相关论文: Sequential Predictions based on Algorithmic Comple…

Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear…

This paper demonstrates that progressive localization, the gradual increase of attention locality from early distributed layers to late localized layers, represents the optimal architecture for creating interpretable large language models…

The present work explores the theoretical limits of Machine Learning (ML) within the framework of Kolmogorov's theory of Algorithmic Probability, which clarifies the notion of entropy as Expected Kolmogorov Complexity and formalizes other…

Time-series prediction or forecasting is critical across many real-world dynamic systems, and recent studies have proposed using Large Language Models (LLMs) for this task due to their strong generalization capabilities and ability to…

We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global…

The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…

Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…

We study a sequential binary prediction setting where the forecaster is evaluated in terms of the calibration distance, which is defined as the $L_1$ distance between the predicted values and the set of predictions that are perfectly…

Markov decision processes (MDP) are finite-state systems with both strategic and probabilistic choices. After fixing a strategy, an MDP produces a sequence of probability distributions over states. The sequence is eventually synchronizing…

We develop deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee. For $\epsilon>1/{\text{{poly}}}\log \Delta$ we obtain two algorithms with…

The occurrence of unknown words in texts significantly hinders reading comprehension. To improve accessibility for specific target populations, computational modelling has been applied to identify complex words in texts and substitute them…

The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…

In some problems there is information about the destination of a moving object. An example is an airliner flying from an origin to a destination. Such problems have three main components: an origin, a destination, and motion in between. To…

Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence $\mathbb{M}=(M_p)_{p\in\mathbb{N}_0}$, have been put forward by A. Lastra, S. Malek and the second author [1], and their validity…

Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by…

Modern challenges of robustness, fairness, and decision-making in machine learning have led to the formulation of multi-distribution learning (MDL) frameworks in which a predictor is optimized across multiple distributions. We study the…

Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…

We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for…

The formal verification and controller synthesis for Markov decision processes that evolve over uncountable state spaces are computationally hard and thus generally rely on the use of approximations. In this work, we consider the…

Despite the fundamental progress in autonomous molecular and materials discovery, data scarcity throughout chemical compound space still severely hampers the use of modern ready-made machine learning models as they rely heavily on the…