arXiv subjects

Pragatheeswaran Vipulanandan

Publications and source records attributed to Pragatheeswaran Vipulanandan.

8 recordsLinked to original sources

arXiv2026

Embedding Semantic Entropy: NLI-Free Semantic Uncertainty Estimation with Geometry-Aware Clustering

Large Language Models (LLMs) often generate fluent yet incorrect responses, making un- certainty estimation important for reliable deployment. Semantic Entropy (SE) estimates uncertainty by clustering responses based on semantic equivalence, but it relies on hard entailment-based clustering. We propose Embedding Semantic Entropy, which replaces entailment-based clustering with K-Medoids in semantic embedding space and uses dynamic cluster selection to account for intra-cluster compactness and inter-cluster separation. We evaluate the method on TriviaQA, SQuAD, NQ-Open, SVAMP, and BioASQ using Falcon- 7B-Instruct, LLaMA-2-7B, LLaMA-2-7B-Chat, and Gemma-7B. Results show competitive AUROC and AUARC performance, suggesting that NLI-based entailment clustering can be replaced with embedding-space clustering with limited degradation while improving the inspectability of semantic grouping. This matters because semantic uncertainty scores depend on underlying semantic groups; by making these groups explicit, compact, and separable in embedding space, Emb-SE turns uncertainty estimation from a black-box en- tailment decision into an inspectable clustering problem.

cs.LG↗

arXiv2026

Rarity of Singletons Matters & Supplementary Materials

Estimating missing-mass and unseen-species counts from finite samples relies heavily on rare-event occupancy statistics, particularly singletons. In small-sample regimes, these statistics can be highly variable, making classical estimators sensitive to sampling fluctuations and potentially unreliable. We propose a fragility-aware (FA) framework that explicitly quantifies this sensitivity and adaptively regularizes conventional missing-mass and unseen-species estimators. Using singleton-based fragility measures derived from probability mass and occupancy counts, we formulate an entropy--Kullback--Leibler (KL) optimization that adjusts the reliance on base estimates according to their fragility. The resulting objectives are strictly concave, admit unique closed-form solutions, and require no Poissonization or asymptotic approximations. The framework provides a lightweight correction to classical estimators, including Good--Turing and Good--Toulmin, while reducing reliance on potentially unstable rare-event statistics. Across 360 experimental configurations spanning synthetic distributions and real-world language corpora, our method remains competitive in stable regimes while improving estimation accuracy and stability in fragmented, long-tailed, and small-sample settings. The findings demonstrate that accounting for the fragility of rare observations can improve the reliability of inference about unobserved species and their associated probability mass.

cs.LG↗

arXiv2026

Embedding Graph Kernel Entropy (EGKE): Fine-grained Hallucination Detection for LLMs from Embeddings

Hallucination detection is critical for ensuring the reliability of Large Language Models (LLMs) in real-world deployments. While recent works, such as Semantic Entropy (SE) and Kernel Language Entropy (KLE), identify hallucinations by measuring semantic disagreement across multiple generated responses using Natural Language Inference (NLI) models, these methods depend on separately loaded NLI classifiers to estimate pairwise semantic similarity, introducing significant computational overhead. We propose Embedding Graph Kernel Entropy (EGKE), a variant of Kernel Language Entropy (KLE) that replaces its NLI-derived semantic graph with a Radial Basis Function (RBF) kernel applied to dense sentence embeddings generated by a BGE embedding model, while retaining KLE's graph Laplacian, heat kernel, and von Neumann entropy formulation unchanged. By computing similarities directly in a continuous embedding space, the proposed method provides a symmetric and computationally efficient alternative to NLI-based semantic comparison. We evaluate our approach across 30 experimental setups (covering multiple question-answer datasets and open-weight LLM families) using both AUROC and AUARC, and demonstrate that this RBF-based method achieves competitive hallucination detection performance against state-of-the-art methods.

cs.LG↗

arXiv2026

New Records for the Hadamard Maximal Determinant Problem

The Hadamard maximal determinant problem seeks an $n\times n$ matrix $X$ with entries in $\{\pm 1\}$, which maximizes the determinant $\vert \det X \vert$ for a given order $n \in \mathbb{N}$. We report matrices attaining new record determinants for orders $n\equiv 3\pmod{4}$ between $103$ and $119$, as well as $n=51$. We provide a proof of optimality within a specific family of circulant--block constructions for $X$. For these orders, we recast the Hadamard problem as a sequence reconstruction problem from a pair of periodic autocorrelation functions, subject to certain arithmetic conditions. We describe several learning--based strategies for reconstruction and provide a comparison with classical simulated annealing--style approaches as a benchmark.

