Related papers: BoolE: Exact Symbolic Reasoning via Boolean Equali…

Modern artificial intelligence excels at statistical interpolation within seen manifolds but fundamentally fails at the exact reasoning required for theoretical physics and mathematics. We identify the "Float Wall" -- a catastrophic…

We consider efficiency in the implementation of deep neural networks. Hardware accelerators are gaining interest as machine learning becomes one of the drivers of high-performance computing. In these accelerators, the directed graph…

Reasoning over structured graphs remains a fundamental challenge for Large Language Models (LLMs), particularly when scaling to large graphs. Existing approaches typically follow the retrieval-augmented generation (RAG) paradigm: first…

We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…

In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a…

Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets…

Recent efforts to improve the performance of neural network (NN) accelerators that meet today's application requirements have given rise to a new trend of logic-based NN inference relying on fixed-function combinational logic (FFCL). This…

Many real-world scientific and industrial applications require the optimization of expensive black-box functions. Bayesian Optimization (BO) provides an effective framework for such problems. However, traditional BO methods are prone to get…

We propose a method of optimizing monotone Boolean circuits by re-writing them in a simpler, equivalent form. We use in total six heuristics: Hill Climbing, Simulated Annealing, and variations of them, which operate on the representation of…

Biclustering is a powerful approach to search for patterns in data, as it can be driven by a function that measures the quality of diverse types of patterns of interest. However, due to its computational complexity, the exploration of the…

Neuro-symbolic AI systems integrate neural perception with symbolic reasoning to enable data-efficient, interpretable, and robust intelligence beyond purely neural models. Although this compositional paradigm has shown superior performance…

Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula's structural…

Mixture-of-Experts models have become a dominant architecture for scaling Large Language Models by activating only a sparse subset of experts per token. However, latency-critical MoE inference faces a fundamental tension: while expert…

Mathematical reasoning is an important research direction in the field of artificial intelligence. This article proposes a novel multi tool application framework for mathematical reasoning, aiming to achieve more comprehensive and accurate…

One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…

In literature, NAND and NOR are two logic gates that display functional completeness, hence regarded as Universal gates. So, the present effort is focused on exploring a library of universal gates in binary that are still unexplored in…

Thread pooling is a common programming idiom in which a fixed set of worker threads are maintained to execute tasks concurrently. The workers repeatedly pick tasks and execute them to completion. Each task is sequential, with possibly…

The formalism of Bayesian model selection provides a very elegant way of ranking different physical models in terms of how compatible they are with a given set of observed data. However, its practical application is often hampered by the…

Optimising the quality-of-results (QoR) of circuits during logic synthesis is a formidable challenge necessitating the exploration of exponentially sized search spaces. While expert-designed operations aid in uncovering effective sequences,…

Inspired by recent successes with parallel optimization techniques for solving Boolean satisfiability, we investigate a set of strategies and heuristics that aim to leverage parallel computing to improve the scalability of neural network…