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Automated vulnerability detection in critical-infrastructure software confronts a fundamental barrier: industrial software is routinely deployed as stripped, symbol-free binaries that deprive conventional Software Composition Analysis of…
Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic…
The canonical anticommutation relations (CAR) for fermion systems can be represented by finite-dimensional matrix algebra, but it is impossible for canonical commutation relations (CCR) for bosons. After description of more simple case with…
We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…
Recent advances in deep learning have led to increasingly complex models with deeper layers and more parameters, reducing interpretability and making their decisions harder to understand. While many methods explain black-box reasoning, most…
The idea of representing symbolic knowledge in connectionist systems has been a long-standing endeavour which has attracted much attention recently with the objective of combining machine learning and scalable sound reasoning. Early work…
The Turing Machine has two implicit properties that depend on its underlying notion of computing: the format is fully determinate and computations are information preserving. Distributed representations lack these properties and cannot be…
The geometric evolution of token representations in large language models (LLMs) presents a fundamental paradox: while human language inherently organizes semantic information in low-dimensional spaces ($\sim 10^1$ dimensions), modern LLMs…
Complex reasoning over tabular data is crucial in real-world data analysis, yet large language models (LLMs) often underperform due to complex queries, noisy data, and limited numerical capabilities. To address these issues, we propose…
The problem of reversing the compilation process, decompilation, is an important tool in reverse engineering of computer software. Recently, researchers have proposed using techniques from neural machine translation to automate the process…
Tsetlin Machine (TM) has been gaining popularity as an inherently interpretable machine leaning method that is able to achieve promising performance with low computational complexity on a variety of applications. The interpretability and…
Multimodal Large Language Models (MLLMs) have demonstrated remarkable reasoning capabilities across modalities such as images and text. However, tabular data, despite being a critical real-world modality, remains relatively underexplored in…
General matrix multiplication (GEMM) is the computational backbone of modern AI workloads, and its efficiency is critically dependent on effective tiling strategies. Conventional approaches employ symmetric tile buffering, where the…
We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic…
Concept Bottleneck Models (CBMs) improve the explainability of black-box Deep Learning (DL) by introducing intermediate semantic concepts. However, standard CBMs often overlook domain-specific relationships and causal mechanisms, and their…
Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to…
Tsetlin Machine (TM) is an interpretable pattern recognition algorithm based on propositional logic, which has demonstrated competitive performance in many Natural Language Processing (NLP) tasks, including sentiment analysis, text…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
Opaque models belonging to the machine learning world are ever more exploited in the most different application areas. These models, acting as black boxes (BB) from the human perspective, cannot be entirely trusted if the application is…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…