Showing 1–50 of 236 results for author: Iyengar, S

Understanding the regulation of star formation within TNG100 galaxies on kpc-scales using machine learning I: Global versus local

Authors: Bryanne McDonough, Sathvika S. Iyengar, Ansa Brew-Smith, Asa F. L. Bluck, Joanna Piotrowska

Abstract: We apply Random Forest and XGBoost machine learning algorithms to determine which galaxy properties most effectively predict star formation and quenching in simulated galaxies. Using spatially-resolved data from approximately 63,000 annular bins across 6,189 TNG100 galaxies, we train classification models to predict quenching states and regression models to predict star formation rate surface dens… ▽ More We apply Random Forest and XGBoost machine learning algorithms to determine which galaxy properties most effectively predict star formation and quenching in simulated galaxies. Using spatially-resolved data from approximately 63,000 annular bins across 6,189 TNG100 galaxies, we train classification models to predict quenching states and regression models to predict star formation rate surface densities. Despite their different algorithmic approaches, both methods produce consistent feature importance rankings, with XGBoost distributing importance more evenly among correlated features. For central galaxies and high-mass satellites, black hole mass dominates quenching predictions, consistent with quenching via active galactic nuclei (AGN) feedback. Classification of low-mass satellites shows overwhelming importance for halo mass, indicating environmental quenching. Star formation predictions are dominated by local stellar mass surface density across all star-forming galaxy types, confirming that active star formation is a local process while quenching is driven by global properties. △ Less

Submitted 16 April, 2026; originally announced April 2026.

Comments: Preprint submitted to Astronomy & Computing

Empowering Future Cybersecurity Leaders: Advancing Students through FINDS Education for Digital Forensic Excellence

Authors: Yashas Hariprasad, Subhash Gurappa, Sundararaj S. Iyengar, Jerry F. Miller, Pronab Mohanty, Naveen Kumar Chaudhary

Abstract: The Forensics Investigations Network in Digital Sciences (FINDS) Research Center of Excellence (CoE), funded by the U.S. Army Research Laboratory, advances Digital Forensic Engineering Education (DFEE) through an integrated research education framework for AI enabled cybersecurity workforce development. FINDS combines high performance computing (HPC), secure software engineering, adversarial analy… ▽ More The Forensics Investigations Network in Digital Sciences (FINDS) Research Center of Excellence (CoE), funded by the U.S. Army Research Laboratory, advances Digital Forensic Engineering Education (DFEE) through an integrated research education framework for AI enabled cybersecurity workforce development. FINDS combines high performance computing (HPC), secure software engineering, adversarial analytics, and experiential learning to address emerging cyber and synthetic media threats. This paper introduces the Multidependency Capacity Building Skills Graph (MCBSG), a directed acyclic graph based model that encodes hierarchical and cross domain dependencies among competencies in AI-driven forensic programming, statistical inference, digital evidence processing, and threat detection. The MCBSG enables structured modeling of skill acquisition pathways and quantitative capacity assessment. Supervised machine learning methods, including entropy-based Decision Tree Classifiers and regression modeling, are applied to longitudinal multi cohort datasets capturing mentoring interactions, laboratory performance metrics, curriculum artifacts, and workshop participation. Feature importance analysis and cross validation identify key predictors of technical proficiency and research readiness. Three year statistical evaluation demonstrates significant gains in forensic programming accuracy, adversarial reasoning, and HPC-enabled investigative workflows. Results validate the MCBSG as a scalable, interpretable framework for data-driven, inclusive cybersecurity education aligned with national defense workforce priorities. △ Less

Submitted 14 March, 2026; v1 submitted 27 February, 2026; originally announced March 2026.

CyberLLM-FINDS 2025: Instruction-Tuned Fine-tuning of Domain-Specific LLMs with Retrieval-Augmented Generation and Graph Integration for MITRE Evaluation

Authors: Vasanth Iyer, Leonardo Bobadilla, S. S. Iyengar

Abstract: Large Language Models (LLMs) such as Gemma-2B have shown strong performance in various natural language processing tasks. However, general-purpose models often lack the domain expertise required for cybersecurity applications. This work presents a methodology to fine-tune the Gemma-2B model into a domain-specific cybersecurity LLM. We detail the processes of dataset preparation, fine-tuning, and s… ▽ More Large Language Models (LLMs) such as Gemma-2B have shown strong performance in various natural language processing tasks. However, general-purpose models often lack the domain expertise required for cybersecurity applications. This work presents a methodology to fine-tune the Gemma-2B model into a domain-specific cybersecurity LLM. We detail the processes of dataset preparation, fine-tuning, and synthetic data generation, along with implications for real-world applications in threat detection, forensic investigation, and attack analysis. Experiments highlight challenges in prompt length distribution during domain-specific fine-tuning. Uneven prompt lengths limit the model's effective use of the context window, constraining local inference to 200-400 tokens despite hardware support for longer sequences. Chain-of-thought styled prompts, paired with quantized weights, yielded the best performance under these constraints. To address context limitations, we employed a hybrid strategy using cloud LLMs for synthetic data generation and local fine-tuning for deployment efficiency. To extend the evaluation, we introduce a Retrieval-Augmented Generation (RAG) pipeline and graph-based reasoning framework. This approach enables structured alignment with MITRE ATT&CK techniques through STIX-based threat intelligence, enhancing recall in multi-hop and long-context scenarios. Graph modules encode entity-neighborhood context and tactic chains, helping mitigate the constraints of short prompt windows. Results demonstrate improved model alignment with tactic, technique, and procedure (TTP) coverage, validating the utility of graph-augmented LLMs in cybersecurity threat intelligence applications. △ Less

Submitted 11 January, 2026; originally announced January 2026.

Comments: 12 pages

Differential Privacy for Secure Machine Learning in Healthcare IoT-Cloud Systems

Authors: N Mangala, Murtaza Rangwala, S Aishwarya, B Eswara Reddy, Rajkumar Buyya, KR Venugopal, SS Iyengar, LM Patnaik

Abstract: Healthcare has become exceptionally sophisticated, as wearables and connected medical devices revolutionize remote patient monitoring, emergency response, medication management, diagnosis, and predictive and prescriptive analytics. Internet of Things and Cloud computing integrated systems (IoT-Cloud) facilitate sensing, automation, and processing for these healthcare applications. While real-time… ▽ More Healthcare has become exceptionally sophisticated, as wearables and connected medical devices revolutionize remote patient monitoring, emergency response, medication management, diagnosis, and predictive and prescriptive analytics. Internet of Things and Cloud computing integrated systems (IoT-Cloud) facilitate sensing, automation, and processing for these healthcare applications. While real-time response is crucial for alleviating patient emergencies, protecting patient privacy is paramount in data-driven healthcare. In this paper, we propose a multi-layer IoT, Edge, and Cloud architecture to enhance emergency healthcare response times by distributing tasks based on response criticality and data permanence requirements. We ensure patient privacy through a Differential Privacy framework applied across several machine learning models: K-means, Logistic Regression, Random Forest, and Naive Bayes. We establish a comprehensive threat model identifying three adversary classes and evaluate Laplace, Gaussian, and hybrid noise mechanisms across varying privacy budgets, with supervised algorithms achieving up to 83.6% accuracy. The proposed hybrid Laplace-Gaussian noise mechanism with adaptive budget allocation provides a balanced approach, offering moderate tails and better privacy-utility trade-offs for both low and high-dimension datasets. At the practical threshold of $\varepsilon$=5.0, supervised algorithms achieve 80-81% accuracy while reducing attribute inference attacks by up to 18% and data reconstruction correlation by 70%. We further enhance security through Blockchain integration, which ensures trusted communication through time-stamping, traceability, and immutability for analytics applications. Edge computing demonstrates 8$\times$ latency reduction for emergency scenarios, validating the hierarchical architecture for time-critical operations. △ Less

Submitted 1 April, 2026; v1 submitted 11 December, 2025; originally announced December 2025.

Future of AI Models: A Computational perspective on Model collapse

Authors: Trivikram Satharasi, S Sitharama Iyengar

Abstract: Artificial Intelligence, especially Large Language Models (LLMs), has transformed domains such as software engineering, journalism, creative writing, academia, and media (Naveed et al. 2025; arXiv:2307.06435). Diffusion models like Stable Diffusion generate high-quality images and videos from text. Evidence shows rapid expansion: 74.2% of newly published webpages now contain AI-generated material… ▽ More Artificial Intelligence, especially Large Language Models (LLMs), has transformed domains such as software engineering, journalism, creative writing, academia, and media (Naveed et al. 2025; arXiv:2307.06435). Diffusion models like Stable Diffusion generate high-quality images and videos from text. Evidence shows rapid expansion: 74.2% of newly published webpages now contain AI-generated material (Ryan Law 2025), 30-40% of the active web corpus is synthetic (Spennemann 2025; arXiv:2504.08755), 52% of U.S. adults use LLMs for writing, coding, or research (Staff 2025), and audits find AI involvement in 18% of financial complaints and 24% of press releases (Liang et al. 2025). The underlying neural architectures, including Transformers (Vaswani et al. 2023; arXiv:1706.03762), RNNs, LSTMs, GANs, and diffusion networks, depend on large, diverse, human-authored datasets (Shi & Iyengar 2019). As synthetic content dominates, recursive training risks eroding linguistic and semantic diversity, producing Model Collapse (Shumailov et al. 2024; arXiv:2307.15043; Dohmatob et al. 2024; arXiv:2402.07712). This study quantifies and forecasts collapse onset by examining year-wise semantic similarity in English-language Wikipedia (filtered Common Crawl) from 2013 to 2025 using Transformer embeddings and cosine similarity metrics. Results reveal a steady rise in similarity before public LLM adoption, likely driven by early RNN/LSTM translation and text-normalization pipelines, though modest due to a smaller scale. Observed fluctuations reflect irreducible linguistic diversity, variable corpus size across years, finite sampling error, and an exponential rise in similarity after the public adoption of LLM models. These findings provide a data-driven estimate of when recursive AI contamination may significantly threaten data richness and model generalization. △ Less

Submitted 29 October, 2025; originally announced November 2025.

