Whitening

Deep neural networks tend to rely on simple features that may be spurious and thus fail to generalize. We study this problem in the setting of linear probes, where a (generalized) linear model is fitted on the representations of a (pretrained) model. We use the connection of these models to the max-margin classifier, and show they favor directions associated with large eigenvalues of the covariance matrix. Whitening removes this preference by equalizing the eigenvalues of the covariance matrix. This observation motivates whitening as a preprocessing step that can reduce reliance on spurious correlations without requiring prior knowledge of their presence or labeled data. We examine the effect of whitening on a synthetic data-generating process and standard spurious correlation benchmarks, and find that it improves robustness. We also find that whitening can improve robustness when added to existing approaches.

Same-instance self-supervised learning (SSL) learns representations by enforcing consistency across two views of the same underlying instance. This principle alone, however, does not determine which downstream tasks remain recoverable from the learned representation. We study this question through \emph{semantic recoverability}, defined as the amount of a task's posterior score captured by the represented function space. We show that, for centered and whitened representations, recoverability exactly determines directional class-distance-normalized variance (CDNV), controls few-shot nearest-centroid classification, and governs the strength of task-relevant semantic directions. The population linear probe and centroid axis coincide, and multiple well-recovered tasks approach a factorial centroid geometry. We then analyze a canonical two-view SSL objective and show that its population optimum spans the leading cross-view-stable modes of the associated two-view operator. This yields a closed-form spectral characterization of semantic recoverability: a downstream task is preserved to the extent that its posterior lies in the selected spectral subspace. We validate these predictions on synthetic and real datasets across several SSL methods, testing the predicted relationships among recoverability, directional geometry, spectral structure, and few-shot transfer. Together, these results give a task-level account of what information survives same-instance SSL and how the retained information appears in downstream geometry and transfer.

Deep vision models often degrade under distribution shift. Test-time adaptation can improve robustness but typically requires iterative optimization, hyperparameter tuning, and multiple forward-backward passes. We propose Zero-Training Fisher Geometry Alignment (ZFGA), a closed-form method that improves robustness under covariate shift without modifying model parameters. ZFGA is based on the observation that distribution shifts distort feature-space geometry. It estimates the Fisher information matrix of the predictive distribution with respect to feature embeddings and applies a linear transformation that aligns test-feature Fisher geometry with a reference geometry computed from clean data. This provides a natural-gradient-inspired preconditioning step in feature space. We evaluate ZFGA on CIFAR-10-C and ImageNet-C using ResNet-50, DINO ViT-S/16, and CLIP ViT-B/32. ZFGA consistently improves over zero-shot inference across all three models, although it is not the strongest method for every model. Covariance whitening performs better on ResNet-50, while Fisher whitening is statistically indistinguishable from ZFGA on CLIP. Across six training-free and gradient-based alternatives (covariance whitening, Fisher whitening, TENT, T3A, LAME, and AdaNPC), ZFGA is the only method that does not substantially harm any of the three model families. The Fisher geometry distortion is also positively correlated with ZFGA gain (Pearson r = 0.366, p = 0.017), providing preliminary evidence that geometric misalignment contributes to robustness degradation. ZFGA requires only forward passes and matrix operations at inference time, offering a lightweight and deterministic alternative to optimization-based test-time adaptation.

Domain adaptation is crucial for addressing distributional shifts that degrade model performance across domains. While most existing research has centered on classification, semi-supervised domain adaptation regression (SSDAR) for continuous-output tasks remains largely unexplored, particularly in practical scenarios with limited labeled target data. To address this gap, we propose semi-supervised domain adaptation regression through whitening transform and dual consistency (WhiteCon), which combines domain-specific whitening transform (DWT) and dual consistency regularization to enhance training stability and domain adaptation. DWT reduces the variance of the model parameters by transforming the feature covariance matrix into an identity matrix, thus stabilizing training under ordinary least squares assumptions. In addition, variance consistency regularization, as part of dual consistency regularization, aligns the variances of weak, strong, and mixup-augmented features to improve resilience against augmentation-induced perturbations. Empirical evaluations on various benchmark datasets under SSDAR settings demonstrate that the proposed WhiteCon achieves state-of-the-art performance compared to existing methods, effectively addressing domain shifts in regression tasks. The code for WhiteCon is available at https://github.com/sejin-sim/WhiteCon.

