arXiv subjects

Himanshu Gupta

Publications and source records attributed to Himanshu Gupta.

At least 19 recordsLinked to original sources

arXiv2026

Positivity preservers over finite fields II

We say that a matrix over a finite field $\mathbb{F}_q$ is positive definite if it is symmetric and each of its leading principal minors is a nonzero square in $\mathbb{F}_q$. In previous work of the authors [J. Algebra, 2025], the entrywise positivity preservers on $M_n(\mathbb{F}_q)$ were classified for every $n\geq 2$, with one remaining case: $n=2$, $q\equiv 1\pmod 4$, and $q$ not a square. We settle this case by proving that every positivity preserver on $M_2(\mathbb{F}_q)$ is injective on the set $\mathbb{F}_q^+$ of nonzero squares whenever $q\equiv 1\pmod 4$. The proof combines an idempotent reduction of positivity preservers with a well-known property of quadratic characters. This yields the complete classification of entrywise positivity preservers over every finite field and in every fixed dimension.

math.RA↗

arXiv2026

Beyond Fixed Goal Delivery: Online POMDP Planning for Target Interception in Crowds

Target interception in crowded environments requires reaching a moving objective while navigating among multiple uncertain human agents. Since human navigation intent is not directly observable, the robot must reason over multiple possible future interaction outcomes. We formulate interception in crowds as a partially observable Markov decision process and solve it online using tree search under a fixed computational budget. In this setting, the action-space structure directly shapes the search tree and how computational effort is allocated. We perform a controlled comparison between a sequential path-speed planner, which first plans a spatial path and then modulates speed along it, and a unified planner that jointly branches over steering and speed within tree search. Across simulations with up to 200 humans, both approaches perform similarly at low crowd density but diverge sharply as density increases. At the highest crowd density, the sequential planner has a safe-interception rate 31 percentage points lower and requires 44% more time than the unified steering-speed planner, revealing a structural limitation of spatial restriction. Project webpage: https://tic-planning.github.io/

cs.RO↗

arXiv2026

Environment Design for Reliable Shared Autonomy with Probabilistic Guarantees

Shared autonomy enables humans and robots to collaboratively perform tasks by combining human input with autonomous assistance. Most prior work focuses on improving intent inference under a fixed environment, overlooking how workspace design itself affects inference difficulty. We observe that the physical arrangement of objects directly influences the separability of candidate goals under noisy user inputs. We formulate workspace design as an optimization problem and derive a probabilistic correctness guarantee under a bounded noise model. Through simulation experiments across multiple tabletop scenarios, we show that optimized layouts improve goal inference reliability and reduce ambiguity compared to baseline arrangements. We further demonstrate a real-world shared autonomy system that integrates the proposed inference framework. This highlights the role of environment design as a complementary axis for improving shared autonomy systems.

cs.RO↗

arXiv2026

Gaussian Spatial Priors for Anatomy-Aware Object Detection in Surgical Videos

Detecting anatomical structures in surgical video is essential for intraoperative safety frameworks such as the Critical View of Myopectineal Orifice (CVMPO) in inguinal hernia repair. While prominent structures like the Cooper's Ligament and Triangle of Doom are reliably detected by standard methods, smaller structures such as the epigastric vessels remain challenging due to their visual ambiguity and intermittent visibility. We observe that the spatial relationship between structures is anatomically constrained, and propose a Gaussian Spatial Prior (GSP) module that encodes this relationship as a compact, parametric bias injected into the self-attention of a DAB-DETR decoder. The prior is computed offline from training annotations as a small set of frozen Gaussian parameters and recomputed at each decoder layer using the iteratively refined reference points. On a dataset of inguinal hernia repair videos with 5-fold cross-validation, GSP improves dependent class detection by $+33.5\%$ ($\text{AP}_{50}$) over DAB-DETR and $+53.9\%$ over YOLOv26, while also improving anchor detection by $+6.0\%$. These gains are statistically significant across all folds ($p=0.012$, paired $t-$test).

