Krish Patel

Dingkun Zhou, Krish Patel, Ajay Kankipati et al.

Emotions conveyed through voice and face shape engagement and context in human AI interaction. Despite rapid progress in omni modal large language models, the holistic evaluation of emotional reasoning with audiovisual cues remains limited. To address this gap, we introduce AV EMO Reasoning, a benchmark designed to systematically assess emotional reasoning abilities in large language models. The framework uses a curated audiovisual corpus comprising synthetic single turn and multi turn dialogues and a real world subset, together with emotion perception and interaction reasoning metrics, to evaluate whether models can understand user emotions and produce appropriate responses. By releasing a systematic evaluation benchmark, AV EMO Reasoning offers a reproducible standard for evaluating emotion aware dialogue and advances toward more natural, adaptive human AI interaction.

Alexander DeLise, Kyle Loh, Krish Patel et al.

Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they remain theoretically opaque, which hinders adoption in contexts where interpretability is paramount. In contrast, linear neural networks serve as a simple yet effective foundation for gaining insight into these complex relationships. In this work, we develop a unified theoretical framework for analyzing linear encoder-decoder architectures through the lens of Bayes risk minimization for solving data-driven scientific machine learning problems. We derive closed-form, rank-constrained linear and affine linear optimal mappings for forward modeling and inverse recovery tasks. Our results generalize existing formulations by accommodating rank-deficiencies in data, forward operators, and measurement processes. We validate our theoretical results by conducting numerical experiments on datasets from simple biomedical imaging, financial factor analysis, and simulations involving nonlinear fluid dynamics via the shallow water equations. This work provides a robust baseline for understanding and benchmarking learned neural network models for scientific machine learning problems.