Why the Third Axis Is Freedom

The deep learning revolution, kicked off by AlexNet, taught us that end-to-end training beats decomposing a problem into hand-designed stages. Generative modeling, however, has remained the exception-despite generative models being remarkably capable, they are still not trained end-to-end. This is because, at its core, generative modeling is about handling distributions with many modes, and existing scalable approaches handle this the same way, by factoring the generation procedure, which prevents end-to-end generation. In this work, we introduce Explorative Modeling, a new paradigm that instead factors the training loop, exploring K candidate matches between model generations and data, and training on the best, so predictions commit to modes rather than blurring them. We find Explorative Models (XMs) useful in two settings. First, increasing exploration adds a third pretraining axis beyond parameters and data for existing generative models-where scaling exploration monotonically improves performance across both continuous and discrete domains (images, video, and language). Notably, gains from exploration increase with scale, climbing from 7% to 36% as data scales and from 13% to 23% as models grow, with efficiency gains more than doubling at 3x the compute. Concretely, exploration improves FLOP efficiency by 4.1x, sample efficiency by 6.2x, parameter efficiency by 47%, lifts the strongest of image-generation recipes to a near-state-of-the-art 1.43 FID on ImageNet without guidance, enables scaling how end-to-end existing models are, and unlocks scaling generalization. Second, XMs enable end-to-end reconstructive generative modeling, matching diffusion on control tasks with 16-256x fewer inference steps. Together, these results establish XMs as both a new pretraining axis for existing generative models and a standalone end-to-end generative modeling paradigm.

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.

Feature attribution methods promise to identify which input features matter for a model output. In generative language models, however, it is often unclear what should count as a feature in the first place. In autoregressive language models, earlier generated tokens are both outputs of the model and inputs to later predictions. In diffusion language models, generation proceeds through iterative denoising or unmasking rather than fixed left-to-right prediction, so local explanation may target a state of diffusion rather than a next token. We argue that this ambiguity is not merely an implementation detail, but a conceptual limitation of carrying classifier-era feature attribution directly into generative language modeling. We introduce the Attribution Contract, a specification for feature-attribution claims that names what output is being explained, which features are eligible to receive attribution, what generative process is assumed, what is held fixed, and what model score is being attributed. The contract clarifies why the same attribution method can answer different questions depending on how it is instantiated. We argue that many disagreements about feature attribution in generative language models are not disagreements about attribution algorithms, but about unstated explanatory contracts. Using autoregressive and diffusion language models as case studies, we show when attribution to earlier generated tokens, intermediate states, or denoising stages is informative, when it is misleading, and why feature-attribution methods in generative language models should be evaluated as method-contract pairs.