arXiv:2606. 21585v4 Announce Type: replace Abstract: A finite agent, a machine's digital twin or any bounded reasoner, infers a fixed and noisy world through finite sensors, so its coherent output is a belief: a probability density over states (the Bayes posterior).
arXiv:2606. 21585v2 Announce Type: replace Abstract: A finite machine's digital twin of a system observes the territory through finite, noisy sensors; we model its coherent output as a belief, a probability density over states, the Bayes posterior, never a point.
arXiv:2606. 12502v1 Announce Type: cross Abstract: We propose that value -- the quantity goal-directed agents create, destroy, and exchange -- is a lawful structural quantity in the same category as information.
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.
arXiv:2310. 09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints.
arXiv:2607. 06570v1 Announce Type: cross Abstract: Value-of-information (VOI) analysis is usually conducted under a single probability measure.
arXiv:2608. 15810v1 Announce Type: new Abstract: Runtime compression of serving state trades quality for capacity with no priced guarantee: systems adapt precision on load signals with no soundness statement, and certified approaches budget request-level risk by a union bound over a pre-declared event count.
arXiv:2608. 16438v1 Announce Type: new Abstract: In a world where valuable artifacts are increasingly created, completed, or processed by LLMs, the central economic question is not only what the LLM can produce, but what \emph{value} remains in the inputs (i.
arXiv:2608. 10650v1 Announce Type: new Abstract: Reducing the number of focal elements of a mass function is classically driven by an intrinsic distance, such as Jaccard or Jousselme, that keeps the approximation close to the original as a body of evidence.
arXiv:2608. 08416v1 Announce Type: new Abstract: Probably Approximately Correct (PAC) learning [Val84] is a fundamental learning model that has been extensively investigated.
arXiv:2607. 11920v1 Announce Type: cross Abstract: Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck.
arXiv:2603. 15384v2 Announce Type: replace-cross Abstract: We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}.
arXiv:2608. 15215v1 Announce Type: cross Abstract: Token-level knowledge distillation (KD) matches two conditional distributions per position, yet the standard objectives compare them pointwise: a Kullback-Leibler gradient is blind to which wrong token receives probability mass.