Progressive Permutation Alignment with Temperature-Controlled Spectral Sharpening

Key points

• 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.1
• We adopt progressive alignment, a layer-wise strategy that follows inter-layer dependencies from input to output.1
• 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.1
• Experiments on MLPs, CNNs, and Neural Radiance Fields (NeRFs) show that the proposed method reliably recovers neuron correspondences and achieves stable alignment across architectures.1

Sources (1)

• [1]Progressive Permutation Alignment with Temperature-Controlled Spectral Sharpening
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 21, 08:26 AM

  In implicit neural representations (INRs), 3D signals are encoded directly in network weights, making stable weight-space operations essential.

  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.

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