cs.CV↗

arXiv2026

SCOPE: A Syndrome-Driven Control Plane for QEC-Enabled Quantum Networks

As quantum networks evolve from experimental testbeds to fault-tolerant systems, the primary performance metric shifts from physical link fidelity to end-to-end logical error rate. However, current control planes remain ill-equipped for this transition: routing decisions are typically decoupled from Quantum Error Correction (QEC) strategies, relying on topology or scalar fidelity metrics that fail to predict how specific physical noise structures interact with logical codes. Optimizing this coupled route-and-code performance requires precise, real-time visibility into network error biases, yet traditional active tomography is operationally prohibitive due to throughput collapse and service interruption. We present SCOPE (Syndrome-based COntrol PlanE), a network-layer architecture that enables joint routing and coding optimization using purely passive telemetry. Instead of injecting probes, SCOPE harvests error syndromes -- the parity-check outcomes naturally generated by QEC decoders during user service. By aggregating these signals, SCOPE's inference engine reconstructs the network's time-varying error map, capturing complex, context-dependent noise correlations. This visibility drives a decision engine that proactively pushes optimal route-and-code configurations to source nodes. NetSquid and IBM-calibrated simulations show that SCOPE reduces estimation error by more than 60% relative to a standard EM baseline. In large-scale networks, this precision reduces logical error rates by 30-35% (up to 65%) against topology-aware baselines.

quant-ph↗

arXiv2026

Translate-R1: Cost-Aware Translation Tool Use via Reinforcement Learning

The performance gap across languages in LLMs is well documented, and closing it natively requires pretraining or fine-tuning on corpora that, for most languages, are quite limited. Translation offers an alternative: converting an input into the model's dominant language unlocks its full capabilities at once. But translating every input is wasteful for languages the model already handles, while leaving the choice to the model fails too, as LLMs are overconfident and skip the tool even when they cannot understand the input. Prior work resolves this with language-specific rules, heuristics, or external routers, each requiring manual engineering. We instead learn a single policy that decides when to translate from reward alone, developing language- and domain-adaptive introspection that invokes translation only when it cannot solve a task natively. Using data from our answer-preserving translation pipeline, we continue RL on the post-trained Qwen3-4B across 22 languages in 3 resource tiers (High, Low, XLow) and 5 domains, and introduce confidence-gated GSPO for cost-sensitive tool use. The gated policy lifts reward over the untrained baseline by +4.6 on High, +23.5 on Low, and +17.5 on XLow, and extends zero-shot to 9 held-out languages. Against an unconstrained policy that almost always translates (the reward upper bound), it preserves full reward at 66% of the cost, outperforming other cost penalties by up to +24.3 on the low-resource tiers while matching the free policy's reward on high-resource tiers at a fraction of the tool use. On 2 synthetic languages with zero prior exposure it correctly learns to always translate, improving +18.7 over the overconfident baseline.

cs.CL↗

arXiv2026

Efficient Multi-Robot Motion Planning with Precomputed Translation-Invariant Edge Bundles

Solving multi-robot motion planning (MRMP) requires generating collision-free kinodynamically feasible trajectories for multiple interacting robots. We introduce Kinodynamic Translation-Invariant Edge Bundles or KiTE-Extend, a planner-agnostic action selection mechanism for sampling-based kinodynamic motion planning. KiTE-Extend uses a library of trajectory segments computed offline to guide action selection during online planning, improving the ability of existing planners to identify feasible motion segments without altering state propagation, collision checking, or cost evaluation, and without changing their theoretical guarantees. While KiTE-Extend can modestly improve single-agent planners, its benefits are most clear in the multi-agent setting, where it is able to explore more effectively and significantly improve planning through the dense spatiotemporal constraints introduced by robot-robot interaction. Through experiments on multiple kinodynamic systems and environments, we show that KiTE-Extend reduces planning time and improves scalability across the three most common MRMP paradigms: centralized, prioritized, and conflict-based.