Recurrent detectors such as bidirectional long short-term memory (Bi-LSTM) networks are low-complexity alternatives to the optimal Bahl-Cocke-Jelinek-Raviv (BCJR) detector for faster-than-Nyquist (FTN) signaling. Motivated by convolutional detectors that build the intersymbol interference (ISI) structure into their architecture, we ask whether processing nested ISI windows in separate recurrent branches improves the bit error rate (BER) of a Bi-LSTM. Across roughly 260 controlled trainings it does not: at a matched parameter budget and a matched readout, the multi-window architecture never significantly beats a plain Bi-LSTM. Nested windowing is an invertible rearrangement that adds no information, extra branches only add bottlenecks, and a distillation diagnostic shows the network is already near optimal for its window. The limitation is therefore the observation model, not the architecture. Keeping the architecture fixed, we pre-whiten the input, restoring the conditional independence that colored matched-filter noise violates, and distill the BCJR soft posterior into the network. With 3.4% more parameters this reaches 1.05 times the BCJR BER at a compression factor of 0.8 and 1.89 times at 0.7, improving to 1.47 times when the whitened window is widened. The 23.7% BER reduction at 0.8 requires an ill-conditioned ISI matrix but is not monotone in the conditioning, and it holds across five independent noise realizations and a symbol-level McNemar test.

We propose Zero-phase Component Analysis (ZCA) whitening as a geometric pre-processing step for the Word Embedding Association Test (WEAT). WEAT is a bias measurement method widely used in both computational social science and AI fairness research. It relies on cosine similarity as a measure of semantic association, which assumes that the embedding space is approximately isotropic. However, prior work has reported that many widely used language models do not satisfy this assumption, raising concerns about the reliability of bias measurements. ZCA whitening transforms the covariance of the embedding space into the identity matrix while minimizing perturbation to the original vectors. This transformation restores the isotropy condition on which WEAT relies. We evaluate our approach on ten standard WEAT test suites and seven models spanning three architectural families, yielding 70 model-task combinations. The results show that ZCA whitening substantially reduces the anisotropy of the embedding spaces across all models. Particularly for highly anisotropic models, we further observe improvements on standard semantic similarity benchmarks, indicating that the calibrated space better captures semantic associations. After calibration, over 30% of WEAT results change significance status, and effect sizes shift in both directions depending on bias category. These shifts suggest that uncalibrated measurements may both overestimate and underestimate the associations encoded in the embedding space. These findings indicate that previously reported bias measurements in anisotropic embedding spaces should be interpreted with caution and may benefit from re-evaluation with calibrated methods. Our approach contributes to restoring the measurement foundation of WEAT across both computational social science and AI fairness research.

Machine-learned surrogates for the AC power flow (ACPF) problem amortize the cost of repeated solves on a fixed network, but lose one to two orders of magnitude of accuracy when a line outage changes the topology. This degradation is an operator shift. The altered admittance matrix changes the input-to-output map, so identical inputs yield a different output distribution. Existing methods correct this with target-topology data and per-topology gradient steps. We ask whether the correction can instead be made statistical and gradient-free. We propose In-Context Whitening (ICW), which trains an ACPF surrogate in an output space whitened by the base topology's first two moments, and adapts it to an unseen N-1 or N-2 topology by re-estimating that whitening from a few hundred solved cases on the new topology. This adaptation is gradient-free, weight-free, and architecture-agnostic. We prove that among affine whiteners the unique choice that preserves the coordinate-wise semantics of the physical output vector is ZCA whitening, so within efficient invertible corrections, two moments are sufficient. Across the IEEE 30-, 118-, and 300-bus systems under N-1 and N-2 contingencies, ICW reduces overall error by 6$\times$ to 28$\times$ over frozen surrogates (up to 54$\times$ per-quantity under N-2) and cuts worst-bus power-balance mismatch by up to 30$\times$, with consistent gains across three backbones. At deployment scale it matches or beats gradient-based adaptation in accuracy while adapting 21$\times$ to 34$\times$ faster, with a cost that parallelizes on commodity CPU cores rather than requiring one GPU per contingency.

