Current literature, aiming to surpass the "Chain-of-Thought" approach, often resorts to external modi operandi involving halting, modifying, and then resuming the generation process to boost Large Language Models’ (LLMs) reasoning capacities. Due to their myopic perspective, they escalate the number of query requests, leading to increased costs, memory, and computational overheads. Addressing this, we propose the Algorithm of Thoughts—a novel strategy that propels LLMs through algorithmic reasoning pathways. By employing algorithmic examples fully in-context, this overarching view of the whole process exploits the innate recurrence dynamics of LLMs, expanding their idea exploration with merely one or a few queries. Our technique outperforms earlier single-query methods and even more recent multi-query strategies that employ an extensive tree search algorithms while using significantly fewer tokens. Intriguingly, our results suggest that instructing an LLM using an algorithm can lead to performance surpassing that of the algorithm itself, hinting at LLM’s inherent ability to weave its intuition into optimized searches. We probe into the underpinnings of our method’s efficacy and its nuances in application. The code and related content can be found in: https://algorithm-of-thoughts.github.io

We study the expressibility and learnability of solution functions of convex optimization and their multi-layer architectural extension. The main results are: (1) the class of solution functions of linear programming (LP) and quadratic programming (QP) is a universal approximant for the smooth model class or some restricted Sobolev space, and we characterize the rate-distortion, (2) the approximation power is investigated through a viewpoint of regression error, where information about the target function is provided in terms of data observations, (3) compositionality in the form of deep architecture with optimization as a layer is shown to reconstruct some basic functions used in numerical analysis without error, which implies that (4) a substantial reduction in rate-distortion can be achieved with a universal network architecture, and (5) we discuss the statistical bounds of empirical covering numbers for LP/QP, as well as a generic optimization problem (possibly nonconvex) by exploiting tame geometry. Our results provide the **first rigorous analysis of the approximation and learning-theoretic properties of solution functions** with implications for algorithmic design and performance guarantees.

Modern power systems will have to face difficult challenges in the years to come: frequent blackouts in urban areas caused by high peaks of electricity demand, grid instability exacerbated by the intermittency of renewable generation, and climate change on a global scale amplified by increasing carbon emissions. While current practices are growingly inadequate, the pathway of artificial intelligence (AI)-based methods to widespread adoption is hindered by missing aspects of trustworthiness. The CityLearn Challenge is an exemplary opportunity for researchers from multi-disciplinary fields to investigate the potential of AI to tackle these pressing issues within the energy domain, collectively modeled as a reinforcement learning (RL) task. Multiple real-world challenges faced by contemporary RL techniques are embodied in the problem formulation. In this paper, we present a novel method using the solution function of optimization as policies to compute the actions for sequential decision-making, while notably adapting the parameters of the optimization model from online observations. Algorithmically, this is achieved by an evolutionary algorithm under a novel trajectory-based guidance scheme. Formally, the global convergence property is established. Our agent ranked first in the latest 2021 CityLearn Challenge, being able to achieve superior performance in almost all metrics while maintaining some key aspects of interpretability.