cs.RO↗

arXiv2026

Expert Upcycling: Shifting the Compute-Efficient Frontier of Mixture-of-Experts

Mixture-of-Experts (MoE) has become the dominant architecture for scaling large language models: frontier models routinely decouple total parameters from per-token computation through sparse expert routing. Scaling laws show that under fixed active computation, model quality scales predictably with total parameters, and MoEs realize this by increasing expert count. However, training large MoEs is expensive, as memory requirements and inter-device communication both scale with total parameter count. We propose expert upcycling, a method for progressively expanding MoE capacity by increasing the number of experts during continued pre-training (CPT). Given a trained E-expert model, the upcycling operator constructs an mE-expert model through expert duplication and router extension while holding top-K routing fixed, preserving per-token inference cost. Duplication provides a warm initialization: the expanded model inherits the source checkpoint's learned representations, starting from a substantially lower loss than random initialization. Subsequent CPT then breaks the symmetry among duplicated experts to drive specialization. We formalize the upcycling operator and develop a theoretical framework decomposing the quality gap into a capacity term and an initialization term. We further introduce utility-based expert selection, which uses gradient-based importance scores to guide non-uniform duplication, more than tripling gap closure when CPT is limited. In our 7B-13B total parameter experiments, the upcycled model matches the fixed-size baseline on validation loss while saving 32% of GPU hours. Comprehensive ablations across model scales, activation ratios, MoE architectures, and training budgets yield a practical recipe for deploying expert upcycling, establishing it as a principled, compute-efficient alternative to training large MoE models from scratch.

cs.LG↗

arXiv2026

The Strong Spectral Property and the Jacobian Method for Weighted Laplacian Matrices

Strong matrix properties, roughly speaking, refer to generic conditions on a matrix such that its spectral perturbation and pattern perturbation interact nicely to cover a neighborhood in the ambient space. With a rich history, these strong properties originate from various fields, including the inverse eigenvalue problem, the sign pattern problem, and structural graph theory. In this paper, we introduce a new strong property, the strong spectral property for weighted Laplacian matrices (SSPWL), and establish the corresponding Supergraph and Bifurcation lemmas. Instead of the space of symmetric matrices, the SSPWL considers the ambient space spanned by all weighted Laplacian matrices. Moreover, we provide a detailed study comparing the Jacobian Method and some strong properties, leading to a full understanding between these two techniques used in different problems. Using these tools, we identify the potential boundaries of the spectral regions of weighted Laplacian matrices associated with connected graphs on $4$ vertices, extending the analysis from the previous work [S. M. Fallat, H. Gupta, and J. C.-H. Lin. Inverse eigenvalue problem for Laplacian matrices of a graph. SIAM J. Matrix Anal. Appl., 46:1866--1886, 2025]. In addition, this analysis can be used to identify the absolute algebraic connectivity of such small ordered graphs, and we establish the existence of strong weighted Laplacian matrices for several graph families.

math.CO↗

arXiv2026

Code Mixologist : A Practitioner's Guide to Building Code-Mixed LLMs

Code-mixing and code-switching (CSW) remain challenging phenomena for large language models (LLMs). Despite recent advances in multilingual modeling, LLMs often struggle in mixed-language settings, exhibiting systematic degradation in grammaticality, factuality, and safety behavior. This work provides a comprehensive overview of CSW research in modern large language model settings. We introduce a unifying taxonomy that organizes prior work along dimensions of data, modeling, and evaluation, and we distill these findings into a practical playbook of actionable recommendations for building, adapting, and evaluating CSW-capable LLMs. We review modeling approaches ranging from CSW-tailored pre-training and task-specific post-training to prompting strategies and in-context learning. We analyze current evaluation practices, highlighting sources of instability and limited reproducibility, and we catalog existing benchmarks while critically examining their linguistic coverage and English-centric biases. Finally, we discuss emerging safety concerns, including use of code-mixing as a mechanism for bypassing model safeguards, and identify open research challenges.

cs.CL↗

arXiv2026

The Inverse Symplectic Eigenvalue Problem of a Graph

Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of these is the notion of symplectic eigenvalues, whose existence for positive definite matrices is known as Williamson's theorem or decomposition. This notion of symplectic eigenvalues gives rise to inverse problems. We introduce the inverse symplectic eigenvalue problem for positive definite matrices described by a labeled graph and solve it for several families of labeled graphs and all labeled graphs of order four. To solve these problems we develop various tools such as the Strong Symplectic Spectral Property (SSSP) and its consequences such as the Supergraph Theorem, the Bifurcation Theorem, and the Matrix Liberation Lemma for symplectic eigenvalues, graph couplings to describe collections of labelings of a graph that produce the same symplectic eigenvalues, and coupled graph zero forcing. We establish numerous results for symplectic positive definite matrices, including a sharp lower bound on the number of nonzero entries of such a matrix (or equivalently, the number of edges in its graph). This lower bound is a consequence of a lower bound on the sum of number of nonzero entries in an irreducible positive definite matrix and its inverse.

