Perturbation: A simple and efficient adversarial tracer for representation learning in language models

We introduce a simple yet powerful framework for training large language models. In contrast to the standard autoregressive next-token prediction based on an exact prefix, we propose a perturbation-based procedure that first transforms the prefix into a semantic neighbor and then conditions on this perturbed variant for next-token prediction. This yields a hierarchical model with a pre-post-additive noise structure. Within this framework, we develop a rigorous theory of extrapolability, namely, the capacity of a model class to make reliable predictions for token sequences that lie outside the empirical support of the training corpus. We evaluate the finite-sample performance of the proposed procedure using both synthetic and real-world language data. Results show that the proposed method consistently improves out-of-support prediction while maintaining competitive in-support performance, demonstrating that perturbation offers a practical route to language modeling.

Language models encounter typos, corrupted text, altered words, and disrupted token order, yet robustness is usually evaluated only through output behavior. We study how six naturalistic and synthetic input perturbations propagate through decoder-only language models at three levels: output behavior, hidden-state geometry, and attention-head function. We evaluate behavioral effects across four GPT-2 and two Qwen2.5 checkpoints by analyzing layerwise geometry using centered kernel alignment and intrinsic dimension, and examine attention-head responses in GPT-2. Perturbation types produce distinguishable metric profiles that are not fully captured by output measures and are only partly consistent across the tested checkpoints. Copying scores are especially associated with activation-patching recovery under token substitution and shuffling. Gradient-guided HotFlip perturbations also cause stronger behavioral and representational disruption than rate-matched random token substitutions in GPT-2; their behavioral effects are consistent across all six tested checkpoints. Our results show that robustness claims based on a single behavioral or representational metric can be misleading, and motivate multi-level evaluation of how perturbations alter language-model computation.

Large language models are sensitive to minor prompt perturbations, yet existing robustness methods usually enforce consistency at the whole-sequence level. This holistic view can hide an important failure mode: a perturbed response may remain globally similar to the clean one while drifting on a critical entity, relation, or conclusion. We introduce S$^2$R$^2$, a segment-level framework for robust LoRA fine-tuning. S$^2$R$^2$ decomposes clean and perturbed generations into semantic segments, aligns them with an optimal-transport objective, and penalises the segments with the largest meaning drift. To connect this output-side objective with model adaptation, we add an adapter-stability regulariser motivated by segment-level attention reallocation, using LoRA norm control as a tractable proxy for limiting perturbation-amplified evidence shifts. A PAC-Bayesian complexity view further explains why controlling adapter growth may support transfer beyond observed perturbations. Experiments on summarisation benchmarks show that S$^2$R$^2$ improves robustness under typographical noise, deletion, synonym replacement, and paraphrasing, while maintaining competitive clean performance and stronger cross-dataset transfer than consistency-based baselines.