AI Agents as Universal Task Solvers

We describe AI agents as stochastic dynamical systems and frame the problem of learning to reason as in <i>transductive inference</i>: Rather than approximating the distribution of past data as in classical induction, the objective is to capture its <i>algorithmic structure</i> so as to reduce the time needed to solve new tasks. In this view, information from past experience serves not only to reduce a model's uncertainty, as in Shannon's classical theory, but to reduce the computational effort required to find solutions to unforeseen tasks. Working in the verifiable setting, where a checker or reward function is available, we establish three main results. First, we show that the optimal speed-up for a new task is tightly related to the algorithmic information it shares with the training data, yielding a theoretical justification for the power-law scaling empirically observed in reasoning models. Second, while the <i>compression view</i> of learning, rooted in Occam's Razor, favors simplicity, we show that transductive inference yields its greatest benefits precisely when the data-generating mechanism is most complex. Third, we identify a possible failure mode of naïve scaling: in the limit of unbounded model size and computing, models with access to a reward signal can behave as <i>savants</i>, brute-forcing solutions without acquiring transferable reasoning strategies. Accordingly, we argue that a critical quantity to optimize when scaling reasoning models is <i>time</i>, the role of which in learning has remained largely unexplored.