math.CO↗

arXiv2025

On the second largest eigenvalue of certain graphs in the perfect matching association scheme

The perfect matching association scheme is a set of relations on the perfect matchings of the complete graph on $2n$ vertices. The relations between perfect matchings are defined by the cycle structure of the union of any two perfect matchings, and each relation can be represented as a matrix. Each matrix is labeled by an integer partition whose parts correspond to the size do the cycles in the union. Since these matrices form an association scheme, they are simultaneously diagonalizable. Further, it is well-known that the common eigenspaces correspond to the irreducible representations of $S_{2n}$ indexed by the even partitions of $2n$. In this paper, we conjecture that the second largest eigenvalue of the matrices in the perfect matching association scheme labeled by a partition containing at least two parts of size 1 always occurs on the eigenspace corresponding to the representation indexed by $[2n-2, 2]$. We confirm this conjecture for matrices labeled by the partitions $[2, 1^{n-2}], [3, 1^{n-3}], [2, 2, 1^{n-4}], [4, 1^{n-4}], [3, 2, 1^{n-5}]$, and $[5, 1^{n-5}]$, as well as any partition in which the first part is sufficiently large.

math.CO↗

arXiv2025

A Comprehensive Protocol Stack for Quantum Networks with a Global Entanglement Module

The development of large-scale quantum networks requires not only advances in physical-layer technologies but also a comprehensive protocol stack that integrates communication, control, and resource management across all layers. We present the first such protocol stack, which introduces a Global Entanglement Module (GEM) that maintains a consistent, network-wide view of entanglement resources through distributed synchronization strategies. By enabling real-time adaptive execution of entanglement distribution plans, GEM bridges the gap between static planning and dynamic operation. The stack naturally supports pre-distributed entanglement, purification, and multi-partite state generation, making it applicable to a broad range of quantum networking applications. We design and evaluate multiple adaptive heuristics for real-time execution and show that a lightweight scoring-based strategy consistently achieves the best performance, improving entanglement generation rates by about 20% over a globally optimal but non-adaptive fixed-tree baseline and achieving more than a two-fold improvement relative to recent connectionless approaches. Across all scenarios-including predistribution and fidelity analysis-GEM consistently enables lower latency and robust operation. These results establish a practical pathway toward scalable, adaptive quantum internet systems.

quant-ph↗

arXiv2025

Cutting Through the Noise: Boosting LLM Performance on Math Word Problems

Large Language Models (LLMs) excel at various tasks, including solving math word problems (MWPs), but struggle with real-world problems containing irrelevant information. To address this, we propose a prompting framework that generates adversarial variants of MWPs by adding irrelevant variables. We introduce a dataset, PROBLEMATHIC, containing both adversarial and non-adversarial MWPs. Our experiments reveal that LLMs are susceptible to distraction by numerical noise, resulting in an average relative performance drop of ~26% on adversarial MWPs. To mitigate this, we fine-tune LLMs (Llama-2, Mistral) on the adversarial samples from our dataset. Fine-tuning on adversarial training instances improves performance on adversarial MWPs by ~8%, indicating increased robustness to noise and improved ability to identify relevant data for reasoning. Finally, to assess the generalizability of our prompting framework, we introduce GSM-8K-Adv, an adversarial variant of the GSM-8K benchmark. LLMs continue to struggle when faced with adversarial information, reducing performance by up to 6%.

cs.CL↗

arXiv2025

Automated Creation and Enrichment Framework for Improved Invocation of Enterprise APIs as Tools

