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Towards a Research Community in Interpretable Reinforcement Learning: the InterpPol Workshop arXiv.cs.SC Pub Date : 2024-04-16 Hector Kohler, Quentin Delfosse, Paul Festor, Philippe Preux
Embracing the pursuit of intrinsically explainable reinforcement learning raises crucial questions: what distinguishes explainability from interpretability? Should explainable and interpretable agents be developed outside of domains where transparency is imperative? What advantages do interpretable policies offer over neural networks? How can we rigorously define and measure interpretability in policies
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Constant-Depth Arithmetic Circuits for Linear Algebra Problems arXiv.cs.SC Pub Date : 2024-04-16 Robert Andrews, Avi Wigderson
We design polynomial size, constant depth (namely, $\mathsf{AC}^0$) arithmetic formulae for the greatest common divisor (GCD) of two polynomials, as well as the related problems of the discriminant, resultant, B\'ezout coefficients, squarefree decomposition, and the inversion of structured matrices like Sylvester and B\'ezout matrices. Our GCD algorithm extends to any number of polynomials. Previously
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Computing with Hypergeometric-Type Terms arXiv.cs.SC Pub Date : 2024-04-15 Bertrand Teguia Tabuguia
Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. We consider such a construction for the monoid of hypergeometric sequences, yielding what we call the ring of hypergeometric-type sequences -- a subring of the ring of holonomic sequences. We present two algorithms in
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Connectivity in Symmetric Semi-Algebraic Sets arXiv.cs.SC Pub Date : 2024-04-15 Cordian Riener, Robin Schabert, Thi Xuan Vu
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a semi-algebraic set are connected. We restrict to the case when all equations and inequalities are invariant under the action of the symmetric group and their degrees at most $d
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Performant Dynamically Typed E-Graphs in Pure Julia arXiv.cs.SC Pub Date : 2024-04-12 Alessandro Cheli, Niklas Heim
We introduce the third major version of Metatheory.jl, a Julia library for general-purpose metaprogramming and symbolic computation. Metatheory.jl provides a flexible and performant implementation of e-graphs and Equality Saturation (EqSat) that addresses the two-language problem in high-level compiler optimizations, symbolics and metaprogramming. We present results from our ongoing optimization efforts
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Complexity of Probabilistic Reasoning for Neurosymbolic Classification Techniques arXiv.cs.SC Pub Date : 2024-04-12 Arthur Ledaguenel, Céline Hudelot, Mostepha Khouadjia
Neurosymbolic artificial intelligence is a growing field of research aiming to combine neural network learning capabilities with the reasoning abilities of symbolic systems. Informed multi-label classification is a sub-field of neurosymbolic AI which studies how to leverage prior knowledge to improve neural classification systems. A well known family of neurosymbolic techniques for informed classification
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Study of Emotion Concept Formation by Integrating Vision, Physiology, and Word Information using Multilayered Multimodal Latent Dirichlet Allocation arXiv.cs.SC Pub Date : 2024-04-12 Kazuki Tsurumaki, Chie Hieida, Kazuki Miyazawa
How are emotions formed? Through extensive debate and the promulgation of diverse theories , the theory of constructed emotion has become prevalent in recent research on emotions. According to this theory, an emotion concept refers to a category formed by interoceptive and exteroceptive information associated with a specific emotion. An emotion concept stores past experiences as knowledge and can predict
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Power Series Composition in Near-Linear Time arXiv.cs.SC Pub Date : 2024-04-08 Yasunori Kinoshita, Baitian Li
We present an algebraic algorithm that computes the composition of two power series in $\mathop{\tilde{\mathrm O}}(n)$ time complexity. The previous best algorithms are $\mathop{\mathrm O}(n^{1+o(1)})$ by Kedlaya and Umans (FOCS 2008) and an $\mathop{\mathrm O}(n^{1.43})$ algebraic algorithm by Neiger, Salvy, Schost and Villard (JACM 2023). Our algorithm builds upon the recent Graeffe iteration approach
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WebPie: A Tiny Slice of Dependent Typing arXiv.cs.SC Pub Date : 2024-04-08 Christophe ScholliersGhent University