Comments: Submitted to Springer Nature. Code Available at https://github.com/t-satharasi/AI-Modal-Collapse-Code-for-Reproduction.git

ACM Class: I.2.0

Collective Communication for 100k+ GPUs

Authors: Min Si, Pavan Balaji, Yongzhou Chen, Ching-Hsiang Chu, Adi Gangidi, Saif Hasan, Subodh Iyengar, Dan Johnson, Bingzhe Liu, Regina Ren, Deep Shah, Ashmitha Jeevaraj Shetty, Greg Steinbrecher, Yulun Wang, Bruce Wu, Xinfeng Xie, Jingyi Yang, Mingran Yang, Kenny Yu, Minlan Yu, Cen Zhao, Wes Bland, Denis Boyda, Suman Gumudavelli, Prashanth Kannan , et al. (14 additional authors not shown)

Abstract: The increasing scale of large language models (LLMs) necessitates highly efficient collective communication frameworks, particularly as training workloads extend to hundreds of thousands of GPUs. Traditional communication methods face significant throughput and latency limitations at this scale, hindering both the development and deployment of state-of-the-art models. This paper presents the NCCLX… ▽ More The increasing scale of large language models (LLMs) necessitates highly efficient collective communication frameworks, particularly as training workloads extend to hundreds of thousands of GPUs. Traditional communication methods face significant throughput and latency limitations at this scale, hindering both the development and deployment of state-of-the-art models. This paper presents the NCCLX collective communication framework, developed at Meta, engineered to optimize performance across the full LLM lifecycle, from the synchronous demands of large-scale training to the low-latency requirements of inference. The framework is designed to support complex workloads on clusters exceeding 100,000 GPUs, ensuring reliable, high-throughput, and low-latency data exchange. Empirical evaluation on the Llama4 model demonstrates substantial improvements in communication efficiency. This research contributes a robust solution for enabling the next generation of LLMs to operate at unprecedented scales. △ Less

Submitted 9 January, 2026; v1 submitted 22 October, 2025; originally announced October 2025.

ACM Class: C.2.4; I.2

Commutative algebra inspired by modularity lifting

Authors: Srikanth B. Iyengar

Abstract: This article gives an overview of some recent results in commutative algebra that are inspired by the work of Wiles, Taylor and Wiles, Diamond, Lenstra and others on the modularity of elliptic curves. This article gives an overview of some recent results in commutative algebra that are inspired by the work of Wiles, Taylor and Wiles, Diamond, Lenstra and others on the modularity of elliptic curves. △ Less

Submitted 27 March, 2026; v1 submitted 13 October, 2025; originally announced October 2025.

Comments: This is submitted to the proceedings of the International Congress of Mathematicians 2026. 11 pages. Comments welcome. Minor corrections, mostly typographical, in this version

MSC Class: 13C10; 13D02 (Primary); 11F80 (Secondary)

The commutative algebra of congruence ideals and applications to number theory

Authors: Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning

Abstract: In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to ``higher codimension''. A critical ingredient is a notion of congruence module in higher codimension: this has turned out to be a key definition whose utility e… ▽ More In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to ``higher codimension''. A critical ingredient is a notion of congruence module in higher codimension: this has turned out to be a key definition whose utility extends beyond the role it plays in the numerical criterion. In this paper we trace the origin of some of the ideas that led to our work, both in number theory and commutative algebra, and new directions that emerge from it. We introduce a related notion of a congruence ideal. When applied to deformation theory of Galois representations and Hecke algebras, which is the setting of Wiles's work on Fermat's Last Theorem, our work leads to the notion of congruence ideals for local deformation rings. This sheds light on the classically studied congruence ideals for global deformation rings and Hecke algebras. We outline applications of the commutative algebra we have developed to: (i) integral modularity lifting theorems in the context of weight one forms, and (ii) factorization formulas for congruence ideals of global deformation rings at augmentations induced by newforms in which local congruence ideals enter as the local terms. The latter leads to surprising relations between these local congruence ideals and local Tamagawa ideals of Bloch-Kato associated to the rank 3 adjoint motive of $f$. △ Less

Submitted 27 March, 2026; v1 submitted 6 October, 2025; originally announced October 2025.

Comments: 52. This version is a significant revision from the first one

MSC Class: 11F80; 13C10; 13D02

Ulrich modules over local rings of dimension two

Authors: Srikanth B. Iyengar, Linquan Ma, Mark E. Walker

Abstract: It is proved that Ulrich modules exist for a large class of local rings of dimension two. This complements earlier work of the authors and Ziquan Zhuang that described complete intersection domains of dimension two that admit no Ulrich modules. As an application, it is proved that, for this class of rings, the length of a nonzero module of finite projective dimension is at least the multiplicity o… ▽ More It is proved that Ulrich modules exist for a large class of local rings of dimension two. This complements earlier work of the authors and Ziquan Zhuang that described complete intersection domains of dimension two that admit no Ulrich modules. As an application, it is proved that, for this class of rings, the length of a nonzero module of finite projective dimension is at least the multiplicity of the local ring. △ Less

Submitted 2 October, 2025; originally announced October 2025.

Comments: 14 pages

MSC Class: 13C13 (primary); 13H10; 13C14; 14F06 (secondary)

LABELING COPILOT: A Deep Research Agent for Automated Data Curation in Computer Vision

Authors: Debargha Ganguly, Sumit Kumar, Ishwar Balappanawar, Weicong Chen, Shashank Kambhatla, Srinivasan Iyengar, Shivkumar Kalyanaraman, Ponnurangam Kumaraguru, Vipin Chaudhary

Abstract: Curating high-quality, domain-specific datasets is a major bottleneck for deploying robust vision systems, requiring complex trade-offs between data quality, diversity, and cost when researching vast, unlabeled data lakes. We introduce Labeling Copilot, the first data curation deep research agent for computer vision. A central orchestrator agent, powered by a large multimodal language model, uses… ▽ More Curating high-quality, domain-specific datasets is a major bottleneck for deploying robust vision systems, requiring complex trade-offs between data quality, diversity, and cost when researching vast, unlabeled data lakes. We introduce Labeling Copilot, the first data curation deep research agent for computer vision. A central orchestrator agent, powered by a large multimodal language model, uses multi-step reasoning to execute specialized tools across three core capabilities: (1) Calibrated Discovery sources relevant, in-distribution data from large repositories; (2) Controllable Synthesis generates novel data for rare scenarios with robust filtering; and (3) Consensus Annotation produces accurate labels by orchestrating multiple foundation models via a novel consensus mechanism incorporating non-maximum suppression and voting. Our large-scale validation proves the effectiveness of Labeling Copilot's components. The Consensus Annotation module excels at object discovery: on the dense COCO dataset, it averages 14.2 candidate proposals per image-nearly double the 7.4 ground-truth objects-achieving a final annotation mAP of 37.1%. On the web-scale Open Images dataset, it navigated extreme class imbalance to discover 903 new bounding box categories, expanding its capability to over 1500 total. Concurrently, our Calibrated Discovery tool, tested at a 10-million sample scale, features an active learning strategy that is up to 40x more computationally efficient than alternatives with equivalent sample efficiency. These experiments validate that an agentic workflow with optimized, scalable tools provides a robust foundation for curating industrial-scale datasets. △ Less

Submitted 26 September, 2025; originally announced September 2025.

Raw2Event: Converting Raw Frame Camera into Event Camera

Authors: Zijie Ning, Enmin Lin, Sudarshan R. Iyengar, Patrick Vandewalle

Abstract: Event cameras offer unique advantages such as high temporal resolution, low latency, and high dynamic range, making them more and more popular for vision tasks under challenging light conditions. However, their high cost, limited resolution, and lack of features such as autofocus hinder their broad adoption, particularly for early-stage development and prototyping. In this work, we present Raw2Eve… ▽ More Event cameras offer unique advantages such as high temporal resolution, low latency, and high dynamic range, making them more and more popular for vision tasks under challenging light conditions. However, their high cost, limited resolution, and lack of features such as autofocus hinder their broad adoption, particularly for early-stage development and prototyping. In this work, we present Raw2Event, a complete hardware-software system that enables real-time event generation from low-cost raw frame-based cameras. By leveraging direct access to raw Bayer data and bypassing traditional image signal processors (ISP), our system is able to utilize the full potential of camera hardware, delivering higher dynamic range, higher resolution, and more faithful output than RGB-based frame-to-event converters. Built upon the DVS-Voltmeter model, Raw2Event features a configurable simulation framework optimized for deployment on embedded platforms. We further design a data acquisition pipeline that supports synchronized recording of raw, RGB, and event streams, facilitating downstream evaluation and dataset creation. Experimental results show that Raw2Event can generate event streams closely resembling those from real event cameras, while benefiting from higher resolution and autofocus capabilities. The system also supports user-intuitive parameter tuning, enabling flexible adaptation to various application requirements. Finally, we deploy the system on a Raspberry Pi for real-time operation, providing a scalable and cost-effective solution for event-based vision research and early-stage system development. The codes are available online: https://anonymous.4open.science/r/raw2event-BFF2/README.md. △ Less

Submitted 8 September, 2025; originally announced September 2025.

