arXiv subjects

Sayan Chakraborty

Publications and source records attributed to Sayan Chakraborty.

At least 19 recordsLinked to original sources

arXiv2026

MINT: Min-Selection Preference Distillation for Balanced Multi-Objective Alignment

Aligning a language agent to several objectives at once is a persistent failure mode of preference-based training: when objectives are combined additively, optimization collapses onto whichever is cheapest to improve and sacrifices the rest, so a support agent learns to sound warm while giving no real help. The root issue is that an additive reward has no notion of balance. We introduce Mint (MIN-selection preference disTillation), a one-line change to preference distillation: rather than ranking sampled candidates by a weighted sum of rewards, we rank them by their weakest objective, distilling the best-balanced candidate over the most lopsided one with an unchanged DPO objective. This is the p -> negative infinity limit of a generalized-mean family spanning additive to worst-case selection. Across cooperative emotional support and adversarial negotiation, min-selection lifts both objectives while sharply cutting their imbalance; on emotional support it raises the weaker axis from 0.37 to 0.64 (p < 10^-40), surpassing human experts and persisting across full multi-turn rollouts. A turn-by-turn analysis yields our central finding: min-selection corrects imbalance in proportion to how imbalanced the reference policy is, and its benefit endures over an interaction precisely as long as that imbalance does.

cs.AI↗

arXiv2025

Hybrid Oscillator-Qudit Quantum Processors: stabilizer states, stabilizer codes, symplectic operations, and non-commutative geometry

We construct stabilizer states and error-correcting codes on combinations of discrete- and continuous-variable systems, generalizing the Gottesman-Kitaev-Preskill (GKP) quantum lattice formalism. Our framework absorbs the discrete phase space of a qudit into a hybrid phase space parameterizable entirely by the continuous variables of a harmonic oscillator. The unit cell of a hybrid quantum lattice grows with the qudit dimension, yielding a way to simultaneously measure an arbitrarily large range of non-commuting position and momentum displacements. Simple hybrid states can be obtained by applying a conditional displacement to a Gottesman-Kitaev-Preskill (GKP) state and a Pauli eigenstate, or by encoding some of the physical qudits of a stabilizer state into a GKP code. The states' oscillator-qudit entanglement cannot be generated using symplectic (i.e., Gaussian-Clifford) operations, distinguishing them as a resource from tensor products of oscillator and qudit stabilizer states. Simple hybrid codes can be thought of as subsystem GKP codes whose gauge factor is entangled with a qudit. Our numerical investigations suggest that such codes can sometimes outperform GKP codes against physical noise, and their decoders can be tuned to accommodate either more qudit or more oscillator errors. We also relate stabilizer codes to non-commutative tori, identifying that a general construction of such tori yields multi-mode multi-qudit extensions of GKP codes. We explicitly calculate these codes' logical dimension and logical operators by utilizing the Morita equivalence between their stabilizer and logical tori. We provide examples using commutation matrices, integer symplectic matrices, and binary codes.

quant-ph↗

arXiv2025

Morita equivalence classes for crossed product of rational rotation algebras

We study the Morita equivalence classes of crossed products of rotation algebras $A_\theta$, where $\theta$ is a rational number, by finite and infinite cyclic subgroups of $\mathrm{SL}(2, \mathbb{Z})$. We show that for any such subgroup $F$, the crossed products $A_\theta \rtimes F$ and $A_{\theta'} \rtimes F$ are strongly Morita equivalent, where both $\theta$ and $\theta'$ are rational. Combined with previous results for irrational values of $\theta$, our result provides a complete classification of the crossed products $A_\theta \rtimes F$ up to Morita equivalence.

math.OA↗

arXiv2025

Towards Robust Offline Evaluation: A Causal and Information Theoretic Framework for Debiasing Ranking Systems

Evaluating retrieval-ranking systems is crucial for developing high-performing models. While online A/B testing is the gold standard, its high cost and risks to user experience require effective offline methods. However, relying on historical interaction data introduces biases-such as selection, exposure, conformity, and position biases-that distort evaluation metrics, driven by the Missing-Not-At-Random (MNAR) nature of user interactions and favoring popular or frequently exposed items over true user preferences. We propose a novel framework for robust offline evaluation of retrieval-ranking systems, transforming MNAR data into Missing-At-Random (MAR) through reweighting combined with black-box optimization, guided by neural estimation of information-theoretic metrics. Our contributions include (1) a causal formulation for addressing offline evaluation biases, (2) a system-agnostic debiasing framework, and (3) empirical validation of its effectiveness. This framework enables more accurate, fair, and generalizable evaluations, enhancing model assessment before deployment.