Dependently typed programming languages have become increasingly relevant in recent years. They have been adopted in industrial strength programming languages and have been extremely successful as the basis for theorem provers. There are however, very few entry level introductions to the theory of language constructs for dependently typed languages, and even less sources on didactical implementations
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Two Algorithms for Computing Rational Univariate Representations of Zero-Dimensional Ideals with Parameters arXiv.cs.SC Pub Date : 2024-03-25 Dingkang Wang, Jingjing Wei, Fanghui Xiao, Xiaopeng Zheng
Two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Different from the rational univariate representation of zero-dimensional ideals without parameters, the number of zeros of zero-dimensional ideals with parameters under various specializations is different, which leads to choosing and checking the separating element
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OSVAuto: semi-automatic verifier for functional specifications of operating systems arXiv.cs.SC Pub Date : 2024-03-20 Yulun Wu, Bohua Zhan, Bican Xia
We present the design and implementation of a tool for semi-automatic verification of functional specifications of operating system modules. Such verification tasks are traditionally done in interactive theorem provers, where the functionalities of the module are specified at abstract and concrete levels using data such as structures, algebraic datatypes, arrays, maps and so on. In this work, we provide
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Hierarchical NeuroSymbolic Approach for Action Quality Assessment arXiv.cs.SC Pub Date : 2024-03-20 Lauren Okamoto, Paritosh Parmar
Action quality assessment (AQA) applies computer vision to quantitatively assess the performance or execution of a human action. Current AQA approaches are end-to-end neural models, which lack transparency and tend to be biased because they are trained on subjective human judgements as ground-truth. To address these issues, we introduce a neuro-symbolic paradigm for AQA, which uses neural networks
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Self-Attention Based Semantic Decomposition in Vector Symbolic Architectures arXiv.cs.SC Pub Date : 2024-03-20 Calvin Yeung, Prathyush Poduval, Mohsen Imani
Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving
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Routing and Scheduling in Answer Set Programming applied to Multi-Agent Path Finding: Preliminary Report arXiv.cs.SC Pub Date : 2024-03-18 Roland Kaminski, Torsten Schaub, Tran Cao Son, Jiří Švancara, Philipp Wanko
We present alternative approaches to routing and scheduling in Answer Set Programming (ASP), and explore them in the context of Multi-agent Path Finding. The idea is to capture the flow of time in terms of partial orders rather than time steps attached to actions and fluents. This also abolishes the need for fixed upper bounds on the length of plans. The trade-off for this avoidance is that (parts
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Reasoning Abilities of Large Language Models: In-Depth Analysis on the Abstraction and Reasoning Corpus arXiv.cs.SC Pub Date : 2024-03-18 Seungpil Lee, Woochang Sim, Donghyeon Shin, Sanha Hwang, Wongyu Seo, Jiwon Park, Seokki Lee, Sejin Kim, Sundong Kim
The existing methods for evaluating the inference abilities of Large Language Models (LLMs) have been results-centric, making it difficult to assess the inference process. We introduce a new approach using the Abstract and Reasoning Corpus (ARC) dataset to evaluate the inference and contextual understanding abilities of large language models in a process-centric manner. ARC demands rigorous logical
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Complexity Classification of Complex-Weighted Counting Acyclic Constraint Satisfaction Problems arXiv.cs.SC Pub Date : 2024-03-14 Tomoyuki Yamakami
We study the computational complexity of counting constraint satisfaction problems (#CSPs) whose constraints assign complex numbers to Boolean inputs when the corresponding constraint hypergraphs are acyclic. These problems are called acyclic #CSPs or succinctly, #ACSPs. We wish to determine the computational complexity of all such #ACSPs when arbitrary unary constraints are freely available. Depending
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ArgMed-Agents: Explainable Clinical Decision Reasoning with Large Language Models via Argumentation Schemes arXiv.cs.SC Pub Date : 2024-03-10 Shengxin Hong, Liang Xiao, Xin Zhang, Jianxia Chen
There are two main barriers to using large language models (LLMs) in clinical reasoning. Firstly, while LLMs exhibit significant promise in Natural Language Processing (NLP) tasks, their performance in complex reasoning and planning falls short of expectations. Secondly, LLMs use uninterpretable methods to make clinical decisions that are fundamentally different from the clinician's cognitive processes
