Related papers: Sharing Equality is Linear
Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive…
It is commonly believed that scaling language models should commit a significant space or time cost, by increasing the parameters (parameter scaling) or output tokens (inference-time scaling). We introduce the third and more…
Semantic Similarity between two sentences can be defined as a way to determine how related or unrelated two sentences are. The task of Semantic Similarity in terms of distributed representations can be thought to be generating sentence…
In this position paper, we would like to offer and defend a new template to study equivalences between programs -- in the particular framework of process algebras for concurrent computation.We believe that our layered model of development…
We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
The problem of scheduling with testing in the framework of explorable uncertainty models environments where some preliminary action can influence the duration of a task. In the model, each job has an unknown processing time that can be…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
Downward translation of equality refers to cases where a collapse of some pair of complexity classes would induce a collapse of some other pair of complexity classes that (a priori) one expects are smaller. Recently, the first downward…
The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only…
The higher order matching problem is the problem of determining whether a term is an instance of another in the simply typed $\lambda$-calculus, i.e. to solve the equation a = b where a and b are simply typed $\lambda$-terms and b is…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
A myriad of applications ranging from engineering and scientific simulations, image and signal processing as well as high-sensitive data retrieval demand high processing power reaching up to teraflops for their efficient execution. While a…
Recently, a new multi-step temporal learning algorithm, called $Q(\sigma)$, unifies $n$-step Tree-Backup (when $\sigma=0$) and $n$-step Sarsa (when $\sigma=1$) by introducing a sampling parameter $\sigma$. However, similar to other…
Performing $n$ steps of $\beta$-reduction to a given term in the $\lambda$-calculus can lead to an increase in the size of the resulting term that is exponential in $n$. The same is true for the possible depth increase of terms along a…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
Large language model (LLM) architectures are often described as functionally hierarchical: Early layers process syntax, middle layers begin to parse semantics, and late layers integrate information. The present work revisits these ideas.…