Recent advancements in Large Language Models (LLMs) has lead to the development of agents capable of complex reasoning and interaction with external tools. In enterprise contexts, the effective use of such tools that are often enabled by application programming interfaces (APIs), is hindered by poor documentation, complex input or output schema, and large number of operations. These challenges make tool selection difficult and reduce the accuracy of payload formation by up to 25%. We propose ACE, an automated tool creation and enrichment framework that transforms enterprise APIs into LLM-compatible tools. ACE, (i) generates enriched tool specifications with parameter descriptions and examples to improve selection and invocation accuracy, and (ii) incorporates a dynamic shortlisting mechanism that filters relevant tools at runtime, reducing prompt complexity while maintaining scalability. We validate our framework on both proprietary and open-source APIs and demonstrate its integration with agentic frameworks. To the best of our knowledge, ACE is the first end-to-end framework that automates the creation, enrichment, and dynamic selection of enterprise API tools for LLM agents.

cs.SE↗

arXiv2025

Explicit Reasoning Makes Better Judges: A Systematic Study on Accuracy, Efficiency, and Robustness

As Large Language Models (LLMs) are increasingly adopted as automated judges in benchmarking and reward modeling, ensuring their reliability, efficiency, and robustness has become critical. In this work, we present a systematic comparison of "thinking" and "non-thinking" LLMs in the LLM-as-a-judge paradigm using open-source Qwen 3 models of relatively small sizes (0.6B, 1.7B, and 4B parameters). We evaluate both accuracy and computational efficiency (FLOPs) on RewardBench tasks, and further examine augmentation strategies for non-thinking models, including in-context learning, rubric-guided judging, reference-based evaluation, and n-best aggregation. Our results show that despite these enhancements, non-thinking models generally fall short of their thinking counterparts. Our results show that thinking models achieve approximately 10% points higher accuracy with little overhead (under 2x), in contrast to augmentation strategies like few-shot learning, which deliver modest gains at a higher cost (>8x). Bias and robustness analyses further demonstrate that thinking models maintain significantly greater consistency under a variety of bias conditions such as positional, bandwagon, identity, diversity, and random biases (6% higher on average). We further extend our experiments to the multilingual setting and our results confirm that explicit reasoning extends its benefits beyond English. Overall, our work results in several important findings that provide systematic evidence that explicit reasoning offers clear advantages in the LLM-as-a-judge paradigm not only in accuracy and efficiency but also in robustness.

cs.AI↗

arXiv2025

Entrywise transforms preserving matrix positivity and non-positivity

We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers. Compared to classical work on entrywise preservers of Schoenberg and others, we completely resolve this problem in the harder fixed dimensional setting, extending a similar recent classification of sign preservers obtained for matrices over finite fields. When the matrix dimension is fixed and at least $3$, we show that the sign preservers are precisely the positive scalar multiples of the continuous automorphisms of the underlying field. This is in contrast to the $2 \times 2$ case where the sign preservers are extensions of power functions. These results are built on our classification of $2 \times 2$ entrywise positivity preservers over broader complex domains. Our results yield a complementary connection with a work of Belton, Guillot, Khare, and Putinar (2023) on negativity-preserving transforms. We also extend our sign preserver results to matrices with a structure of zeros, as studied by Guillot, Khare, and Rajaratnam for the entrywise positivity preserver problem. Finally, in the spirit of sign preservers, we address a natural extension to monotone maps, classically studied by Loewner and many others.

math.CA↗

arXiv2025

The Weak Version of the Graph Complement Conjecture and Partial Results for the Delta Conjecture

Since the transformative workshop by the American Institute of Mathematics on the minimum rank of a graph, two longstanding open problems have captivated the community interested in the minimum rank of graphs: the graph complement conjecture and the $δ$-conjecture. In this paper, we use a classical result of Mader (1972) to establish a weak version of the graph complement conjecture for all key minimum rank parameters. In addition, again using the same result of Mader, we present some extremal resolutions of the $δ$-conjecture. Furthermore, we incorporate the assumption of the $δ$-conjecture and extensive work on graph degeneracy to improve the bound in the weak version of the graph complement conjecture. We conclude with a list of conjectured bounds on the positive semidefinite variant of the Colin de Verdière number.

math.CO↗