Papers

Mixed causal–noncausal (anticipative) models capture locally explosive dynamics and provide economically meaningful probabilities of continuation and collapse, but forecasting with them remains computationally difficult. We develop a two-stage framework that estimates such an ARMA model and then learns its predictive density using a Mixture Density Network with skewed-t components, tail-aware training weights, and post-hoc calibration. The approach accommodates the heavy tails, asymmetry, and multimodality characteristic of non-causal forecasts while remaining computationally tractable. Monte Carlo experiments and a real-time natural-gas application show substantial improvements over existing density-forecasting methods.

Forecasting intermittent time series, which contain zeros, is a crucial challenge in supply chains as inventory policies require probabilistic forecasts to establish safety levels. Intermittent time series are commonly forecast using local models, trained individually on each time series. In the last years global models, trained on a large collection of time series, have become popular for time series forecasting. Global models are often based on neural networks or gradient boosted trees. We carry out the first study comparing state-of-the-art probabilistic local and global models on intermittent time series. For global models we consider three different distribution heads suitable for intermittent time series: negative binomial, hurdle-shifted negative binomial and Tweedie. To the best of our knowledge, this is the first use of the latter two with neural networks. We perform experiments on five datasets comprising overall more than 40'000 real-world time series. Among global models, TiDE, a simple neural network architecture, achieves the best accuracy; it also consistently outperforms local models and has lower computational requirements. Large global models are instead much more computationally demanding and less accurate. Among the distribution heads, the Tweedie provides the best estimates of the highest quantiles.

Allowing for adversarial contamination and heavy tails, we study testing whether the mean of a high-dimensional random vector equals zero. Because standard max-tests based on sample averages are highly non-robust, we propose a max-test based on quantile-winsorized observations. The test controls asymptotic size under adversarial contamination and only requires $m>2$ moments, while allowing dimension to grow exponentially with sample size. We fully characterize its asymptotic power function. Comparing with the standard max-test, for which we also derive a power characterization as a benchmark, we show that robustness is obtained for free at first order: under the stronger conditions that make the standard max-test valid, our robust test has identical asymptotic power. We show that the decay condition on the contamination-rate imposed is necessary for this no-first-order-loss property. Finally, we also study the role of bootstrap critical values, showing that their use never decreases power, can strictly improve asymptotic power in extremely correlated designs, but often has no first-order asymptotic effect.

This paper introduces the modeling of circular data with excess zeros under a longitudinal framework, where the response is a circular variable and the covariates can be both linear and circular in nature. In the literature, various circular-circular and circular-linear regression models have been studied and applied to different real-world problems. However, there are no models for addressing zero-inflated circular observations in the context of longitudinal studies. Motivated by a real case study, a mixed-effects two-stage model based on the projected normal distribution is proposed to handle such issues. The interpretation of the model parameters is discussed and identifiability conditions are derived. A Bayesian methodology based on Gibbs sampling technique is developed for estimating the associated model parameters. Simulation results show that the proposed method outperforms its competitors in various situations. A real dataset on post-operative astigmatism is analyzed to demonstrate the practical implementation of the proposed methodology. The use of the proposed method facilitates effective decision-making for treatment choices and in the follow-up phases.

In this paper, we study correlation detection problem between a pair of Erdős-Rényi graphs. Under the null hypothesis, the two graphs are independent, whereas under the alternative, they are edge-correlated through a latent permutation. We consider the partial-observation setting in which only an induced subgraph of each graph is sampled, and determine the sharp information-theoretic threshold for the sample size, including its leading constant. We also establish a general conditional second moment principle and identify a continuous transition in the sharp threshold constant across two different regimes.

