相关论文: Maximal Sharing in the Lambda Calculus with letrec

The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical…

Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can…

Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs, but it is not clear that they exploit their full capacity for all inputs. We introduce the s-Trace method…

We propose an implementation of lambda+, a recently introduced simply typed lambda-calculus with pairs where isomorphic types are made equal. The rewrite system of lambda+ is a rewrite system modulo an equivalence relation, which makes its…

For the partition graph $G_n$ on the set of partitions of $n$, we study the stratification induced by the local simplex dimension $\dim_{\mathrm{loc}}(\lambda)$, defined as the maximal dimension of a simplex of the clique complex…

In classic distributed graph problems, each instance on a graph specifies a space of feasible solutions (e.g. all proper ($\Delta+1$)-list-colorings of the graph), and the task of distributed algorithm is to construct a feasible solution…

Since the very beginning of the theory of linear logic it is known how to represent the $\lambda$-calculus as linear logic proof nets. The two systems however have different granularities, in particular proof nets have an explicit notion of…

In a setting where segmentation models have to be built for multiple datasets, each with its own corresponding label set, a straightforward way is to learn one model for every dataset and its labels. Alternatively, multi-task architectures…

Let $\lambda(G)$ be the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree. Let $\lambda_{\rm e}(G)$ be the smallest number of edges that can be removed from…

Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context…

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…

We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…

In order to improve precision and efficiency sharing analysis should track both freeness and linearity. The abstract unification algorithms for these combined domains are suboptimal, hence there is scope for improving precision. This paper…

For a graph $G$ on $v(G)$ vertices let $m_k(G)$ denote the number of matchings of size $k$, and consider the partition function $M_{G}(\lambda)=\sum_{k=0}^nm_k(G)\lambda^k$. In this paper we show that if $G$ is a $d$--regular graph and…

We study the problem of finding and monitoring fixed-size subgraphs in a continually changing large-scale graph. We present the first approach that (i) performs worst-case optimal computation and communication, (ii) maintains a total memory…

The linear complementarity problem (LCP) is a general set membership problem that includes quadratic cone programming as a special case. In this work we consider a homogeneous embedding of the LCP, which encodes both the optimality…

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…

Consider a channel with a given input alphabet size and a given input distribution. Our aim is to degrade or upgrade it to a channel with at most L output letters. The paper contains four main results. The first result, from which the paper…

Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…

Influence Maximization (IM) is a crucial problem in data science. The goal is to find a fixed-size set of highly-influential seed vertices on a network to maximize the influence spread along the edges. While IM is NP-hard on commonly-used…