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Search papers from 30+ top conferences, including NeurIPS, ICLR, ICML, CVPR, ACL and AAAI. Filter by keyword, then open any paper for its abstract, authors and links.

arXiv

Boundary Density Likelihood for Direct Event-Time Supervision

Clark Peng, Tolga Dinçer

Event detection turns long recordings into a sparse set of ranked timestamps. Yet many sequence models are trained for samplewise segmentation and only convert predicted states into events after training. We ask whether training directly for the evaluated output improves detection. Boundary Density Likelihood (BDL) assigns one unit of target mass to each annotated event, preserves that mass through smoothing and temporal downsampling, and uses a Poisson objective to estimate expected event mass in each output bin; local peaks become ranked detections. In a prespecified five-fold nested sleep study, BDL-Hard raises pooled out-of-fold mAP from 0.586 to 0.705 over interval segmentation (+11.9 percentage points; 95% interval [10.8, 13.0]) and strict one-minute AP from 0.071 to 0.286 (4.0x; +21.5 points), improving on every outer fold. A separate held-out rerun reproduces the direction of the effect. A matched boundary-BCE detector reaches 0.702 mAP, showing that direct boundary supervision and event decoding account for most of the gain, with a smaller contribution from the Poisson objective. The same trend appears with an offline convolutional model; causal, Transformer, and patient-grouped seizure experiments leave broader generalization unresolved. Our results support training on event times when timestamps define the evaluated output.

arXiv

Path Planning of Cleaning Robot with Reinforcement Learning

Woohyeon Moon, Bumgeun Park, Sarvar Hussain Nengroo, Taeyoung Kim, Dongsoo Har

Recently, as the demand for cleaning robots has steadily increased, therefore household electricity consumption is also increasing. To solve this electricity consumption issue, the problem of efficient path planning for cleaning robot has become important and many studies have been conducted. However, most of them are about moving along a simple path segment, not about the whole path to clean all places. As the emerging deep learning technique, reinforcement learning (RL) has been adopted for cleaning robot. However, the models for RL operate only in a specific cleaning environment, not the various cleaning environment. The problem is that the models have to retrain whenever the cleaning environment changes. To solve this problem, the proximal policy optimization (PPO) algorithm is combined with an efficient path planning that operates in various cleaning environments, using transfer learning (TL), detection nearest cleaned tile, reward shaping, and making elite set methods. The proposed method is validated with an ablation study and comparison with conventional methods such as random and zigzag. The experimental results demonstrate that the proposed method achieves improved training performance and increased convergence speed over the original PPO. And it also demonstrates that this proposed method is better performance than conventional methods (random, zigzag).

arXiv

Tracing the Heart: An Evidence-Linked Pipeline for Heart-Failure Feature Engineering

Soorya Ram Shimgekar, Michelle Hu, Dorisa Shehi, Daniel Kang, Roy Ka-Wei Lee, Koustuv Saha, Christian Poellabauer, Christopher Lee, Sajeev Singh, Piyum Zonooz, Navin Kumar, Zeeshan Ahmed, Priyadarshini Kachroo

Electronic health record (EHR) feature engineering is a major bottleneck in clinical research and AI, accounting for 39-45% of data scientists' workload. This is especially pronounced in heart failure, which affects an estimated 6.7 million U.S. adults and requires integrating fragmented EHR data with disease-specific, guideline-based clinical reasoning. Existing rule-based and large language model (LLM)-based approaches offer only partial automation with limited maintainability and evidence traceability. We developed the Nimblemind Multi-Agent System (nMAS), an evidence-linked, rubric-grounded pipeline for automated heart-failure feature engineering, and evaluated it on 500 dummy patient records from nine EHR source tables. nMAS generated 132 structured and 70 rubric-scored aggregated features, verified for structural integrity, rubric compliance, and provenance, and audited by a restricted LLM. Adding the aggregated features improved held-out AUROC from 0.895 to 0.963 for HFrEF and 0.870 to 0.910 for HFpEF phenotyping, and an independent LLM-based rubric assessment of evidence support and methodological soundness scored the features at 81.5% of maximum points. These results demonstrate the feasibility of automated, auditable feature engineering for complex cardiovascular EHR data, though evaluation was limited to a single-institution cohort and external validation is needed.