Comments: Submitted to IEEE Transactions on Robotics (Special Section on Event-based Vision for Robotics), under review. This version is submitted for peer review and may be updated upon acceptance

Unstable elements in cohomology and a question of Lescot

Authors: Srikanth B. Iyengar, Sarasij Maitra, Tim Tribone

Abstract: In his work on the Bass series of syzygy modules of modules over a commutative noetherian local ring $R$, Lescot introduces a numerical invariant, denoted $σ(R)$, and asks whether it is finite for any $R$. He proves that this is so when $R$ is Gorenstein or Golod. In the present work many new classes of rings $R$ for which $σ(R)$ is finite are identified. The new insight is that $σ(R)$ is related… ▽ More In his work on the Bass series of syzygy modules of modules over a commutative noetherian local ring $R$, Lescot introduces a numerical invariant, denoted $σ(R)$, and asks whether it is finite for any $R$. He proves that this is so when $R$ is Gorenstein or Golod. In the present work many new classes of rings $R$ for which $σ(R)$ is finite are identified. The new insight is that $σ(R)$ is related to the natural map from the usual cohomology of the module to its stable cohomology, which permits the use of multiplicative structures to study the question of finiteness of $σ(R)$. △ Less

Submitted 30 July, 2025; originally announced July 2025.

Comments: 25 pages

MSC Class: 13D02; 13D07

Intelligibility of Text-to-Speech Systems for Mathematical Expressions

Authors: Sujoy Roychowdhury, H. G. Ranjani, Sumit Soman, Nishtha Paul, Subhadip Bandyopadhyay, Siddhanth Iyengar

Abstract: There has been limited evaluation of advanced Text-to-Speech (TTS) models with Mathematical eXpressions (MX) as inputs. In this work, we design experiments to evaluate quality and intelligibility of five TTS models through listening and transcribing tests for various categories of MX. We use two Large Language Models (LLMs) to generate English pronunciation from LaTeX MX as TTS models cannot proce… ▽ More There has been limited evaluation of advanced Text-to-Speech (TTS) models with Mathematical eXpressions (MX) as inputs. In this work, we design experiments to evaluate quality and intelligibility of five TTS models through listening and transcribing tests for various categories of MX. We use two Large Language Models (LLMs) to generate English pronunciation from LaTeX MX as TTS models cannot process LaTeX directly. We use Mean Opinion Score from user ratings and quantify intelligibility through transcription correctness using three metrics. We also compare listener preference of TTS outputs with respect to human expert rendition of same MX. Results establish that output of TTS models for MX is not necessarily intelligible, the gap in intelligibility varies across TTS models and MX category. For most categories, performance of TTS models is significantly worse than that of expert rendition. The effect of choice of LLM is limited. This establishes the need to improve TTS models for MX. △ Less

Submitted 5 June, 2025; originally announced June 2025.

Comments: Accepted at Interspeech 2025

State Dependent Optimization with Quantum Circuit Cutting

Authors: Xinpeng Li, Ji Liu, Jeffrey M. Larson, Shuai Xu, Sundararaja Sitharama Iyengar, Paul Hovland, Vipin Chaudhary

Abstract: Quantum circuits can be reduced through optimization to better fit the constraints of quantum hardware. One such method, initial-state dependent optimization (ISDO), reduces gate count by leveraging knowledge of the input quantum states. Surprisingly, we found that ISDO is broadly applicable to the downstream circuits produced by circuit cutting. Circuit cutting also requires measuring upstream… ▽ More Quantum circuits can be reduced through optimization to better fit the constraints of quantum hardware. One such method, initial-state dependent optimization (ISDO), reduces gate count by leveraging knowledge of the input quantum states. Surprisingly, we found that ISDO is broadly applicable to the downstream circuits produced by circuit cutting. Circuit cutting also requires measuring upstream qubits and has some flexibility of selection observables to do reconstruction. Therefore, we propose a state-dependent optimization (SDO) framework that incorporates ISDO, our newly proposed measure-state dependent optimization (MSDO), and a biased observable selection strategy. Building on the strengths of the SDO framework and recognizing the scalability challenges of circuit cutting, we propose non-separate circuit cutting-a more flexible approach that enables optimizing gates without fully separating them. We validate our methods on noisy simulations of QAOA, QFT, and BV circuits. Results show that our approach consistently mitigates noise and improves overall circuit performance, demonstrating its promise for enhancing quantum algorithm execution on near-term hardware. △ Less

Submitted 5 June, 2025; originally announced June 2025.

Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Tasks

Authors: Debargha Ganguly, Vikash Singh, Sreehari Sankar, Biyao Zhang, Xuecen Zhang, Srinivasan Iyengar, Xiaotian Han, Amit Sharma, Shivkumar Kalyanaraman, Vipin Chaudhary

Abstract: Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated for… ▽ More Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic guarantees. This paper addresses this epistemological gap by comprehensively investigating failure modes and uncertainty quantification (UQ) in LLM-generated formal artifacts. Our systematic evaluation of five frontier LLMs reveals Satisfiability Modulo Theories (SMT) based autoformalization's domain-specific impact on accuracy (from +34.8% on logical tasks to -44.5% on factual ones), with known UQ techniques like the entropy of token probabilities failing to identify these errors. We introduce a probabilistic context-free grammar (PCFG) framework to model LLM outputs, yielding a refined uncertainty taxonomy. We find uncertainty signals are task-dependent (e.g., grammar entropy for logic, AUROC>0.93). Finally, a lightweight fusion of these signals enables selective verification, drastically reducing errors (14-100%) with minimal abstention, transforming LLM-driven formalization into a reliable engineering discipline. △ Less

Submitted 26 May, 2025; originally announced May 2025.

The spectrum of local dualisable modular representations

Authors: Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova

Abstract: For a point $\mathfrak{p}$ in the spectrum of the cohomology ring of a finite group $G$ over a field $k$, we calculate the spectrum for the subcategory of dualisable objects inside the tensor triangulated category of $\mathfrak{p}$-local and $\mathfrak{p}$-torsion objects in the (big) stable module category of the group algebra $kG$. For a point $\mathfrak{p}$ in the spectrum of the cohomology ring of a finite group $G$ over a field $k$, we calculate the spectrum for the subcategory of dualisable objects inside the tensor triangulated category of $\mathfrak{p}$-local and $\mathfrak{p}$-torsion objects in the (big) stable module category of the group algebra $kG$. △ Less

Submitted 25 May, 2025; originally announced May 2025.

Comments: 15 pages

MSC Class: 20C20 (primary); 18G80; 20J06 (secondary)

AI Greenferencing: Routing AI Inferencing to Green Modular Data Centers with Heron

Authors: Tella Rajashekhar Reddy, Palak, Rohan Gandhi, Anjaly Parayil, Chaojie Zhang, Mike Shepperd, Liangcheng Yu, Jayashree Mohan, Srinivasan Iyengar, Shivkumar Kalyanaraman, Debopam Bhattacherjee

Abstract: AI power demand is growing unprecedentedly thanks to the high power density of AI compute and the emerging inferencing workload. On the supply side, abundant wind power is waiting for grid access in interconnection queues. In this light, this paper argues bringing AI workload to modular compute clusters co-located in wind farms. Our deployment right-sizing strategy makes it economically viable to… ▽ More AI power demand is growing unprecedentedly thanks to the high power density of AI compute and the emerging inferencing workload. On the supply side, abundant wind power is waiting for grid access in interconnection queues. In this light, this paper argues bringing AI workload to modular compute clusters co-located in wind farms. Our deployment right-sizing strategy makes it economically viable to deploy more than 6 million high-end GPUs today that could consume cheap, green power at its source. We built Heron, a cross-site software router, that could efficiently leverage the complementarity of power generation across wind farms by routing AI inferencing workload around power drops. Using 1-week ofcoding and conversation production traces from Azure and (real) variable wind power traces, we show how Heron improves aggregate goodput of AI compute by up to 80% compared to the state-of-the-art. △ Less

Submitted 15 May, 2025; originally announced May 2025.

Using random perturbations to infer the structure of feedback control in gene expression

Authors: Seshu Iyengar, Andreas Hilfinger

Abstract: Feedback in cellular processes is typically inferred through cellular responses to experimental perturbations. Modular response analysis provides a theoretical framework for translating specific perturbations into feedback sensitivities between cellular modules. However, in large-scale drug perturbation studies the effect of any given drug may not be known and may not only affect one module at a t… ▽ More Feedback in cellular processes is typically inferred through cellular responses to experimental perturbations. Modular response analysis provides a theoretical framework for translating specific perturbations into feedback sensitivities between cellular modules. However, in large-scale drug perturbation studies the effect of any given drug may not be known and may not only affect one module at a time. Here, we analyze the response of gene expression models to random perturbations that affect multiple modules simultaneously. In the deterministic regime we analytically show how cellular responses to infinitesimal random perturbations can be used to infer the nature of feedback regulation in gene expression, as long as the effects of perturbations are statistically independent between modules. We numerically extend this deterministic analysis to the response of average abundances of stochastic gene expression models to finite perturbations. Across a large sample of stochastic models, the response of average abundances generally obeyed predicted bounds from the deterministic analysis, but dramatic deviations occurred in systems with bimodal or fat-tailed stationary state distributions. These discrepancies demonstrate how deterministic analyses can fail to capture the effect of perturbations on averages of stochastic cellular feedback systems--even in the linear response regime. △ Less

Submitted 7 May, 2025; originally announced May 2025.

