arXiv subjects

Aditya Singh

Publications and source records attributed to Aditya Singh.

At least 19 recordsLinked to original sources

arXiv2026

Anharmonic Lattice Dynamics and Anisotropic Electron-Phonon Coupling in Quasi-1-Dimensional Charge Density Wave Ta2NiSe7

The microscopic origin of charge density wave formation in quasi one dimensional Ta2NiSe7 remains actively debated, particularly regarding the relative contributions of Fermi surface nesting, electron phonon coupling, and lattice instabilities. Here, we combine temperature and orientation dependent polarized Raman spectroscopy with first principles calculations to uncover the anisotropic electronic and lattice interactions governing the CDW state in Ta2NiSe7. Heat capacity and electrical transport measurements identify an incommensurate CDW transition at 61 K. Raman spectroscopy reveals pronounced in plane anisotropy, with e ph coupling strength along intrachain b axis exceeding five times that along interchain c axis, whereas lattice anharmonicity is enhanced by threefold along c axis. First principles calculations identify Ta2 Se octahedral vibrations and Ta Se electronic states near the Fermi level as dominant channels mediating the anisotropic e ph interaction. Exceptionally strong and directional e ph coupling along b axis establishes lattice driven electronic instability as the primary mechanism underlying CDW modulation and highlights the dominance of intrachain interactions in strongly coupled Ta2NiSe7. Despite this strong coupling, the CDW remains incommensurate, indicating that lattice anharmonicity provides an additional degree of freedom. Enhanced anharmonicity along c axis suggests that anisotropic phonon phonon interactions reshape the free energy landscape and contribute to stabilizing incommensurate phase. These findings reveal a cooperative interplay between anisotropic e ph coupling and lattice anharmonicity in governing CDW formation in low dimensional quantum materials.

cond-mat.mtrl-sci↗

arXiv2026

Characterisations of finite groups with exponent $q$ via their power graphs

The power graph $P(G)$ of a finite group $G$ is the graph with vertex set $G$ and edge set $E(P(G))=\{uv:\ u,v \in G,\ u \neq v,\ u \in \langle v \rangle \ \text{or}\ v \in \langle u \rangle\},$ where $\langle x\rangle$ denotes the cyclic subgroup generated by $x$. In this paper, we characterise all the finite groups with exponent $q$ whose power graphs are friendship graphs, firefly-type graphs, or torch graphs. We prove that the power graph of a finite group $G$ with exponent $q$ is a friendship graph if and only if $q=3$. In particular, in the abelian case, this is equivalent to $G\cong\mathbb{Z}_3^{n}$. We further show that, among all the symmetric and alternating groups, only $S_3$ and $A_4$ have firefly-type power graphs, whereas no finite group has a power graph isomorphic to a torch graph. Finally, we determine the generalised distance spectra $D_{\alpha}$-spectra of these graph classes.

math.CO↗

arXiv2026

Not All Attention Is Equal: A Quantitative Survey of the EEI Trade-off

Attention mechanisms have driven machine learning for a decade, from neural machine translation to language models that do general-purpose reasoning. This survey covers four connected threads: their formulation for sequence-to-sequence tasks, adaptation to computer vision, efficiency innovations that address the quadratic bottleneck, and advances in interpretability. We define three criteria: efficiency, expressiveness, and interpretability, and compare twenty-one methods using an EEI scoring framework. Scores come from a single rater with an assumed +/-1-point perturbation range. A deterministic Monte Carlo analysis with 200,000 samples shows that, under this perturbation model, rank changes of more than one position occur in 67-70% of samples on average. A rank-matched null model reproduces a similar stability profile, so the results support coarse tier-level comparisons rather than fine-grained rankings. The survey traces attention from Bahdanau-Luong alignment through the Transformer and into vision architectures. It reviews fixed and learned sparse attention, linear attention, IO-aware exact algorithms including FlashAttention, and state-space alternatives including Mamba. It also covers induction heads, superposition, and the attention-SSM duality. We further provide a structured narrative review, a benchmark synthesis with cross-study caveats, a five-problem research gap analysis, and a 2015-2026 evolution timeline. We conclude by framing attention research as an expansion of the efficiency-expressiveness-interpretability frontier and identifying future directions including unified efficiency benchmarks, learned routing for hybrid architectures, length generalization, and scalable mechanistic interpretability.

