Related papers: The Relative Monadic Metalanguage
In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities;…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
Periodic or quasi-periodic phenomena reveal intrinsic characteristics in various natural processes, such as weather patterns, movement behaviors, traffic flows, and biological signals. Given that these phenomena span multiple modalities,…
Autoregressive Large Language Models (LLMs) demonstrate exceptional performance in language understanding and generation. However, their application in text embedding tasks has been relatively slow, along with the analysis of their semantic…
Nominal abstract syntax and higher-order abstract syntax provide a means for describing binding structure which is higher-level than traditional techniques. These approaches have spawned two different communities which have developed along…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
Recent advances in large language models (LLMs) and multimodal LLMs (MLLMs) have led to strong reasoning ability across a wide range of tasks. However, their ability to perform mathematical reasoning from spoken input remains underexplored.…
Humans naturally interpret numbers non-literally, effortlessly combining context, world knowledge, and speaker intent. We investigate whether large language models (LLMs) interpret numbers similarly, focusing on hyperbole and pragmatic halo…
As Large Multimodal Models (LMMs) become more capable, there is growing interest in evaluating their reasoning processes alongside their final outputs. However, most benchmarks remain focused on English, overlooking languages with rich…
Data visualizations like charts are fundamental tools for quantitative analysis and decision-making across fields, requiring accurate interpretation and mathematical reasoning. The emergence of Multimodal Large Language Models (MLLMs)…
We introduce I-RAVEN-X, a symbolic benchmark designed to evaluate generalization and robustness in analogical and mathematical reasoning for Large Language Models (LLMs) and Large Reasoning Models (LRMs). I-RAVEN-X extends I-RAVEN by…
We introduce a new method to improve existing multilingual sentence embeddings with Abstract Meaning Representation (AMR). Compared with the original textual input, AMR is a structured semantic representation that presents the core concepts…
Multimodal Mathematical Reasoning (MMR) has recently attracted increasing attention for its capability to solve mathematical problems involving both textual and visual modalities. However, current models still face significant challenges in…
Combining large language models with logical reasoning enhances their capacity to address problems in a robust and reliable manner. Nevertheless, the intricate nature of logical reasoning poses challenges when gathering reliable data from…
This paper describes a categorical interpretation of the Wolfram Language and introduces a simple implementation of monadic types and the "do" notation. The monadic style of programming combined with the many built in functions of the…
Large Language Models (LLMs) demonstrate robust capabilities across various fields, leading to a paradigm shift in LLM-enhanced Recommender System (RS). Research to date focuses on point-wise and pair-wise recommendation paradigms, which…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…