Progressive Permutation Alignment with Temperature-Controlled Spectral Sharpening

Yuta Horioka, Naoya Chiba, Yuki Uranishi

In implicit neural representations (INRs), 3D signals are encoded directly in network weights, making stable weight-space operations essential. However, permutation symmetry causes independently trained yet functionally equivalent models to appear distant in weight space, often inducing large loss barriers under linear interpolation. Existing neuron alignment methods either commit early to discrete matches and become trapped in inconsistent local optima or rely on computationally expensive gradient optimization over continuous relaxations, both of which are unreliable in challenging cases such as NeRF. We adopt progressive alignment, a layer-wise strategy that follows inter-layer dependencies from input to output. At each layer, a correlation matrix is estimated and aligned with a discrete anchor obtained by the Hungarian algorithm, after which temperature-controlled spectral annealing gradually sharpens the correlation structure toward a permutation matrix. This update is deterministic and lightweight, avoiding the inner-loop gradient optimization required by continuous relaxation methods. A final refinement stage further optimizes the network layer-by-layer via weight matching,…