Mathematics & Machine Learning Seminar

Modern neural models exhibit strong empirical performance yet lack a structural theory explaining when their predictions are stable, interpretable, or reliable. This issue is especially pronounced in large language models, where small perturbations in input or context can induce large and difficult-to-predict changes in output, suggesting an underlying sensitivity that is not captured by standard statistical uncertainty measures.

In this talk, I present a tensor-network–based framework for analyzing neural architectures that draws on tools from quantum many-body theory and operator factorization. By representing model computations as structured contractions of local maps, we obtain quantitative notions of sensitivity, information propagation, and effective complexity. This viewpoint yields principled diagnostics for fragility in regression networks, time-series models, and language models, and provides a way to distinguish regimes in which inference behaves predictably from those in which it becomes unstable.

I will further discuss how such structural characterizations may inform the design of reliable learning systems and connect to emerging work on reinforcement learning–driven mathematical reasoning, where the stability of learned inference procedures is essential. More broadly, the aim is to argue that tensor-network methods offer a bridge between empirical deep learning practice and mathematically analyzable models, and to outline open questions at the interface of statistical learning theory, physics-inspired representations, and reliable AI.