Rethinking Evaluation for Principled Generalization Using a Kripkean Challenge to Meaning as Use

Recent advances in large language models (LLMs) have brought impressive performance across diverse tasks; however, shortcomings remain in logical reasoning, including inconsistencies under linguistic variation. To improve the reasoning capacity of LLMs, we must be able to accurately measure their reasoning capacity. Current benchmarks primarily report single accuracy numbers on selected reasoning tasks. Such a performance-based evaluation methodology says little about a model's generalization capacity in reasoning. To address this limitation, we argue for a different evaluation paradigm, called competence-based evaluation (CBE), which tests whether models reliably apply the same competence across a family of problems. A parameterized generator scales complexity while keeping the required competence fixed, and matched answer-preserving presentations test correctness beyond one formulation. We instantiate CBE on elementary ordering tasks, scaling input size while varying presentations of the same ordering rule. Across six GPT and Qwen models, performance is reasonably good over bounded complexity ranges, but even strong models fail the competence condition across the tested family. Chain-of-thought and GRPO extend strong performance without resolving all tested failures; supervised LoRA shows little held-out transfer. CBE provides diagnostic profiles and an evaluation protocol that can grow with future models.

This position paper argues that many behaviours framed as either "stochastic parroting" or "advanced reasoning" are better explained as context-directed extrapolation from training-data priors, and that ML and NLP research communities would benefit from evaluations that distinguish remembering and basic extrapolation from genuine application-level generalisation. Our central contribution is an actionable evaluation checklist and design patterns that make these distinctions testable in practice. Our framework posits that LLMs extrapolate from training data priors while using context to guide the model to the appropriate priors; we call this "context-directed extrapolation." Specifically, this context direction is achieved through examples in base models, leading to in-context learning, while instruction tuning allows analogous task specification via prompts rather than explicit examples. We argue that adopting this more realistic framework and controls for improving evaluation would better calibrate claims about LLM "reasoning," refocus research on how LLM performance interacts with training data and generalisability to out-of-domain tasks, and reduce miscalibration in deployment and policy decisions.

Generalization in large language models (LLMs) is the ability to produce consistent and semantically stable outputs when the same input is expressed in different ways. Existing work typically evaluates generalization through aggregate accuracy on a single prompt format, task, or set of variations, which conflates robustness with overall benchmark performance. In this work, we show generalization evaluation at the level of individual examples, across multiple input variants, and across different aspects of model behavior, focusing on variability rather than reducing performance to a score that can be improved through narrow training or other ways that obfuscate generalization evaluation. Following this view, we introduce the Stability-Aware Generalization Objective (SAGO), a framework that measures how much model behavior changes for the same input under different variations and benchmarks, capturing variability across several dimensions including generation consistency, internal activations, confidence, and response mirroring. We show that many commonly used models exhibit statistically significant and consistent generalization instability: no model generalizes uniformly, behavioral axes capture independent failure modes, and cross-dataset variation can reverse model rankings.