Related papers: Bottom-up rewriting for words and terms
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
There is no free lunch, no single learning algorithm that will outperform other algorithms on all data. In practice different approaches are tried and the best algorithm selected. An alternative solution is to build new algorithms on demand…
Always-on edge systems must keep learning as conditions change under tight compute budgets and must detect unreliable predictions. Bayesian binary neural networks are attractive in this setting, but mean-field Bernoulli posteriors can…
Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite…
In hierarchical text classification, we perform a sequence of inference steps to predict the category of a document from top to bottom of a given class taxonomy. Most of the studies have focused on developing novels neural network…
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF…
In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)$\to$Learn from the category of parameterized…
Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (Blankenship and Falk. "Infinitely constrained optimization…
We introduce a coinductive definition of infinitary term rewriting. The setup is surprisingly simple, and has in contrast to the usual definitions of infinitary rewriting, neither need for ordinals nor for metric convergence. While the idea…
A supervised learning algorithm searches over a set of functions $A \to B$ parametrised by a space $P$ to find the best approximation to some ideal function $f\colon A \to B$. It does this by taking examples $(a,f(a)) \in A\times B$, and…
The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain…
Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…