Related papers: Evolving the Incremental {\lambda} Calculus into a…

In-context learning (ICL) in Large Language Models (LLMs) has emerged as a powerful new learning paradigm. However, its underlying mechanism is still not well understood. In particular, it is challenging to map it to the "standard" machine…

Automatic math correction aims to check students' solutions to mathematical problems via artificial intelligence technologies. Most existing studies focus on judging the final answer at the problem level, while they ignore detailed feedback…

In-context learning (ICL) is a few-shot learning paradigm that involves learning mappings through input-output pairs and appropriately applying them to new instances. Despite the remarkable ICL capabilities demonstrated by Large Language…

Numerical solutions for flows in partially saturated porous media pose challenges related to the non-linearity and elliptic-parabolic degeneracy of the governing Richards' equation. Iterative methods are therefore required to manage the…

Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…

Just as the $\lambda$-calculus uses three primitives (abstraction, application, variable) as the foundation of functional programming, inheritance-calculus uses three primitives (record, definition, inheritance) as the foundation of…

Incremental Learning is well known machine learning approach wherein the weights of the learned model are dynamically and gradually updated to generalize on new unseen data without forgetting the existing knowledge. Incremental learning…

Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…

With the increasing capabilities of large language models (LLMs), in-context learning (ICL) has emerged as a new paradigm for natural language processing (NLP), where LLMs make predictions based on contexts augmented with a few examples. It…

Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the…

Claims about recursive self-improvement in AI often slide from repeated internal revision to the possibility of qualitatively stronger capability without clearly distinguishing the underlying computational regimes. This paper gives a formal…

Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…

Class-incremental learning (CIL) aims to enable models to continuously learn new classes while overcoming catastrophic forgetting. The introduction of pre-trained models has brought new tuning paradigms to CIL. In this paper, we revisit…

Since the observation in 2006 that it is possible to embed IPC into the atomic polymorphic lambda-calculus (a predicative fragment of system F with universal instantiations restricted to atomic formulas) different such embeddings appeared…

Continual instruction tuning enables large language models (LLMs) to learn incrementally while retaining past knowledge, whereas existing methods primarily focus on how to retain old knowledge rather than on selecting which new knowledge to…

In a previous paper an asymptotic expansion for lambda_d in powers of 1/d was developed. The results of computer computations for some terms in the expansion, as well as various quantities associated to the expansion, are herein presented.…

Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…

Modern machine learning approaches excel in static settings where a large amount of i.i.d. training data are available for a given task. In a dynamic environment, though, an intelligent agent needs to be able to transfer knowledge and…

Along the lines of the Abramsky ``Proofs-as-Processes'' program, we present an interpretation of multiplicative linear logic as typing system for concurrent functional programming. In particular, we study a linear multiple-conclusion…

Large Language Models (LLMs) have emerged as powerful tools for accelerating scientific discovery, yet their static knowledge and hallucination issues hinder autonomous research applications. Recent advances integrate LLMs into agentic…