Nonclassical states of light induced via measurement in a bimodalsystem

Authors: R. Chakrabarti, S. V. Iyengar, B. V. Jenisha

Abstract: We investigate generation of nonclassical photon states via conditional measurement process in a two mode coupled waveguide. Interaction of the fields takes place in a waveguide beamsplitter due to the overlap between normal modes supported therein. A quadratic Hamiltonian of two degrees of freedom describes the hopping interaction. An initial two mode squeezed state undergoes a unitary evolution… ▽ More We investigate generation of nonclassical photon states via conditional measurement process in a two mode coupled waveguide. Interaction of the fields takes place in a waveguide beamsplitter due to the overlap between normal modes supported therein. A quadratic Hamiltonian of two degrees of freedom describes the hopping interaction. An initial two mode squeezed state undergoes a unitary evolution governed by the interaction Hamiltonian for a specified time. Following this the bipartite state is subjected to a projective measurement that detects $n$-th Fock state in one subsystem. The post-measurement excitation rendered in the residual subsystem depends on the prior time of interaction between the modes as well as the interaction strength. The Wigner quasiprobability distribution of an arbitrary post-selection state is computed. Its nonclassicality is examined via the negativity of the Wigner distribution. The sub-Poissonian nature of the photon statistics is revealed by the Mandel parameter. The dynamically generated squeezing is evidenced in the post-measurement state. In the ultrastrong coupling regime the parity even and odd states display markedly \textit{different} nonclassical properties. The nonclassicality of the post-measurement states obtained here may be \textit{controlled} by varying the interaction strength and the time span of interaction between the modes. △ Less

Submitted 11 April, 2025; originally announced April 2025.

Journal ref: J. Phys. B: At. Mol. Opt. Phys. 58 085401 (2025)

Sub-nm Curvature Unlocks Quantum Flexoelectricity in Graphene

Authors: Sathvik Ajay Iyengar, James G. McHugh, Jonathan P. Salvage, Robert Vajtai, Alan Dalton, Manoj Tripathi, Pulickel M. Ajayan, Vincent Meunier

Abstract: Flexoelectricity, polarization induced by strain gradients, is especially pronounced in two-dimensional (2D) materials due to their mechanical flexibility and sensitivity to mechanical deformation. In nanostructures with sub-nm curvature, this effect is governed by quantum-mechanical polarization and electrostatic modulation, not merely classical lattice distortion. Here, we present the first dire… ▽ More Flexoelectricity, polarization induced by strain gradients, is especially pronounced in two-dimensional (2D) materials due to their mechanical flexibility and sensitivity to mechanical deformation. In nanostructures with sub-nm curvature, this effect is governed by quantum-mechanical polarization and electrostatic modulation, not merely classical lattice distortion. Here, we present the first direct experimental and theoretical demonstration of large intrinsic quantum flexoelectricity in graphene nanowrinkles, exhibiting polarization densities (P_{th} ~ 4 C/m^{2}, P_{exp} ~ 1 C/m^{2}) that exceed those of mesoscale systems by 5 to 7 orders of magnitude. These nanowrinkles, with sub-nm radii of curvature at their apex, undergo atomic-level buckling and result in localized strain fields, as confirmed by sub-micron Raman spectroscopy. These curvatures create an asymmetry to π-orbital interactions across the atomic layer, which, in turn, leads to localized polarization densities. Kelvin probe force microscopy reveals curvature-dependent work function shifts consistent with flexoelectric polarization, while conductive atomic force microscopy detects reproducible flexoelectric currents exhibiting a threshold voltage (Φth ~1 V) that matches the band offset predicted by ab initio calculations (~1.2 V). Together, these results confirm how flexoelectric dipoles reshape the local electronic potential. Graphene nanowrinkles thus provide a pristine platform for uncovering quantum-mechanical flexoelectricity: a fundamentally ubiquitous effect, whose study in the simplest crystalline material can illuminate electromechanical behavior across condensed matter, soft matter, and biological systems. △ Less

Submitted 27 June, 2025; v1 submitted 27 March, 2025; originally announced March 2025.

Comments: 29 pages, 5 main figures, 12 supplementary figures

Composition based machine learning to predict phases & strength of refractory high entropy alloys

Authors: M. Sreenidhi Iyengar, M. K Anirudh, P. H. Anantha Desik, M. P. Phaniraj

Abstract: Refractory high-entropy alloys can function at temperatures exceeding those of nickel-based superalloys. Aluminum, as an alloying element, contributes multiple advantageous characteristics to various high-temperature alloys. The Aluminum containing RHEAs have the potential of being the best high temperature materials. In the present study we use the machine learning(ML) technique to determine the… ▽ More Refractory high-entropy alloys can function at temperatures exceeding those of nickel-based superalloys. Aluminum, as an alloying element, contributes multiple advantageous characteristics to various high-temperature alloys. The Aluminum containing RHEAs have the potential of being the best high temperature materials. In the present study we use the machine learning(ML) technique to determine the phase and yield strength of aluminum containing RHEAs. In this regard, we created the Al-RHEA dataset from the published [1] compilation of RHEA data. We applied multiple ML algorithms to the training set and determined that the CatBoost algorithm gave the best performance. We optimized the hyperparameters of this algorithm and tested it for robustness using cross-validation methods. The CatBoost model predicts the yield strength of test data accurately (R2=0.98). The algorithm was applied to estimate the yield strength for alloy compositions absent from our current dataset, achieving accurate predictions for these unrecorded alloys indicating that the model has learnt the underlying rules to predict the yield strength sufficiently. We then predict the effect of varying aluminum content on yield strength of RHEA. The model predictions were rationalized in view of published data on Al-RHEAs. We also developed the CatBoost classifier model that predicts the phases formed in the alloy of a given composition accurately. The cause for errors in phase prediction is discussed. △ Less

Submitted 27 March, 2025; originally announced March 2025.

Comments: 27 pages including 7 figure, 7 tables & Graphical abstract

Distributed LLMs and Multimodal Large Language Models: A Survey on Advances, Challenges, and Future Directions

Authors: Hadi Amini, Md Jueal Mia, Yasaman Saadati, Ahmed Imteaj, Seyedsina Nabavirazavi, Urmish Thakker, Md Zarif Hossain, Awal Ahmed Fime, S. S. Iyengar

Abstract: Language models (LMs) are machine learning models designed to predict linguistic patterns by estimating the probability of word sequences based on large-scale datasets, such as text. LMs have a wide range of applications in natural language processing (NLP) tasks, including autocomplete and machine translation. Although larger datasets typically enhance LM performance, scalability remains a challe… ▽ More Language models (LMs) are machine learning models designed to predict linguistic patterns by estimating the probability of word sequences based on large-scale datasets, such as text. LMs have a wide range of applications in natural language processing (NLP) tasks, including autocomplete and machine translation. Although larger datasets typically enhance LM performance, scalability remains a challenge due to constraints in computational power and resources. Distributed computing strategies offer essential solutions for improving scalability and managing the growing computational demand. Further, the use of sensitive datasets in training and deployment raises significant privacy concerns. Recent research has focused on developing decentralized techniques to enable distributed training and inference while utilizing diverse computational resources and enabling edge AI. This paper presents a survey on distributed solutions for various LMs, including large language models (LLMs), vision language models (VLMs), multimodal LLMs (MLLMs), and small language models (SLMs). While LLMs focus on processing and generating text, MLLMs are designed to handle multiple modalities of data (e.g., text, images, and audio) and to integrate them for broader applications. To this end, this paper reviews key advancements across the MLLM pipeline, including distributed training, inference, fine-tuning, and deployment, while also identifying the contributions, limitations, and future areas of improvement. Further, it categorizes the literature based on six primary focus areas of decentralization. Our analysis describes gaps in current methodologies for enabling distributed solutions for LMs and outline future research directions, emphasizing the need for novel solutions to enhance the robustness and applicability of distributed LMs. △ Less

Submitted 20 March, 2025; originally announced March 2025.

EnCortex: A General, Extensible and Scalable Framework for Decision Management in New-age Energy Systems

Authors: Millend Roy, Vaibhav Balloli, Anupam Sobti, Srinivasan Iyengar, Shivkumar Kalyanaraman, Tanuja Ganu, Akshay Nambi

Abstract: With increased global warming, there has been a significant emphasis to replace fossil fuel-dependent energy sources with clean, renewable sources. These new-age energy systems are becoming more complex with an increasing proportion of renewable energy sources (like solar and wind), energy storage systems (like batteries), and demand side control in the mix. Most new-age sources being highly depen… ▽ More With increased global warming, there has been a significant emphasis to replace fossil fuel-dependent energy sources with clean, renewable sources. These new-age energy systems are becoming more complex with an increasing proportion of renewable energy sources (like solar and wind), energy storage systems (like batteries), and demand side control in the mix. Most new-age sources being highly dependent on weather and climate conditions bring about high variability and uncertainty. Energy operators rely on such uncertain data to make different planning and operations decisions periodically, and sometimes in real-time, to maintain the grid stability and optimize their objectives (cost savings, carbon footprint, etc.). Hitherto, operators mostly rely on domain knowledge, heuristics, or solve point problems to take decisions. These approaches fall short because of their specific assumptions and limitations. Further, there is a lack of a unified framework for both research and production environments at scale. In this paper, we propose EnCortex to address these challenges. EnCortex provides a general, easy-to-use, extensible, and scalable energy decision framework that enables operators to plan, build and execute their real-world scenarios efficiently. We show that using EnCortex, we can define and compose complex new-age scenarios, owing to industry-standard abstractions of energy entities and the modularity of the framework. EnCortex provides a foundational structure to support several state-of-the-art optimizers with minimal effort. EnCortex supports both quick developments for research prototypes and scaling the solutions to production environments. We demonstrate the utility of EnCortex with three complex new-age real-world scenarios and show that significant cost and carbon footprint savings can be achieved. △ Less

Submitted 10 March, 2025; originally announced March 2025.

