arXiv subjects

Rahul Singh

Publications and source records attributed to Rahul Singh.

At least 37 records · Page 2Linked to original sources

arXiv2026

Program Evaluation with Remotely Sensed Outcomes

We study causal inference in experiments and quasi-experiments, where the economic outcome is imperfectly measured by a remotely sensed variable. The remotely sensed variable is low-cost, scalable, and predictive of the economic outcome in observational data; examples include satellite imagery and mobile phone activity. We model the remotely sensed variable as post-outcome: variation in the economic outcome causes variation in the remotely sensed variable. For example, changes in environmental quality cause changes in satellite imagery, not vice versa. Under this assumption, we propose a formula to nonparametrically identify the causal parameter by combining experimental and observational data. We develop a method for n^{-1/2} inference that is robust to misspecification and that does not restrict the algorithms used to process remotely sensed variables.

econ.EM↗

arXiv2026

On Gaussian approximation for entropy-regularized Q-learning with function approximation

In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial stepsize $k^{-ω}$, $ω\in (1/2,1)$. Assuming that the sequence of observed triples $(s_k,a_k,s_{k+1})_{k \geq 0}$ forms a uniformly geometrically ergodic Markov chain, and under suitable regularity conditions for the projected soft Bellman equation, we establish a Gaussian approximation bound in the convex distance with rate of order $n^{-1/4}$, up to polylogarithmic factors in $n$, where $n$ is the number of samples used by the algorithm. To obtain this result, we combine a linearization of the soft Bellman recursion with a Gaussian approximation for the leading martingale term. Finally, we derive high-order moment bounds for the algorithm's last iterate, which might be of independent interest.

stat.ML↗

arXiv2026

Regret and Sample Complexity of Online Q-Learning via Concentration of Stochastic Approximation with Time-Inhomogeneous Markov Chains

We present the first regret bound for classical online Q-learning in infinite-horizon discounted Markov decision processes (MDPs), without relying on optimism or bonus terms. We first analyze Boltzmann Q-learning with decaying temperature and show that its regret depends critically on the suboptimality gap of the MDP: for sufficiently large gaps, the regret is sublinear, while for small gaps it deteriorates and can approach linear growth. To address this limitation, we study a Smoothed $ε_n$-Greedy exploration scheme that combines $ε_n$-greedy and Boltzmann exploration, for which we prove a gap-robust regret bound of near-$\tilde{O}(N^{9/10})$. We also obtain sample complexity guarantees, with both regret and sample complexity bounds holding with high probability. To analyze these algorithms, we develop a high-probability concentration bound for contractive Markovian stochastic approximation with iterate- and time-dependent transition dynamics. This bound may be of independent interest as the contraction factor in our framework is allowed to converge to one asymptotically.

cs.LG↗

arXiv2026

Policy Gradient Methods for Non-Markovian Reinforcement Learning

We study policy gradient methods for reinforcement learning in non-Markovian decision processes (NMDPs), where observations and rewards depend on the entire interaction history. To handle this dependence, the agent maintains an internal state that is recursively updated to provide a compact summary of past observations and actions. In contrast to approaches that treat the agent state dynamics as fixed or learn it via predictive objectives, we propose a reward-centric formulation that jointly optimizes the agent state dynamics and the control policy to maximize the expected cumulative reward. To this end, we consider a class of Agent State-Markov (ASM) policies, comprising an agent state dynamics and a control policy that maps the agent state to actions. We establish a novel policy gradient theorem for ASM policies, extending the classical policy gradient results from the Markovian setting to episodic and infinite-horizon discounted NMDPs. Building on this gradient expression, we propose the Agent State-Markov Policy Gradient (ASMPG) algorithm, which leverages the recursive structure of the agent state dynamics for efficient optimization. We establish finite-time and almost sure convergence guarantees, and empirically demonstrate that, on a range of non-Markovian tasks, ASMPG outperforms baselines that learn state representations via predictive objectives.

cs.LG↗

arXiv2026

Emergent topological phase from a one-dimensional network of defects

Symmetry-protected topological phases of matter, characterized by non-trivial band topology, are spectrally gapped and show non-trivial boundary phenomena. Here, we show that scattering states when interjected by an array of periodically modulated defects can result in emergent topological phases whose properties can be tuned by modulating the defect strengths. We dub this the Su-Schrieffer-Heeger network. We show that a scattering-matrix network model can capture the emergent symmetries and nontrivial winding of the quasienergy bands, which lead to distinct transport signatures and can be further periodically driven to realize a robust Thouless charge pump. We show that a microscopic lattice model embedded with a defect superlattice yields Bloch minibands that directly map to the network problem. We further verify that the physics we report is stable to disorder and point out concrete experimental solid-state platforms where it is readily realizable. Our work, in contrast to engineering atomic Hamiltonians, shows that defect engineering on metallic platforms can lead to emergent topological phases of quantum matter.