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Learning Guided Automated Reasoning: A Brief Survey arXiv.cs.SC Pub Date : 2024-03-06 Lasse Blaauwbroek, David Cerna, Thibault Gauthier, Jan Jakubův, Cezary Kaliszyk, Martin Suda, Josef Urban
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In practice, such systems however face large combinatorial explosion, and therefore include many heuristics and choice points that considerably influence their performance
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Saturating Sorting without Sorts arXiv.cs.SC Pub Date : 2024-03-06 Pamina Georgiou, Márton Hajdu, Laura Kovács
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted first-order logic and integrate sortedness/permutation properties within our first-order formalization. Rather than focusing on sorting lists of elements of specific
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Deep Neural Network for Constraint Acquisition through Tailored Loss Function arXiv.cs.SC Pub Date : 2024-03-04 Eduardo Vyhmeister, Rocio Paez, Gabriel Gonzalez
The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain relatively scarce. Furthermore, the intricate task of modeling demands expertise and is prone to errors, thus constraint acquisition methods offer a solution by automating
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Communication Optimal Unbalanced Private Set Union arXiv.cs.SC Pub Date : 2024-02-26 Jean-Guillaume DumasUGA, LJK, CASC, Alexis GalanCASC, Bruno GrenetCASC, Aude MaignanCASC, Daniel S. Roche
We consider the private set union (PSU) problem, where two parties each hold a private set of elements, and they want one of the parties (the receiver) to learn the union of the two sets and nothing else. Our protocols are targeted for the unbalanced case where the receiver's set size is larger than the sender's set size, with the goal of minimizing the costs for the sender both in terms of communication
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Optimal Pseudorandom Generators for Low-Degree Polynomials Over Moderately Large Fields arXiv.cs.SC Pub Date : 2024-02-19 Ashish Dwivedi, Zeyu Guo, Ben Lee Volk
We construct explicit pseudorandom generators that fool $n$-variate polynomials of degree at most $d$ over a finite field $\mathbb{F}_q$. The seed length of our generators is $O(d \log n + \log q)$, over fields of size exponential in $d$ and characteristic at least $d(d-1)+1$. Previous constructions such as Bogdanov's (STOC 2005) and Derksen and Viola's (FOCS 2022) had either suboptimal seed length
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Fast interpolation and multiplication of unbalanced polynomials arXiv.cs.SC Pub Date : 2024-02-15 Pascal Giorgi, Bruno Grenet, Armelle Perret du Cray, Daniel S. Roche
We consider the classical problems of interpolating a polynomial given a black box for evaluation, and of multiplying two polynomials, in the setting where the bit-lengths of the coefficients may vary widely, so-called unbalanced polynomials. Writing s for the total bit-length and D for the degree, our new algorithms have expected running time $\tilde{O}(s \log D)$, whereas previous methods for (resp
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Computing Krylov iterates in the time of matrix multiplication arXiv.cs.SC Pub Date : 2024-02-12 Vincent Neiger, Clément Pernet, Gilles Villard
Krylov methods rely on iterated matrix-vector products $A^k u_j$ for an $n\times n$ matrix $A$ and vectors $u_1,\ldots,u_m$. The space spanned by all iterates $A^k u_j$ admits a particular basis -- the \emph{maximal Krylov basis} -- which consists of iterates of the first vector $u_1, Au_1, A^2u_1,\ldots$, until reaching linear dependency, then iterating similarly the subsequent vectors until a basis
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Ensuring trustworthy and ethical behaviour in intelligent logical agents arXiv.cs.SC Pub Date : 2024-02-12 Stefania Costantini
Autonomous Intelligent Agents are employed in many applications upon which the life and welfare of living beings and vital social functions may depend. Therefore, agents should be trustworthy. A priori certification techniques (i.e., techniques applied prior to system's deployment) can be useful, but are not sufficient for agents that evolve, and thus modify their epistemic and belief state, and for
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Towards a Parallel Summation Algorithm arXiv.cs.SC Pub Date : 2024-02-07 Shaoshi Chen, Ruyong Feng, Manuel Kauers, Xiuyun Li
We propose a summation analog of the paradigm of parallel integration. Using this paradigm, we make some first steps towards an indefinite summation algorithm applicable to summands that rationally depend on the summation index and a P-recursive sequence and its shifts. Under the assumption that the corresponding difference field has no unnatural constants, we are able to compute a bound on the normal