cs.IR↗

arXiv2024

Resilient Learning-Based Control Under Denial-of-Service Attacks

In this paper, we have proposed a resilient reinforcement learning method for discrete-time linear systems with unknown parameters, under denial-of-service (DoS) attacks. The proposed method is based on policy iteration that learns the optimal controller from input-state data amidst DoS attacks. We achieve an upper bound for the DoS duration to ensure closed-loop stability. The resilience of the closed-loop system, when subjected to DoS attacks with the learned controller and an internal model, has been thoroughly examined. The effectiveness of the proposed methodology is demonstrated on an inverted pendulum on a cart.

eess.SY↗

arXiv2024

Enhancing the Harrow-Hassidim-Lloyd (HHL) algorithm in systems with large condition numbers

Although the Harrow-Hassidim-Lloyd (HHL) algorithm offers an exponential speedup in system size for treating linear equations of the form $A\vec{x}=\vec{b}$ on quantum computers when compared to their traditional counterparts, it faces a challenge related to the condition number ($\mathcal{\kappa}$) scaling of the $A$ matrix. In this work, we address the issue by introducing the post-selection-improved HHL (Psi-HHL) framework that operates on a simple yet effective premise: subtracting mixed and wrong signals to extract correct signals while providing the benefit of optimal scaling in the condition number of $A$ (denoted as $\mathcal{\kappa}$) for large $\mathcal{\kappa}$ scenarios. This approach, which leads to minimal increase in circuit depth, has the important practical implication of having to use substantially fewer shots relative to the traditional HHL algorithm. The term `signal' refers to a feature of $|x\rangle$. We design circuits for overlap and expectation value estimation in the Psi-HHL framework. We demonstrate performance of Psi-HHL via numerical simulations. We carry out two sets of computations, where we go up to 26-qubit calculations, to demonstrate the ability of Psi-HHL to handle situations involving large $\mathcal{\kappa}$ matrices via: (a) a set of toy matrices, for which we go up to size $64 \times 64$ and $\mathcal{\kappa}$ values of up to $\approx$ 1 million, and (b) application to quantum chemistry, where we consider matrices up to size $256 \times 256$ that reach $\mathcal{\kappa}$ of about 393. The molecular systems that we consider are Li$_{\mathrm{2}}$, KH, RbH, and CsH.

physics.atom-ph↗

arXiv2024

Optimizing Oscilloscope based Acquisition for Pulsed Optically Detected Magnetic Resonance Measurements

Ensembles of nitrogen vacancy (NV) defect centers in diamond have emerged as a promising platform for fundamental studies and applications in quantum sensing and quantum information processing. Here, we demonstrate the use of a digital oscilloscope for acquiring pulsed optically detected magnetic resonance (ODMR) data from an ensemble of NV centers in diamond. The oscilloscope facilitates improved signal visualization, and simplifies system debugging. We show that on-board waveform averaging in the oscilloscope enables more efficient measurements. The detection scheme, and data processing are optimized to allow fast acquisition of high quality data. The system noise, and its impact on the measurements is analyzed in detail. The data processing method is shown to effectively suppress a broad range of noise spectral components, thereby reducing the total noise in the processed data. Furthermore, the introduction of an analog low pass filter in the signal path is shown to improve the measurement by removing aliasing. The framework developed in this work can be extended to other detection techniques and material platforms for ODMR. We expect that the insights developed here will guide the design, and development of dedicated instruments for ODMR in future.

