arXiv subjects

Aditya Singh

Publications and source records attributed to Aditya Singh.

At least 37 records · Page 2Linked to original sources

arXiv2026

A Note on Chaos in Hayward Black Holes with String Fluids

In this work, we first examine the onset of thermodynamic chaos in Hayward AdS black holes with string fluids, emphasizing the effects of temporal and spatially periodic perturbations. We apply Melnikov's approach to examine the perturbed Hamiltonian dynamics and detect the onset of chaotic behavior. In the case of temporal perturbations induced by thermal quenches, chaos occurs for perturbation amplitude $γ$ exceeding a critical threshold, determined by charge $q$ and the string fluid parameter. From the equation of state of the black hole, a general condition is established indicating that under temporal perturbations, the existence of charge is an essential prerequisite for chaos. However, regardless of the presence of charge, spatial perturbations result in chaotic behavior. Further next, we compute the Lyapunov exponent associated with the thermodynamic system to further quantify chaotic behavior beyond the threshold condition. We demonstrate that the string fluid density and the Hayward regularization parameter have a considerable effect on the amplitude of the Lyapunov exponent, showing the control of thermal instability by regular geometry corrections and matter sources. These results highlight the rich nonlinear dynamics arising from the interplay of geometric regularization, matter content, and phase-space instability.

gr-qc↗

arXiv2026

Unified Hydrodynamic Analogue of Aharonov-Bohm and Lense-Thirring Effects

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.

physics.flu-dyn↗

arXiv2026

T2I-BiasBench: A Multi-Metric Framework for Auditing Demographic and Cultural Bias in Text-to-Image Models

Text-to-image (T2I) generative models achieve impressive visual fidelity but inherit and amplify demographic imbalances and cultural biases embedded in training data. We introduce T2I-BiasBench, a unified evaluation framework of thirteen complementary metrics that jointly captures demographic bias, element omission, and cultural collapse in diffusion models - the first framework to address all three dimensions simultaneously. We evaluate three open-source models - Stable Diffusion v1.5, BK-SDM Base, and Koala Lightning - against Gemini 2.5 Flash (RLHF-aligned) as a reference baseline. The benchmark comprises 1,574 generated images across five structured prompt categories. T2I-BiasBench integrates six established metrics with seven additional measures: four newly proposed (Composite Bias Score, Grounded Missing Rate, Implicit Element Missing Rate, Cultural Accuracy Ratio) and three adapted (Hallucination Score, Vendi Score, CLIP Proxy Score). Three key findings emerge: (1) Stable Diffusion v1.5 and BK-SDM exhibit bias amplification (>1.0) in beauty-related prompts; (2) contextual constraints such as surgical PPE substantially attenuate professional-role gender bias (Doctor CBS = 0.06 for SD v1.5); and (3) all models, including RLHF-aligned Gemini, collapse to a narrow set of cultural representations (CAS: 0.54-1.00), confirming that alignment techniques do not resolve cultural coverage gaps. T2I-BiasBench is publicly released to support standardized, fine-grained bias evaluation of generative models. The project page is available at: https://gyanendrachaubey.github.io/T2I-BiasBench/

cs.CV↗

arXiv2026

V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functions

Ensuring safety in autonomous systems requires controllers that aim to satisfy state-wise constraints without relying on online interaction.While existing Safe Offline RL methods typically enforce soft expected-cost constraints, they struggle to ensure strict state-wise safety. Conversely, Control Barrier Functions (CBFs) offer a principled mechanism to enforce forward invariance, but often rely on expert-designed barrier functions or knowledge of the system dynamics. We introduce Value-Guided Offline Control Barrier Functions (V-OCBF), a framework that learns a neural CBF entirely from offline demonstrations. Unlike prior approaches, V-OCBF does not assume access to the dynamics model; instead, it derives a recursive finite-difference barrier update, enabling model-free learning of a barrier that propagates safety information over time. Moreover, V-OCBF incorporates an expectile-based objective that avoids querying the barrier on out-of-distribution actions and restricts updates to the dataset-supported action set. The learned barrier is then used with a Quadratic Program (QP) formulation to synthesize real-time safe control. Across multiple case studies, V-OCBF yields substantially fewer safety violations than baseline methods while maintaining strong task performance, highlighting its scalability for offline synthesis of safety-critical controllers without online interaction or hand-engineered barriers.