arXiv

An Optimal Agnostic PAC Algorithm

Markus Engelund Mathiasen, Jian Qian, Nikita Zhivotovskiy

Let $H\subseteq\{-1,+1\}^X$ be a class of finite VC dimension $d\ge1$. Writing $L$ for the binary risk and $L^*=\min_{h\in H}L(h)$, we construct a learner achieving the statistically optimal risk bound: from an i.i.d.\ sample of size $n$, for every $0<δ\le 1/2$, with probability at least $1-δ$, \[ L(\widehat h) \le L^*+ 7\cdot10^8\left( \sqrt{\frac{L^*(d+\log(1/δ))}{n}} +\frac{d+\log(1/δ)}{n} \right). \] This settles the sample complexity of agnostic PAC learning up to universal constants at every fixed $L^*$, matching the lower bounds of Devroye, Györfi, and Lugosi [A Probabilistic Theory of Pattern Recognition, Springer, 1996].

arXiv

Scalable estimation of VARMA models

Daniel Paulin, Victor Elvira

Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags. We introduce an estimation framework that removes this computational barrier: each optimization iteration is independent of the series length $T$. The framework combines a partial-autocorrelation reparametrization that guarantees stationarity and invertibility by construction, Gaussian priors on the reparametrized coefficients with separate scales for diagonal and off-diagonal entries, and losses that depend on the data only through fixed-size sufficient statistics, evaluated by a Parseval (Fourier) identity at near-linear cost in the truncation length. This yields two point estimators: a regularized least-squares fit and a covariance-marginalized maximum-a-posteriori estimator. We prove that both recover the infinite-autoregressive representation of the true process at a near-parametric rate in fixed dimension, so the truncation introduces no asymptotic bias. The same machinery extends, at the same leading cost, to seasonal dynamics, exogenous regressors (VARMAX), and rolling-window refits. Empirically, the estimators stay close to the oracle forecast error from $d=10$ to $d=40$ (where classical conditional MLE returns non-invertible fits whose forecasts diverge) and match or beat VAR, Bayesian-VAR, component-wise ARMA, and sparse-VARMA baselines on retail-demand, meteorological, and air-quality data. This brings likelihood-based VARMA estimation, at a per-iteration cost independent of the series length, to the problem sizes where practitioners have so far relied on VAR models.

arXiv

Optimal Rates for Learning with Monotone Adversaries

Anay Mehrotra

A monotone adversary observes an i.i.d. labeled sample and appends a finite number of further examples of its choice, every one of them labeled correctly by the target hypothesis. The learner sees a uniform shuffle of the combined sample and is scored on the original distribution. Every example is correctly labeled, but the insertions depend on the clean sample, so the combined sample is not exchangeable. Larsen, Pabbaraju, and Shetty, who introduced this model, showed that empirical risk minimization attains expected error $O((d/n)\log(n/d))$ for classes of VC dimension $d$, and that every known optimal learner can be pushed away from the $Θ(d/n)$ rate, optimal for PAC learning. They asked whether the extra logarithm is an artifact of those particular algorithms or an inherent consequence of the lack of exchangeability. We show that this additional cost is inherent beyond VC dimension one. In the worst case over classes of VC dimension $d$ and over known finite insertion budgets, the minimax expected error is $Θ(1/n)$ at $d=1$ and $Θ((d/n)\log(n/d))$ for $d\geq 2$. The same rates hold with Littlestone dimension $d_{\mathrm L}$ in place of $d$, so the clean online-to-batch rate $O(d_{\mathrm L}/n)$ is unattainable as well. Thus, somewhat counterintuitively, adding correctly labeled examples can make learning harder by a logarithmic factor, even for classes that admit finite mistake bounds in online learning. The dimension-one upper bound is achieved by a simple improper learner whose analysis adapts the leave-one-out argument underlying the one-inclusion graph. All of our lower bounds are elementary and come from a single construction: an explicit class and prior on which two target hypothesis, which differ a point of nonnegligible mass, produce the same sample.