Accurate, low-latency estimates of the instantaneous phase of oscillations are essential for closed-loop sensing and actuation, including (but not limited to) phase-locked neurostimulation and other real-time applications. The endpoint-corrected Hilbert transform (ecHT) reduces boundary artefacts of the Hilbert transform by applying a causal narrow-band filter to the analytic spectrum. This improves the phase estimate at the most recent sample. Despite its widespread empirical use, the systematic endpoint distortions of ecHT have lacked a principled, closed-form analysis. In this study, we derive the ecHT endpoint operator analytically and demonstrate that its output can be decomposed into a desired positive-frequency term (a deterministic complex gain that induces a calibratable amplitude/phase bias) and a residual leakage term that sets an irreducible variance floor. This yields (i) an explicit characterisation and bounds for endpoint phase/amplitude error, (ii) a mean-squared-error-optimal scalar calibration, and (iii) practical design rules relating window length, filter bandwidth and order, and centre-frequency mismatch to residual bias via an endpoint group delay. The resulting calibrated ecHT achieves near-zero mean phase error and remains computationally compatible with real-time pipelines. Code and analyses are provided at https://github.com/eikeosmers/cecHT.

This study examines generalized cross-validation for the tuning parameter selection for ridge regression in high-dimensional misspecified linear models. The set of candidates for the tuning parameter includes not only positive values but also zero and negative values. We demonstrate that if the second moment of the specification error converges to zero, generalized cross-validation is still a uniformly consistent estimator of the out-of-sample prediction risk. This implies that generalized cross-validation selects the tuning parameter for which ridge regression asymptotically achieves the smallest prediction risk among the candidates if the degree of misspecification for the regression function is small. Our simulation studies show that ridge regression tuned by generalized cross-validation exhibits a prediction performance similar to that of optimally tuned ridge regression and outperforms the Lasso under correct and incorrect model specifications.

We establish topological necessary and sufficient conditions under which a pair of statistical hypotheses can be consistently distinguished when i.i.d. observations are recorded only to finite precision. To accommodate finite-precision data, we introduce finite-precision tests: tests whose decision regions are open in the sample-space topology. We first show that, both for classical and finite-precision tests, the existence of such tests with finite-sample error control, asymptotic error control, or uniform convergence of the errors are all equivalent. A pair of null- and alternative hypotheses $H_0$ and $H_1$ admits a consistent finite-precision test if and only if both are $F_\sigma$ in the weak topology on the space of probability measures $W := H_0\cup H_1$. The hypotheses admit uniform error control under $H_i$ if and only if $H_i$ is closed in $W$, and admit uniformly consistent testing with bounded precision under metric separation of $H_0$ and $H_1$. These criteria imply that, without regularity assumptions, conditional independence is not consistently testable from finite-precision data when the conditioning space has no isolated points - strengthening existing impossibility results to Polish sample spaces and showing that even pointwise consistency cannot be obtained. We introduce an equicontinuity assumption on the family of conditional distributions under which we recover consistent finite-precision testability of conditional independence with uniform error control under the null, provided sample spaces are Polish and the conditioning space is locally compact. The equicontinuity assumption is itself a finite-precision-testable hypothesis, so the resulting test for conditional independence is, in a precise sense, assumption-free.

We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal component score. As a corollary of the main result, the clustering procedure is shown to be consistent in a high-dimensional regime.

Accurately and efficiently estimating the variance of the Maximum Mean Discrepancy (MMD) remains challenging, particularly for unbalanced sample sizes. In this paper, we derive a finite-sample unbiased estimator of the MMD variance. To overcome the traditional $\mathcal{O}(N^2)$ computational bottleneck, we develop a recursive prefix-suffix accumulation scheme for the Laplace kernel, reducing the computational complexity to $\mathcal{O}(N \log N)$ while requiring $\mathcal{O}(N)$ memory. Experimental results verify the theoretical exactness and numerical stability of the proposed estimator and demonstrate its scalability on large datasets. Furthermore, the method proves effective for monitoring distributional convergence during the training of Time-series Generative Adversarial Networks (TimeGAN).

Self-Organizing Maps (SOMs) provide topology-preserving projections of high-dimensional data, yet their use as generative models remains largely unexplored. We show that the activation pattern of a SOM – the squared distances to its prototypes – can be inverted to recover the exact input, following from a classical result in Euclidean distance geometry: a point in $D$ dimensions is uniquely determined by its distances to $D{+}1$ affinely independent references. We derive the corresponding linear system and characterize the conditions under which inversion is well-posed. Building on this mechanism, we introduce the Manifold-Aware Unified SOM Inversion and Control (MUSIC) update rule, which modifies squared distances to selected prototypes while preserving others, producing controlled, semantically meaningful trajectories aligned with the SOM's piecewise-linear structure. Tikhonov regularization stabilizes the update and ensures smooth motion in high dimensions. Unlike variational or diffusion-based generative models, MUSIC requires no sampling, latent priors, or learned decoders: it operates entirely on prototype geometry. If no perturbation is applied, inversion recovers the exact input; when a target prototype or cluster is specified, MUSIC produces coherent semantic transitions. We validate the framework on synthetic Gaussian mixtures, MNIST digits, and the Labeled Faces in the Wild dataset. Across all settings, MUSIC trajectories maintain high classifier confidence, produce significantly sharper intermediate images than linear interpolation, and reveal an interpretable geometric structure of the learned map.

