Human Supervision as an Information Bottleneck: A Unified Theory of Error Floors in Human-Guided Learning

Recent advances in large reasoning models (LRMs) have shown that reinforcement learning with verifiable rewards (RLVR) can substantially improve reasoning in mathematics and code, where outcomes can be checked automatically. Extending this progress to open-ended and agentic tasks remains difficult because reliable rewards are harder to obtain and direct human supervision cannot keep pace with the scale and complexity of model-generated experience. This paper studies how LRMs can continue to improve as human supervision gradually recedes from the learning loop. We examine two connected dimensions of this problem. The reward axis traces the development from per-instance human judgments to reusable verifiers and rewards that operate even without human feedback. The experience axis examines how learning can progress from human-curated tasks and environments toward self-generated curricula, constructed environments, and autonomous co-evolution. We connect these dimensions through a five-level ladder from L0 to L4 that identifies which parts of the learning process remain under continued human control. Our analysis further highlights the risks introduced by increasingly autonomous rewards and experience generation, including reward hacking, feedback drift, curriculum collapse, and environment errors. Consequently, we also provide the evaluation around three complementary objects: policy capability, feedback fidelity, and experience quality. This analysis provides a structured account of current approaches to scaling LRMs beyond human supervision and the open problems involved in developing self-sustaining learning systems toward superintelligence. Furthermore, we maintain a continuously updated GitHub repository to track the latest advances.

Some limits on what language models know are not gaps in data coverage but structural properties of learning from text. We introduce the information shadow: the region of phenomena that a text-trained learner cannot acquire regardless of scale, comprising (I) structures language cannot express, (II) functions that are statistically non-identifiable from the training distribution, and (III) functions that are representable but unreachable by gradient-based training. We give each type a probe that is decisive because the premise of the shadow is, in that setting, provable. For Type I, Language Compression Residuals compare a text learner, which sees only a lossy text-like encoding of the signal, against a full-signal learner, which sees the underlying signal directly. The text learner sits at a computable expressibility ceiling while the full-signal learner pulls away by a gap that stays flat across 300x more data, so the deficit is a property of the channel, not of training. For Type II, the Counterfactual Distinction Test trains models on data exactly consistent with two incompatible rules. Across a provable string task and a language-like agreement task, behavior on counterfactuals is set by the model's inductive bias, while 5% disambiguating data steers the learned rule bidirectionally to either target (r = +/-1.0, p < 1e-10). For Type III, Basin Escape Mapping exhibits a function that is representable at 100% (by hand construction) yet reached 0% of the time by standard training and instantly from a nearby initialization, with width scaling providing no help (p = 1.6 x 10^-14). Each effect is isolated by a control that rules out a capacity or modality artifact. We release the probe suite and discuss implications for benchmark design, capability auditing, and shadow-aware uncertainty.

Large Language Models (LLMs) are frequently portrayed as general-purpose solvers capable of solving arbitrary tasks. We argue that this view overlooks a fundamental constraint: language is a compressed and capacity-limited interface for conveying task information. Modelling User--System interaction as a bilevel cheap-talk game, we analyse how latent tasks are encoded into prompts and reinterpreted under alignment and safety constraints. We introduce a conceptual decomposition separating task inference from execution and derive PAC-Bayes bounds that distinguish finite-sample estimation error from irreducible structural limitations. Our first main result establishes an expressivity floor: language acts as a capacity-limited communication channel, and whenever the informational complexity of a task family exceeds the capacity of that channel, distinct tasks become unavoidably indistinguishable to the Solver, inducing a strictly positive error floor that cannot be eliminated by additional data, optimisation, or model scaling alone. We then establish an objective-misalignment floor: when alignment constraints restrict the admissible output set, the User-ideal distribution may lie outside the feasible class, inducing an irreducible distortion. Together, these results yield a formal negative conclusion: prompt-conditioned LLMs are not universal problem solvers through prompting alone, as there exist task families for which correct behaviour is provably unattainable even in the infinite-data regime. More broadly, our analysis shows the limits of prompt-based generalisation arise from information-constrained communication and alignment-constrained objectives. This suggests that interfaces beyond natural language, including multimodal observations and, external memory, may reduce the inherent LLM limitations by increasing the task-relevant information available to the System.