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SymbolicAI: A framework for logic-based approaches combining generative models and solvers arXiv.cs.SC Pub Date : 2024-02-01 Marius-Constantin Dinu, Claudiu Leoveanu-Condrei, Markus Holzleitner, Werner Zellinger, Sepp Hochreiter
We introduce SymbolicAI, a versatile and modular framework employing a logic-based approach to concept learning and flow management in generative processes. SymbolicAI enables the seamless integration of generative models with a diverse range of solvers by treating large language models (LLMs) as semantic parsers that execute tasks based on both natural and formal language instructions, thus bridging
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Creative Telescoping for Hypergeometric Double Sums arXiv.cs.SC Pub Date : 2024-01-29 Peter Paule, Carsten Schneider
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which guarantees the applicability of our method for many input sums. In addition, we elaborate new techniques to optimize the underlying key task of our method to compute
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Open Source Prover in the Attic arXiv.cs.SC Pub Date : 2024-01-22 Zoltán KovácsThe Private University College of Education of the Diocese of Linz, Austria, Alexander VujicThe Private University College of Education of the Diocese of Linz, Austria
The well known JGEX program became open source a few years ago, but seemingly, further development of the program can only be done without the original authors. In our project, we are looking at whether it is possible to continue such a large project as a newcomer without the involvement of the original authors. Is there a way to internationalize, fix bugs, improve the code base, add new features?
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Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD arXiv.cs.SC Pub Date : 2024-01-24 Tereso del Río, Matthew England
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from having them made separately for each problem via a machine learning model. This study reports lessons on such use of machine learning in symbolic computation, in
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Symbolic Equation Solving via Reinforcement Learning arXiv.cs.SC Pub Date : 2024-01-24 Lennart Dabelow, Masahito Ueda
Machine-learning methods are gradually being adopted in a great variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks like simplifying mathematical terms, calculating formal derivatives, or finding exact solutions of algebraic equations. Traditional software packages for these purposes
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Solving with GeoGebra Discovery an Austrian Mathematics Olympiad problem: Lessons Learned arXiv.cs.SC Pub Date : 2024-01-22 Belén Ariño-MoreraDepartamento de Economía Financiera y Contabilidad, Universidad Rey Juan Carlos, Madrid, Spain, Zoltán KovácsThe Private University College of Education of the Diocese of Linz, Austria, Tomás RecioEscuela Politécnica Superior, Universidad Antonio de Nebrija, Madrid, Spain, Piedad TolmosDepartamento de Economía Financiera y Contabilidad, Universidad Rey Juan Carlos, Madrid, Spain
We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost instantaneous, automated solution of the proposed problem; the measure of its complexity, according to some recent proposals; the automated discovery of a generalization
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Showing Proofs, Assessing Difficulty with GeoGebra Discovery arXiv.cs.SC Pub Date : 2024-01-22 Zoltán KovácsThe Private University College of Education of the Diocese of Linz, Austria, Tomás RecioEscuela Politécnica Superior, Universidad Antonio de Nebrija, Madrid, Spain, M. Pilar VélezEscuela Politécnica Superior, Universidad Antonio de Nebrija, Madrid, Spain
In our contribution we describe some on-going improvements concerning the Automated Reasoning Tools developed in GeoGebra Discovery, providing different examples of the performance of these new features. We describe the new ShowProof command, that outputs both the sequence of the different steps performed by GeoGebra Discovery to confirm a certain statement, as well as a number intending to grade the
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3D Space Trajectories and beyond: Abstract Art Creation with 3D Printing arXiv.cs.SC Pub Date : 2024-01-22 Thierry Dana-PicardJerusalem College of Technology, Matias TejeraJohannes Kepler University Linz, Austria, Eva UlbrichJohannes Kepler University Linz, Austria
We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse direction and tricircular moves in 2D and 3D, to explore complex visualisations of extraplanetary movements. These moves are studied in a plane setting. Then, adding increasing
