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The growing demand for automated graph algorithm reasoning has attracted increasing attention in the large language model (LLM) community. Recent LLM-based graph reasoning methods typically decouple task descriptions from graph data,…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
Deductive verification has become a mature paradigm for the verification of industrial software. Applying deductive verification, however, requires that every function in the code base is annotated with a function contract specifying its…
Auxiliary tasks facilitate learning in situations where data is scarce or the principal task of interest is extremely complex. This idea is primarily inspired by the improved generalization capability induced by solving multiple tasks…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
Large Language Models (LLMs) have recently developed new advanced functionalities. Their effectiveness relies on statistical learning and generalization capabilities. However, they face limitations in internalizing the data they process and…
Abstractive compression utilizes smaller langauge models to condense query-relevant context, reducing computational costs in retrieval-augmented generation (RAG). However,retrieved documents often include information that is either…
We address the challenge of extracting structured information from business documents without detailed annotations. We propose Deep Conditional Probabilistic Context Free Grammars (DeepCPCFG) to parse two-dimensional complex documents and…
Efficiently querying Description Logic (DL) ontologies is becoming a vital task in various data-intensive DL applications. Considered as a basic service for answering object queries over DL ontologies, instance checking can be realized by…
In-context learning (ICL) has emerged as a powerful paradigm for easily adapting Large Language Models (LLMs) to various tasks. However, our understanding of how ICL works remains limited. We explore a simple model of ICL in a controlled…
Abstract Interpretation approximates the semantics of a program by mimicking its concrete fixpoint computation on an abstract domain $\mathbb{A}$. The abstract (post-) fixpoint computation is classically divided into two phases: the…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…
Sentence matching is widely used in various natural language tasks such as natural language inference, paraphrase identification, and question answering. For these tasks, understanding logical and semantic relationship between two sentences…
Core spanners are a class of document spanners that capture the core functionality of IBM's AQL. FC is a logic on strings built around word equations that when extended with constraints for regular languages can be seen as a logic for core…
The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most…
Partial functions are common abstractions in formal specification notations such as Z, B and Alloy. Conversely, executable programming languages usually provide little or no support for them. In this paper we propose to add partial…
Final-answer-based metrics are commonly used for evaluating large language models (LLMs) on math word problems, often taken as proxies for reasoning ability. However, such metrics conflate two distinct sub-skills: abstract formulation…
We study methods for automated parsing of informal mathematical expressions into formal ones, a main prerequisite for deep computer understanding of informal mathematical texts. We propose a context-based parsing approach that combines…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…