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Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative,…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
We propose abstract compilation for precise static type analysis of object-oriented languages based on coinductive logic programming. Source code is translated to a logic program, then type-checking and inference problems amount to queries…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular…
In the practical deployment of machine learning (ML) models, missing data represents a recurring challenge. Missing data is often addressed when training ML models. But missing data also needs to be addressed when deciding predictions and…
In a reversible language, any forward computation can be undone by a finite sequence of backward steps. Reversible computing has been studied in the context of different programming languages and formalisms, where it has been used for…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
Distributed storage systems with replication are well known for storing large amount of data. A large number of replication is done in order to provide reliability. This makes the system expensive. Various methods have been proposed over…
Automatic static cost analysis infers information about the resources used by programs without actually running them with concrete data, and presents such information as functions of input data sizes. Most of the analysis tools for logic…
While machine learning models are usually assumed to always output a prediction, there also exist extensions in the form of reject options which allow the model to reject inputs where only a prediction with an unacceptably low certainty…
We design and conduct a simple experiment to study whether neural networks can perform several steps of approximate reasoning in a fixed dimensional latent space. The set of rewrites (i.e. transformations) that can be successfully performed…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Reversible computation requires that intermediate data be explicitly undone rather than discarded. In quantum programming, this principle appears as uncomputation, usually treated as a technical cleanup mechanism. We instead present…
Due to the increasing use of machine learning in practice it becomes more and more important to be able to explain the prediction and behavior of machine learning models. An instance of explanations are counterfactual explanations which…
Computation codes in network information theory are designed for the scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. K\"orner and Marton showed for distributed…
Concurrent pattern calculus (CPC) drives interaction between processes by comparing data structures, just as sequential pattern calculus drives computation. By generalising from pattern matching to pattern unification, interaction becomes…
We present a straightforward source-to-source transformation that introduces justifications for user-defined constraints into the CHR programming language. Then a scheme of two rules suffices to allow for logical retraction (deletion,…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…