cs.AI↗

arXiv2026

$RD_α$-Spectra of Joined Union Graphs with Applications to Power Graphs of Finite Groups

The \emph{generalized reciprocal distance matrix} of a graph $\mathscr{G}$, denoted by $RD_α(\mathscr{G})$, is defined as $RD_α(\mathscr{G})=α\,RT_r(\mathscr{G})+(1-α)\,RD(\mathscr{G}), \, α\in[0,1],$ where $RT_r(\mathscr{G})$ represents the diagonal matrix of reciprocal vertex transmissions, and $RD(\mathscr{G})$ is the Harary (reciprocal distance) matrix of $\mathscr{G}$. In this paper, we investigate the $RD_α$-spectrum of graphs obtained through the joined union operation. We derive explicit formulas for the characteristic polynomial of $RD_α(\mathscr{G})$ when $\mathscr{G}$ is formed as a joined union of regular graphs. These results provide closed-form expressions for the corresponding spectra of several important graph classes. Moreover, we show that the power graphs of the dihedral group $D_{2n}$ and the generalized quaternion group $Q_{4n}$ admit representations as joined union graphs. Using this structural characterization, we determine the $RD_α$-spectra of power graphs arising from various classes of finite groups, including cyclic groups $\mathbb{Z}_n$, dihedral groups $D_{2n}$, generalized quaternion groups $Q_{4n}$, elementary abelian $p$-groups, and certain non-abelian groups of order $pq$.

math.CO↗

arXiv2026

Highly Autonomous Cyber-Capable Agents: Anticipating Capabilities, Tactics, and Strategic Implications

This report introduces the concept of "Highly Autonomous Cyber-Capable Agents" (HACCAs), AI systems capable of autonomously conducting multi-stage cyber campaigns at a level comparable to today's top criminal hacking groups or state-affiliated threat actors, and analyzes the security implications of their emergence. The report: (1) Defines what HACCAs are and forecasts when they might arrive, establishing a clear framework for an autonomous cyber agent that can operate across the full attack lifecycle without meaningful human direction; (2) Identifies five core operational tactics, detailing how HACCAs could sustain themselves in the wild, from autonomous infrastructure setup and credential harvesting to detection evasion and adaptive shutdown avoidance; (3) Analyzes the strategic implications, including how HACCAs could intensify interstate cyber competition, lower the barrier to entry for sophisticated operations, and proliferate advanced offensive capabilities to criminal groups and less-resourced state actors; (4) Flags two tail risks that deserve serious attention: the potential for autonomous cyber operations to trigger inadvertent cyber-nuclear escalation, and the possibility of sustained loss of control over rogue HACCA deployments; (5) Proposes seven policy recommendations across three goals: understanding the emerging threat, defending against HACCAs, and ensuring their responsible development and deployment.

cs.CY↗

arXiv2026

Generalized Momenta-Based Koopman Formalism for Robust Control of Euler-Lagrangian Systems

This paper presents a novel Koopman operator formulation for Euler Lagrangian dynamics that employs an implicit generalized momentum-based state space representation, which decouples a known linear actuation channel from state dependent dynamics and makes the system more amenable to linear Koopman modeling. By leveraging this structural separation, the proposed formulation only requires to learn the unactuated dynamics rather than the complete actuation dependent system, thereby significantly reducing the number of learnable parameters, improving data efficiency, and lowering overall model complexity. In contrast, conventional explicit formulations inherently couple inputs with the state dependent terms in a nonlinear manner, making them more suitable for bilinear Koopman models, which are more computationally expensive to train and deploy. Notably, the proposed scheme enables the formulation of linear models that achieve superior prediction performance compared to conventional bilinear models while remaining substantially more efficient. To realize this framework, we present two neural network architectures that construct Koopman embeddings from actuated or unactuated data, enabling flexible and efficient modeling across different tasks. Robustness is ensured through the integration of a linear Generalized Extended State Observer (GESO), which explicitly estimates disturbances and compensates for them in real time. The combined momentum-based Koopman and GESO framework is validated through comprehensive trajectory tracking simulations and experiments on robotic manipulators, demonstrating superior accuracy, robustness, and learning efficiency relative to state of the art alternatives.

