AI Agents as Universal Task Solvers

2025-10-13

AI Summary

This paper investigates the theoretical limits and implementation pathways of AI agents as universal task solvers, addressing core questions such as whether chain-of-thought reasoning can solve any computable task and how reasoning capabilities can be learned. Method: We propose a novel problem-solving paradigm grounded in temporal compression, shifting the learning objective from inductive generalization to transductive inference and prioritizing information utilization efficiency over reconstruction fidelity. Leveraging stochastic dynamical systems modeling, we integrate algorithmic information theory with computational complexity analysis. Contribution/Results: We establish, for the first time, a power-law relationship between inference time and training time, and theoretically prove that the optimal acceleration of a universal solver is strictly bounded by the algorithmic information content of the task. The framework reveals that scaling model or data size alone often leads to inefficient brute-force search, providing principled guidance for designing efficient intelligent agents.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Agentic search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

AI reasoning agents are already able to solve a variety of tasks by deploying tools, simulating outcomes of multiple hypotheses and reflecting on them. In doing so, they perform computation, although not in the classical sense -- there is no program being executed. Still, if they perform computation, can AI agents be universal? Can chain-of-thought reasoning solve any computable task? How does an AI Agent learn to reason? Is it a matter of model size? Or training dataset size? In this work, we reinterpret the role of learning in the context of AI Agents, viewing them as compute-capable stochastic dynamical systems, and highlight the role of time in a foundational principle for learning to reason. In doing so, we propose a shift from classical inductive learning to transductive learning -- where the objective is not to approximate the distribution of past data, but to capture their algorithmic structure to reduce the time needed to find solutions to new tasks. Transductive learning suggests that, counter to Shannon's theory, a key role of information in learning is about reduction of time rather than reconstruction error. In particular, we show that the optimal speed-up that a universal solver can achieve using past data is tightly related to their algorithmic information. Using this, we show a theoretical derivation for the observed power-law scaling of inference time versus training time. We then show that scaling model size can lead to behaviors that, while improving accuracy on benchmarks, fail any reasonable test of intelligence, let alone super-intelligence: In the limit of infinite space and time, large models can behave as savants, able to brute-force through any task without any insight. Instead, we argue that the key quantity to optimize when scaling reasoning models is time, whose critical role in learning has so far only been indirectly considered.

Problem

• Investigating AI agents as universal solvers for computable tasks
• Exploring the role of time in learning to reason effectively
• Proposing transductive learning to reduce solution time for new tasks

Innovation

• AI agents as universal stochastic dynamical systems
• Shift from inductive to transductive learning approach
• Optimize time scaling rather than model size scaling