Inferential Theory of Learning as a Framework for Test-Time Computation in Foundation Models

Foundation models are billion-parameter neural networks that are trained under statistical learning principles to reason inductively regarding multifarious tasks at inference. However, foundation models are increasingly deployed in settings where the statistical principles that they were trained on may not hold. During deployment, users intervene in these systems' functionality through prompts, instructions, demonstrations, analogies, retrieval, tool calls, memory, verification, search, and multi-step reasoning. These operations change the effective knowledge state available at inference time, all of which are not well described by induction alone. This paper argues that Michalski’s Inferential Theory of Learning (ITL) provides a useful conceptual basis for describing deployed foundation models as multistrategy, goal-directed inference systems. In ITL, learning is modeled as the transformation of knowledge through transmutations such as generalization, specialization, abstraction, concretion, association, discrimination, explanation, derivation, reformulation, insertion, deletion, replication, and sorting. We reinterpret these classical transmutations in the context of modern test-time computation techniques, showing that the functionality of reasoning models, intelligent prompting, retrieval-augmented generation, tool use, memory, and agentic search can be understood as transmutation programs over knowledge states. We then identify limitations of classical ITL for contemporary machine learning and propose a probabilistic extension in which transmutations are stochastic operators selected under uncertainty and cost. Finally, we connect this view to a system-level information bottleneck principle, quantifying the new knowledge that is acquired during the inference process. The resulting framework positions ITL as a bridge between statistical learning, symbolic reasoning, abductive explanations, prompting, and agentic foundation models.