Homological properties of the module of differentials

Authors: Jürgen Herzog, Benjamin Briggs, Srikanth B. Iyengar

Abstract: These notes were produced by Jürgen Herzog to accompany his lectures in Recife, Brazil, in 1980, on the homological algebra of noetherian local rings. They are are concerned with two conjectures made by Wolmer Vasconcelos: if the conormal module of a local ring has finite projective dimension, or if the module of differentials, taken over an appropriate field, has finite projective dimension, then… ▽ More These notes were produced by Jürgen Herzog to accompany his lectures in Recife, Brazil, in 1980, on the homological algebra of noetherian local rings. They are are concerned with two conjectures made by Wolmer Vasconcelos: if the conormal module of a local ring has finite projective dimension, or if the module of differentials, taken over an appropriate field, has finite projective dimension, then the ring must be complete intersection. The notes present an accessible and self-contained account of the strongest results known at the time in connection with these problems; this includes a number of ideas that have not appeared elsewhere. In the last section, Herzog turns his attention to the cotangent complex, and conjectures himself that if the cotangent complex of a local ring has bounded homology groups, then the ring must be complete intersection. Among other results, he proves that the conjecture holds for local rings of characteristic zero over which all modules have rational Poincaré series. Sadly Jürgen Herzog passed away in April of 2024. The notes in this form have been prepared in his memory, newly typeset and lightly edited. A short appendix has been added to survey some of the results of the intervening decades. △ Less

Submitted 19 February, 2025; originally announced February 2025.

Comments: To appear in a volume dedicated to Wolmer Vasconcelos

MSC Class: 13D07 (primary) 16E45; 13D02; 13D40 (secondary)

A freeness criterion for complexes with derived actions

Authors: Sylvain Brochard, Srikanth B. Iyengar, Chandrashekhar B. Khare

Abstract: Inspired by the patching method of Calegari and Geraghty, and a conjecture of de Smit that has been proved by the first author, we present a conjectural freeness criterion without patching for complexes over commutative noetherian local rings with derived actions, and verify it in several cases. Inspired by the patching method of Calegari and Geraghty, and a conjecture of de Smit that has been proved by the first author, we present a conjectural freeness criterion without patching for complexes over commutative noetherian local rings with derived actions, and verify it in several cases. △ Less

Submitted 18 February, 2025; originally announced February 2025.

Comments: 17 pages

MSC Class: 13C10 (primary); 13D02; 11F80 (secondary)

SPIRIT: Short-term Prediction of solar IRradIance for zero-shot Transfer learning using Foundation Models

Authors: Aditya Mishra, Ravindra T, Srinivasan Iyengar, Shivkumar Kalyanaraman, Ponnurangam Kumaraguru

Abstract: Traditional solar forecasting models are based on several years of site-specific historical irradiance data, often spanning five or more years, which are unavailable for newer photovoltaic farms. As renewable energy is highly intermittent, building accurate solar irradiance forecasting systems is essential for efficient grid management and enabling the ongoing proliferation of solar energy, which… ▽ More Traditional solar forecasting models are based on several years of site-specific historical irradiance data, often spanning five or more years, which are unavailable for newer photovoltaic farms. As renewable energy is highly intermittent, building accurate solar irradiance forecasting systems is essential for efficient grid management and enabling the ongoing proliferation of solar energy, which is crucial to achieve the United Nations' net zero goals. In this work, we propose SPIRIT, a novel approach leveraging foundation models for solar irradiance forecasting, making it applicable to newer solar installations. Our approach outperforms state-of-the-art models in zero-shot transfer learning by about 70%, enabling effective performance at new locations without relying on any historical data. Further improvements in performance are achieved through fine-tuning, as more location-specific data becomes available. These findings are supported by statistical significance, further validating our approach. SPIRIT represents a pivotal step towards rapid, scalable, and adaptable solar forecasting solutions, advancing the integration of renewable energy into global power systems. △ Less

Submitted 9 November, 2025; v1 submitted 14 February, 2025; originally announced February 2025.

The Query/Hit Model for Sequential Hypothesis Testing

Authors: Mahshad Shariatnasab, Stefano Rini, Farhad Shirani, S. Sitharama Iyengar

Abstract: This work introduces the Query/Hit (Q/H) learning model. The setup consists of two agents. One agent, Alice, has access to a streaming source, while the other, Bob, does not have direct access to the source. Communication occurs through sequential Q/H pairs: Bob sends a sequence of source symbols (queries), and Alice responds with the waiting time until each query appears in the source stream (hit… ▽ More This work introduces the Query/Hit (Q/H) learning model. The setup consists of two agents. One agent, Alice, has access to a streaming source, while the other, Bob, does not have direct access to the source. Communication occurs through sequential Q/H pairs: Bob sends a sequence of source symbols (queries), and Alice responds with the waiting time until each query appears in the source stream (hits). This model is motivated by scenarios with communication, computation, and privacy constraints that limit real-time access to the source. The error exponent for sequential hypothesis testing under the Q/H model is characterized, and a querying strategy, the Dynamic Scout-Sentinel Algorithm (DSSA), is proposed. The strategy employs a mutual information neural estimator to compute the error exponent associated with each query and to select the query with the highest efficiency. Extensive empirical evaluations on both synthetic and real-world datasets -- including mouse movement trajectories, typesetting patterns, and touch-based user interactions -- are provided to evaluate the performance of the proposed strategy in comparison with baselines, in terms of probability of error, query choice, and time-to-detection. △ Less

Submitted 1 February, 2025; originally announced February 2025.

Do We Really Need to Design New Byzantine-robust Aggregation Rules?

Authors: Minghong Fang, Seyedsina Nabavirazavi, Zhuqing Liu, Wei Sun, Sundararaja Sitharama Iyengar, Haibo Yang

Abstract: Federated learning (FL) allows multiple clients to collaboratively train a global machine learning model through a server, without exchanging their private training data. However, the decentralized aspect of FL makes it susceptible to poisoning attacks, where malicious clients can manipulate the global model by sending altered local model updates. To counter these attacks, a variety of aggregation… ▽ More Federated learning (FL) allows multiple clients to collaboratively train a global machine learning model through a server, without exchanging their private training data. However, the decentralized aspect of FL makes it susceptible to poisoning attacks, where malicious clients can manipulate the global model by sending altered local model updates. To counter these attacks, a variety of aggregation rules designed to be resilient to Byzantine failures have been introduced. Nonetheless, these methods can still be vulnerable to sophisticated attacks or depend on unrealistic assumptions about the server. In this paper, we demonstrate that there is no need to design new Byzantine-robust aggregation rules; instead, FL can be secured by enhancing the robustness of well-established aggregation rules. To this end, we present FoundationFL, a novel defense mechanism against poisoning attacks. FoundationFL involves the server generating synthetic updates after receiving local model updates from clients. It then applies existing Byzantine-robust foundational aggregation rules, such as Trimmed-mean or Median, to combine clients' model updates with the synthetic ones. We theoretically establish the convergence performance of FoundationFL under Byzantine settings. Comprehensive experiments across several real-world datasets validate the efficiency of our FoundationFL method. △ Less

Submitted 28 January, 2025; originally announced January 2025.

Comments: To appear in NDSS 2025

An Agentic Approach to Automatic Creation of P&ID Diagrams from Natural Language Descriptions

Authors: Shreeyash Gowaikar, Srinivasan Iyengar, Sameer Segal, Shivkumar Kalyanaraman

Abstract: The Piping and Instrumentation Diagrams (P&IDs) are foundational to the design, construction, and operation of workflows in the engineering and process industries. However, their manual creation is often labor-intensive, error-prone, and lacks robust mechanisms for error detection and correction. While recent advancements in Generative AI, particularly Large Language Models (LLMs) and Vision-Langu… ▽ More The Piping and Instrumentation Diagrams (P&IDs) are foundational to the design, construction, and operation of workflows in the engineering and process industries. However, their manual creation is often labor-intensive, error-prone, and lacks robust mechanisms for error detection and correction. While recent advancements in Generative AI, particularly Large Language Models (LLMs) and Vision-Language Models (VLMs), have demonstrated significant potential across various domains, their application in automating generation of engineering workflows remains underexplored. In this work, we introduce a novel copilot for automating the generation of P&IDs from natural language descriptions. Leveraging a multi-step agentic workflow, our copilot provides a structured and iterative approach to diagram creation directly from Natural Language prompts. We demonstrate the feasibility of the generation process by evaluating the soundness and completeness of the workflow, and show improved results compared to vanilla zero-shot and few-shot generation approaches. △ Less

Submitted 17 December, 2024; originally announced December 2024.

Comments: Accepted at the AAAI'25 Workshop on AI to Accelerate Science and Engineering (AI2ASE)

A large language model-type architecture for high-dimensional molecular potential energy surfaces

Authors: Xiao Zhu, Srinivasan S. Iyengar

Abstract: Computing high-dimensional potential energy surfaces for molecular systems and materials is considered to be a great challenge in computational chemistry with potential impact in a range of areas including the fundamental prediction of reaction rates. In this paper, we design and discuss an algorithm that has similarities to large language models in generative AI and natural language processing. S… ▽ More Computing high-dimensional potential energy surfaces for molecular systems and materials is considered to be a great challenge in computational chemistry with potential impact in a range of areas including the fundamental prediction of reaction rates. In this paper, we design and discuss an algorithm that has similarities to large language models in generative AI and natural language processing. Specifically, we represent a molecular system as a graph which contains a set of nodes, edges, faces, etc. Interactions between these sets, which represent molecular subsystems in our case, are used to construct the potential energy surface for a reasonably sized chemical system with 51 nuclear dimensions. For this purpose, a family of neural networks that pertain to the graph-theoretically obtained subsystems get the job done for this 51 nuclear dimensional system. We then ask if this same family of lower-dimensional graph-based neural networks can be transformed to provide accurate predictions for a 186-dimensional potential energy surface. We find that our algorithm does provide accurate results for this larger-dimensional problem with sub-kcal/mol accuracy for the higher-dimensional potential energy surface problem. Indeed, as a result of these developments, here we produce the first efforts towards a full-dimensional potential energy surface for the protonated 21-water cluster (186 nuclear dimensions) at CCSD level accuracy. △ Less

Submitted 26 December, 2025; v1 submitted 4 December, 2024; originally announced December 2024.