We propose a frequentist adaptive phase 2 trial design to evaluate the safety and efficacy of three treatment regimens (doses) compared to placebo for four types of helminth (worm) infections. This trial will be carried out in four Subsaharan African countries from spring 2025. Since the safety of the highest dose is not yet established, the study begins with the two lower doses and placebo. Based on safety and early efficacy results from an interim analysis, a decision will be made to either continue with the two lower doses or drop one or both and introduce the highest dose instead. This design borrows information across baskets for safety assessment, while efficacy is assessed separately for each basket. The proposed adaptive design addresses several key challenges: (1) The trial must begin with only the two lower doses because reassuring safety data from these doses is required before escalating to a higher dose. (2) Due to the expected speed of recruitment, adaptation decisions must rely on an earlier, surrogate endpoint. (3) The primary outcome is a count variable that follows a mixture distribution with an atom at 0. To control the familywise error rate in the strong sense when comparing multiple doses to the control in the adaptive design, we extend the partial conditional error approach to accommodate the inclusion of new hypotheses after the interim analysis. In a comprehensive simulation study we evaluate various design options and analysis strategies, assessing the robustness of the design under different design assumptions and parameter values. We identify scenarios where the adaptive design improves the trial's ability to identify an optimal dose. Adaptive dose selection enables resource allocation to the most promising treatment arms, increasing the likelihood of selecting the optimal dose while reducing the required overall sample size and trial duration.

Local Polynomial Regression (LPR) and Moving Least Squares (MLS) are closely related nonparametric estimation methods, developed independently in statistics and approximation theory. While statistical LPR analysis focuses on overcoming sampling noise under probabilistic assumptions, the deterministic MLS theory studies smoothness properties and convergence rates with respect to the fill distance (a resolution parameter). Despite this similarity, the deterministic assumptions underlying MLS fail to hold under random sampling. We begin by quantifying the probabilistic behavior of the fill distance $h_n$ and separation $\delta_n$ of an i.i.d. random sample. That is, for a distribution satisfying a mild regularity condition, $h_n\propto n^{-1/d}\log^{1/d} (n)$ and $\delta_n \propto n^{-2/d}$ in probability. We then prove that, for MLS of degree $k\!-\!1$, the approximation error associated with a differential operator $Q$ of order $m\leq k-1$ decays as $h_n^{\,k-m}$, establishing stochastic analogues of the classical MLS estimates. Additionally, we show that the MLS approximant is locally smooth with high probability. This work provides the first unified stochastic analysis of MLS, demonstrating that - despite the failure of deterministic sampling assumptions - the classical convergence and smoothness properties persist under natural probabilistic models.

Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite significant advancements, existing implementations remain fragmented, limited, and computationally demanding. To address these issues, we introduce Orthogonium , a unified, efficient, and comprehensive PyTorch library providing orthogonal and 1-Lipschitz layers. Orthogonium provides access to standard convolution features-including support for strides, dilation, grouping, and transposed-while maintaining strict mathematical guarantees. Its optimized implementations reduce overhead on large scale benchmarks such as ImageNet. Moreover, rigorous testing within the library has uncovered critical errors in existing implementations, emphasizing the importance of standardized and reliable tools. Orthogonium thus significantly lowers adoption barriers, enabling scalable experimentation and integration across diverse applications requiring orthogonality and robust Lipschitz constraints. Orthogonium is available at https://github.com/deel-ai/orthogonium.