cond-mat.mes-hall↗

arXiv2026

q-Opers and Bethe Ansatz for Open Spin Chains I

In in a nutshell, the classical geometric $q$-Langlands duality can be viewed as a correspondence between the space of $(G,q)$-opers and the space of solutions of $^L\mathfrak{g}$ XXZ Bethe Ansatz equations. The latter describe spectra of closed spin chains with twisted periodic boundary conditions and, upon the duality, the twist elements are identified with the $q$-oper connections on a projective line in a certain gauge. In this work, we initiate the geometric study of Bethe Ansatz equations for spin chains with open boundary conditions. We introduce the space of $q$-opers whose defining sections are invariant under reflection through the unit circle in a selected gauge. The space of such reflection-invariant $q$-opers in the presence of certain nondegeneracy conditions is thereby described by the corresponding Bethe Ansatz problem. We compare our findings with the existing results in integrable systems and representation theory. This paper discusses the type-A construction leaving the general case for the upcoming work.

math.AG↗

arXiv2026

Testing for lack of fit in paired comparison data

Linear stochastic transitivity is a central assumption in paired comparison models that is rarely verified in practice. Empirical violations, however, are common and can substantially affect inference and ranking. We develop a class of tests for detecting lack of fit in cardinal paired comparison models, where lack of fit is characterized by the presence of cyclical preferences among subsets of items. We propose a suite of tests adapted to different regimes governing the growth of the comparison graph. For a fixed number of items, the proposed procedures exhibit substantially improved power relative to the classical Kendall--Smith test and its cardinal analogue. We further extend the framework to high--dimensional, sparse comparison graphs near the connectivity threshold in random graph models. The theoretical analysis characterizes the behavior of the tests under both the null and alternative, with particular emphasis on limits of detectability and consistency. Simulation studies corroborate the theoretical findings, and applications to real data uncover substantial and previously unrecognized intransitivity and structural lack of fit.

stat.ME↗

arXiv2026

High-Probability Bounds for SGD under the Polyak-Lojasiewicz Condition with Markovian Noise

We present the first uniform-in-time high-probability bound for SGD under the PL condition, where the gradient noise contains both Markovian and martingale difference components. This significantly broadens the scope of finite-time guarantees, as the PL condition arises in many machine learning and deep learning models while Markovian noise naturally arises in decentralized optimization and online system identification problems. We further allow the magnitude of noise to grow with the function value, enabling the analysis of many practical sampling strategies. In addition to the high-probability guarantee, we establish a matching $1/k$ decay rate for the expected suboptimality. Our proof technique relies on the Poisson equation to handle the Markovian noise and a probabilistic induction argument to address the lack of almost-sure bounds on the objective. Finally, we demonstrate the applicability of our framework by analyzing three practical optimization problems: token-based decentralized linear regression, supervised learning with subsampling for privacy amplification, and online system identification.

cs.LG↗

arXiv2026

Shiksha Copilot: Teacher-AI Collaboration for Curating and Customizing Lesson Plans in Low-Resource Schools

This study investigates Shiksha copilot, an AI-assisted lesson planning tool deployed in government schools across Karnataka, India. The system combined LLMs and human expertise through a structured process in which English and Kannada lesson plans were co-created by curators and AI; teachers then further customized these curated plans for their classrooms using their own expertise alongside AI support. Drawing on a large-scale mixed-methods study involving 1,043 teachers and 23 curators, we examine how educators collaborate with AI to generate context-sensitive lesson plans, assess the quality of AI-generated content, and analyze shifts in teaching practices within multilingual, low-resource environments. Our findings show that teachers used Shiksha copilot both to meet administrative documentation needs and to support their teaching. The tool eased bureaucratic workload, reduced lesson planning time, and lowered teaching-related stress, while promoting a shift toward activity-based pedagogy. However, systemic challenges such as staffing shortages and administrative demands constrained broader pedagogical change. We frame these findings through the lenses of teacher-AI collaboration and communities of practice to examine the effective integration of AI tools in teaching. Finally, we propose design directions for future teacher-centered EdTech, particularly in multilingual and Global South contexts.