Comments: 31 pages, 35 figures

Journal ref: Phys. Rev. X, 2026

Quantum circuit and mapping algorithms for wavepacket dynamics: case study of anharmonic hydrogen bonds in protonated and hydroxide water clusters

Authors: Debadrita Saha, Philip Richerme, Srinivasan S. Iyengar

Abstract: The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here we present two algorithms that, in conjunction with other methods developed by us, will form the basis for performing quantum nuclear dynamics in arbitrary dimensions. For one algorithm, we present a direct map between the Born-Oppenhe… ▽ More The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here we present two algorithms that, in conjunction with other methods developed by us, will form the basis for performing quantum nuclear dynamics in arbitrary dimensions. For one algorithm, we present a direct map between the Born-Oppenheimer Hamiltonian describing the wavepacket time-evolution and the control parameters of a spin-lattice Hamiltonian that describes the dynamics of qubit states in an ion-trap quantum computer. This map is exact for three qubits, and when implemented, the dynamics of the spin states emulate those of the nuclear wavepacket. However, this map becomes approximate as the number of qubits grow. In a second algorithm we present a general quantum circuit decomposition formalism for such problems using a method called the Quantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits, at the cost of increased circuit complexity. The resultant circuit is implemented on IBM's quantum simulator (QASM) for 3-7 qubits. In both cases the wavepacket dynamics is found to be in good agreement with the classical result and the corresponding vibrational frequencies obtained from the wavepacket density time-evolution, are in agreement to within a few tenths of a wavenumbers. △ Less

Submitted 4 December, 2024; originally announced December 2024.

Journal ref: J. Chem. Theory and Comput. 21, 3814 (2025)

Proxy-small objects present compactly generated categories

Authors: Benjamin Briggs, Srikanth B. Iyengar, Greg Stevenson

Abstract: We develop a correspondence between presentations of compactly generated triangulated categories as localizations of derived categories of ring spectra and proxy-small objects, and explore some consequences. In addition, we give a characterization of proxy-smallness in terms of coproduct preservation of the associated corepresentable functor `up to base change'. We develop a correspondence between presentations of compactly generated triangulated categories as localizations of derived categories of ring spectra and proxy-small objects, and explore some consequences. In addition, we give a characterization of proxy-smallness in terms of coproduct preservation of the associated corepresentable functor `up to base change'. △ Less

Submitted 17 December, 2024; v1 submitted 11 November, 2024; originally announced November 2024.

Comments: 17 pages; minor changes and additions

MSC Class: 18G80; 13D09

SELP: Generating Safe and Efficient Task Plans for Robot Agents with Large Language Models

Authors: Yi Wu, Zikang Xiong, Yiran Hu, Shreyash S. Iyengar, Nan Jiang, Aniket Bera, Lin Tan, Suresh Jagannathan

Abstract: Despite significant advancements in large language models (LLMs) that enhance robot agents' understanding and execution of natural language (NL) commands, ensuring the agents adhere to user-specified constraints remains challenging, particularly for complex commands and long-horizon tasks. To address this challenge, we present three key insights, equivalence voting, constrained decoding, and domai… ▽ More Despite significant advancements in large language models (LLMs) that enhance robot agents' understanding and execution of natural language (NL) commands, ensuring the agents adhere to user-specified constraints remains challenging, particularly for complex commands and long-horizon tasks. To address this challenge, we present three key insights, equivalence voting, constrained decoding, and domain-specific fine-tuning, which significantly enhance LLM planners' capability in handling complex tasks. Equivalence voting ensures consistency by generating and sampling multiple Linear Temporal Logic (LTL) formulas from NL commands, grouping equivalent LTL formulas, and selecting the majority group of formulas as the final LTL formula. Constrained decoding then uses the generated LTL formula to enforce the autoregressive inference of plans, ensuring the generated plans conform to the LTL. Domain-specific fine-tuning customizes LLMs to produce safe and efficient plans within specific task domains. Our approach, Safe Efficient LLM Planner (SELP), combines these insights to create LLM planners to generate plans adhering to user commands with high confidence. We demonstrate the effectiveness and generalizability of SELP across different robot agents and tasks, including drone navigation and robot manipulation. For drone navigation tasks, SELP outperforms state-of-the-art planners by 10.8% in safety rate (i.e., finishing tasks conforming to NL commands) and by 19.8% in plan efficiency. For robot manipulation tasks, SELP achieves 20.4% improvement in safety rate. Our datasets for evaluating NL-to-LTL and robot task planning will be released in github.com/lt-asset/selp. △ Less

Submitted 13 February, 2025; v1 submitted 28 September, 2024; originally announced September 2024.

Comments: This paper has been accepted for presentation at the 2025 IEEE International Conference on Robotics and Automation (ICRA), May 19-23, 2025, Atlanta, USA, and for inclusion in the conference proceeding

Proof of Thought : Neurosymbolic Program Synthesis allows Robust and Interpretable Reasoning

Authors: Debargha Ganguly, Srinivasan Iyengar, Vipin Chaudhary, Shivkumar Kalyanaraman

Abstract: Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework that enhances the reliability and transparency of LLM outputs. Our approach bridges LLM-generated ideas with formal logic verification, employing a custom inte… ▽ More Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework that enhances the reliability and transparency of LLM outputs. Our approach bridges LLM-generated ideas with formal logic verification, employing a custom interpreter to convert LLM outputs into First Order Logic constructs for theorem prover scrutiny. Central to our method is an intermediary JSON-based Domain-Specific Language, which by design balances precise logical structures with intuitive human concepts. This hybrid representation enables both rigorous validation and accessible human comprehension of LLM reasoning processes. Key contributions include a robust type system with sort management for enhanced logical integrity, explicit representation of rules for clear distinction between factual and inferential knowledge, and a flexible architecture that allows for easy extension to various domain-specific applications. We demonstrate Proof of Thought's effectiveness through benchmarking on StrategyQA and a novel multimodal reasoning task, showing improved performance in open-ended scenarios. By providing verifiable and interpretable results, our technique addresses critical needs for AI system accountability and sets a foundation for human-in-the-loop oversight in high-stakes domains. △ Less

Submitted 23 October, 2024; v1 submitted 25 September, 2024; originally announced September 2024.

Comments: 38th Conference on Neural Information Processing Systems (NeurIPS 2024) System 2 Reasoning At Scale Workshop

Quantum nuclear dynamics on a distributed set of ion-trap quantum computing systems

Authors: Anurag Dwivedi, A. J. Rasmusson, Philip Richerme, Srinivasan S. Iyengar

Abstract: Quantum nuclear dynamics with wavepacket time-evolution is classically intractable and viewed as a promising avenue for quantum information processing. Here, we use an IonQ 11-qubit trapped-ion quantum computer, Harmony, to study the quantum wavepacket dynamics of a shared-proton within a short-strong hydrogen-bonded system. We also provide the first application of distributed quantum computing fo… ▽ More Quantum nuclear dynamics with wavepacket time-evolution is classically intractable and viewed as a promising avenue for quantum information processing. Here, we use an IonQ 11-qubit trapped-ion quantum computer, Harmony, to study the quantum wavepacket dynamics of a shared-proton within a short-strong hydrogen-bonded system. We also provide the first application of distributed quantum computing for chemical dynamics problems, where the distributed set of quantum processes is constructed using a tensor network formalism. For a range of initial states, we experimentally drive the ion-trap system to emulate the quantum nuclear wavepacket as it evolves along the potential surface generated from electronic structure. Following the experimental creation of the nuclear wavepacket, we extract measurement observables such as its time-dependent spatial projection and its characteristic vibrational frequencies to good agreement with classical results. Vibrational eigenenergies obtained from quantum computational are in agreement with those obtained from classical simulations to within a fraction of a kcal/mol, thus suggesting chemical accuracy. Our approach opens a new paradigm for studying the quantum chemical dynamics and vibrational spectra of molecules and also provides the first demonstration for parallel quantum computation on a distributed set of ion-trap quantum computers. △ Less

Submitted 7 June, 2024; originally announced June 2024.

Journal ref: J. Am. Chem. Soc. 146, 29355 (2024)

Locally dualisable modular representations and local regularity

Authors: Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova

Abstract: This work concerns the stable module category of a finite group over a field of characteristic dividing the group order. The minimal localising tensor ideals correspond to the non-maximal homogeneous prime ideals in the cohomology ring of the group. Given such a prime ideal, a number of characterisations of the dualisable objects in the corresponding tensor ideal are given. One characterisation of… ▽ More This work concerns the stable module category of a finite group over a field of characteristic dividing the group order. The minimal localising tensor ideals correspond to the non-maximal homogeneous prime ideals in the cohomology ring of the group. Given such a prime ideal, a number of characterisations of the dualisable objects in the corresponding tensor ideal are given. One characterisation of interest is that they are exactly the modules whose restriction along a corresponding $π$-point are finite dimensional plus projective. A key insight is the identification of a special property of the stable module category that controls the cohomological behaviour of local dualisable objects. This property, introduced in this work for general triangulated categories and called local regularity, is related to strong generation. A major part of the paper is devoted to developing this notion and investigating its ramifications for various special classes of objects in tensor triangulated categories. △ Less

Submitted 22 April, 2024; originally announced April 2024.