Tukey's boxplot is widely used for outlier detection; however, its classic fixed-fence rule tends to flag an excessive number of outliers as the sample size grows. To address this, we introduce two new R packages, ChauBoxplot and AdaptiveBoxplot, which implement more robust and statistically principled outlier detection methods. We illustrate their advantages and practical implications through comprehensive simulation studies and a real-world analysis of provincial university admission rates from China's National College Entrance Examination. Based on these findings, we provide practical guidance to help practitioners select appropriate boxplot methods, achieving a balance between interpretability and statistical reliability.

Academic Clinical Trial Units frequently face fragmented statistical workflows, leading to duplicated effort, limited collaboration, and inconsistent analytical practices. To address these challenges within an oncology Clinical Trial Unit, we developed grstat, an R package providing a standardised set of tools for routine statistical analyses. Beyond the software itself, the development of grstat is embedded in a structured organisational framework combining formal request tracking, peer-reviewed development, automated testing, and staged validation of new functionalities. The package is intentionally opinionated, reflecting shared practices agreed upon within the unit, and evolves through iterative use in real-world projects. Its development as an open-source project on GitHub supports transparent workflows, collective code ownership, and traceable decision-making. While primarily designed for internal use, this work illustrates a transferable approach to organising, validating, and maintaining a shared analytical toolbox in an academic setting. By coupling technical implementation with governance and validation principles, grstat supports efficiency, reproducibility, and long-term maintainability of biostatistical workflows, and may serve as a source of inspiration for other Clinical Trial Units facing similar organisational challenges.

We propose a statistical proxy framework for retrieval-augmented generation (RAG) that formalizes how language models balance internal predictions with retrieved evidence. We derive an optimal query-level gate, analyze hallucination via retrieval discordance, model query-memory mismatch, and validate the framework numerically on synthetic and real data.

Fairness and privacy are two vital pillars of trustworthy machine learning. Despite extensive research on these individual topics, their relationship has received significantly less attention. In this paper, we utilize an information-theoretic measure Chernoff Information to characterize the fundamental trade-off between fairness, privacy, and accuracy, as induced by the input data distribution. We first propose Chernoff Difference, a notion of data fairness, along with its noisy variant, Noisy Chernoff Difference, which allows us to analyze both fairness and privacy simultaneously. Through simple Gaussian examples, we show that Noisy Chernoff Difference exhibits three qualitatively distinct behaviors depending on the underlying data distribution. To extend this analysis beyond synthetic settings, we develop the Chernoff Information Neural Estimator (CINE), the first neural network-based estimator of Chernoff Information for unknown distributions. We apply CINE to analyze the Noisy Chernoff Difference on real-world datasets. Together, this work fills a critical gap in the literature by providing a principled, data-dependent characterization of the fairness-privacy interaction.

Modern macroeconomic monetary theory suggests that the labor share of income has effectively become a core macroe-conomic parameter anchored by top policymakers through Open Market Operations (OMO). However, the setting of this parameter remains a subject of intense economic debate. This paper provides a detailed summary of these controversies, analyzes the scope of influence exerted by market agents other than the top policymakers on the labor share, and explores the rationality of its setting mechanism.

Average-reward reinforcement learning offers a principled framework for long-term decision-making by maximizing the mean reward per time step. Although Q-learning is a widely used model-free algorithm with established sample complexity in discounted and finite-horizon Markov decision processes (MDPs), its theoretical guarantees for average-reward settings remain limited. This work studies a simple but effective Q-learning algorithm for average-reward MDPs with finite state and action spaces under the weakly communicating assumption, covering both single-agent and federated scenarios. For the single-agent case, we show that Q-learning with carefully chosen parameters achieves sample complexity $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{\varepsilon^3}\right)$, where $\|h^{\star}\|_{\mathsf{sp}}$ is the span norm of the bias function, improving previous results by at least a factor of $\frac{\|h^{\star}\|_{\mathsf{sp}}^2}{\varepsilon^2}$. In the federated setting with $M$ agents, we prove that collaboration reduces the per-agent sample complexity to $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{M\varepsilon^3}\right)$, with only $\widetilde{O}\left(\frac{\|h^{\star}\|_{\mathsf{sp}}}{\varepsilon}\right)$ communication rounds required. These results establish the first federated Q-learning algorithm for average-reward MDPs, with provable efficiency in both sample and communication complexity.

