The performance of textual neural models often degrades when their inputs are corrupted by noise such as typos, OCR errors, or dropped words. We study the degradation rate across neural models, both sentence embeddings and decoder-only LLMs, and find that how consistent it is depends on the scale of the noise: under word-level noise, models with very different architectures decline along nearly the same curve, while under character-level noise they separate. We further identify the determining factor to be the training objective, not the architecture: eight encoders spanning six pretraining paradigms are scattered initially, and collapse onto a common curve after a short contrastive training recipe. We trace the word/character split to tokenization: a single character edit forces the tokenizer to re-segment the surrounding word, disturbing the token sequence far more than dropping a whole word does. This finding and its underlying mechanism provide a practical means to predict a model's robustness to noise without any noisy evaluation, and to install robustness at a chosen noise scale through noise-augmented training.
Prompting steers large language models (LLMs) and vision-language models (VLMs) without weight updates, but it remains unclear how instruction changes reshape internal representations to produce behavior. We introduce a nested geometric decomposition framework that treats prompting as a transformation of the representational geometry of the content following the prompt. For each prompt pair, we align representations of the same stimuli under two prompts using increasingly expressive stimulus-invariant maps: translation, rigid transformation with uniform scaling, sequential axis scaling, affine transformation, and nonlinear transformation. We then causally test each map by replacing a single layer's prompt-A hidden state for held-out stimuli with its mapped counterpart and measuring recovery of prompt-B representational geometry and behavior. Across three LLMs, three VLMs, and six text or image datasets spanning style, emotion, scene content, and number, prompts consistently reshape representations toward the instructed task structure. Cross-validated variance decomposition shows that much prompt-induced activation change is captured by shape-preserving maps, especially translation and rigid transformation with uniform scaling, while tier profiles reveal model- and task-specific routing strategies across layers. Crucially, although translation and rigid tiers already improve behavioral agreement, affine transformation is the first tier to nearly recover target-prompt task geometry and yields corresponding behavioral gains. This suggests that cross-dimensional linear mixing is a key mechanism by which prompts reorganize representations toward instructed task structure. Our framework decomposes prompt-induced representational change into interpretable geometric components and reveals how models route task-relevant structure to produce prompt-driven behavior.