Comments: 34 pages

MSC Class: 20C20 (primary); 18G80; 20J06 (secondary)

Non-existence of Ulrich modules over Cohen-Macaulay local rings

Authors: Srikanth B. Iyengar, Linquan Ma, Mark E. Walker, Ziquan Zhuang

Abstract: Over a Cohen-Macaulay local ring, the minimal number of generators of a maximal Cohen-Macaulay module is bounded above by its multiplicity. In 1984 Ulrich asked whether there always exist modules for which equality holds; such modules are known nowadays as Ulrich modules. We answer this question in the negative by constructing families of two dimensional Cohen-Macaulay local rings that have no Ulr… ▽ More Over a Cohen-Macaulay local ring, the minimal number of generators of a maximal Cohen-Macaulay module is bounded above by its multiplicity. In 1984 Ulrich asked whether there always exist modules for which equality holds; such modules are known nowadays as Ulrich modules. We answer this question in the negative by constructing families of two dimensional Cohen-Macaulay local rings that have no Ulrich modules. Some of these examples are Gorenstein normal domains; others are even complete intersection domains, though not normal. △ Less

Submitted 12 March, 2025; v1 submitted 22 March, 2024; originally announced March 2024.

Comments: 13 pages. The Introduction has been expanded, and a few minor corrections have been made in the text. This is slated to appear in the Commun. Am. Math. Soc

MSC Class: 13C13 (primary); 13H10; 13C14; 14F06 (secondary)

Locally dualizable modules abound

Authors: Jon F. Carlson, Srikanth B. Iyengar

Abstract: It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of the derived category of $A$ than those that are obtained as retracts of images of perfect $A$-complexes. An analogous result is established dealing with the stable… ▽ More It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of the derived category of $A$ than those that are obtained as retracts of images of perfect $A$-complexes. An analogous result is established dealing with the stable module category of the group algebra, over a countable field of positive characteristic $p$, of an elementary abelian $p$-group of rank at least 3. △ Less

Submitted 4 January, 2024; originally announced January 2024.

Comments: 7 pages

MSC Class: 13D09 (primary); 18G80; 14F08 (secondary

Congruence modules in higher codimension and zeta lines in Galois cohomology

Authors: Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning, Eric Urban

Abstract: This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence modules, and a more refined version of a result tracking the change of congruence modules under deformation is proved. Number theoretic applications include the const… ▽ More This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence modules, and a more refined version of a result tracking the change of congruence modules under deformation is proved. Number theoretic applications include the construction of canonical lines in certain Galois cohomology groups arising from adjoint motives of Hilbert modular forms. △ Less

Submitted 21 November, 2023; originally announced November 2023.

Comments: 22 pages

MSC Class: 11F80 (primary); 11F33; 13D02 (secondary)

Synergy of machine learning with quantum computing and communication

Authors: Debasmita Bhoumik, Susmita Sur-Kolay, Latesh Kumar K. J., Sundaraja Sitharama Iyengar

Abstract: Machine learning in quantum computing and communication provides intensive opportunities for revolutionizing the field of Physics, Mathematics, and Computer Science. There exists an aperture of understanding behind this interdisciplinary domain and a lack of core understanding renders an opportunity to explore the machine learning techniques for this domain. This paper gives a comprehensive review… ▽ More Machine learning in quantum computing and communication provides intensive opportunities for revolutionizing the field of Physics, Mathematics, and Computer Science. There exists an aperture of understanding behind this interdisciplinary domain and a lack of core understanding renders an opportunity to explore the machine learning techniques for this domain. This paper gives a comprehensive review of state-of-the-art approaches in quantum computing and quantum communication in the context of Artificial Intelligence and machine learning models. The paper reviews the classical ML models that have been employed in various ways for quantum computation such as quantum error correction, quantum communication, quantum cryptography, and mapping quantum algorithms to the existing hardware. The paper also illustrates how the relevant current challenges can be transformed into future research avenues. △ Less

Submitted 5 October, 2023; originally announced October 2023.

Lattices over finite group schemes and stratification

Authors: Tobias Barthel, Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova

Abstract: This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full subcategory of all $G$-modules projective over $R$ generated by the lattices. The stable category of such $G$-modules is a rigidly-compactly generated, tensor triang… ▽ More This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full subcategory of all $G$-modules projective over $R$ generated by the lattices. The stable category of such $G$-modules is a rigidly-compactly generated, tensor triangulated category. The main result is that this stable category is stratified and costratified by the natural action of the cohomology ring of $G$. Applications include formulas for computing the support and cosupport of tensor products and the module of homomorphisms, and a classification of the thick ideals in the stable category of lattices. △ Less

Submitted 14 October, 2023; v1 submitted 30 July, 2023; originally announced July 2023.

Comments: 35 pages. The Introductions, and sections 2 and 5 have been rewritten significantly

Report number: MPIM-Bonn-2023 MSC Class: 16G30 (primary); 18G80; 20C10; 20J06 (secondary)

Bottom-up Integration of TMDCs with Pre-Patterned Device Architectures via Transfer-free Chemical Vapor Deposition

Authors: Lucas M. Sassi, Sathvik Ajay Iyengar, Anand B. Puthirath, Yuefei Huang, Xingfu Li, Tanguy Terlier, Ali Mojibpour, Ana Paula C. Teixeira, Palash Bharadwaj, Chandra Sekhar Tiwary, Robert Vajtai, Saikat Talapatra, Boris Yakobson, Pulickel M. Ajayan

Abstract: Two-dimensional (2D) transition metal dichalcogenides (TMDCs) remain a topic of immense interest. Specifically, given their low operational switching costs, they find many niche applications in new computing architectures with the promise of continued miniaturization. However, challenges lie in Back End of Line (BEOL) integration temperature and time compliance regarding current requirements for c… ▽ More Two-dimensional (2D) transition metal dichalcogenides (TMDCs) remain a topic of immense interest. Specifically, given their low operational switching costs, they find many niche applications in new computing architectures with the promise of continued miniaturization. However, challenges lie in Back End of Line (BEOL) integration temperature and time compliance regarding current requirements for crystal growth. Additionally, deleterious and time-consuming transfer processes and multiple steps involved in channel/contact engineering can cripple device performance. This work demonstrates kinetics-governed in-situ growth regimes (surface or edge growth from gold) of WSe2 and provides a mechanistic understanding of these regimes via energetics across various material interfaces. As a proof-of-concept, field effect transistors (FET) with an in-situ grown WSe2 channel across Au contacts are fabricated, demonstrating a 2D semiconductor transistor via a transfer-free method within the 450-600 C 2h-time window requirement BEOL integration. We leverage directional edge growth to fabricate contacts with robust thickness-dependent Schottky-to-Ohmic behavior. By transitioning between Au and SiO2 growth substrates in situ, this work achieves strain-induced subthreshold swing of 140 mV/decade, relatively high mobility of 107 +- 19 cm2V-1s-1, and robust ON/OFF ratios 10^6 in the fabricated FETs. △ Less

Submitted 23 May, 2023; originally announced May 2023.

Comments: 32 pages, 5 Figures

Structural, optical, and thermal properties of BN thin films grown on diamond via pulsed laser deposition

Authors: Abhijit Biswas, Gustavo A. Alvarez, Tao Li, Joyce Christiansen-Salameh, Eugene Jeong, Anand B. Puthirath, Sathvik Ajay Iyengar, Chenxi Li, Tia Gray, Xiang Zhang, Tymofii S. Pieshkov, Harikishan Kannan, Jacob Elkins, Robert Vajtai, A. Glen Birdwell, Mahesh R. Neupane, Elias J. Garratt, Bradford B. Pate, Tony G. Ivanov, Yuji Zhao, Zhiting Tian, Pulickel M. Ajayan

Abstract: Heterostructures based on ultrawide-bandgap (UWBG) semiconductors (bandgap >4.0 eV), boron nitride (BN) and diamond are important for next-generation high-power electronics. However, in-situ hetero-epitaxy of BN/diamond or vice-versa remains extremely challenging, due to their non-trivial growth kinetics. Here, we have grown BN thin film on (100) single crystal diamond by pulsed laser deposition a… ▽ More Heterostructures based on ultrawide-bandgap (UWBG) semiconductors (bandgap >4.0 eV), boron nitride (BN) and diamond are important for next-generation high-power electronics. However, in-situ hetero-epitaxy of BN/diamond or vice-versa remains extremely challenging, due to their non-trivial growth kinetics. Here, we have grown BN thin film on (100) single crystal diamond by pulsed laser deposition and investigated its structural and magnetic properties, optical refractive index, and thermal conductivity. Structural characterizations confirm the mixed (stable hexagonal and metastable cubic) phase growth. Film shows diamagnetic behavior at room temperature. It displays anisotropic refractive index within the visible-to-near-infrared wavelength range. The room temperature cross-plane thermal conductivity of BN is ~1.53 W/(mK), and the thermal conductance of the BN/diamond interface is ~20 MW/(m2K). Our findings are useful for various device related applications based on UWBG BN/diamond heterostructures. △ Less

Submitted 20 September, 2023; v1 submitted 22 May, 2023; originally announced May 2023.

