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While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem…
Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication when the identical underlying arithmetic problem is presented as numerals, number words, images, or in audio…
Understanding how policy is debated and justified in parliament is a fundamental aspect of the democratic process. However, the volume and complexity of such debates mean that outside audiences struggle to engage. Meanwhile, Large Language…
In recent years, large language models (LLMs) have shown remarkable capabilities in various artificial intelligence problems. However, they fail to plan reliably, even when prompted with a detailed definition of the planning task. Attempts…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
Metaphors are everywhere. They appear extensively across all domains of natural language, from the most sophisticated poetry to seemingly dry academic prose. A significant body of research in the cognitive science of language argues for the…
Large Language Models (LLMs) increasingly exhibit strong reasoning abilities, often attributed to their capacity to generate chain-of-thought-style intermediate reasoning. Recent work suggests that exposure to code can further enhance these…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving…
We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitative relations. To define the simulations, we…
The math abilities of large language models can represent their abstract reasoning ability. In this paper, we introduce and open-source our math reasoning LLMs InternLM-Math which is continue pre-trained from InternLM2. We unify…
Large language models (LLMs) have demonstrated remarkable potential across numerous applications and have shown an emergent ability to tackle complex reasoning tasks, such as mathematical computations. However, even for the simplest…
Mathematical reasoning in large language models (LMs) has garnered significant attention in recent work, but there is a limited understanding of how these models process and store information related to arithmetic tasks within their…
Recent advances in large language models (LLMs) have shown impressive progress in mathematical reasoning tasks. However, current evaluation benchmarks predominantly focus on the accuracy of final answers, often overlooking the crucial…
Large Language Models (LLMs) achieve impressive performance in a wide range of tasks, even if they are often trained with the only objective of chatting fluently with users. Among other skills, LLMs show emergent abilities in mathematical…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…