Foundations¶
The static objects of energy-based modeling, before anything moves. These examples are fast, CPU-friendly, and involve no training: they build the intuition the rest of the curriculum rests on.
- Energies: an energy is an unnormalised negative log-density; everything follows from its gradient \(-\nabla_x E\), the score of the model.
- Datasets: the synthetic 2D targets you sample and train against.
- Schedulers: the parameter schedules samplers and losses consume.
- Interpolants: the probability paths behind flow and diffusion sampling.
Theory: The Energy-Based View, and for the paths, Interpolants and Couplings.
Next: Sampling, where these objects start to move.
| Example | Summary | Level |
|---|---|---|
| Energy Landscapes | An energy E(x) defines a density p(x) proportional to exp(-E(x)); evaluate it and its force field -grad E. | intro |
| Custom Energies | Subclass BaseModel with any differentiable map (N, d) -> (N,); gradients, sampling, and losses come for free. | intro |
| Dataset Gallery | The eight synthetic 2D targets: one constructor contract, standard benchmarks from the flow and EBM literature. | intro |
| Scheduler Anatomy | Linear, cosine, and exponential schedules, and how a sampler advances a scheduled parameter per step. | intro |
| Interpolant Anatomy | The path x_t = alpha(t) x1 + sigma(t) x0 and its conditional velocity, for the linear, cosine, and VP schedules. | intro |