Related papers: Randomized Distributed Decision
Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability…
We introduce the problem of simultaneously learning all powers of a Poisson Binomial Distribution (PBD). A PBD of order $n$ is the distribution of a sum of $n$ mutually independent Bernoulli random variables $X_i$, where $\mathbb{E}[X_i] =…
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…
We connect three distinct lines of research that have recently explored extensions of the classical LOCAL model of distributed computing: A. distributed quantum computing and non-signaling distributions [e.g. STOC 2024], B.…
Languages encode distinct abstractions and inductive priors, yet most large language models (LLMs) overlook this diversity by reasoning in a single dominant language. In this work, we introduce x1, a family of reasoning models that can…
There have been many recent advances in the structure and measurement of distributed language models: those that map from words to a vector-space that is rich in information about word choice and composition. This vector-space is the…
The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A rational stochastic language is a probability distribution over a free monoid…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its…
Property-based random testing a la QuickCheck requires building efficient generators for well-distributed random data satisfying complex logical predicates, but writing these generators can be difficult and error prone. We propose a…
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this…
In this paper, we present the first known example of a locally checkable labeling problem (LCL) that admits asymptotic distributed quantum advantage in the LOCAL model of distributed computing: our problem can be solved in $O(\log n)$…
"Help bits" are some limited trusted information about an instance or instances of a computational problem that may reduce the computational complexity of solving that instance or instances. In this paper, we study the value of help bits in…
Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…
We study the task, for a given language $L$, of enumerating the (generally infinite) sequence of its words, without repetitions, while bounding the delay between two consecutive words. To allow for delay bounds that do not depend on the…
In distributed machine learning, data is dispatched to multiple machines for processing. Motivated by the fact that similar data points often belong to the same or similar classes, and more generally, classification rules of high accuracy…
Learning to read words aloud is a major step towards becoming a reader. Many children struggle with the task because of the inconsistencies of English spelling-sound correspondences. Curricula vary enormously in how these patterns are…