Related papers: Random Context and Semi-Conditional Insertion-Dele…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…
Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…
Large language models (LLMs) achieved remarkable performance across various tasks. However, they face challenges in managing long documents and extended conversations, due to significantly increased computational requirements, both in…
Larger language models become simultaneously better and worse at handling contextual information -- better at ignoring false claims, worse at ignoring irrelevant tokens. We formalize this apparent paradox through the first scaling laws for…
A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
Contextual information at inference time, such as demonstrations, retrieved knowledge, or interaction history, can substantially improve large language models (LLMs) without parameter updates, yet its theoretical role remains poorly…
Generating rational and generally accurate responses to tasks, often accompanied by example demonstrations, highlights Large Language Model's (LLM's) remarkable In-Context Learning (ICL) capabilities without requiring updates to the model's…
In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some…
This article summarizes principles and ideas from the emerging area of applying \textit{conditional computation} methods to the design of neural networks. In particular, we focus on neural networks that can dynamically activate or…
Large language models (LLMs) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs…
Large Language Models (LLMs) excel at reasoning, traditionally requiring high-quality large-scale data and extensive training. Recent works reveal a very appealing Less-Is-More phenomenon where very small, carefully curated high-quality…
Heterogeneous nonmonotonic multi-context systems (MCS) permit different logics to be used in different contexts, and link them via bridge rules. We investigate the role of symmetry detection and symmetry breaking in such systems to…
Recent research in machine teaching has explored the instruction of any concept expressed in a universal language. In this compositional context, new experimental results have shown that there exist data teaching sets surprisingly shorter…
Sentence compression is the task of creating a shorter version of an input sentence while keeping important information. In this paper, we extend the task of compression by deletion with the use of contextual embeddings. Different from…
In this paper, we present two techniques for use in context-aware systems: Semantic Decomposition, which sequentially decomposes input prompts into a structured and hierarchal information schema in which systems can parse and process…
This paper studies the counting problem in random dynamical systems. We noticed that the nature of counting in the random setting is completely different than that of the deterministic systems in the sense that non-exponential growth is…
RRULES is presented as an improvement and optimization over RULES, a simple inductive learning algorithm for extracting IF-THEN rules from a set of training examples. RRULES optimizes the algorithm by implementing a more effective mechanism…
We phrase parsing with context-free expressions as a type inhabitation problem where values are parse trees and types are context-free expressions. We first show how containment among context-free and regular expressions can be reduced to a…