arXiv:2609. 27860v1 Announce Type: new Abstract: A pointwise-unbiased one-bit compressor reconstructs every real input in expectation while transmitting one bit.
arXiv:2604. 10727v2 Announce Type: replace-cross Abstract: Classical information-theoretic learning bounds typically rely on KL mutual information and moment-generating-function (MGF) arguments, which are well matched to bounded or sub-Gaussian losses but can be ineffective when losses or rewards are heavy-tailed.
arXiv:2608. 08416v1 Announce Type: new Abstract: Probably Approximately Correct (PAC) learning [Val84] is a fundamental learning model that has been extensively investigated.
The paper introduces a pragmatic information theory that unifies communication, control, and decision-making through the isoteleia mapping, which formalizes equifinality by treating distinct semantic paths that lead to the same optimal action as pragmatically equivalent. It establishes a three-tier hierarchy of syntactic, semantic, and pragmatic information, defines pragmatic entropy, mutual information, channel capacity, and rate-distortion, and proves coding theorems that generalize Shannon’s results. The authors also present pragmatic value and cost of information, a Lagrangian dual framework for cross-layer optimization, and a pragmatic efficiency bound that quantifies the maximum net utility for resource-constrained intelligent systems, extending the theory to continuous messages and dynamic settings.
We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distribution over $\mathcal{X} \times \{0,1\}$, as in clas...
arXiv:2606. 00703v1 Announce Type: cross Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible.
arXiv:2609.24260v1 Announce Type: cross Abstract: We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distrib...
arXiv:2606. 10458v1 Announce Type: cross Abstract: We derive the optimal quantizer of a real-valued random variable $W$ with distribution $P_W$ such that 1) the distribution of the quantization output $X$ that can take $k$ values follows any specified distribution $P_X$ over $\{1,\ldots,k\}$, and 2) the minimum mean squared error (MMSE) of estimating $W$ from $X$ is minimized.
arXiv:2605. 05189v2 Announce Type: replace-cross Abstract: How many key-value associations can a $d\times d$ linear memory store?
arXiv:2601. 20970v3 Announce Type: replace-cross Abstract: The maximum-entropy remote sampling problem (MERSP) is to select a subset of $s$ random variables from a set of $n$ random variables, so as to maximize the information concerning a set of target random variables that are not directly observable.
arXiv:2607. 17232v1 Announce Type: cross Abstract: Classical rate-distortion (RD) theory has long established the fundamental limits of lossy compression by quantifying the minimum number of bits required to represent a source under a prescribed distortion constraint.
arXiv:2608. 15472v1 Announce Type: cross Abstract: The problem of networked information aggregation, studied in Kearns et al.