cs.RO↗

arXiv2026

Deep Robust Koopman Learning from Noisy Data

Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However, real-world data is often noisy, making it difficult to obtain an accurate and unbiased approximation of the Koopman operator. The Koopman operator generated from noisy datasets is typically corrupted by noise-induced bias that severely degrades prediction and downstream tracking performance. In order to address this drawback, this paper proposes a novel autoencoder-based neural architecture to jointly learn the appropriate lifting functions and the reduced-bias Koopman operator from noisy data. The architecture initially learns the Koopman basis functions that are consistent for both the forward and backward temporal dynamics of the system. Subsequently, by utilizing the learned forward and backward temporal dynamics, the Koopman operator is synthesized with a reduced bias making the method more robust to noise compared to existing techniques. Theoretical analysis is used to demonstrate significant bias reduction in the presence of training noise. Dynamics prediction and tracking control simulations are conducted for multiple serial manipulator arms, including performance comparisons with leading alternative designs, to demonstrate its robustness under various noise levels. Experimental studies with the Franka FR3 7-DoF manipulator arm are further used to demonstrate the effectiveness of the proposed approach in a practical setting.

cs.RO↗

arXiv2025

Robust Superconductivity and High Upper Critical Fields in Epitaxial cubic W2N Thin Films

Transition Metal Nitrides are a versatile class of materials, combining chemical robustness, high hardness, and superconducting behaviour with critical temperatures between 2 to 10 K. While several binary TMNs have been explored, superconductivity in stoichiometric W2N has remained largely unexplored. Here, we report on superconducting thin films of stoichiometric W2N, demonstrating a distinctly high upper critical field of 8.5 T, uncommon among binary TMNs. This robust superconducting response under high magnetic fields highlights the technological relevance of W2N for integrated quantum and cryogenic electronic platforms. Overall, these results position stoichiometric W2N as a promising addition to the TMN superconducting landscape, opening new avenues for functional materials design based on chemically stable and mechanically resilient nitrides.

cond-mat.supr-con↗

arXiv2025

Automatically Finding Rule-Based Neurons in OthelloGPT

OthelloGPT, a transformer trained to predict valid moves in Othello, provides an ideal testbed for interpretability research. The model is complex enough to exhibit rich computational patterns, yet grounded in rule-based game logic that enables meaningful reverse-engineering. We present an automated approach based on decision trees to identify and interpret MLP neurons that encode rule-based game logic. Our method trains regression decision trees to map board states to neuron activations, then extracts decision paths where neurons are highly active to convert them into human-readable logical forms. These descriptions reveal highly interpretable patterns; for instance, neurons that specifically detect when diagonal moves become legal. Our findings suggest that roughly half of the neurons in layer 5 can be accurately described by compact, rule-based decision trees ($R^2 > 0.7$ for 913 of 2,048 neurons), while the remainder likely participate in more distributed or non-rule-based computations. We verify the causal relevance of patterns identified by our decision trees through targeted interventions. For a specific square, for specific game patterns, we ablate neurons corresponding to those patterns and find an approximately 5-10 fold stronger degradation in the model's ability to predict legal moves along those patterns compared to control patterns. To facilitate future work, we provide a Python tool that maps rule-based game behaviors to their implementing neurons, serving as a resource for researchers to test whether their interpretability methods recover meaningful computational structures.

cs.LG↗

arXiv2025

Noncommutative Geometry and the Thermodynamic Fate of Black Holes

We study the thermodynamics of black holes in the framework of non-commutative geometry, where spacetime fuzziness is modelled by smeared Lorentzian distributions. Corrected black hole solutions with this quantum fuzziness are obtained, and their thermodynamic analysis is performed. We show that the conventional first law of black hole thermodynamics is violated since the entropy deviates from the Bekenstein-Hawking form. Introducing a correction to the mass restores consistency, yielding a modified first law compatible with Bekenstein-Hawking entropy. Next, we investigate the effects of spacetime non-commutativity on the thermodynamic universality of these black holes. We demonstrate that non-commutativity modifies the standard universality relations of black holes and can induce thermodynamic stability by altering the underlying microscopic interactions. Our results suggest that quantum features of spacetime can have significant macroscopic consequences for black hole thermodynamics.