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The Locus Story of a Rocking Camel in a Medical Center in the City of Freistadt arXiv.cs.SC Pub Date : 2024-01-22 Anna KäferböckThe Private University College of Education of the Diocese of Linz, Austria, Zoltán KovácsThe Private University College of Education of the Diocese of Linz, Austria
We give an example of automated geometry reasoning for an imaginary classroom project by using the free software package GeoGebra Discovery. The project is motivated by a publicly available toy, a rocking camel, installed at a medical center in Upper Austria. We explain how the process of a false conjecture, experimenting, modeling, a precise mathematical setup, and then a proof by automated reasoning
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Towards Automatic Transformations of Coq Proof Scripts arXiv.cs.SC Pub Date : 2024-01-22 Nicolas MagaudLab. ICube CNRS Université de Strasbourg, France
Proof assistants like Coq are increasingly popular to help mathematicians carry out proofs of the results they conjecture. However, formal proofs remain highly technical and are especially difficult to reuse. In this paper, we present a framework to carry out a posteriori script transformations. These transformations are meant to be applied as an automated post-processing step, once the proof has been
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EFO: the Emotion Frame Ontology arXiv.cs.SC Pub Date : 2024-01-19 Stefano De Giorgis, Aldo Gangemi
Emotions are a subject of intense debate in various disciplines. Despite the proliferation of theories and definitions, there is still no consensus on what emotions are, and how to model the different concepts involved when we talk about - or categorize - them. In this paper, we propose an OWL frame-based ontology of emotions: the Emotion Frames Ontology (EFO). EFO treats emotions as semantic frames
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Hypergeometric Solutions of Linear Difference Systems arXiv.cs.SC Pub Date : 2024-01-16 Moulay Barkatou, Mark van Hoeij, Johannes Middeke, Yi Zhou
We extend Petkov\v{s}ek's algorithm for computing hypergeometric solutions of scalar difference equations to the case of difference systems $\tau(Y) = M Y$, with $M \in {\rm GL}_n(C(x))$, where $\tau$ is the shift operator. Hypergeometric solutions are solutions of the form $\gamma P$ where $P \in C(x)^n$ and $\gamma$ is a hypergeometric term over $C(x)$, i.e. ${\tau(\gamma)}/{\gamma} \in C(x)$. Our
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Submodule approach to creative telescoping arXiv.cs.SC Pub Date : 2024-01-16 Mark van Hoeij
This paper proposes ideas to speed up the process of creative telescoping, particularly when the telescoper is reducible. One can interpret telescoping as computing an annihilator $L \in D$ for an element $m$ in a $D$-module $M$. The main idea is to look for submodules of $M$. If $N$ is a non-trivial submodule of $M$, constructing the minimal operator $R$ of the image of $m$ in $M/N$ gives a right-factor
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Interpretable Concept Bottlenecks to Align Reinforcement Learning Agents arXiv.cs.SC Pub Date : 2024-01-11 Quentin Delfosse, Sebastian Sztwiertnia, Wolfgang Stammer, Mark Rothermel, Kristian Kersting
Reward sparsity, difficult credit assignment, and misalignment are only a few of the many issues that make it difficult, if not impossible, for deep reinforcement learning (RL) agents to learn optimal policies. Unfortunately, the black-box nature of deep networks impedes the inclusion of domain experts who could interpret the model and correct wrong behavior. To this end, we introduce Successive Concept
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Computing greatest common divisor of several parametric univariate polynomials via generalized subresultant polynomials arXiv.cs.SC Pub Date : 2023-12-31 Hoon Hong, Jing Yang
In this paper, we tackle the following problem: compute the gcd for several univariate polynomials with parametric coefficients. It amounts to partitioning the parameter space into ``cells'' so that the gcd has a uniform expression over each cell and constructing a uniform expression of gcd in each cell. We tackle the problem as follows. We begin by making a natural and obvious extension of subresultant
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Hypergeometric-Type Sequences arXiv.cs.SC Pub Date : 2023-12-30 Bertrand Teguia Tabuguia
We introduce hypergeometric-type sequences. They are linear combinations of interlaced hypergeometric sequences (of arbitrary interlacements). We prove that they form a subring of the ring of holonomic sequences. An interesting family of sequences in this class are those defined by trigonometric functions with linear arguments in the index and $\pi$, such as Chebyshev polynomials, $\left(\sin^2\left(n\
