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Toward the Optimal Regret-Instability Trade-off in Multi-Armed Bandits

arXiv:2608.17841v1 Announce Type: cross Abstract: Multi-armed bandit algorithms are evaluated by regret, yet comparable regret can coexist with different allocations across independent runs. We study the trade-off between worst-case regret $mathcal{R}_{K,T}$ and instability $mathcal S_{K,T}$, defined as the largest standard…

Backward through Time, Algebraically

arXiv:2608.17087v1 Announce Type: new Abstract: Linear temporal logic is a modal extension of propositional logic that allows one to state how a system should behave over time. Its canonical domain is the booleans, but discretely-valued judgements are of little use…

Low-dimensional topology of deep neural networks

arXiv:2606.31856v2 Announce Type: replace Abstract: We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of $d = 3$, i.e., $mathbb{R}^3$ as representation space. This allows us to track how a neural network…