hep-th↗

arXiv2025

Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions

Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time, they can become overly conservative when the nominal policy lacks safety awareness. Conversely, solving State-Constrained Optimal Control Problems (SC-OCPs) via dynamic programming offers formal guarantees but is intractable in high-dimensional systems. In this work, we propose a novel two-stage framework that combines gradient-based Model Predictive Control (MPC) with CBF-based safety filtering for co-optimizing safety and performance. In the first stage, we relax safety constraints as penalties in the cost function, enabling fast optimization via gradient-based methods. This step improves scalability and avoids feasibility issues associated with hard constraints. In the second stage, we modify the resulting controller using a CBF-based Quadratic Program (CBF-QP), which enforces hard safety constraints with minimal deviation from the reference. Our approach yields controllers that are both performant and provably safe. We validate the proposed framework on two case studies, showcasing its ability to synthesize scalable, safe, and high-performance controllers for complex, high-dimensional autonomous systems.

eess.SY↗

arXiv2025

Black Holes in Lorentz-Violating Gravity: Thermodynamics, Geometry, and Particle Dynamics

We investigate the thermodynamics, topology, and geometry of black holes in Lorentz-violating gravity. Modifications in the theory by perturbative parameter lead to coupled changes in horizon structure and thermodynamic behaviour, allowing us to derive generalized universal relations and explore implications for the Weak Gravity Conjecture. The thermodynamic topology reveals distinct topological charges, with photon spheres identified as robust topological defects. Our analysis shows that the Ruppeiner curvature remains universally negative across thermodynamic ensembles, indicating dominant attractive interactions among microstructures. This ensemble-independent behaviour highlights a fundamental thermodynamic universality in Lorentz-violating settings. Together, these results provide a consistent and rich framework for understanding black hole microphysics and gravitational consistency in modified theories. We further study the motion of timelike test particles in these black hole spacetimes by analyzing the effective potential shaped by the Lorentz-violating couplings. The resulting dynamics reveal the existence of bound orbits and stable circular trajectories, with the location of the innermost stable circular orbit and turning points significantly influenced by the parameters $\ell_{1,2}$, and the cosmological constant. Numerical simulations of trajectories in the $x-y,\,x-z$, and 3D planes show precessing, bounded, and plunging orbits, depending on the particle's specific energy and angular momentum. These results highlight how Lorentz-violating effects alter the structure of geodesic motion and provide potential observational signatures in the dynamics of massive particles near black holes.

gr-qc↗

arXiv2025

Thermodynamic Curvature and Topological Insights of Hayward Black Holes with String Fluids

In this paper, we study the influence of string fluids on the extended thermodynamic structure and microscopic interactions of Hayward black holes by employing thermodynamic geometry as an empirical tool. Using the novel equation of state obtained for regular black holes surrounded by string fluids, we analyze the extended phase space with enthalpy as the central thermodynamic potential. By examining the behavior of the normalized Ruppeiner curvature scalar $R_N$ in the temperature-volume $(T,V)$ plane, we analyzed the influence of the string fluid parameters on the microstructure of the black hole. Our analysis reveals that the presence of string fluids significantly modifies the dominant microscopic interactions, transitioning from attractive to repulsive regimes depending on the charge and volume of the black hole. We see that the thermodynamic curvature effectively detects critical points and phase transitions, reflecting the nature of repulsive or attractive interactions among black hole microstructures. We further investigate thermodynamic topology to provide a novel classification scheme for stability and phase behavior, delineating local stable and unstable regions in parameter space. We investigate the thermodynamic topology of Hayward-AdS black holes surrounded by string fluids, showing that the number and type of topological charges depend on the parameters $ε$ and $b$, revealing phase transitions and stability characteristics encoded in the global topological charge $W$. This integrated study of the thermodynamic geometry and topology structure enhances the understanding of Hayward black holes surrounded by string fluids, showing overall thermodynamic stability and configuration with significant implications for holographic duality and potential astrophysical observations.

gr-qc↗

arXiv2025

Lattice Mismatch Driven In Plane Strain Engineering for Enhanced Upper Critical Fields in Mo2N Superconducting Thin Films

