Persistence of non-identifiability at the reconstruction noise floor

Determine whether non-identifiability between IFS parameter sets and density maps persists as the density-map tolerance decreases from the currently analyzed level to the reconstruction noise floor, by conducting a second-solution analysis that drives a solution far from the true parameters down to that floor.

Background

The paper establishes that substantially different affine-map parameter sets can produce nearly identical density maps, demonstrating non-identifiability at density-map tolerances down to approximately 0.013 in density L2 distance. However, the matched rendering procedure has a reconstruction noise floor of approximately 2.7×10-6 in density SSE because of finite stochastic trajectory sampling. The unresolved issue is whether distinct, far-from-truth parameter solutions continue to exist when reconstruction is required to approach this much smaller noise-floor tolerance. The paper specifies that resolving the issue would require finding a second solution whose parameters remain far from the true parameters while its reconstruction error is reduced to the noise floor.

References

Non-identifiability near the noise floor is undetermined. We quantified non-identifiability down to an achievable tolerance (density $L_2\approx0.013$; Section~\ref{sec:identifiability}). Whether it persists as the tolerance shrinks to the reconstruction noise floor ($\sim2.7\times10{-6}$ in density SSE; Section~\ref{sec:oracle}) is undetermined; settling it would require a second-solution analysis that drives a solution far from the truth down to the floor, which we leave for future work.

— Amortized Set Prediction for Inverse IFS Reconstruction from Density Maps  (2608.24175 - Yamaguti, 25 Aug 2026) in Section 6, subsection “Limitations” (first bullet)