arXiv

BaKron: Efficient Quantization with Kronecker-Factored Hessians

Johann Birnick, Rayan Saab

We accelerate a family of algorithms for neural network quantization whose geometry is informed by any Kronecker-factored approximation of the Hessian. GPTQ-style adaptive rounding typically uses one-sided information derived from input activations. Two-sided Kronecker-factored Hessian approximations can additionally capture correlations across output coordinates, but applying GPTQ directly in the vectorized weight domain is computationally expensive. Building on the two-sided adaptive-rounding formulation used by BoA and YAQA, we introduce BaKron, an efficient solver that combines anti-diagonal parallelism with a recursive divide-and-conquer construction. For an $m\times n$ weight matrix, BaKron uses $O(m+n)$ sequential steps while reducing the total work from $O(m^2n^2)$ to $O(mn(m+n))$. Thus, it matches the cubic scaling of GPTQ while exploiting richer curvature information. Moreover, BaKron is modular with respect to both the base quantizer and the Hessian estimator. We also provide practical benchmarks, consider a range of Hessians that BaKron can be called with, find an efficient technique to compute these Hessians, and evaluate the algorithm experimentally.

arXiv

Surv-IPTB: An Attention-Based Model for Estimating Individual Probability of Treatment Benefit with Survival Data

Lev V. Utkin, Stanislav K. Kogan, Andrei V. Konstantinov

This work presents a novel attention-based framework for estimating the Individual Probability of Treatment Benefit (IPTB) in survival analysis contexts. The proposed model, called Surv-IPTB, directly quantifies the probability that a specific patient will experience extended survival time under treatment versus control. We reformulate IPTB estimation as a binary classification problem, leveraging pairwise patient comparisons across treatment and control cohorts. The framework incorporates a principled handling of right-censored observations through imprecise probability representations, where uncertain treatment effects are characterized by interval-valued probabilities. An attention mechanism with learnable query-key transformations enables flexible, data-driven aggregation of pairwise comparisons, while simultaneously learning soft class probabilities for censored cases. Through extensive experiments on synthetic datasets with complex nonlinear structures, including spiral, bell-shaped, and circular feature spaces, we demonstrate that our approach maintains robust performance across varying censoring rates and treatment effect strengths. The model consistently outperforms meta-learner baselines (T-learner and S-learner) equipped with random survival forests, Cox proportional hazards, and Beran estimators, particularly in challenging nonlinear scenarios where conventional methods exhibit significant degradation. The results establish the proposed attention-based framework as a scalable and statistically principled solution for personalized treatment benefit assessment in survival settings. The code implementing the model is publicly available.

arXiv

The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity

Iosif Lytras, Nikolaos Makras, Sotirios Sabanis

We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures. To handle the superlinear regime, taming techniques are employed to produce a stable, explicit scheme. We derive non-asymptotic convergence bounds in Wasserstein-2 distance, with all constants tracked explicitly in terms of dimension and inverse temperature, improving upon the currently known rates for subgradient-based Langevin algorithms. We further provide excess risk estimates for the associated optimisation problem. We verify the assumptions, with explicit constants, for the regularized pretraining potential of a LLM in the GPT-2 lineage and the boosted coordinate-wise variant of SG-TULA pretrains the former competitively against finetuned AdamW and Muon, for which no comparable non-asymptotic guarantees are presently available.

arXiv

Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learning

Farzana Nasrin

Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure. While substantial progress has been made in the statistical analysis of PDs, existing literature often treats diagrams as static objects and provide limited frameworks for probabilistic modeling and stochastic evolution on PD space. We introduce a reinforcement learning framework for stochastic dynamics on PD space, where diagrams evolve through topology aware local edit operations. The dynamics define controlled Markov processes on spaces of finite PDs with variable cardinality. We establish conditions under which the induced Markov chains are irreducible, aperiodic, and geometrically ergodic, implying the existence of unique stationary probability laws on PD space. To guide the dynamics toward scientifically relevant topological targets, we formulate objectives that encompass distribution matching, task specific topological statistics, and structure-preserving compression. The resulting rewards balance task specific distributional targets, diagram fidelity, and complexity reduction, and yield a framework for adaptive topological simplification and probabilistic modeling. Experiments on synthetic and neuroimaging PDs demonstrate that the proposed framework can preserve dominant topological structure while reducing diagram complexity.

