Akshay Seshadri

Mattia J. Villani, Pranav Deshpande, Akshay Seshadri et al.

Large Language Models (LLMs) often generate factually incorrect outputs, commonly termed hallucinations, that undermine trust and limit deployment in high-stakes settings. Existing hallucination detection methods typically require multiple forward passes, or access to model internals. In this work, we provide theoretical background and empirical evidence that the distribution of token-level entropies, beyond the mean captured by perplexity or length-normalised entropy, serves as a fingerprint of hallucination, with distributional shape and tail behaviour carrying independent signal. We formalize hallucination detection as a statistical hypothesis test and propose the Calibrated Entropy Score (CES), a lightweight algorithm requiring only a single forward pass and black-box access to token logits. CES combines the mean signal with the maximum signal of the generated entropy through a calibrated reference CDF, producing scores that are directly comparable across models and tasks. We establish finite-sample calibration guarantees via a novel random-length Dvoretzky--Kiefer--Wolfowitz inequality, and also prove that CES detects hallucinations with probability converging to one exponentially fast in the generation length. Across eight QA benchmarks and ten generator models spanning open-source and API access models, CES achieves the highest detection performance among all single-pass black-box methods while providing formal error guarantees that existing heuristics lack. Remarkably, CES is statistically indistinguishable from multi-sample methods that require far greater computational cost, closing the gap between lightweight and expensive detection and making it suitable for real-time, large-scale deployment.

Tyler Chen, Archan Ray, Akshay Seshadri et al.

The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive in big data applications. This was improved in recent works proposing quantum and quantum-inspired classical algorithms to approximate the $k$-means algorithm locally, in time depending only logarithmically on the number of data points (along with data dependent parameters) [q-means: A quantum algorithm for unsupervised machine learning, Kerenidis, Landman, Luongo, and Prakash, NeurIPS 2019; Do you know what $q$-means?, Cornelissen, Doriguello, Luongo, Tang, QTML 2025]. In this work, we describe a simple randomized mini-batch $k$-means algorithm and a quantum algorithm inspired by the classical algorithm. We demonstrate that the worst case guarantees of these algorithms can significantly improve upon the bounds for algorithms in prior work. Our improvements are due to a careful use of uniform sampling, which preserves certain symmetries of the $k$-means problem that are not preserved in previous algorithms that use data norm-based sampling.

Tyler Chen, Akshay Seshadri, Mattia J. Villani et al.

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature dimension) number of model evaluations. To address this, many model-agnostic randomized estimators have been developed, the most influential and widely used being the KernelSHAP method (Lundberg & Lee, 2017). While related estimators such as unbiased KernelSHAP (Covert & Lee, 2021) and LeverageSHAP (Musco & Witter, 2025) are known to satisfy theoretical guarantees, bounds for KernelSHAP have remained elusive. We describe a broad and unified framework that encompasses KernelSHAP and related estimators constructed using both with and without replacement sampling strategies. We then prove strong non-asymptotic theoretical guarantees that apply to all estimators from our framework. This provides, to the best of our knowledge, the first theoretical guarantees for KernelSHAP and sheds further light on tradeoffs between existing estimators. Through comprehensive benchmarking on small and medium dimensional datasets for Decision-Tree models, we validate our approach against exact Shapley values, consistently achieving low mean squared error with modest sample sizes. Furthermore, we make specific implementation improvements to enable scalability of our methods to high-dimensional datasets. Our methods, tested on datasets such MNIST and CIFAR10, provide consistently better results compared to the KernelSHAP library.