math.CO↗

arXiv2026

Do LLMs Understand Context? A Knowledge Graph-Based Evaluation Framework

While large language models (LLMs) have achieved remarkable linguistic capabilities, a profound question lingers at their core: do these models truly comprehend context or simply excel at pattern matching on an unprecedented scale? Contextual understanding in LLMs refers to the ability to correctly extract relevant information from a given context, integrate it into a coherent internal representation, and reason over it to produce factually consistent and contextually grounded responses. However, traditional methods such as BiLingual Evaluation Understudy (BLEU) and perplexity simply measure surface-level performance. This reveals a critical gap in question answering (QA), where responses must be contextually grounded rather than simply being memorized associations. To fill this void, we propose a novel knowledge graph (KG) based evaluation framework for LLM contextual understanding in QA. Central to this is Semantic Structural Similarity for KGs (S3KG), a hybrid similarity measure combining structural and semantic signals into a single score. In addition, a diagnostic analysis framework is developed to identify and categorize reasoning errors at the triplet level, enabling fine-grained analysis of model failures. Together, across nine benchmarks, S3KG achieves F1 gains of up to $+7.6$ points over the strongest baseline and AUROC up to $0.973$.

cs.AI↗

arXiv2026

Evaluation of Contextual Understanding in Large Language Models

Large Language Models (LLMs) demonstrate impressive performance across diverse NLP tasks, yet their ability to exhibit genuine contextual understanding remains uncertain. Traditional evaluation metrics such as perplexity, BiLingual Evaluation Understudy (BLEU), or surface-level accuracy fail to reveal how well LLMs extract, integrate, and reason over contextual information--a gap particularly critical in question answering, where models must align responses with contextually grounded knowledge rather than memorized associations. We propose a novel knowledge graph-based evaluation framework introducing Semantic Structural Similarity for KGs (S3KG), a hybrid similarity measure integrating structural and semantic similarity into a continuous evaluation score, alongside a diagnostic framework for categorizing reasoning errors. To validate this pipeline, we evaluate S3KG against established metrics on a curated question-answer (QA) benchmark, demonstrating its effectiveness in measuring correctness, faithfulness, and interpretability in LLM-generated responses.

cs.CL↗

arXiv2026

A Graph Neural Network Model for Real-Time Gesture Recognition Based on sEMG Signals

For seemless control of advanced hand prostheses and augmented reality, accurate and immediate hand gestures recognition is essential. Surface electromyography (sEMG) signals obtained from the forearm are commonly employed for this purpose. In this paper, we present a novel approach for sEMG representation that utilizes graph networks which contain information about muscle activation patterns in the forearm. Based on these graph networks, we have developed a machine learning algorithm capable of real-time hand gesture recognition using a graph neural network. The algorithm's performance was evaluated using sEMG signals acquired from myoband, which has 8 electrodes placed around the forearm, involving 8 healthy subjects. The proposed method demonstrated an average classification accuracy of 99\%, surpassing the performance of state-of-the-art techniques. The average time for both graph construction and prediction stood at 48ms utilizing a M1 pro CPU, rendering the approach well-suited for real-time applications.

cs.AI↗

arXiv2026

Semantic Uncertainty Quantification of Hallucinations in LLMs: A Quantum Tensor Network Based Method

Large language models (LLMs) exhibit strong generative capabilities but remain vulnerable to confabulations, fluent yet unreliable outputs that vary arbitrarily even under identical prompts. Leveraging a quantum tensor network based pipeline, we propose a quantum physics inspired uncertainty quantification framework that accounts for aleatoric uncertainty in token sequence probability for semantic equivalence based clustering of LLM generations. This offers a principled and interpretable scheme for hallucination detection. We further introduce an entropy maximization strategy that prioritizes high certainty, semantically coherent outputs and highlights entropy regions where LLM decisions are likely to be unreliable, offering practical guidelines for when human oversight is warranted. We evaluate the robustness of our scheme under different generation lengths and quantization levels, dimensions overlooked in prior studies, demonstrating that our approach remains reliable even in resource constrained deployments. A total of 116 experiments on TriviaQA, NQ, SVAMP, and SQuAD across multiple architectures including Mistral-7B, Mistral-7B-instruct, Falcon-rw-1b, LLaMA-3.2-1b, LLaMA-2-13b-chat, LLaMA-2-7b-chat, LLaMA-2-13b, and LLaMA-2-7b show consistent improvements in AUROC and AURAC over state of the art baselines.

cs.CL↗