arXiv

Improving the Realism of Synthetic Clinical Benchmarks Under Utility Constraints

Omid Bazgir, Md Nasir, Jacob Hoffman, Yang Yang, Manu Agrawal, Anusua Trivedi, Vinay Rao Dandin, Chris Gibbons, Christine Swisher

Synthetic clinical benchmarks for enterprise AI agents can pass existing utility checks and still remain structurally unrealistic, especially in privacy-sensitive healthcare settings where operational data are hard to access. We study how to improve such benchmarks without breaking the downstream utility checks already used in practice. We formulate benchmark revision as utility-constrained realism improvement: dataset changes should increase realism while staying above an operational utility floor. We instantiate this idea on a care-gap benchmark derived from Synthea-generated patients exercised through demonstration electronic health record workflows and then processed by the same downstream pipeline as operational data. Realism is measured through missingness structure, simplicity, structural plausibility, and population alignment. The baseline benchmark is extremely thin: sampled-pair missingness is 79.44%, only 12.75% of rows are actionable, 38.94% of patients have zero actionable measures, and top-three token concentration reaches 100.0%. Two deterministic revisions improve these panels while remaining above the current utility floor, whereas a naive densification control preserves unrealistic templating. We further show that internal benchmark realism and source fidelity to an aggregate operational reference are related but distinct objectives. These results suggest that synthetic benchmark quality should be optimized explicitly, with utility treated as one constraint rather than as sufficient evidence of realism.

arXiv

Hypothesis Testing with Conditional Queries: Learnability and the Value of Interaction

Zonghuan Xu

Model evaluations may fix all tests before observing any responses or select later tests using earlier responses. We study this choice in a conditional-query model on a finite outcome space $\mathcal{X}$ with $|\mathcal{X}|=N$. We first ask which pairs of distribution classes can be reliably distinguished. We then ask how many additional queries are required to match an adaptive tester when all queried events must be fixed in advance. We show that learnability holds if and only if the two classes have positive separation in their pairwise conditional probabilities. When this separation is zero, the optimal worst-case error is exactly $1/2$ at every finite query budget. For any $T$-query adaptive policy and any $ρ\in (0,1)$, we construct a randomized non-adaptive procedure using $O(N^2(T + \log(1/ρ)))$ pair queries chosen before any response is observed. Its simulated transcript is within $ρ$ in total variation of the adaptive transcript, uniformly over all distributions in the model. We also construct a matching family with constant adaptive query complexity and $Ω_\varepsilon(N^2)$ non-adaptive query complexity. Consequently, the worst-case fixed-error adaptivity gap is $Θ_\varepsilon(N^2)$. Thus interaction can reduce the required number of tests by a quadratic factor, but the apparent exponential branching of an interactive evaluation does not yield an exponential query advantage.

arXiv

RxnCLF: Contrastive Transformation-Aware Reaction Foundation Model for Improved Reactivity Prediction

Yiting Zheng, Cheng Fang, Anthony Donofrio, Haote Li

Reaction yield prediction remains challenging because labeled data are scarce and reaction space is both combinatorially large and sparsely populated, limiting the generalization of existing reaction representations. String-, fingerprint-, and graph-based reaction encodings only partially capture chemical transformations, making accurate prediction difficult for reactions with complex substrates. We propose reaction contrastive learning foundation (RxnCLF), a self-supervised contrastive framework for reaction representation learning. RxnCLF is built on a condensed reaction graph (CRG) that unifies reactant and product information into a single graph, enabling the model to learn explicit and enriched transformation structure rather than disconnected graphs. Pretrained on 1.7 million Pistachio reactions, RxnCLF learns a compact and continuous latent space that captures both reaction-center features and broader side chain contexts, making it transformation-aware and chemically interpretable. Fine-tuned on multiple yield prediction benchmarks, including Buchwald-Hartwig, Pd-catalyzed BH coupling, and proprietary HTE C-N coupling and amide formation datasets, RxnCLF consistently outperforms graph and sequence-based baselines, improving R2 and achieving the best performance overall. Our results highlight the promise of CRG-based RxnCLF as a scalable reaction foundation model, with the potential to generalize across broader reaction spaces and support diverse downstream reaction informatics tasks, including regioselectivity prediction, enantioselectivity prediction, and reaction condition optimization.

