Related papers: SDDs are Exponentially More Succinct than OBDDs

Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…

Large language models (LLMs) have transformed natural language processing but face critical deployment challenges in device-edge systems due to resource limitations and communication overhead. To address these issues, collaborative…

In this paper we show that a CNF cannot be compiled into an Ordered Binary Decision Diagram (OBDD) of fixed-parameter size parameterized by the primal graph treewidth of the CNF. Thus we provide a parameterized separation between OBDDs and…

Word embeddings -- distributed word representations that can be learned from unlabelled data -- have been shown to have high utility in many natural language processing applications. In this paper, we perform an extrinsic evaluation of five…

Binary decision diagram (BDD) and zero-suppressed binary decision diagram (ZDD) are data structures to represent a family of (sub)sets compactly, and it can be used as succinct indexes for a family of sets. To build BDD/ZDD representing a…

We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…

The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing…

Context: Embedded Domain-Specific Languages (EDSLs) are a common and widely used approach to DSLs in various languages, including Haskell and Scala. There are two main implementation techniques for EDSLs: shallow embeddings and deep…

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are based on semi-definite programming (\textit{SDP}), which is generally…

Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…

In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and…

Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…

String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…

We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed. The architecture is inspired by the notion of Deep Operator Networks (DeepONets), which is based on…

Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules…

This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…