quant-ph↗

arXiv2023

Symmetrized non-commutative tori revisited

For the flip action of $\mathbb{Z}_2$ on an $n$-dimensional noncommutative torus $A_θ,$ using an exact sequence by Natsume, we compute the K-theory groups of $A_θ\rtimes \mathbb{Z}_2$. The novelty of our method is that it also provides an explicit basis of $\mathrm{K}_{0}(A_θ\rtimes \mathbb{Z}_2),$ for any $θ.$ As an application, for a simple $n$-dimensional torus $A_θ,$ using classification techniques, we determine the isomorphism class of $A_θ\rtimes \mathbb{Z}_2$ in terms of the isomorphism class of $A_θ.$

math.OA↗

arXiv2022

$K$-theory of non-commutative Bernoulli Shifts

For a large class of C*-algebras $A$, we calculate the $K$-theory of reduced crossed products $A^{\otimes G}\rtimes_rG$ of Bernoulli shifts by groups satisfying the Baum--Connes conjecture. In particular, we give explicit formulas for finite-dimensional C*-algebras, UHF-algebras, rotation algebras, and several other examples. As an application, we obtain a formula for the $K$-theory of reduced C*-algebras of wreath products $H\wr G$ for large classes of groups $H$ and $G$. Our methods use a generalization of techniques developed by the second named author together with Joachim Cuntz and Xin Li, and a trivialization theorem for finite group actions on UHF algebras developed in a companion paper by the third and fourth named authors.

math.OA↗

arXiv2022

Higher dimensional Bott classes and the stability of rotation relations

Let $Θ=(θ_{jk})_{n\times n}$ be a real skew-symmetric $n\times n$ matrix for $n\geq 2$. Under some mild non-integrality conditions on $Θ,$ we construct Rieffel-type projections as higher dimensional Bott classes in the $n$-dimensional noncommutative torus $\mathcal{A}_Θ.$ These projections generate $\operatorname{K}_0(\mathcal{A}_Θ)$ when $Θ$ is strongly totally irrational. As an application, when $Θ$ is strongly totally irrational, we show that: For any $\varepsilon>0,$ there exists $δ>0$ (depending only on $\varepsilon$ and $Θ$) satisfying the following: For any unital simple separable $C^*$-algebra $\mathcal{A}$ with tracial rank at most one, and for any $n$-tuple of unitaries $u_1,u_2,\dots,u_n$ in $\mathcal{A}$, if $u_1,u_2,\dots,u_n$ satisfy certain trace conditions and \begin{eqnarray*}\|u_ku_j-e^{2πiθ_{jk}}u_ju_k\|<δ,\,j,k=1,2,\dots,n, \end{eqnarray*} then there exists an $n$-tuple of unitaries $\tilde{u}_1,\tilde{u}_2,\dots,\tilde{u}_n$ in $\mathcal{A}$ such that \begin{eqnarray*}\tilde{u}_k\tilde{u}_j=e^{2πiθ_{jk}}\tilde{u}_j\tilde{u}_k\, {\rm and}\, \|\tilde{u}_j-u_j\|<\varepsilon,\, j,k=1,2,\dots,n. \end{eqnarray*} We also show that these trace conditions are also necessary in the above application.

math.OA↗

arXiv2021

Tracing projective modules over noncommutative orbifolds

For an action of a finite cyclic group $F$ on an $n$-dimensional noncommutative torus $A_θ,$ we give sufficient conditions when the fundamental projective modules over $A_θ$, which determine the range of the canonical trace on $A_θ,$ extend to projective modules over the crossed product C*-algebra $A_θ\rtimes F.$ Our results allow us to understand the range of the canonical trace on $A_θ\rtimes F$, and determine it completely for several examples including the crossed products of 2-dimensional noncommutative tori with finite cyclic groups and the flip action of $\mathbb{Z}_2$ on any $n$-dimensional noncommutative torus. As an application, for the flip action of $\mathbb{Z}_2$ on a simple $n$-dimensional torus $A_θ$, we determine the Morita equivalence class of $A_θ\rtimes \mathbb{Z}_2,$ in terms of the Morita equivalence class of $A_θ.$

math.OA↗

arXiv2020

Building an Automated and Self-Aware Anomaly Detection System

Organizations rely heavily on time series metrics to measure and model key aspects of operational and business performance. The ability to reliably detect issues with these metrics is imperative to identifying early indicators of major problems before they become pervasive. It can be very challenging to proactively monitor a large number of diverse and constantly changing time series for anomalies, so there are often gaps in monitoring coverage, disabled or ignored monitors due to false positive alarms, and teams resorting to manual inspection of charts to catch problems. Traditionally, variations in the data generation processes and patterns have required strong modeling expertise to create models that accurately flag anomalies. In this paper, we describe an anomaly detection system that overcomes this common challenge by keeping track of its own performance and making changes as necessary to each model without requiring manual intervention. We demonstrate that this novel approach outperforms available alternatives on benchmark datasets in many scenarios.