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Joint symbolic aggregate approximation of time series arXiv.cs.SC Pub Date : 2023-12-30 Xinye Chen
The increasing availability of temporal data poses a challenge to time-series and signal-processing domains due to its high numerosity and complexity. Symbolic representation outperforms raw data in a variety of engineering applications due to its storage efficiency, reduced numerosity, and noise reduction. The most recent symbolic aggregate approximation technique called ABBA demonstrates outstanding
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Adaptive Flip Graph Algorithm for Matrix Multiplication arXiv.cs.SC Pub Date : 2023-12-28 Yamato Arai, Yuma Ichikawa, Koji Hukushima
This study proposes the "adaptive flip graph algorithm", which combines adaptive searches with the flip graph algorithm for finding fast and efficient methods for matrix multiplication. The adaptive flip graph algorithm addresses the inherent limitations of exploration and inefficient search encountered in the original flip graph algorithm, particularly when dealing with large matrix multiplication
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Symbolic Security Verification of Mesh Commissioning Protocol in Thread (extended version) arXiv.cs.SC Pub Date : 2023-12-20 Pankaj Upadhyay, Subodh Sharma, Guangdong Bai
The Thread protocol (or simply Thread ) is a popular networking protocol for the Internet of Things (IoT). It allows seamless integration of a set of applications and protocols, hence reducing the risk of incompatibility among different applications or user protocols. Thread has been deployed in many popular smart home products by the majority of IoT manufacturers, such as Apple TV, Apple HomePod mini
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LoKit (revisited): A Toolkit for Building Distributed Collaborative Applications arXiv.cs.SC Pub Date : 2023-12-19 Uwe M. Borghoff
LoKit is a toolkit based on the coordination language LO. It allows to build distributed collaborative applications by providing a set of generic tools. This paper briefly introduces the concept of the toolkit, presents a subset of the LoKit tools, and finally demonstrates its power by discussing a sample application built with the toolkit.
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Physical Symbolic Optimization arXiv.cs.SC Pub Date : 2023-12-06 Wassim Tenachi, Rodrigo Ibata, Foivos I. Diakogiannis
We present a framework for constraining the automatic sequential generation of equations to obey the rules of dimensional analysis by construction. Combining this approach with reinforcement learning, we built $\Phi$-SO, a Physical Symbolic Optimization method for recovering analytical functions from physical data leveraging units constraints. Our symbolic regression algorithm achieves state-of-the-art
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Robust Clustering using Hyperdimensional Computing arXiv.cs.SC Pub Date : 2023-12-05 Lulu Ge, Keshab K. Parhi
This paper addresses the clustering of data in the hyperdimensional computing (HDC) domain. In prior work, an HDC-based clustering framework, referred to as HDCluster, has been proposed. However, the performance of the existing HDCluster is not robust. The performance of HDCluster is degraded as the hypervectors for the clusters are chosen at random during the initialization step. To overcome this
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Here Is Not There: Measuring Entailment-Based Trajectory Similarity for Location-Privacy Protection and Beyond arXiv.cs.SC Pub Date : 2023-12-02 Zilong Liu, Krzysztof Janowicz, Kitty Currier, Meilin Shi, Jinmeng Rao, Song Gao, Ling Cai, Anita Graser
While the paths humans take play out in social as well as physical space, measures to describe and compare their trajectories are carried out in abstract, typically Euclidean, space. When these measures are applied to trajectories of actual individuals in an application area, alterations that are inconsequential in abstract space may suddenly become problematic once overlaid with geographic reality
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${L}^{\infty}$-norm computation for linear time-invariant systems depending on parameters arXiv.cs.SC Pub Date : 2023-12-01 Alban Quadrat, Fabrice Rouillier, Grace Younes
This paper focuses on representing the $L^{\infty}$-norm of finite-dimensional linear time-invariant systems with parameter-dependent coefficients. Previous studies tackled the problem in a non-parametric scenario by simplifying it to finding the maximum $y$-projection of real solutions $(x, y)$ of a system of the form $\Sigma=\{P=0, \, \partial P/\partial x=0\}$, where $P \in \Z[x, y]$. To solve this
