Related papers: Resetting Infinite Time Blum-Shub-Smale-Machines
This paper delves into the problem of computing robust controlled invariants for monotone continuous-time systems, with a specific focus on lower-closed specifications. We consider the classes of state monotone (SM) and control-state…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
Large language models (LLMs) with advanced cognitive capabilities are emerging as agents for various reasoning and planning tasks. Traditional evaluations often focus on specific reasoning or planning questions within controlled…
Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (Blankenship and Falk. "Infinitely constrained optimization…
We present a novel approach for solving quantified bit-vector formulas in Satisfiability Modulo Theories (SMT) based on computing symbolic inverses of bit-vector operators. We derive conditions that precisely characterize when bit-vector…
In this paper, we analyze the convergence %semi-convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of…
While LLMs have demonstrated remarkable potential in time series forecasting, their practical deployment remains constrained by excessive computational demands and memory footprints. Existing LLM-based approaches typically suffer from three…
Accurate models of quantum processors are essential for understanding, calibrating, and improving their performance. In practice, model construction must balance physical detail against the experimental and computational effort required to…
In a recent study (Ref. [1]), quantum annealing was reported to exhibit a scaling advantage for approximately solving Quadratic Unconstrained Binary Optimization (QUBO). However, this claim critically depends on the choice of classical…
Despite significant efforts towards extending the AGM paradigm of belief change beyond finitary logics, the computational aspects of AGM have remained almost untouched. We investigate the computability of AGM contraction on non-finitary…
Large Language Models (LLMs) exhibit nonlinear relationships between performance, cost, and token usage. This paper presents a quantitative study on structured prompting using BRAID (Bounded Reasoning for Au tonomous Inference and…
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush--Kuhn--Tucker (KKT) system at each iteration of the…
Despite the growing prevalence of large language model (LLM) architectures, a crucial concern persists regarding their energy and power consumption, which still lags far behind the remarkable energy efficiency of the human brain. Recent…
This paper records some apparently new results for the partition of integer intervals [1, n] into weakly sum-free subsets. These were produced using a method closely related to that used by Schur in 1917. New lower bounds can be produced in…
Large language models (LLMs) have demonstrated exceptional proficiency in understanding and generating human language, but efficient inference on resource-constrained embedded devices remains challenging due to large model sizes and…
The rapid advancement of Large Language Models (LLMs) necessitates a deep understanding of their fundamental performance limits. This paper investigates the limits of LLM inference, focusing on hardware-imposed bottlenecks in…
Fine-tuning all parameters of large language models (LLMs) necessitates substantial computational power and extended time. Latest advancements in parameter-efficient fine-tuning (PEFT) techniques, such as Adapter tuning and LoRA, allow for…
Recent studies have demonstrated that test-time compute scaling effectively improves the performance of small language models (sLMs). However, prior research has mainly examined test-time compute scaling with an additional larger model as a…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
In this paper we show that the computational complexity of the Iterative Thresholding and K-residual-Means (ITKrM) algorithm for dictionary learning can be significantly reduced by using dimensionality-reduction techniques based on the…