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Large language models (LLMs) represent words through contextual word embeddings encoding different language properties like semantics and syntax. Understanding these properties is crucial, especially for researchers investigating language…

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…

Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify…

Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…

Linked lists have long served as a valuable teaching tool in programming. However, the question arises: Are they truly practical for everyday program use? In most cases, it appears that array-based data structures offer distinct advantages,…

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…

While many EDA tasks already involve graph-based data, existing LLMs in EDA primarily either represent graphs as sequential text, or simply ignore graph-structured data that might be beneficial like dataflow graphs of RTL code. Recent…

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…

Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…

Scientific knowledge is growing rapidly, making it difficult to track progress and high-level conceptual links across broad disciplines. While tools like citation networks and search engines help retrieve related papers, they lack the…

The ongoing development of Lean 4's Mathlib has produced a macroscopic structural complexity that interweaves logical, mathematical, and infrastructural dependencies. We present a network analysis of this library, extracting its dependency…

Traditional software engineering programming paradigms are mostly object or procedure oriented, driven by deterministic algorithms. With the advent of deep learning and cognitive sciences there is an emerging trend for data-driven…

Efficiency is essential to support responsiveness w.r.t. ever-growing datasets, especially for Deep Learning (DL) systems. DL frameworks have traditionally embraced deferred execution-style DL code that supports symbolic, graph-based Deep…

Large language models (LLMs) often struggle with complex mathematical tasks, prone to "hallucinating" incorrect answers due to their reliance on statistical patterns. This limitation is further amplified in average Small LangSLMs with…

We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. With the advances of deep learning, current link prediction methods commonly compute features from subgraphs centered…

Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…

We live in a world driven by data. The amount of it outgrows anyone's ability to oversee it or even observe its scope. Along with all the advances in the space of data management, there is still a significant lack of formalism and…

The task of link prediction for knowledge graphs is to predict missing relationships between entities. Knowledge graph embedding, which aims to represent entities and relations of a knowledge graph as low dimensional vectors in a continuous…

While there exist a plethora of deep learning tools and frameworks, the fast-growing complexity of the field brings new demands and challenges, such as more flexible network design, speedy computation on distributed setting, and…