Large-scale neural network training increasingly relies on matrix-aware optimizers that exploit the structure of weight parameters beyond element-wise adaptation. However, existing matrix-aware methods such as Muon have an underappreciated vulnerability: their core operation, Newton-Schulz iteration, depends critically on input conditioning, yet the raw momentum matrices exhibit severe coordinate-wise scale heterogeneity. In this paper, we first verify this scale heterogeneity through a chi-square uniformity test, showing that intra-matrix scale imbalance is prevalent across Transformer layers and that coordinate whitening effectively corrects it. Motivated by this finding, we propose Zeta, a dual whitening optimizer that applies coordinate whitening and spectral whitening in a strictly ordered pipeline. The ordering is not a tunable choice but follows from a mathematical dependency: coordinate whitening establishes the statistical isotropy that spectral whitening requires to function reliably. We further prove that this dual pipeline strictly reduces orthogonalization error relative to pure spectral methods by improving the condition number of the input. Empirically, Zeta matches or surpasses strong baselines across language modeling (0.6B to 8B parameters), mixture-of-experts architectures, and vision tasks, demonstrating that resolving scale imbalance before orthogonalization leads to faster convergence and better generalization. Code is available at https://github.com/AIGCodeOS/aigcode_zeta_optimizer.

Generalized segmentation of medical images prevents performance degradation when different imaging devices and clinical protocols are used across multiple domains. The Whitening Transform-based Probabilistic Shape Regularization Extractor (WT-PSE), published in IEEE Transactions on Medical Imaging in 2024, addresses this challenge by employing feature decorrelation and Wasserstein distance-based knowledge distillation to achieve robust cross-domain segmentation. This study systematically examines improvements to the WT-PSE learning framework. Four limitations in the original implementation are identified: limited training augmentations that fail to simulate real scanner variations, reliance on per-pixel binary cross-entropy loss that is sensitive to edge noise, the absence of a scheduled loss weighting strategy that may destabilize early training, and the lack of ablation switches for controlled scientific comparison. To address these issues, we propose four enhancements: (1) domain-adaptive augmentation including random erasing, gamma correction, and salt-and-pepper noise; (2) a hybrid BCE and Dice loss function for improved edge-aware segmentation under noisy conditions; (3) a curriculum-based Dice weight scheduling strategy; and (4) command-line control flags for systematic ablation studies. Experiments on the fundus optic disc segmentation benchmark demonstrate that the improved pipeline achieves a final epoch optic-disc Dice score of 0.956 and an ASD score of 13.31, outperforming the baseline epoch-5 Dice score of 0.939. These results indicate that training-level improvements can provide consistent performance gains without modifying the underlying WT-PSE architecture.

The Gauss-Newton matrix is widely viewed as a positive semidefinite approximation of the Hessian, yet mounting empirical evidence shows that Gauss-Newton descent outperforms Newton's method. We adopt a function space perspective to analyze this phenomenon. We show that the generalized Gauss-Newton (GGN) matrix projects the Newton direction in function space onto the model's tangent space, while a Jacobian-only variant obtained by applying the least squares Gauss-Newton matrix to non-least squares losses projects the function space loss gradient onto this same tangent space. Both projections eliminate distortions from the model's parameterization. Specifically, the evolution of the prediction-target mismatch depends on the model's parameterization through the matrix $JJ^\top$ where $J$ is the Jacobian of the model with respect to its parameters. The projections effectively replace $JJ^\top$ with the identity. We call this effect error whitening. Once the parameterization is removed, the prediction-target mismatch evolves according to dynamics dictated by the structure of the loss and the projection produced by the optimizer. Error whitening is a special property of Gauss-Newton descent that rigorously distinguishes it from Newton's method. We empirically demonstrate that Gauss-Newton optimizers follow the theoretically predicted function space dynamics and outperforms Newton's method, Adam, and Muon across case studies spanning supervised learning, physics-informed deep learning, and approximate dynamic programming.

Muon orthogonalizes matrix updates, but multi-head attention naturally operates at the level of heads. This granularity mismatch raises the question of whether Muon should be applied to the full attention projection, to individual heads, or to intermediate head groups. We study this question through a one-step descent comparison between full-matrix Muon and group-wise Muon. Our analysis reveals a trade-off between the \textbf{group-wise whitening gain} from group-wise updates and the \textbf{grouping-induced norm cost}, an additional update-norm cost caused by replacing full-matrix whitening with group-wise whitening. Motivated by this trade-off, we propose \textbf{Group Muon}, which treats head group size and grouping rule as optimizer hyperparameters. On GPT-2 Small trained on FineWeb, appropriate grouping improves validation loss over both full-QKV Muon and fully head-wise MuonSplit.