cs.CY↗

arXiv2026

Serving Compound Inference Systems on Datacenter GPUs

Applications in emerging domains such as XR are being built as compound inference systems, where multiple ML models are composed in the form of a task graph to service each request. Serving these compound systems efficiently raises two questions: how to apportion end-to-end latency and accuracy budgets between different tasks in a compound inference system, and how to allocate resources effectively for different models with varying resource requirements. We present JigsawServe, the first serving framework that jointly optimizes for latency, accuracy, and cost in terms of GPU resources by adaptively choosing model variants and performing fine-grained resource allocation by spatially partitioning the GPUs for each task of a compound inference system. Analytical evaluation of a system with a large number of GPUs shows that JigsawServe can increase the maximum serviceable demand (in requests per second) by 11.3x when compared to the closest prior work. Our empirical evaluation shows that for a large range of scenarios, JigsawServe consumes only 43.3% of the available GPU resources while meeting accuracy SLOs with less than 0.6% latency SLO violations. All of the features in JigsawServe contribute to this high efficiency -- sacrificing any one feature of accuracy scaling, GPU spatial partitioning, or task-graph-informed resource budgeting significantly reduces efficiency.

cs.DC↗

arXiv2026

Scalable Digital Compute-in-Memory Ising Machines for Robustness Verification of Binary Neural Networks

Verification of binary neural network (BNN) robustness is NP-hard, as it can be formulated as a combinatorial search for an adversarial perturbation that induces misclassification. Exact verification methods therefore scale poorly with problem dimension, motivating the use of hardware-accelerated heuristics and unconventional computing platforms, such as Ising solvers, that can efficiently explore complex energy landscapes and discover high-quality solutions. In this work, we reformulate BNN robustness verification as a quadratic unconstrained binary optimization (QUBO) problem and solve it using a digital compute-in-memory (DCIM) SRAM-based Ising machine. Instead of requiring globally optimal solutions, we exploit imperfect solutions produced by the DCIM Ising machine to extract adversarial perturbations and thereby demonstrate the non-robustness of the BNN. The proposed architecture stores quantized QUBO coefficients in approximately 9.1~Mb of SRAM and performs annealing in memory via voltage-controlled pseudo-read dynamics, enabling iterative updates with minimal data movement. Experimental projections indicate that the proposed approach achieves a $178\times$ acceleration in convergence rate and a $1538\times$ improvement in power efficiency relative to conventional CPU-based implementations.

cs.ET↗

arXiv2026

Resource-Efficient Emulation of Majorana Zero Mode Braiding on a Superconducting Trijunction

Topological superconductivity could host quasiparticles that are key candidates for fault-tolerant quantum computation due to their immunity to noise as they obey non-Abelian exchange statistics. For example, in the case of Majorana Zero Modes (MZM), braiding enables two topologically protected quantum gates. While their direct manipulation in solid-state systems remains experimentally challenging, digital emulation of MZM behavior has provided insight as well as a deeper understanding of controlling these topological quantum systems. This emulation is typically accomplished by mapping the topological and trivial phases of a Majorana system to ferromagnetic and paramagnetic Hamiltonians of a spin-glass model. This approach usually relies on adiabatic evolution of superconducting Hamiltonians, which require circuits with very large depths. In this work, we present a resource-efficient method to emulate MZM braiding in a trijunction geometry using a quantum processor. We introduce direct braiding operators which simulate the evolution more efficiently, reducing the quantum gate overhead. We then further generalize this method to emulate braiding operations in extended trijunction architectures based on Kitaev chains.

quant-ph↗

arXiv2026

Robustness Verification of Binary Neural Networks: An Ising and Quantum-Inspired Framework

Binary neural networks (BNNs) are increasingly deployed in edge computing applications due to their low hardware complexity and high energy efficiency. However, verifying the robustness of BNNs against input perturbations, including adversarial attacks, remains computationally challenging because the underlying decision problem is inherently combinatorial. In this paper, we propose an Ising- and quantum-inspired framework for BNN robustness verification. We show that, for a broad class of BNN architectures, robustness verification can be formulated as a Quadratic Constrained Boolean Optimization (QCBO) problem and subsequently transformed into a Quadratic Unconstrained Boolean Optimization (QUBO) instance amenable to Ising and quantum-inspired solvers. We demonstrate the feasibility of this formulation on binarized MNIST by solving the resulting QUBOs with a free energy machine (FEM) solver and simulated annealing. We also show the deployment of this framework on quantum annealing and digital annealing platforms. Our results highlight the potential of quantum-inspired computing and Ising computing as a pathway toward trustworthy AI systems.

