differentiates between fake and real news in a self-supervised manner. Extensive experiments demonstrate that our self-supervised framework achieves superior performance compared to other state-of-the-art methodologies, even with limited labelled datasets while improving generalizability.

cs.CL↗

arXiv2025

Audio Prototypical Network For Controllable Music Recommendation

Traditional recommendation systems represent user preferences in dense representations obtained through black-box encoder models. While these models often provide strong recommendation performance, they lack interpretability for users, leaving users unable to understand or control the system's modeling of their preferences. This limitation is especially challenging in music recommendation, where user preferences are highly personal and often evolve based on nuanced qualities like mood, genre, tempo, or instrumentation. In this paper, we propose an audio prototypical network for controllable music recommendation. This network expresses user preferences in terms of prototypes representative of semantically meaningful features pertaining to musical qualities. We show that the model obtains competitive recommendation performance compared to popular baseline models while also providing interpretable and controllable user profiles.

cs.IR↗

arXiv2025

LiSTEN: Learning Soft Token Embeddings for Neural Audio LLMs

Foundation models based on large language models (LLMs) have shown great success in handling various tasks and modalities. However, adapting these models for general-purpose audio-language tasks is challenging due to differences in acoustic environments and task variations. In this work, we introduce LiSTEN Learning Soft Token Embeddings for Neural Audio LLMs), a framework for adapting LLMs to speech and audio tasks. LiSTEN uses a dynamic prompt selection strategy with learnable key-value pairs, allowing the model to balance general and task-specific knowledge while avoiding overfitting in a multitask setting. Our approach reduces dependence on large-scale ASR or captioning datasets, achieves competitive performance with fewer trainable parameters, and simplifies training by using a single-stage process. Additionally, LiSTEN enhances interpretability by analyzing the diversity and overlap of selected prompts across different tasks.

cs.AI↗

arXiv2025

Infinitely Many Counter Examples of a Conjecture of Franu\v{s}i\'c and Jadrijevi\'c

Let $d$ be a square-free integer such that $d \equiv 15 \pmod{60}$ and the Pell's equation $x^2 - dy^2 = -6$ is solvable in rational integers $x$ and $y$. In this paper, we prove that there exist infinitely many Diophantine quadruples in $\mathbb{Z}[\sqrt{d}]$ with the property $D(n)$ for certain $n$'s. As an application of it, we `unconditionally' prove the existence of infinitely many rings $\mathbb{Z}[\sqrt{d}]$ for which the conjecture of Franu\v{s}i\'c and Jadrijevi\'c (Conjecture 1.1) does `not' hold. This conjecture states a relationship between the existence of a Diophantine quadruple in $\mathcal{R}$ with the property $D(n)$ and the representability of $n$ as a difference of two squares in $\mathcal{R}$, where $\mathcal{R}$ is a commutative ring with unity.

math.NT↗

arXiv2025

Quality Concerns Caused by Quality Control -- deformation of silicon strip detector modules in thermal cycling tests

The ATLAS experiment at the Large Hadron Collider (LHC) is currently preparing to replace its present Inner Detector (ID) with the upgraded, all-silicon Inner Tracker (ITk) for its High-Luminosity upgrade (HL-LHC). The ITk will consist of a central pixel tracker and the outer strip tracker, consisting of about 19,000 strip detector modules. Each strip module is assembled from up to two sensors, and up to five flexes (depending on its geometry) in a series of gluing, wirebonding and quality control steps. During detector operation, modules will be cooled down to temperatures of about -35C (corresponding to the temperature of the support structures on which they will be mounted) after being initially assembled and stored at room temperature. In order to ensure compatibility with the detector's operating temperature range, modules are subjected to thermal cycling as part of their quality control process. Ten cycles between -35C and +40C are performed for each module, with full electrical characterisation tests at each high and low temperature point. As part of an investigation into the stress experienced by modules during cooling, it was observed that modules generally showed a change in module shape before and after thermal cycling. This paper presents a summary of the discovery and understanding of the observed changes, connecting them with excess module stress, as well as the resulting modifications to the module thermal cycling procedure.

hep-ex↗

arXiv2025

A Transfer Framework for Enhancing Temporal Graph Learning in Data-Scarce Settings

Dynamic interactions between entities are prevalent in domains like social platforms, financial systems, healthcare, and e-commerce. These interactions can be effectively represented as time-evolving graphs, where predicting future connections is a key task in applications such as recommendation systems. Temporal Graph Neural Networks (TGNNs) have achieved strong results for such predictive tasks but typically require extensive training data, which is often limited in real-world scenarios. One approach to mitigating data scarcity is leveraging pre-trained models from related datasets. However, direct knowledge transfer between TGNNs is challenging due to their reliance on node-specific memory structures, making them inherently difficult to adapt across datasets. To address this, we introduce a novel transfer approach that disentangles node representations from their associated features through a structured bipartite encoding mechanism. This decoupling enables more effective transfer of memory components and other learned inductive patterns from one dataset to another. Empirical evaluations on real-world benchmarks demonstrate that our method significantly enhances TGNN performance in low-data regimes, outperforming non-transfer baselines by up to 56\% and surpassing existing transfer strategies by 36\%

cs.LG↗

arXiv2025

Granite Vision: a lightweight, open-source multimodal model for enterprise Intelligence

We introduce Granite Vision, a lightweight large language model with vision capabilities, specifically designed to excel in enterprise use cases, particularly in visual document understanding. Our model is trained on a comprehensive instruction-following dataset, including document-related tasks, such as content extraction from tables, charts, diagrams, sketches, and infographics, as well as general image tasks. The architecture of Granite Vision is centered around visual modality alignment with a decoder-only, 2 billion parameter Granite large language model. Additionally, we introduce a dedicated safety classification approach in test-time that leverages a sparse set of attention vectors to identify potential harmful inputs. Despite its lightweight architecture, Granite Vision achieves strong results in standard benchmarks related to visual document understanding, as well as on the LiveXiv benchmark, which is designed to avoid test set contamination by using a constantly updated corpus of recently published Arxiv papers. We are releasing the model under the Apache-2 license, allowing for both research and commercial use, while offering complete visibility into the training data and other relevant details. See https://huggingface.co/ibm-granite/ for model weights.

cs.CV↗