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AI Agents as Universal Task Solvers

Alessandro Achille, Stefano Soatto

TL;DR

The paper reframes AI agents as universal task solvers through a transductive learning lens, arguing that time is the central resource for reasoning and introducing the notion of proper time. It extends Levin–Solomonoff universality to stochastic dynamical systems, derives scaling laws under a Generalized Hilberg Conjecture that predict how inference speed scales with training data, and analyzes memory, prompting, and tool-use to understand where learning is essential. It also proposes maximalistic models of computation to accelerate reasoning by automating and abstracting frequent subroutines. Collectively, the work delineates when scaling improves reasoning versus when brute-force computation dominates, guiding time-aware design of future AI agents and prompting regimes for swift, general problem solving.

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.

AI Agents as Universal Task Solvers

TL;DR

The paper reframes AI agents as universal task solvers through a transductive learning lens, arguing that time is the central resource for reasoning and introducing the notion of proper time. It extends Levin–Solomonoff universality to stochastic dynamical systems, derives scaling laws under a Generalized Hilberg Conjecture that predict how inference speed scales with training data, and analyzes memory, prompting, and tool-use to understand where learning is essential. It also proposes maximalistic models of computation to accelerate reasoning by automating and abstracting frequent subroutines. Collectively, the work delineates when scaling improves reasoning versus when brute-force computation dominates, guiding time-aware design of future AI agents and prompting regimes for swift, general problem solving.

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.
Paper Structure (28 sections, 19 theorems, 66 equations, 3 figures)

This paper contains 28 sections, 19 theorems, 66 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Can an LLM-powered AI Agent be a universal solver?
  3. Intelligence is about time
  4. Scaling laws for speed.
  5. Maximizing a Continuous Reward
  6. Dynamical Systems as Computation
  7. Notation
  8. Proper Time
  9. Side note: Multiple successful paths
  10. Universal Solvers
  11. Universal Solvers and Sampling
  12. Scaling Laws for Speed
  13. Hilberg's conjecture for scaling
  14. Scaling Laws for Time
  15. Memory-Time Trade-Off
  16. ...and 13 more sections

Key Result

theorem 1

Information is Speedinfo-speed The maximum speed-up a task universal solver can achieve in finding an optimal solution $h$ to a task from training on a dataset $D$, is where $I(h : D)$ is the algorithmic mutual information between the data and the solution.

Figures (3)

  • Figure 1: Scaling law inversion curve showing information vs. model scale
  • Figure :
  • Figure :

Theorems & Definitions (30)

  • theorem 1
  • theorem 2
  • definition 1
  • theorem 3
  • theorem 4
  • definition 2
  • theorem 5
  • lemma 1
  • proof : Proof sketch
  • lemma 2
  • ...and 20 more