Comments: 16 pages, 4 figures

Journal ref: Phys. Rev. Materials 7, 094602 (2023)

The Privacy-Utility Tradeoff in Rank-Preserving Dataset Obfuscation

Authors: Mahshad Shariatnasab, Farhad Shirani, S. Sitharma Iyengar

Abstract: Dataset obfuscation refers to techniques in which random noise is added to the entries of a given dataset, prior to its public release, to protect against leakage of private information. In this work, dataset obfuscation under two objectives is considered: i) rank-preservation: to preserve the row ordering in the obfuscated dataset induced by a given rank function, and ii) anonymity: to protect us… ▽ More Dataset obfuscation refers to techniques in which random noise is added to the entries of a given dataset, prior to its public release, to protect against leakage of private information. In this work, dataset obfuscation under two objectives is considered: i) rank-preservation: to preserve the row ordering in the obfuscated dataset induced by a given rank function, and ii) anonymity: to protect user anonymity under fingerprinting attacks. The first objective, rank-preservation, is of interest in applications such as the design of search engines and recommendation systems, feature matching, and social network analysis. Fingerprinting attacks, considered in evaluating the anonymity objective, are privacy attacks where an attacker constructs a fingerprint of a victim based on its observed activities, such as online web activities, and compares this fingerprint with information extracted from a publicly released obfuscated dataset to identify the victim. By evaluating the performance limits of a class of obfuscation mechanisms over asymptotically large datasets, a fundamental trade-off is quantified between rank-preservation and user anonymity. Single-letter obfuscation mechanisms are considered, where each entry in the dataset is perturbed by independent noise, and their fundamental performance limits are characterized by leveraging large deviation techniques. The optimal obfuscating test-channel, optimizing the privacy-utility tradeoff, is characterized in the form of a convex optimization problem which can be solved efficiently. Numerical simulations of various scenarios are provided to verify the theoretical derivations. △ Less

Submitted 11 May, 2023; originally announced May 2023.

Quantum Computing with dartboards

Authors: Ishaan Ganti, Srinivasan S. Iyengar

Abstract: We present a physically appealing and elegant picture for quantum computing using rules constructed for a game of darts. A dartboard is used to represent the state space in quantum mechanics and the act of throwing the dart is shown to have close similarities to the concept of measurement, or collapse of the wavefunction in quantum mechanics. The analogy is constructed in arbitrary dimensional spa… ▽ More We present a physically appealing and elegant picture for quantum computing using rules constructed for a game of darts. A dartboard is used to represent the state space in quantum mechanics and the act of throwing the dart is shown to have close similarities to the concept of measurement, or collapse of the wavefunction in quantum mechanics. The analogy is constructed in arbitrary dimensional spaces, that is using arbitrary dimensional dartboards, and for for such arbitrary spaces this also provides us a ``visual'' description of uncertainty. Finally, connections of qubits and quantum computing algorithms is also made opening the possibility to construct analogies between quantum algorithms and coupled dart-throw competitions. △ Less

Submitted 24 April, 2023; originally announced May 2023.

Journal ref: J. Phys. Chem. A, 127 , 7853 (2023)

Non-linear optics at twist interfaces in h-BN/SiC heterostructures

Authors: Abhijit Biswas, Rui Xu, Gustavo A. Alvarez, Jin Zhang, Joyce Christiansen-Salameh, Anand B. Puthirath, Kory Burns, Jordan A. Hachtel, Tao Li, Sathvik Ajay Iyengar, Tia Gray, Chenxi Li, Xiang Zhang, Harikishan Kannan, Jacob Elkins, Tymofii S. Pieshkov, Robert Vajtai, A. Glen Birdwell, Mahesh R. Neupane, Elias J. Garratt, Tony Ivanov, Bradford B. Pate, Yuji Zhao, Hanyu Zhu, Zhiting Tian , et al. (2 additional authors not shown)

Abstract: Understanding the emergent electronic structure in twisted atomically thin layers has led to the exciting field of twistronics. However, practical applications of such systems are challenging since the specific angular correlations between the layers must be precisely controlled and the layers have to be single crystalline with uniform atomic ordering. Here, we suggest an alternative, simple and s… ▽ More Understanding the emergent electronic structure in twisted atomically thin layers has led to the exciting field of twistronics. However, practical applications of such systems are challenging since the specific angular correlations between the layers must be precisely controlled and the layers have to be single crystalline with uniform atomic ordering. Here, we suggest an alternative, simple and scalable approach where nanocrystalline two-dimensional (2D) film on three-dimensional (3D) substrates yield twisted-interface-dependent properties. Ultrawide-bandgap hexagonal boron nitride (h-BN) thin films are directly grown on high in-plane lattice mismatched wide-bandgap silicon carbide (4H-SiC) substrates to explore the twist-dependent structure-property correlations. Concurrently, nanocrystalline h-BN thin film shows strong non-linear second-harmonic generation and ultra-low cross-plane thermal conductivity at room temperature, which are attributed to the twisted domain edges between van der Waals stacked nanocrystals with random in-plane orientations. First-principles calculations based on time-dependent density functional theory manifest strong even-order optical nonlinearity in twisted h-BN layers. Our work unveils that directly deposited 2D nanocrystalline thin film on 3D substrates could provide easily accessible twist-interfaces, therefore enabling a simple and scalable approach to utilize the 2D-twistronics integrated in 3D material devices for next-generation nanotechnology. △ Less

Submitted 4 November, 2023; v1 submitted 24 April, 2023; originally announced April 2023.

Comments: 33 pages, 4 figures

Journal ref: Adv. Mater. 2023, 2304624

High Frobenius pushforwards generate the bounded derived category

Authors: Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank, Alapan Mukhopadhyay, Josh Pollitz

Abstract: This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme $X$ of prime characteristic. The main result is that when the Frobenius map on $X$ is finite, for any compact generator $G$ of $\mathsf{D}(X)$ the Frobenius pushforward $F ^e_*G$ generates the bounded derived category whenever $p^e$ is larger than the codepth of $X$, an invariant that is a m… ▽ More This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme $X$ of prime characteristic. The main result is that when the Frobenius map on $X$ is finite, for any compact generator $G$ of $\mathsf{D}(X)$ the Frobenius pushforward $F ^e_*G$ generates the bounded derived category whenever $p^e$ is larger than the codepth of $X$, an invariant that is a measure of the singularity of $X$. The conclusion holds for all positive integers $e$ when $X$ is locally complete intersection. The question of when one can take $G=\mathcal{O}_X$ is also investigated. For smooth projective complete intersections it reduces to a question of generation of the Kuznetsov component. △ Less

Submitted 6 January, 2026; v1 submitted 31 March, 2023; originally announced March 2023.

Comments: 32 pages; minor revision. To appear in Forum of Mathematics, Sigma

MSC Class: 14A30 (primary); 13A35; 14G17; 13D09

Journal ref: Forum of Mathematics, Sigma 14 (2026) e12

A class of Gorenstein algebras and their dualities

Authors: Wassilij Gnedin, Srikanth B. Iyengar, Henning Krause

Abstract: In the recent paper "The Nakayama functor and its completion for Gorenstein algebras", a class of Gorenstein algebras over commutative noetherian rings was introduced, and duality theorems for various categories of representations were established. The manuscript on hand provides more context to the results presented in the aforementioned work, identifies new classes of Gorenstein algebras, and ex… ▽ More In the recent paper "The Nakayama functor and its completion for Gorenstein algebras", a class of Gorenstein algebras over commutative noetherian rings was introduced, and duality theorems for various categories of representations were established. The manuscript on hand provides more context to the results presented in the aforementioned work, identifies new classes of Gorenstein algebras, and explores their behaviour under standard operations like taking tensor products and tilting. △ Less

Submitted 8 March, 2023; originally announced March 2023.

Comments: 34 pages. To appear in the Proceedings of ICRA 2020

MSC Class: 16GXX (Primary) 16E35; 16E65; 13H10 (Secondary)

Local dualisable objects in local algebra

Authors: Dave Benson, Srikanth B. Iyengar, Henning Krause, Julia Pevtsova

Abstract: We discuss dualisable objects in minimal subcategories of compactly generated tensor triangulated categories, paying special attention to the derived category of a commutative noetherian ring. A cohomological criterion for detecting these local dualisable objects is established. Generalisations to other related contexts are discussed. We discuss dualisable objects in minimal subcategories of compactly generated tensor triangulated categories, paying special attention to the derived category of a commutative noetherian ring. A cohomological criterion for detecting these local dualisable objects is established. Generalisations to other related contexts are discussed. △ Less

Submitted 16 February, 2023; originally announced February 2023.

Comments: 15 pages

MSC Class: 13D09 (primary); 18G80; 14F08 (secondary)

Analogy between Boltzmann machines and Feynman path integrals

Authors: Srinivasan S. Iyengar, Sabre Kais

Abstract: We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We find that this equivalence allows the interpretation that the hidden layers in Boltzmann machines and other neural network formalisms are in fact discrete version… ▽ More We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We find that this equivalence allows the interpretation that the hidden layers in Boltzmann machines and other neural network formalisms are in fact discrete versions of path elements that are present within the Feynman path-integral formalism. Since Feynman paths are the natural and elegant depiction of interference phenomena germane to quantum mechanics, it appears that in machine learning, the goal is to find an appropriate combination of ``paths'', along with accumulated path-weights, through a network that cumulatively capture the correct $x \rightarrow y$ map for a given mathematical problem. As a direct consequence of this analysis, we are able to provide general quantum circuit models that are applicable to both Boltzmann machines and to Feynman path integral descriptions. Connections are also made to inverse quantum scattering problems which allow a robust way to define ``interpretable'' hidden layers. △ Less

Submitted 15 January, 2023; originally announced January 2023.

Journal ref: Journal of Chemical Theory and Computation 2023 19 (9), 2446-2454