Optimizers that exploit the matrix structure of gradients are central to modern LLM pre-training, with two distinct frontiers: explicit Kronecker-factored preconditioning -- most recently KL-Shampoo, which estimates the preconditioner via KL divergence minimization -- and orthogonalization of the gradient momentum, exemplified by Muon and analyzed as steepest descent under the spectral norm. The two routes are typically developed in isolation. We make a structural observation about KL-Shampoo's Kronecker preconditioners: their eigenvalue spectra exhibit a \emph{spike-and-flat} shape -- a few dominant eigenvalues followed by an approximately uniform tail -- across layers and training stages, holding exactly under a rank-$ρ$ signal-plus-noise gradient model. We exploit this structure by restricting one of KL-Shampoo's Kronecker factors to a parametric family aligned with the spike-and-flat shape: full spectral structure on a tracked $r$-dimensional subspace, single shared eigenvalue across the remaining $n-r$ directions. On these directions, we apply orthogonalization. An identity shows that this orthogonalization recovers the algebraic form of full KL-Shampoo's preconditioner. On four pre-training scales (GPT-2 124M / 350M, LLaMA 134M / 450M), Pro-KLShampoo consistently outperforms KL-Shampoo at every subspace rank we test in validation loss, peak per-GPU memory, and wallclock time to reach each loss level.

Linear models are widely used in computational neuroimaging to identify biomarkers associated with brain pathologies. However, interpreting the learned weights remains challenging, as they do not always yield clinically meaningful insights. This difficulty arises in part from the inherent correlation between brain regions, which causes linear weights to reflect shared rather than region-specific contributions. In particular, some groups of regions, including homologous structures in the left and right hemispheres, are known to exhibit strong anatomical correlations. In this work, we leverage this prior neuroanatomical knowledge to introduce a whitening approach applied to groups of regions with known shared variance, designed to disentangle overlapping information across correlated brain measures. We additionally propose a regularized variant that allows controlled tuning of the degree of decorrelation. We evaluate this method using region-of-interest features in two psychiatric classification tasks, distinguishing individuals with bipolar disorder or schizophrenia from healthy controls. Importantly, unlike PCA or ICA which use whitening as a dimensionality reduction step, our approach decorrelates anatomically informed pairs of neuroanatomical regions while retaining the full input signal, making it specifically suited for feature interpretation rather than feature selection. Our findings demonstrate that whitening improves the interpretability of model weights while preserving predictive performance, providing a robust framework for linking linear model outputs to neurobiological mechanisms.

Delayed loss spikes have been reported in neural-network training, but existing theory mainly explains earlier non-monotone behavior caused by overly large fixed learning rates. We study one stylized hypothesis: normalization can postpone instability by gradually increasing the effective learning rate during otherwise stable descent. To test this hypothesis at theorem level, we analyze batch-normalized linear models. Our flagship result concerns whitened square-loss linear regression, where we derive explicit no-rising-edge and delayed-onset conditions, bound the waiting time to directional onset, and show that the rising edge self-stabilizes within finitely many iterations. Combined with a square-loss decomposition, this yields a concrete delayed-spike mechanism in the whitened regime. For logistic regression, under highly restrictive active-margin assumptions, we prove only a supporting finite-horizon directional precursor in a knife-edge regime, with an optional appendix-only loss lower bound under an extra non-degeneracy condition. The paper should therefore be read as a stylized mechanism study rather than a general explanation of neural-network loss spikes. Within that scope, the results isolate one concrete delayed-instability pathway induced by batch normalization.

Activation-aware low-rank factorization techniques yield strong compression results but are generally confined to linear layers, while existing whitening-based theory typically makes an implicit full-rank assumption on activations. We introduce a layer representation framework that extends activation-aware factorization beyond linear layers, including standard and grouped convolutions. Within this framework, our whitening-based formulation is more general than prior ones, naturally covering rank-deficient activations, and yields an optimal low-rank projection that attains the reconstruction error of the best low-rank approximation to layer activations. The resulting singular spectrum provides a closed-form per-layer distortion proxy, which we use to allocate per-layer ranks under explicit FLOP or parameter-count budgets via a Lagrangian relaxation with negligible overhead. Together, these components form BALF, an end-to-end pipeline for efficient vision model compression. Across CNNs and vision transformers on CIFAR-10 and ImageNet-1K, BALF generally achieves higher accuracy than SVD-based factorization baselines at matched FLOP or parameter count targets and remains competitive with other fine-tuning-free compression techniques.