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Nested Integrals and Rationalizing Transformations arXiv.cs.SC Pub Date : 2023-11-28 Clemens G. Raab
A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are discussed. We also include a short discussion comparing the holonomic systems approach and the differential field approach. For simplification to rational integrands
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Hybrid Intervals and Symbolic Block Matrices arXiv.cs.SC Pub Date : 2023-11-28 Mike Ghesquiere, Stephen M. Watt
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects, showing how to add matrices with blocks of different symbolic sizes in a general way while avoiding a combinatorial explosion of cases. The present article introduces
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The Inverse of the Complex Gamma Function arXiv.cs.SC Pub Date : 2023-11-28 David J. Jeffrey, Stephen M. Watt
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
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Efficient Local Search for Nonlinear Real Arithmetic arXiv.cs.SC Pub Date : 2023-11-24 Zhonghan Wang, Bohua Zhan, Bohan Li, Shaowei Cai
Local search has recently been applied to SMT problems over various arithmetic theories. Among these, nonlinear real arithmetic poses special challenges due to its uncountable solution space and potential need to solve higher-degree polynomials. As a consequence, existing work on local search only considered fragments of the theory. In this work, we analyze the difficulties and propose ways to address
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Geometric Fiber Classification of Morphisms and a Geometric Approach to Cylindrical Algebraic Decomposition arXiv.cs.SC Pub Date : 2023-11-17 Rizeng Chen
Cylindrical Algebraic Decomposition (CAD) is a classical construction in real algebraic geometry. The original cylindrical algebraic decomposition was proposed by Collins, using the classical elimination theory. In this paper, we first study the geometric fibers cardinality classification problem of morphisms of affine varieties (over a field of characteristic 0), using a constructive version of Grothendieck's
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ACL2 Proofs of Nonlinear Inequalities with Imandra arXiv.cs.SC Pub Date : 2023-11-15 Grant PassmoreImandra Inc.
We present a proof-producing integration of ACL2 and Imandra for proving nonlinear inequalities. This leverages a new Imandra interface exposing its nonlinear decision procedures. The reasoning takes place over the reals, but the proofs produced are valid over the rationals and may be run in both ACL2 and ACL2(r). The ACL2 proofs Imandra constructs are extracted from Positivstellensatz refutations
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Formal Verification of Zero-Knowledge Circuits arXiv.cs.SC Pub Date : 2023-11-15 Alessandro CoglioKestrel Institute and Aleo Systems Inc., Eric McCarthyKestrel Institute and Aleo Systems Inc., Eric W. SmithKestrel Institute
Zero-knowledge circuits are sets of equality constraints over arithmetic expressions interpreted in a prime field; they are used to encode computations in cryptographic zero-knowledge proofs. We make the following contributions to the problem of ensuring that a circuit correctly encodes a computation: a formal framework for circuit correctness; an ACL2 library for prime fields; an ACL2 model of the
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Computing Implicitizations of Multi-Graded Polynomial Maps arXiv.cs.SC Pub Date : 2023-11-13 Joseph Cummings, Benjamin Hollering
In this paper, we focus on computing the kernel of a map of polynomial rings $\varphi$. This core problem in symbolic computation is known as implicitization. While there are extremely effective Gr\"obner basis methods used to solve this problem, these methods can become infeasible as the number of variables increases. In the case when the map $\varphi$ is multigraded, we consider an alternative approach
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On the Existence of Telescopers for P-recursive Sequences arXiv.cs.SC Pub Date : 2023-11-10 Lixin Du
We extend the criterion on the existence of telescopers for hypergeometric terms to the case of P-recursive sequences. This criterion is based on the concept of integral bases and the generalized Abramov-Petkovsek reduction for P-recursive sequences.
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Stability Problems on D-finite Functions arXiv.cs.SC Pub Date : 2023-11-10 Shaoshi Chen, Ruyong Feng, Zewang Guo, Wei Lu
This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators satisfied by iterated integrals of D-finite functions and determine bounds and exact formula for stability indices of several special classes of differential operators.