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Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
We introduce LADDER (Learning through Autonomous Difficulty-Driven Example Recursion), a framework which enables Large Language Models to autonomously improve their problem-solving capabilities through self-guided learning by recursively…
We address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees. We propose a transformation technique whose objective is the…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems,…
Letter-string analogy is an important analogy learning task which seems to be easy for humans but very challenging for machines. The main idea behind current approaches to solving letter-string analogies is to design heuristic rules for…
We propose a novel distributed iterative linear inverse solver method. Our method, PolyLin, has significantly lower communication cost, both in terms of number of rounds as well as number of bits, in comparison with the state of the art at…
SMT-based program analysis and verification often involve reasoning about program features that have been specified using quantifiers; incorporating quantifiers into SMT-based reasoning is, however, known to be challenging. If quantifier…
Although Score Distillation Sampling (SDS) has exhibited remarkable performance in conditional 3D content generation, a comprehensive understanding of its formulation is still lacking, hindering the development of 3D generation. In this…
The normalizing layer has become one of the basic configurations of deep learning models, but it still suffers from computational inefficiency, interpretability difficulties, and low generality. After gaining a deeper understanding of the…
We introduce an operator on classes of regular languages, the star-free closure. Our motivation is to generalize standard results of automata theory within a unified framework. Given an arbitrary input class $C$, the star-free closure…
A core component of a successful artificial general intelligence would be the rapid creation and manipulation of grounded compositional abstractions and the demonstration of expertise in the family of recursive hierarchical syntactic…
The paper presents a new control algorithm for unstable linear systems with input delay. In comparison with known analogues, the control law has been designed, which is a modification of the Smith predictor, and is the simplest one to…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
Large Language Model (LLM)-based applications are increasingly deployed across various domains, including customer service, education, and mobility. However, these systems are prone to inaccurate, fictitious, or harmful responses, and their…
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
We use the classical interpretation of the braid group $B_3$ as a central extension of the modular group $\text{PSL}_2\left(\mathbb{Z}\right)$ to establish new and fundamental properties of $B_3$ using the theory of continued fractions. In…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
Strings are widely used in programs, especially in web applications. Integer data type occurs naturally in string-manipulating programs, and is frequently used to refer to lengths of, or positions in, strings. Analysis and testing of…