arXiv

MetaboLLM: a metabolomics-specialized large language model for biochemical knowledge integration and predictive metabolite graph construction

Dohyun Ku, Min Gu Kwak, Francisco J. Pasquel, Jing Li

Metabolomics knowledge is distributed across heterogeneous resources and remains difficult to translate into predictive representations. We developed MetaboLLM, a metabolomics-specialized large language model adapted through continual pretraining, supervised fine-tuning, and structured retrieval, together with MetaboLLM-GIN, which converts generated biochemical descriptions into metabolite graphs for patient-level prediction using a graph isomorphism network. Across four backbone families, MetaboLLM outperformed corresponding base and medically adapted models on metabolomics knowledge, relational, and description tasks, and transferred to an external public benchmark. MetaboLLM-GIN achieved the highest AUC for stress hyperglycemia prediction after coronary artery bypass grafting (0.8616) and postmenopausal hormone-regimen classification (0.8123), outperforming conventional models, alternative graph constructions, and graphs generated from unadapted or non-retrieval LLM configurations. Model interpretation further produced biologically meaningful findings in both applications. These results show that domain-specialized language models can organize heterogeneous biochemical knowledge into predictive and interpretable metabolite graph representations.

arXiv

Minimax Optimal Early-Stopped Gradient Descent for Gaussian Mixture Classification

Alex Buna, Shirley Xiaoqi Liu, Patrick Rebeschini

In overparameterised classification, training data can be linearly separable even when the underlying distribution is not. In this setting, gradient descent (GD) on the logistic loss diverges in norm while converging in direction to a max-margin interpolating classifier, whose implicit bias can be statistically suboptimal. In this work, we show that early stopping can overcome this suboptimality: in a Gaussian mixture model with label-flipping noise, GD stopped at an appropriate oracle time achieves minimax-optimal excess zero-one risk for covariance spectra with fast and continuous decay, including polynomial and exponential spectral decays. Our analysis combines a sharp upper bound for the early-stopped iterate with a matching statistical lower bound over arbitrary classifiers, yielding optimal rates that are validated by experiments. A central technical contribution is a new calibration result that converts excess logistic risk into excess zero-one risk; it handles the model misspecification induced by the label-flipping noise, and removes the square-root rate in standard bounds. We also establish a lower bound for linear interpolators, showing that interpolation can require exponentially more samples than early stopping to achieve the same excess risk.

arXiv

A Six-Dimensional Taxonomy of Post-Training Adaptation Techniques with Applications in AI Governance

Fardin Afdideh, Fernando Seoane, Farhad Abtahi

Post-training adaptation has become central to modern machine learning practice and includes techniques such as retraining, fine-tuning, parameter-efficient adaptation, alignment, retrieval augmentation, model editing, unlearning, calibration, and Multimodal Instruction Tuning. However, the literature remains fragmented across technique families, model classes, and deployment contexts, making it difficult to compare methods or describe how a trained model has been modified. This survey synthesizes the post-training adaptation literature and introduces a six-dimensional taxonomy organized by mechanism, goal, data requirement, persistence, structural scope, and model type. The taxonomy distinguishes commonly conflated terms such as fine-tuning, retrieval augmentation, and prompting, and shows how adaptation strategies evolve from traditional machine learning through deep learning, foundation models, large language models, and multimodal large language models. It also maps relationships among techniques, including inheritance, supersession, hybridization, and layered deployment stacks. The resulting vocabulary can support technical documentation, model-change tracking, and governance analysis. The survey concludes by identifying open challenges in evaluation, reproducibility, persistent inference-time adaptation, unlearning, multimodal adaptation, and governance-aware post-training workflows.

arXiv

Timestep-Conditioned Transformers for Global Weather Forecasting

Sam Levang, Fran Bartolic, Ty Dickinson, Chase Dwelle, Paulius Rauba, Viktor Cikojevic

