Noise2Noise (N2N) trains denoisers on pairs of independently corrupted observations, eliminating clean references. We stress-test two natural conjectures about why the L1 loss outperforms L2 here. First, the hypothesis that the L1 loss confers robustness via parameter sparsity confuses the loss with Lasso regularization: an explicit Lasso penalty produces the predicted sparsity yet fails to reproduce L1's cross-noise behavior, while L1- and L2-trained weight distributions are indistinguishable. Second, the population optima of the two losses coincide exactly for symmetric signal posteriors and nearly so for concentrated ones. Measured differences are therefore dominated by optimization dynamics (bounded-influence gradients), which we probe with gradient statistics and contaminated-target training. On Kodak24 with five synthetic noise families, the L1 loss holds a statistically significant edge over L2, below 1 dB PSNR, holding across three seeds on 13 of the 14 noise columns. On real camera noise the loss is not the decisive variable in distribution: on official SIDD validation blocks, synthetic-Gaussian-trained N2N models gain only 0.8 to 3.7 dB over the noisy input regardless of loss, while retraining on SIDD's own noisy pairs, never reading ground truth, gains 9.4 to 11.0 dB, far ahead of BM3D. All metrics are on raw network outputs, and the study makes no leaderboard claim. The training pair distribution, not the loss, carries the inductive bias. That design rule applies wherever clean references are unobtainable, from microscopy to industrial inspection sensors.
Single-image self-supervised denoising replaces unavailable clean targets with surrogate targets constructed from noisy observations. Its effectiveness therefore depends on how closely the surrogate objective remains aligned with supervised denoising, especially when noise is correlated, spatially nonstationary, or unknown. We express the discrepancy between a broad class of MSE-based self-supervised objectives and supervised MSE as a parameter-independent constant and a trace interaction between the surrogate-target residual and the prediction error. The corresponding gradient discrepancy is determined by the gradient of this interaction. This formulation provides a common view of paired-noise, blind-spot, weak-noise, re-corruption, and sub-image methods, while revealing that a small global interaction may conceal substantial positive and negative regional interactions through spatial cancellation. Building on these observations, we propose LoTA-N2N, a two-stage zero-shot adaptation framework. Stage 1 trains a denoiser on complementary sub-image pairs and freezes it to construct detached clean-sub-image proxies. Stage 2 estimates the residual--prediction interaction using these proxies and suppresses its patch-wise absolute magnitude. We show that the local construction prevents spatial cancellation and upper-bounds the magnitude of the corresponding global interaction. Experiments across natural, confocal, and X-ray images, complemented by iteration-matched controls, controlled noise shifts, and gradient diagnostics, show consistent gains over MSE-only adaptation under IID, spatially varying, and mixed noise. Overall, LoTA-N2N demonstrates that estimated local interaction and spatial cancellation control provide effective design principles for single-image self-supervised denoising without paired clean targets, repeated acquisitions, or a predefined re-corruption model.
Label noise is common in medical imaging datasets due to factors such as inter-rater variability, annotation errors, and ambiguous cases. This can severely undermine the reliability and clinical effectiveness of machine learning models trained using those datasets. To address this challenge, we introduce Lightweight Noise Correction (LiNC), which adds a single trainable trust parameter per training sample and learns when to use the observed label and when to defer to the model during a standard training loop. The key idea is to train using a convex combination of the observed label and the model's own predictive distribution, controlled by a per-sample trust parameter. We show that the gradient of this objective drives trust values in opposite directions for clean versus noisy samples in the early training phase, yielding separable trust distributions. We use a 3-component Gaussian Mixture Model over the trust values to separate them into clean, ambiguous, and noisy cases and then execute a short soft-correction phase on the noisy cases and a final hard correction phase. Experiments on ten 2D datasets from MedMNISTv2 under label noise of up to 50% show consistent gains in accuracy and strong mislabel detection. LiNC adds negligible asymptotic overhead: the training-time complexity remains dominated by the base network, with additional memory growing linearly with the size of the training set.
Refurbishment-based noisy-label learning mixes an observed label with a model-derived pseudo target, typically using one sample-wise cleanliness score to control both branches. This creates a hidden coupling: reducing trust in the observed label automatically increases trust in the pseudo target. We show that this complementarity can replace one unreliable signal with another because a pseudo target learned from corrupted supervision may reproduce the noise it is meant to correct. Our representation diagnostics provide a consistent account of this mismatch: noisy supervision redirects deeper layers more strongly, whereas shallower relations remain comparatively stable and provide information beyond the loss posterior. We therefore propose TRACE, a Two-Source Reliability Assessment framework for Label Correction and Sample Reweighting. TRACE assesses the observed label using loss fit, shallow relation stability, and prediction agreement, while separately assessing the pseudo target using model confidence. Its source-specific scores control target correction and supervision strength without assuming complementary reliability. Across synthetic and real-world noisy benchmarks, TRACE improves representative refurbishment baselines and yields more reliable pseudo supervision.