Decomposing how prompting steers behavior

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.

Do vision models perceive illusory motion in static images like humans?

Understanding human motion processing is essential for building reliable, human-centered computer vision systems. Although deep neural networks (DNNs) achieve strong performance in optical flow estimation, they remain less robust than humans and rely on fundamentally different computational strategies. Visual motion illusions provide a powerful probe into these mechanisms, revealing how human and machine vision align or diverge. While recent DNN-based motion models can reproduce dynamic illusions such as reverse-phi, it remains unclear whether they can perceive illusory motion in static images, exemplified by the Rotating Snakes illusion. We evaluate several representative optical flow models on Rotating Snakes and show that most fail to generate flow fields consistent with human perception. Under simulated conditions mimicking saccadic eye movements, only the human-inspired Dual-Channel model exhibits the expected rotational motion, with the closest correspondence emerging during the saccade simulation. Ablation analyses further reveal that both luminance-based and higher-order color--feature--based motion signals contribute to this behavior and that a recurrent attention mechanism is critical for integrating local cues. Our results highlight a substantial gap between current optical-flow models and human visual motion processing, and offer insights for developing future motion-estimation systems with improved correspondence to human perception and human-centric AI.