cs.LG↗

arXiv2020

Some remarks on $K_0$ of noncommutative tori

Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibers are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of $K_0$ of all noncommutative tori.

math.OA↗

arXiv2020

Root Cause Detection Among Anomalous Time Series Using Temporal State Alignment

The recent increase in the scale and complexity of software systems has introduced new challenges to the time series monitoring and anomaly detection process. A major drawback of existing anomaly detection methods is that they lack contextual information to help stakeholders identify the cause of anomalies. This problem, known as root cause detection, is particularly challenging to undertake in today's complex distributed software systems since the metrics under consideration generally have multiple internal and external dependencies. Significant manual analysis and strong domain expertise is required to isolate the correct cause of the problem. In this paper, we propose a method that isolates the root cause of an anomaly by analyzing the patterns in time series fluctuations. Our method considers the time series as observations from an underlying process passing through a sequence of discretized hidden states. The idea is to track the propagation of the effect when a given problem causes unaligned but homogeneous shifts of the underlying states. We evaluate our approach by finding the root cause of anomalies in Zillows clickstream data by identifying causal patterns among a set of observed fluctuations.

cs.LG↗

arXiv2019

Development of Embedded Speed Control System for DC Servo Motor using Wireless Communication

In this experiment, a closed-loop discrete time system for speed control of a permanent magnet DC motor with discrete PI controller is implemented in embedded platform. The design & analysis of the system is based on the mathematical model of the DC motor obtained by system identification technique. After that the closed loop system is distributed through a wireless network created by means of Bluetooth without any change in the discrete controller. The network connects the controller on one side with the sensor, actuator & the plant on the other side. Then the performance of the closed loop system is observed with the wireless network in two configurations : with point-to-point connection between two nodes and a network structure with two intermediate nodes among the controller side node & the plant side node. It has been observed that the performance degrades with only the PI controller a little bit in point to point configuration and the performance severely degrades in intermediate node configuration. To tackle this issue time delay is measured in the WNCS and then a digital smith predictor structure is implemented to obtain better performance. It has been observed that in point to point configuration the time delay remains almost constant and in intermediate node configuration the time delay is varying. Hence the digital smith predictor fails to perform reasonably in intermediate node configuration. An online time delay measurement & estimation procedure has been implemented and proposed in this research. We have implemented an adaptive digital smith predictor using the online time delay measurement and identification. The implemented smith predictor provides good results for both intermediate node and point to point connection. An stability analysis of the DC motor system with variation of delay has been discussed.

eess.SY↗

arXiv2019

Online Delay Estimation and Adaptive Compensation in Wireless Networked System: An Embedded Control Design

In the present work, an embedded PI controller is designed for speed regulation of DC servomotor over a wireless network. The embedded controller integrates PI controller with a proposed time-delay estimator and an adaptive digital Smith predictor for its real time operation, which is the novelty of the work. The real time or rather online operation of the developed embedded controller over wireless network is possible mainly due to the contributions in terms of proposing a new empirical formula for time-delay estimation, viable approximation of time-delay, discretization scheme in developing the proposed adaptive Smith predictor. The proposed embedded design validates that the deterioration of control performance due to random network-induced delay are mitigated in real time. The embedded controller is designed and tested for a short-range of 100 meters, and wireless technology chosen is suitable for biomedical applications.

eess.SY↗

arXiv2019

Smooth Connes--Thom isomorphism, cyclic homology, and equivariant quantisation

Using a smooth version of the Connes--Thom isomorphism in Grensing's bivariant K-theory for locally convex algebras, we prove an equivariant version of the Connes--Thom isomorphism in periodic cyclic homology. As an application, we prove that periodic cyclic homology is invariant with respect to equivariant strict deformation quantization.

math.KT↗

arXiv2019

A note on crossed products of rotation algebras

We compute the $K$-theory of crossed products of rotation algebras $\mathcal{A}_θ$, for any real angle $θ$, by matrices in $\mathrm{SL}(2,\mathbb{Z})$ with infinite order. Using techniques of continuous fields, we show that the canonical inclusion of $\mathcal{A}_θ$ into the crossed products is injective at the level of $K_0$-groups. We then give an explicit set of generators for the $K_0$-groups and compute the tracial ranges concretely.

math.OA↗