cs.LG↗

arXiv2026

Spectral Properties of Power Graphs of Metacyclic Groups

For a group $\Omega$, the associated power graph $P(\Omega)$ is defined as the graph whose vertices are the elements of $\Omega$, with two distinct vertices $u,v\in \Omega$ being adjacent if either $u=v^m$ or $v=u^n$ for some $m,n \in \mathbb{N}$. In this paper, we completely characterise the structure of the power graph associated with the class of metacyclic groups. Building on this structural description, we derive explicit expressions for the characteristic polynomials of the adjacency, Laplacian, and signless Laplacian matrices. Moreover, we obtain lower and upper bounds for the spectral radii of the adjacency and signless Laplacian matrices.

math.CO↗

arXiv2026

Joint Utilization of Geospatial and census proxies for Autoencoder-Assisted Downscaling (JUGAAD) of socioeconomic indicators in India

Monitoring poverty and food security indicators is imperative for addressing socioeconomic challenges in developing nations. A limitation is mismatches in scale between data sources: census data provide geographic coverage, while socioeconomic indicators are derived from infrequently conducted surveys at coarse resolutions, posing a methodological challenge. This study introduces a deep learning framework, JuGAAD, using Indian census and survey data from 2001 and 2011 as a case study. We employ a three-step process: census and geospatial data are averaged into intermediate village-cluster-scale tessellations to reduce noise and regularize administrative boundary changes; an autoencoder compresses high-dimensional National Sample Survey Office (NSSO) data into a low-dimensional latent representation; and a regression model maps upscaled census and geospatial data to this representation. This function is applied to fine-grained census data to generate high-resolution predictions, validated against ground-truth district-level NSSO indicators. Results confirm the methodology predicts socioeconomic indicators at fine scales with strong accuracy.

cs.LG↗

arXiv2026

Noncommutative black holes: Topological bulk-boundary correspondence and Binary Merger Bounds

We investigate the thermodynamic topology of charged AdS black holes in a non-commutative spacetime sourced by Lorentzian-smeared matter distributions. Since exact analytical solutions for the critical thermodynamic quantities are not available, we employ a perturbative expansion in the non-commutative parameter and validate the resulting expressions through numerical analysis. Using the generalized off-shell free-energy framework, we explore the topological structure of the thermodynamic phase space and evaluate the corresponding winding number that characterizes the phase transitions. Our results reveal that non-commutative effects introduce qualitative modifications to the thermodynamic behavior compared with the standard Reissner-Nordstr\"om AdS black hole. Furthermore, we demonstrate that the bulk and boundary descriptions possess an identical global thermodynamic topology, providing strong evidence for the correspondence between their topological structures. We also investigate the lower bound on the remnant mass implied by the second law of black-hole thermodynamics and observe that non-commutative corrections modify key thermodynamic quantities, with particular emphasis on the entropy and the final black-hole mass.

gr-qc↗

arXiv2026

Model Forensics: Investigating Whether Concerning Behavior Reflects Misalignment

A central goal of safety research is determining whether a model is misaligned. Prior work has largely focused on detecting concerning behavior. But behavior alone does not establish misalignment: a concerning action can arise from benign causes such as confusion. This motivates model forensics: investigating whether the action was driven by malign intent. In this paper, we propose a baseline protocol for model forensics consisting of two steps, iterated as needed. First, we read the chain of thought (CoT) to generate hypotheses about what drives model behavior. Second, we make edits to the prompt or environment to test these hypotheses. While the CoT is not always faithful, it is a rich source of unsupervised insight that can guide the collection of more rigorous evidence. To evaluate our protocol, we create a suite of six agentic environments where models exhibit concerning behavior, and apply it to each. We establish that Kimi K2 Thinking takes shortcuts due to a genuine disposition towards low-effort actions, by showing this hypothesis successfully predicts its behavior. Through counterfactual experiments, we show DeepSeek R1 deceives out of a desire to be consistent with a previous instance of itself. Our methods nonetheless leave significant room for refinement. For example, when we test whether Kimi K2 Thinking believes it is violating user intent, we find no evidence of such a belief, but without positive controls we cannot confirm our tests would detect it. Overall, we find our simple protocol provides a strong baseline that we hope future work will improve upon. More broadly, our work is a concrete step in developing the growing field of model forensics.