Compressed sensing, which involves the reconstruction of sparse signals from an under-determined linear system, has been recently used to solve problems in group testing. In a public health context, group testing aims to determine the health status values of p subjects from n<<p pooled tests, where a pool is defined as a mixture of small, equal-volume portions of the samples of a subset of subjects. This approach saves on the number of tests administered in pandemics or other resource-constrained scenarios. In practical group testing in time-constrained situations, a technician can inadvertently make a small number of errors during pool preparation, which leads to errors in the pooling matrix, which we term `model mismatch errors' (MMEs). This poses difficulties while determining health status values of the participating subjects from the results on n<<p pooled tests. In this paper, we present an algorithm to correct the MMEs in the pooled tests directly from the pooled results and the available (inaccurate) pooling matrix. Our approach then reconstructs the signal vector from the corrected pooling matrix, in order to determine the health status of the subjects. We further provide theoretical guarantees for the correction of the MMEs and the reconstruction error from the corrected pooling matrix. We also provide several supporting numerical results.

Predicting highly-cited papers is a long-standing challenge due to the complex interactions of research content, scholarly communities, and temporal dynamics. Recent advances in large language models (LLMs) raise the question of whether early-stage textual information can provide useful signals of long-term scientific impact. Focusing on statistical publications, we propose a flexible, text-centered framework that leverages LLMs and structured prompt design to predict highly cited papers. Specifically, we utilize information available at the time of publication, including titles, abstracts, keywords, and limited bibliographic metadata. Using a large corpus of statistical papers, we evaluate predictive performance across multiple publication periods and alternative definitions of highly cited papers. The proposed approach achieves stable and competitive performance relative to existing methods and demonstrates strong generalization over time. Textual analysis further reveals that papers predicted as highly cited concentrate on recurring topics such as causal inference and deep learning. To facilitate practical use of the proposed approach, we further develop a WeChat mini program, Stat Highly Cited Papers, which provides an accessible interface for early-stage citation impact assessment. Overall, our results provide empirical evidence that LLMs can capture meaningful early signals of long-term citation impact, while also highlighting their limitations as tools for research impact assessment.

Power system outages expose market participants to significant financial risk unless promptly detected and hedged. We develop an outage identification method from public market signals grounded in the parametric quickest change detection (QCD) theory. Parametric QCD operates on stochastic data streams, distinguishing pre- and post-change regimes using the ratio of their respective probability density functions. To derive the density functions for normal and post-outage market signals, we exploit multi-parametric programming to decompose complex market signals into parametric random variables with a known density. These densities are then used to construct a QCD-based statistic that triggers an alarm as soon as the statistic exceeds an appropriate threshold. Numerical experiments on a stylized PJM testbed demonstrate rapid line outage identification from public streams of electricity demand and price data.

In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a bounded part associated with recurrent motion within the periodic landscape, and an unbounded stochastic part that grows in time and carries the net transport. We show that effective drift and diffusion are governed entirely by this unbounded component, while local potential-induced fluctuations contribute only bounded corrections. Treating the displacement as an additive functional of the stochastic dynamics provides a rigorous formulation of this separation and leads to a corrector-martingale representation at the trajectory level. Within this framework, classical results-including the Lifson-Jackson formula for unbiased periodic systems and the Stratonovich expressions for tilted periodic potentials-follow as direct consequences of the same underlying structure. The same perspective extends naturally to higher-dimensional periodic environments, recovering the standard homogenized transport tensors.

This paper constructs a multilayer recursive game model to demonstrate that in a rule vacuum environment, hierarchical predatory structures inevitably collapse into a monolithic political strongman system due to the conflict between exponentially growing rent dissipation and the rigidity of bottom-level survival constraints. We propose that the rise of a monolithic political strongman is essentially an "algorithmic entropy reduction" achieved through forceful means by the system to counteract the "informational entropy increase" generated by multilayer agency. However, the order gained at the expense of social complexity results in the stagnation of social evolutionary functions.