Transition metal nitrides are a fascinating class of hard coating material that provide an excellent platform for investigating superconductivity and fundamental electron phonon interactions. In this work the structural morphological and superconducting properties have been studied for Mo2N thin films deposited via direct current magnetron sputtering on cplane Al2O3 and MgO substrates to elucidate the effect of internal strain on superconducting properties. High resolution X Ray diffraction and time of flight elastic recoil detection analysis confirms the growth of single phase Mo2N thin films exhibiting epitaxial growth with twin domain structure. Low temperature electrical transport measurements reveal superconducting transitions at 5.2 K and 5.6 K with corresponding upper critical fields of 5 T and 7 T for the films deposited on Al2O3 and MgO, respectively. These results indicate strong type II superconductivity and the observed differences in superconducting properties are attributed to substrate induced strain which leads to higher e ph coupling for the film on MgO substrate. These findings highlight the tunability of superconducting properties in Mo2N films through strategic substrate selection.

cond-mat.supr-con↗

arXiv2025

A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems

As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult. Learning-based methods, such as Constrained Reinforcement Learning (CRL), achieve strong performance but lack formal safety guarantees due to safety being enforced as soft constraints, limiting their use in safety-critical settings. Conversely, formal methods such as Hamilton-Jacobi (HJ) Reachability Analysis and Control Barrier Functions (CBFs) provide rigorous safety assurances but often neglect performance, resulting in overly conservative controllers. To bridge this gap, we formulate the co-optimization of safety and performance as a state-constrained optimal control problem, where performance objectives are encoded via a cost function and safety requirements are imposed as state constraints. We demonstrate that the resultant value function satisfies a Hamilton-Jacobi-Bellman (HJB) equation, which we approximate efficiently using a novel physics-informed machine learning framework. In addition, we introduce a conformal prediction-based verification strategy to quantify the learning errors, recovering a high-confidence safety value function, along with a probabilistic error bound on performance degradation. Through several case studies, we demonstrate the efficacy of the proposed framework in enabling scalable learning of safe and performant controllers for complex, high-dimensional autonomous systems.

cs.RO↗

arXiv2025

Concept Incongruence: An Exploration of Time and Death in Role Playing

Consider this prompt "Draw a unicorn with two horns". Should large language models (LLMs) recognize that a unicorn has only one horn by definition and ask users for clarifications, or proceed to generate something anyway? We introduce concept incongruence to capture such phenomena where concept boundaries clash with each other, either in user prompts or in model representations, often leading to under-specified or mis-specified behaviors. In this work, we take the first step towards defining and analyzing model behavior under concept incongruence. Focusing on temporal boundaries in the Role-Play setting, we propose three behavioral metrics--abstention rate, conditional accuracy, and answer rate--to quantify model behavior under incongruence due to the role's death. We show that models fail to abstain after death and suffer from an accuracy drop compared to the Non-Role-Play setting. Through probing experiments, we identify two main causes: (i) unreliable encoding of the "death" state across different years, leading to unsatisfactory abstention behavior, and (ii) role playing causes shifts in the model's temporal representations, resulting in accuracy drops. We leverage these insights to improve consistency in the model's abstention and answer behaviors. Our findings suggest that concept incongruence leads to unexpected model behaviors and point to future directions on improving model behavior under concept incongruence.

cs.CL↗

arXiv2025

CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions

Control Barrier Functions (CBFs) are a practical approach for designing safety-critical controllers, but constructing them for arbitrary nonlinear dynamical systems remains a challenge. Recent efforts have explored learning-based methods, such as neural CBFs (NCBFs), to address this issue. However, ensuring the validity of NCBFs is difficult due to potential learning errors. In this letter, we propose a novel framework that leverages split-conformal prediction to generate formally verified neural CBFs with probabilistic guarantees based on a user-defined error rate, referred to as CP-NCBF. Unlike existing methods that impose Lipschitz constraints on neural CBF-leading to scalability limitations and overly conservative safe sets--our approach is sample-efficient, scalable, and results in less restrictive safety regions. We validate our framework through case studies on obstacle avoidance in autonomous driving and geo-fencing of aerial vehicles, demonstrating its ability to generate larger and less conservative safe sets compared to conventional techniques.

eess.SY↗