cs.LG↗

arXiv2026

The Voronoi Bottleneck: Capacity-Aware Dense Retrieval for Product Search

Dense embedding retrieval compresses all relevance information into a single inner product, imposing a fundamental geometric limit -- the Voronoi Bottleneck -- on the number of query-document relevance patterns expressible at fixed embedding dimension (d). We make three contributions. (1) Unified capacity theory. We prove that Voronoi complexity and sign-rank are equivalent for top-1 retrieval, yielding tight dimension bounds and a computable diagnostic, the Capacity Utilization Score (CUS), that predicts per-query retrieval failure with AUC (> 0.8) without relevance labels. (2) Diagnosis. CUS identifies two capacity regimes -- moderate ((\delta \gtrsim 1)), where density-aware training yields measurable gains, and vacuous ((\delta \ll 1)), where it does not -- giving practitioners an a priori check before investing in retraining. (3) DART training. We introduce AT-DW-InfoNCE, an Adaptive-Temperature Density-Weighted contrastive objective with formally derived optimal weighting (\alpha^* = 2.0). On a 100K-query synthetic product-search corpus with controlled relevance structure, DART improves +1.9 Recall@100 over a same-data InfoNCE baseline ((84.9 \pm 0.0) vs. (83.0 \pm 0.3); 8 seeds, (p < 0.001)), outperforming focal loss and temperature-schedule alternatives. DART requires zero inference-time overhead -- it is a drop-in training objective that improves any dual-encoder system.

cs.IR↗

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

$RD_\alpha$-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 $RD_\alpha(\mathscr{G})$, is defined as $RD_\alpha(\mathscr{G})=\alpha\,RT_r(\mathscr{G})+(1-\alpha)\,RD(\mathscr{G}), \, \alpha\in[0,1],$ 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 $RD_\alpha$-spectrum of graphs obtained through the joined union operation. We derive explicit formulas for the characteristic polynomial of $RD_\alpha(\mathscr{G})$ 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 $RD_\alpha$-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

AdaptNC: Adaptive Nonconformity Scores for Conformal Prediction under Distribution Shift

Rigorous uncertainty quantification is essential for the safe deployment of autonomous systems in unconstrained environments. Conformal Prediction (CP) provides a distribution-free framework for this task, yet its standard formulations rely on exchangeability assumptions that are violated by the distribution shifts inherent in real-world robotics. Existing online CP methods maintain target coverage by adaptively scaling the conformal threshold, but typically employ a static nonconformity score function. We show that this fixed geometry leads to highly conservative, volume-inefficient prediction regions when environments undergo structural shifts. To address this, we propose $\textbf{AdaptNC}$, a framework for the joint online adaptation of both the nonconformity score parameters and the conformal threshold. AdaptNC leverages an adaptive reweighting scheme to optimize score functions, and introduces a replay buffer mechanism to mitigate the coverage instability that occurs during score transitions. We evaluate AdaptNC on diverse robotic benchmarks involving multi-agent policy changes, environmental changes and sensor degradation. Our results demonstrate that AdaptNC significantly reduces prediction region volume compared to state-of-the-art threshold-only baselines while maintaining target coverage levels.

cs.LG↗

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

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↗

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

MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control

Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge. Existing approaches based on multi-agent reinforcement learning (MARL), safety filtering, or Model Predictive Control (MPC) either lack strict safety guarantees, suffer from conservatism, or fail to scale effectively. We propose MAD-PINN, a decentralized physics-informed machine learning framework for solving the multi-agent state-constrained optimal control problem (MASC-OCP). Our method leverages an epigraph-based reformulation of SC-OCP to simultaneously capture performance and safety, and approximates its solution via a physics-informed neural network. Scalability is achieved by training the SC-OCP value function on reduced-agent systems and deploying them in a decentralized fashion, where each agent relies only on local observations of its neighbours for decision-making. To further enhance safety and efficiency, we introduce an Hamilton-Jacobi (HJ) reachability-based neighbour selection strategy to prioritize safety-critical interactions, and a receding-horizon policy execution scheme that adapts to dynamic interactions while reducing computational burden. Experiments on multi-agent navigation tasks demonstrate that MAD-PINN achieves superior safety-performance trade-offs, maintains scalability as the number of agents grows, and consistently outperforms state-of-the-art baselines.

cs.RO↗