Generative models are steered with knobs -- prompts, guidance scales, property tags. Turn one as hard as you like and, past a point, it stops moving the property you care about. We find that ceiling is not a shortcoming of the model but a budget, set by the training data before the model is trained: a property's movable range splits in two -- the part a knob can reach, and a second, significant part that only examples -- concrete instances of what you want more of -- can reach. That second part is usually much larger, but not always, and the same budget says so in advance. Reaching that second part takes a different move: instead of turning a knob, you show the model examples, composed from what it already learned rather than added to its training. A cheap audit of the training data measures the budget; we give a recipe for building the example set that reaches all of it. This buys two things a knob can't. Reach: it moves a property across the whole budget, not just the part a knob reaches. Expressiveness: it steers toward targets you can only specify by example -- including ones you can't put into words. We turn these into a handful of falsifiable claims and verify them in two unrelated domains, image and crystal-structure generation -- marking where a knob is enough, and where only examples will do.
The standard way to read latent knowledge out of a model, a linear probe confirmed by a steering recovery, can systematically overstate what a vision-language model (VLM) actually grounds in the image. We show this on spatial reasoning, where the error is invisible to both probing and steering yet exposed by a one-line causal control: replacing the image with a gray blank. Probes decode the within-axis answer at 73--97% across axes, and a training-free projection lifts a near-chance axis from 59% to 79%, exactly the signature of unlocking latent knowledge. The blank-image arbiter refutes it, revealing three grounding regimes that probing conflates: an axis can be grounded (vision-dependent, correct), a prior (vision-independent, with its decode and its apparent recovery a directional default rather than perception), or, surprisingly, inverted: decodable, causally controllable, but deployed with the wrong sign, so the model scores below chance and the error requires looking. The taxonomy holds across the studied VLMs: in fourteen models spanning six language-model families and 2B--27B, horizontal is grounded, vertical is a prior, and depth is inverted, with the inversion emerging at scale within families. The decode-versus-deploy inversion replicates on seven of eight models across five families, and the minimal edit that re-deploys it varies with geometry: a training-free rotation matches a trained edit on the cleanest model, while distributed inversions need a trained low-rank edit, tracing a per-model correction-complexity spectrum. The cheap, self-calibrating arbiter cleanly separates grounded perception, inverted perception, and prior substitution; we argue it should be a default control for latent-knowledge and steering claims in VLMs.
Sparse Autoencoders (SAEs) have shown promise for analyzing language models, but applying them to vision-language models (VLMs) often yields representations that are difficult to use as controllable cross-modal steering directions. We introduce the Joint Sparse Autoencoder (JSAE), which uses an explicit alignment constraint to jointly factorize sequence-pooled vision and language activations into shared, interpretable image/caption-level features. Applied to LLaVA, JSAE recovers cross-modal features for recognizable concepts (e.g., food and animals). Through bidirectional interventions (additive steering and suppression), we observe a layer-dependent asymmetry under our protocol: additive steering peaks at mid-to-late (pre-output) layers and weakens at both ends, whereas suppression scores remain within a comparable range across all probed layers within statistical noise. Experiments on three VLMs, namely LLaVA-v1.6-Mistral-7B, Llama3-LLaVA-8B, and the MoE-based Qwen3-VL-30B, show related layer-localized effects across architectures. Together, these results suggest that explicitly aligned sparse representations support more controllable intervention-based analysis of multimodal features, within an identifiable layer range, than the unconstrained alternatives tested here.