Can machines think efficiently?

We introduce the Generalized Turing Test (GTT), a formal framework for comparing the capabilities of arbitrary agents via indistinguishability. For agents A and B, we define the Turing comparator A $\geq$ B to hold if B, acting as a distinguisher, cannot reliably distinguish between interactions with A (instructed to imitate B) and another instance of B. This yields a dataset- and task-agnostic notion of relative intelligence. We study the comparator's structure, including conditions under which it is transitive and therefore induces an ordering over equivalence classes, and we define and analyze variants with querying, bounded interaction, and fixed distinguishers. To complement the theory, we instantiate the framework on a collection of modern models, empirically evaluating pairwise indistinguishability across thousands of trials. The resulting comparisons exhibit a stratified structure consistent with existing rankings, hinting that the proposed framework yields meaningful empirical orderings. Our results position indistinguishability as a unifying lens for reasoning about intelligence, suggesting a foundation for evaluation and, potentially, training objectives that are inherently independent of fixed datasets or benchmarks.

This paper examines Turing's 1948 report, "Intelligent Machinery", as an important conceptual source for the later imitation games. Its first contribution is to identify and integrate the design concepts underlying the 1948 chess-based imitation game: the possibility that intelligent machines may make mistakes, the exclusion of irrelevant physical features, the role of the human judge, and Turing's claim that intellectual activity consists mainly of search. The paper's second contribution is to argue that restricting the human contestant to a rather poor chess player increases the role of intellectual search and makes human behaviour more comparable to machine behaviour. This interpretation presents the 1948 game as a human-approximates-machine game and suggests that the imitation game framework can be used not only to ask whether machines imitate humans, but also to examine when human intelligence becomes machine-like under specific task constraints.

Intelligence is constituted by \textit{process} (iterative activity through which output emerges), not in the output itself. Generative AI (GenAI) is trained on \textit{traces} (textual and visual residues of human cognitive processes), reproducing samples from a distribution of those traces. Its outputs resemble reasoning, problem-solving, and creativity, yet the activity that produces such outputs in humans remains largely absent. Current GenAI is, therefore, weakly equivalent to the cognition it imitates, matching outputs while process stays absent or opaque. The cognitive sciences have long distinguished between weak and strong equivalence. Here, we define \textit{strong} equivalence across seven process features, assessable against human and machine cognition. Our process-based account addresses a symmetric risk: GenAI tools that outsource a person's generative processes may leave critical capacities unbuilt. We specify design principles for GenAI that instantiate more process and preserve rather than erode human judgment and creativity, and outline process audits that make strong equivalence testable.