Neural Radiance Fields (NeRF) — implicit volumetric scene representation L1-082
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
NeRF represents a scene as an MLP F_theta: (x, y, z, theta, phi) -> (sigma, c) mapping a 3D position and view direction to volumetric density and RGB color. Rendering a pixel casts a ray and numerically integrates the classical volume-rendering equation along quadrature samples; training fits theta by back-propagating photometric error on K posed reference images.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- false
- Stability:
- conditional
- κ:
- 12000
Strongly non-convex MLP fitting. Unique 3D scene only when K views cover the scene with sufficient baseline and pose accuracy; view-dependent effects (specularity, transparency) can be absorbed into radiance ambiguously. Pose error, lighting drift, and under-covered regions cause floaters, baked-in artifacts, and depth collapse.
Solvability C
- Solver class:
- SGD / Adam on MLP weights with hierarchical sampling; accelerated variants (Instant-NGP hashgrid, TensoRF factorisation, Plenoxels voxel grid)
- Convergence rate q:
- 1.5
- Complexity:
- O(N_rays * N_samp * F_theta_cost); Instant-NGP reduces F_theta_cost by ~100x via hash grid