Related papers: Almost-catalytic Computation
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the…
Autonomous tuning of particle accelerators is an active and challenging field of research with the goal of enabling novel accelerator technologies cutting-edge high-impact applications, such as physics discovery, cancer research and…
Through in-context learning (ICL), large-scale language models are effective few-shot learners without additional model fine-tuning. However, the ICL performance does not scale well with the number of available training samples as it is…
Continual Learning (CL) is a process in which there is still huge gap between human and deep learning model efficiency. Recently, many CL algorithms were designed. Most of them have many problems with learning in dynamic and complex…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
We study local computation algorithms (LCA) for maximum matching. An LCA does not return its output entirely, but reveals parts of it upon query. For matchings, each query is a vertex $v$; the LCA should return whether $v$ is matched -- and…
The continual learning (CL) ability is vital for deploying large language models (LLMs) in the dynamic world. Existing methods devise the learning module to acquire task-specific knowledge with parameter-efficient tuning (PET) block and the…
In a seminal work, Buhrman et al. (STOC 2014) defined the class $CSPACE(s,c)$ of problems solvable in space $s$ with an additional catalytic tape of size $c$, which is a tape whose initial content must be restored at the end of the…
Post-training model compression is essential for enhancing the portability of Large Language Models (LLMs) while preserving their performance. While several compression approaches have been proposed, less emphasis has been placed on…
In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete…
The increasing use of Advanced Language Models (ALMs) in diverse sectors, particularly due to their impressive capability to generate top-tier content following linguistic instructions, forms the core of this investigation. This study…
Correlation Clustering (CC) is a foundational problem in unsupervised learning that models binary similarity relations using labeled graphs. While classical CC has been widely studied, many real-world applications involve more nuanced…
We are interested in the intersection of approximation algorithms and complexity theory, in particular focusing on the complexity class APX. Informally, APX $\subseteq$ NPO is the complexity class comprising optimization problems where the…
Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
Large language models (LLMs) have demonstrated strong capabilities in processing long contexts, enabling them to tackle tasks involving long textual inputs such as multi-turn conversations, legal documents, or retrieved documents in…
We introduce \textbf{AAC} (Architecturally Admissible Compressor), a differentiable landmark-selection module for ALT (A*, Landmarks, and Triangle inequality) shortest-path heuristics whose outputs are admissible by construction: each…
We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory $\mathrm{APC}_2$ of…