Generalization Is Stability, Not Accuracy: Multi-Axis Evaluation of LLMs
Most LLM benchmarks treat generalization as aggregate accuracy on fixed prompts, which can hide per-example fragility when the same user intent is rephrased. This paper reframes generalization as behavioral stability across semantically equivalent input variations and proposes SAGO, a per-prompt, multi-axis framework that tracks changes in generation consistency, internal activations, confidence/uncertainty, and response mirroring. By evaluating eleven open- and closed-source models across six datasets and three variation families, the authors show that instability is heterogeneous, axis-specific, and not resolved by scale, challenging the assumption that high benchmark scores imply reliable generalization.
The reframing of generalization from aggregate accuracy to per-instance behavioral stability is conceptually sharp and empirically actionable. SAGO convincingly demonstrates that current instruction-tuned LLMs exhibit statistically significant instability under semantically equivalent variations, and that failure profiles differ across models, datasets, and behavioral axes. However, the empirical claims are undercut by an extremely small base sample ($N=16$ prompts per dataset), ad hoc normalization constants tied to the observed empirical range, and incomplete coverage on closed-source models due to API restrictions. The framework is a genuine advance in diagnostic breadth, but its statistical basis is thinner than the significance stars suggest.
The central thesis—that aggregate accuracy obscures per-instance behavioral flipping—is well-argued and strongly supported by the multi-axis design. The dissociation between axes is compelling: for example, one model can achieve the lowest generation inconsistency in the pool while simultaneously registering the highest confidence drift, showing that robustness is not unidimensional. The inclusion of internal activation geometry ($\Delta_{X_{\mathrm{Act}}}$) alongside surface-output metrics gives SAGO diagnostic reach that single-signal benchmarks lack. The finding that larger models do not automatically resolve instability is an important corrective to scale-centric narratives.
The most pressing limitation is sample size: the study rests on only $N=16$ base prompts per dataset (96 total), which is a fragile foundation for one-sided $t$-tests and broad population-level claims about model families. The authors justify this with a bootstrap ablation, but the variance inherent in 16 prompts remains a serious threat to external validity.
Normalization for unbounded metrics relies on constants ($R_{\mathrm{Prob}}=250$, $R_{\mathrm{Ent}}=10$) derived from the same evaluation data, limiting cross-study comparability. Additionally, social-register mirroring depends on GPT-4o-mini as a judge without reported temperature or prompt-chain details, and closed-source model conclusions are incomplete because activation and sequence log-probability axes are unavailable via API.
The paper positions itself clearly against prior robustness literature, distinguishing SAGO from single-perturbation and aggregate OOD studies. The evidence for axis independence and cross-dataset ranking reversal is quantitative and specific: within-model instability can span a $3.7\times$ range across datasets, and one architecture's advancement can yield worse generation stability than its predecessor. However, the paper does not quantitatively compare SAGO outputs against existing robustness benchmarks (e.g., PromptBench or DecodingTrust), so it is difficult to judge whether the framework reveals new failure modes or primarily re-packages known fragility in finer granularity. The statistical tolerance-threshold testing ($\varepsilon=0.05$) is sensible in principle, but with $N=16$ the effect-size estimates carry high variance.
The authors publish a reference implementation, specify deterministic decoding ($T=0$), list exact model versions, and report GPU hardware. Variation families are documented with concrete strength-level examples in Appendix A, and the SGS computation is described with sufficient algebra to replicate. Reproduction is hampered, however, by undisclosed random seeds for variation generation, proprietary API-dependent judges for mirroring, and normalization constants tied to empirical ranges observed in this study. Because activation and log-probability axes are blocked for closed-source APIs, exact replication of the full multi-axis comparison requires hardware access that matches the open-source setup. Releasing per-prompt delta matrices and judge prompts would significantly lower barriers.
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.
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