Existing machine-learning weather forecasting models rely on predetermined and fixed autoregressive timesteps. The choice of model timestep involves a fundamental trade-off: shorter timesteps (e.g. 1 to 6 hours) finely resolve atmospheric dynamics within the diurnal cycle but increase error accumulation for a given forecast horizon, while longer timesteps (e.g. 24 hours) reduce error accumulation but limit the usability of short-range forecasts where sub-daily predictability is high. In this work, we present GEM-3, a probabilistic global weather model that addresses this trade-off through explicit multi-timestep inference. With a single set of trained weights, the model timestep can be configured at inference time to balance predictability and usability across a broad forecast horizon. Additionally, we find that mixed-timestep training consistently improves rollout stability relative to timestep-specialist models. Under the hood, GEM-3 is a lightweight neighborhood-attention transformer with ~134M parameters on an equirectangular grid with a number of architectural advancements beyond its predecessor GEM-2. The result is a practical forecasting system that couples near-SOTA medium-range probabilistic skill, stable extended-range rollouts, efficient training and inference, and decision-relevant diagnostics.

arXiv

TS-RAG: Retrieval Augmented Generation for Time Series Forecasting

Yixiong Xiao, Congxi Xiao, Jingbo Zhou

While deep learning models, particularly transformer-based architectures, have shown impressive performance in time series forecasting, the application of retrieval-augmented generation (RAG) in this domain remains limited. Since RAG has proven effective in enhancing the capabilities of large language models by incorporating relevant external information, retrieving similar time series sequences as references might also improve accuracy in time series forecasting tasks. However, most time series models are constrained by limited training data, smaller parameter scales, and a lack of the extensive generative capabilities found in large language models. Simply concatenating reference sequences into the prompt, as done in language models, may not yield the expected results. To address these challenges, we propose a novel approach, TS-RAG, which leverages RAG to enhance forecasting performance. The framework introduces specially designed reference tokens to effectively fuse information from the input sequence with that from retrieved similar sequences, enabling a more robust capture of complex temporal dynamics. Experimental results demonstrate that TS-RAG achieves consistent state-of-the-art performance across several real-world forecasting benchmarks.

arXiv

Robot Learning from Human Demonstrations: Handwritten Alphabet Trajectories and Human-Likeness Evaluation

Alperen Kenan, Paul Bremner, Manuel Giuliani

Learning from demonstration (LfD) provides a developmental framework through which robots can develop motor skills by observing and imitating human dynamics, reducing reliance on explicit programming to teach a skill to a robot. The resulting human-like robot motion is recognised as a key factor in building trust and enabling natural collaboration in human-robot interaction. This paper presents a framework for learning human-like robot motion from demonstration, including data collection, probabilistic trajectory learning, and perceptual user evaluation. A dataset of 3,142 handwriting demonstrations was collected from 22 participants across all 52 Latin alphabet character-case combinations via a touchscreen teleoperation interface, capturing planar position, contact force, and timing. Building on the widely used Gaussian Mixture Model and Gaussian Mixture Regression approach for learning from demonstration, the framework is extended in this work by incorporating force and normalised time dimensions to enable richer representation of human dynamics, and adapting it to handle non-continuous, multi-segment trajectories, enabling generalisation across demonstrations. A user study with 21 participants evaluated the perceived human-likeness of the generated trajectories using a continuous scale anchored between robotic and human-like motion, normalised to 0-100 where 50 represents the neutral midpoint. The generated trajectories achieved an overall human-likeness score of 71.50 (SD=22.56), indicating that the majority of trajectories were perceived as more human-like. Participants identified geometric positioning and trajectory sequence as the most influential perceptual factors, and reported positive attitudes toward human-like robot behaviour. The datasets are released as open-source, providing a reproducible benchmark for developing and evaluating human-like robot motion methods.

arXiv

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update

Mikhail Solonko, Molozhavenko Alexander, Maxim Rakhuba

We study Muon, a recently proposed matrix-aware optimization method, in the context of the Stiefel manifold. This manifold consists of matrices with orthonormal columns and is ubiquitous in machine learning and scientific computing. Existing extensions of Muon to this manifold rely on heuristic, approximate, or iterative updates with varying computational efficiency. We show that the corresponding Stiefel Muon update admits an exact closed-form solution and use this result to develop Skewon, a practical algorithm for orthogonality-constrained optimization with an efficient implementation. We further establish first-order convergence guarantees for Skewon in the smooth non-convex setting.

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