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Developing prompt-based methods with Large Language Models (LLMs) requires making numerous decisions, which give rise to a combinatorial search problem over hyper-parameters. This exhaustive evaluation can be time-consuming and costly. In this paper, we propose an adaptive approach to explore this space. We are exploiting the fact that often only few samples are needed to identify clearly superior or inferior settings, and that many evaluation tests are highly correlated. We lean on multi-armed bandits to sequentially identify the next (method, validation sample)-pair to evaluate and utilize low-rank matrix factorization to fill in missing evaluations. We carefully assess the efficacy of our approach on several competitive benchmark problems and show that it can identify the top-performing method using only 5-15% of the typical resources—resulting in 85-95% LLM cost savings. Our code is available at https://github.com/kilian-group/banditeval. 

Abstract Recent advancements in wearable sensor technologies have enabled real-time monitoring of physiological and biochemical signals, opening new opportunities for personalized healthcare applications. However, conventional wearable devices often depend on rigid electronics components for signal transduction, processing, and wireless communications, leading to compromised signal quality due to the mechanical mismatches with the soft, flexible nature of human skin. Additionally, current computing technologies face substantial challenges in efficiently processing these vast datasets, with limitations in scalability, high power consumption, and a heavy reliance on external internet resources, which also poses security risks. To address these challenges, we have developed a miniaturized, standalone, chip-less wearable neuromorphic system capable of simultaneously monitoring, processing, and analyzing multimodal physicochemical biomarker data (i.e., metabolites, cardiac activities, and core body temperature). By leveraging scalable printing technology, we fabricated artificial synapses that function as both sensors and analog processing units, integrating them alongside printed synaptic nodes into a compact wearable system embedded with a medical diagnostic algorithm for multimodal data processing and decision making. The feasibility of this flexible wearable neuromorphic system was demonstrated in sepsis diagnosis and patient data classification, highlighting the potential of this wearable technology for real-time medical diagnostics. 

Abstract Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as$${{{{{{{\mathcal{O}}}}}}}}({T}^{2}\times {{{{{{{\rm{polylog}}}}}}}}(n))$$ $O\left(T^2\times \mathrm{polylog}\left(n\right)\right)$, wherenis the size of the models andTis the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems. 

Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic study of such algorithms. In particular, we show that the dynamics of a d -dimensional Schrödinger equation with η particles can be simulated with gate complexity O ~ ( η d F poly ( log ⁡ ( g ′ / ϵ ) ) ) , where ϵ is the discretization error, g ′ controls the higher-order derivatives of the wave function, and F measures the time-integrated strength of the potential. Compared to the best previous results, this exponentially improves the dependence on ϵ and g ′ from poly ( g ′ / ϵ ) to poly ( log ⁡ ( g ′ / ϵ ) ) and polynomially improves the dependence on T and d , while maintaining best known performance with respect to η . For the case of Coulomb interactions, we give an algorithm using η 3 ( d + η ) T poly ( log ⁡ ( η d T g ′ / ( Δ ϵ ) ) ) / Δ one- and two-qubit gates, and another using η 3 ( 4 d ) d / 2 T poly ( log ⁡ ( η d T g ′ / ( Δ ϵ ) ) ) / Δ one- and two-qubit gates and QRAM operations, where T is the evolution time and the parameter Δ regulates the unbounded Coulomb interaction. We give applications to several computational problems, including faster real-space simulation of quantum chemistry, rigorous analysis of discretization error for simulation of a uniform electron gas, and a quadratic improvement to a quantum algorithm for escaping saddle points in nonconvex optimization. 

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity p o l y ( 1 / ϵ ) , where ϵ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be p o l y ( d , log ⁡ ( 1 / ϵ ) ) , where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.