cs.ET↗

arXiv2026

Cross-Frequency Bispectral EEG Analysis of Reach-to-Grasp Planning and Execution

Neural control of grasping arises from nonlinear interactions across multiple brain rhythms, yet EEG-based motor decoding has largely relied on linear, second-order spectral features. Here, we examine whether higher-order cross-frequency dynamics distinguish motor planning from execution during natural reach-to-grasp behavior. EEG was recorded in a cue-based paradigm during executed precision and power grips, enabling stage-resolved analysis of preparatory and execution-related neural activity. Cross-frequency bispectral analysis was used to compute bicoherence matrices across canonical frequency band pairs, from which magnitude- and phase-based features were extracted. Classification, permutation-based feature selection, and within-subject statistical testing showed that execution is characterized by substantially stronger and more discriminative nonlinear coupling than planning, with dominant contributions from beta- and gamma-driven interactions. In contrast, decoding of precision versus power grips achieved comparable performance during planning and execution, indicating that grasp-type representations emerge during planning and persist into execution. Spatial and spectral analyses further revealed that informative bispectral features reflect coordinated activity across prefrontal, central, and occipital regions. Despite substantial feature redundancy, effective dimensionality reduction preserved decoding performance. Together, these findings demonstrate that nonlinear cross-frequency coupling provides an interpretable and robust marker of motor planning and execution, extending bispectral EEG analysis to ecologically valid grasping and supporting its relevance for brain-computer interfaces and neuroprosthetic control.

eess.SP↗

arXiv2026

Knock Out Slow Extraction Using Betatron Sidebands at High Harmonics

Radio frequency knock out resonant slow extraction is a standard method for extracting stored particle beams from synchrotrons by transverse excitation. Excitation signals comprising many betatron sidebands have shown to reduce intensity fluctuations of the extracted beam spill and are used at several facilities. In this contribution, the effect of individual sidebands at different harmonics on the spill quality is systematically studied using efficient noise excitation signals fully covering the respective sidebands. Particle tracking simulations show a clear correlation between the chosen excitation frequency and the spill quality. This relation is attributed to the spectrum of particle motion shortly before their extraction, and an empiric relation between the spectrum, the excitation frequency, and the resulting spill quality is given. Experiments show an additional reduction of pile-up when using higher excitation frequencies. These insights have implications for an optimal design of excitation waveforms and hardware for Knock Out extraction systems.

physics.acc-ph↗

arXiv2026

Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety

We present a formula for the Poincaré dual in the flag manifold of the equivariant fundamental class of any regular nilpotent or regular semisimple Hessenberg variety as a polynomial in terms of certain Chern classes. We then develop a type-independent proof of the Giambelli formula for the Peterson variety, and use this formula to compute the intersection multiplicity of a Peterson variety with an opposite Schubert variety corresponding to a Coxeter word. Finally, we develop an equivariant Chevalley formula for the cap product of a divisor class with a fundamental class, and a dual Monk rule, for the Peterson variety.

math.AG↗

arXiv2026

Extensible Post Quantum Cryptography Based Authentication

Cryptography underpins the security of modern digital infrastructure, from cloud services to health data. However, many widely deployed systems will become vulnerable after the advent of scalable quantum computing. Although quantum-safe cryptographic primitives have been developed, such as lattice-based digital signature algorithms (DSAs) and key encapsulation mechanisms (KEMs), their unique structural and performance characteristics make them unsuitable for existing protocols. In this work, we introduce a quantum-safe single-shot protocol for machine-to-machine authentication and authorization that is specifically designed to leverage the strengths of lattice-based DSAs and KEMs. Operating entirely over insecure channels, this protocol enables the forward-secure establishment of tokens in constrained environments. By demonstrating how new quantum-safe cryptographic primitives can be incorporated into secure systems, this study lays the groundwork for scalable, resilient, and future-proof identity infrastructures in a quantum-enabled world.

cs.CR↗

arXiv2025

Canonical correlation regression with noisy data

We study instrumental variable regression in data rich environments. The goal is to estimate a linear model from many noisy covariates and many noisy instruments. Our key assumption is that true covariates and true instruments are repetitive, though possibly different in nature; they each reflect a few underlying factors, however those underlying factors may be misaligned. We analyze a family of estimators based on two stage least squares with spectral regularization: canonical correlations between covariates and instruments are learned in the first stage, which are used as regressors in the second stage. As a theoretical contribution, we derive upper and lower bounds on estimation error, proving optimality of the method with noisy data. As a practical contribution, we provide guidance on which types of spectral regularization to use in different regimes.

econ.EM↗