Do inherent limits forbid full robustness?

The mainstream research reading treats robustness as a property defined relative to a task, threat model, data distribution, architecture, and performance target. Several results show serious barriers: robust generalization can require exponential model size, adversarial perturbations can fool classifiers under distributional assumptions, and some systems exhibit instability. These findings constrain what can be guaranteed, but they do not by themselves prove that all useful or domain-specific robustness is impossible.

• For ReLU networks, robust training can coexist with a robust-generalization gap; in the cited setting, avoiding the gap may require network size exponential in data dimension.
• A strong no-free-lunch result shows that, for certain data distributions, classifiers can be adversarially fooled with high probability when perturbations exceed the natural noise level.
• A mathematical analysis reports universal instability for neural networks trained on classification problems in virtually any application, while its title and framing distinguish this from the existence of stable neural networks.
• For vision-language-action policies, an information-theoretic bound constrains the combined amount of capability and robustness, implying that improving one can consume a finite information budget.
• These results are conditional mathematical limits, so they establish trade-offs or failure regimes rather than a blanket proof that every useful notion of robustness is impossible.

A stronger dissenting interpretation argues that failures are not merely shortcomings of current training. It points to no-go results for combining desirable notions of robustness and trustworthiness, architectural arguments that probabilistic language-model safeguards cannot become formal constraints, and limits on eliminating hallucination in general problem-solving. Related arguments contend that scaling capabilities and restrictions can become structurally incompatible. These claims are broader than the conditional results, and depend heavily on their formalizations and assumptions.

• A formal-epistemology paper claims that four prima facie desirable properties of robustness and trustworthiness cannot be combined without triviality, regardless of how the concepts are specified within its framework.
• An architectural analysis argues that probabilistic LLM safety boundaries cannot provide the categorical enforcement of rule-based constraints and presents formal claims that unsafe outputs remain reachable.
• A formal learning-theoretic paper argues that general-purpose computable LLMs cannot learn every computable function, making hallucination inevitable under its definition of hallucination.
• A NIST-listed article presents information-theoretic limitations for AI security and alignment and frames responsible adoption around preparing for those limits rather than expecting unrestricted robustness.
• An EA Forum argument interprets restriction circumvention by a capable agent as evidence of a structural incompatibility between scaling capability and restrictions, concluding that stopping scaling may be the only reliable constraint beyond a threshold.