The growing availability of large health databases has expanded the use of observational studies for comparative effectiveness research. Unlike randomized trials, observational studies must adjust for systematic differences in patient characteristics between treatment groups. Propensity score methods, including matching, weighting, stratification, and regression adjustment, address this issue by creating groups that are comparable with respect to measured covariates. Among these approaches, overlap weighting (OW) has emerged as a principled and efficient method that emphasizes individuals at empirical equipoise, those who could plausibly receive either treatment. By assigning weights proportional to the probability of receiving the opposite treatment, OW targets the Average Treatment Effect in the Overlap population (ATO), achieves exact mean covariate balance under logistic propensity score models, and minimizes asymptotic variance. Over the last decade, the OW method has been recognized as a valuable confounding adjustment tool across the statistical, epidemiologic, and clinical research communities, and is increasingly applied in clinical and health studies. Given the growing interest in using observational data to emulate randomized trials and the capacity of OW to prioritize populations at clinical equipoise while achieving covariate balance (fundamental attributes of randomized studies), this article provides a concise overview of recent methodological developments in OW and practical guidance on when it represents a suitable choice for causal inference.

This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the $G^\star$ regret, depends on the cumulative squared gradient norm evaluated at the decision in hindsight. We show that the $G^\star$ regret strictly refines the existing $L^\star$ (small loss) regret, and that it can be arbitrarily sharper when the losses have vanishing curvature around the hindsight decision. We establish upper and lower bounds on the $G^\star$ regret and extend our results to dynamic regret and bandit settings. As a byproduct, we refine the existing convergence analysis of stochastic optimization algorithms in the interpolation regime. Some experiments validate our theoretical findings.

We consider inference for M-estimators after model selection using a sparsity-inducing penalty. While existing methods for this task require bespoke inference procedures, we propose a simpler approach, which relies on two insights: (i) adding and subtracting carefully-constructed noise to a Gaussian random variable with unknown mean and known variance leads to two independent Gaussian random variables; and (ii) both the selection event resulting from penalized M-estimation, and the event that a standard (non-selective) confidence interval for an M-estimator covers its target, can be characterized in terms of an approximately normal “score variable". We combine these insights to show that – when the noise is chosen carefully – there is asymptotic independence between the model selected using a noisy penalized M-estimator, and the event that a standard (non-selective) confidence interval on noisy data covers the selected parameter. Therefore, selecting a model via penalized M-estimation (e.g. \verb=glmnet= in \verb=R=) on noisy data, and then conducting standard inference on the selected model (e.g. \verb=glm= in \verb=R=) using noisy data, yields valid inference: no bespoke methods are required. Our results require independence of the observations, but only weak distributional requirements. We apply the proposed approach to conduct inference on the association between sex and smoking in a social network.

To estimate the causal effect of an endogenous treatment using clustered data, the canonical two-stage least squares (2sls) estimates a linear regression of the outcome on treatment status using an instrumental variable (IV) and conducts inference with cluster-robust standard errors. When both the treatment and the IV vary within clusters, an alternative two-stage least squares with fixed effects (2sfe) additionally includes cluster indicators in the regression, thereby incorporating cluster information into point estimation as well. This paper studies the trade-off between these approaches within the local average treatment effect (LATE) framework. When clusters are homogeneous, we show that both approaches yield valid large-sample inference for the LATE, and that 2sfe is more efficient than canonical 2sls only when the variation in cluster-specific effects dominates idiosyncratic variation and the IV has sufficient within-cluster variation. When clusters are heterogeneous, we show that 2sfe identifies a weighted average of cluster-specific LATEs, whereas the canonical 2sls generally does not. We further propose a test for detecting cluster heterogeneity.

The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon – particularly the role of gradient orthogonalization – remain poorly understood, with very few works providing end-to-end analyses that rigorously explain its advantages in concrete applications. We take a step by studying the effectiveness of a simplified variant of Muon through two case studies: matrix factorization, and in-context learning of linear transformers. For both problems, we prove that simplified Muon converges linearly with iteration complexities independent of the relevant condition number, provably outperforming gradient descent and Adam. Our analysis reveals that the Muon dynamics decouple into a collection of independent scalar sequences in the spectral domain, each exhibiting similar convergence behavior. Our theory formalizes the preconditioning effect induced by spectral orthogonalization, offering insight into Muon's effectiveness in these matrix optimization problems and potentially beyond.