Ben-Gurion University of the Negev

A GNN weight matrix acts on graph-propagated features, so an update that is well normalized in parameter space can still be amplified by graph structure into a large representation-level perturbation. GraphMuon moves Muon's matrix orthogonalization into a metric defined by the covariance of the propagated layer inputs and scales each step by its induced effect on the layer representation. On three large-scale OGB benchmarks it reaches AdamW's validation-loss target in 1/2.32 to 1/1.32 of the wall-clock time, a 1.32x to 2.42x speedup.

A GNN weight matrix acts on graph-propagated features, so an update that is well normalized in parameter space can still be amplified by graph structure into a large representation-level perturbation. GraphMuon moves Muon's matrix orthogonalization into a metric defined by the covariance of the propagated layer inputs and scales each step by its induced effect on the layer representation. On three large-scale OGB benchmarks it reaches AdamW's validation-loss target in 1/2.32 to 1/1.32 of the wall-clock time, a 1.32x to 2.42x speedup.

High-stakes regression decisions need a point estimate, a risk interval and an option to abstain, yet interval methods and selective prediction each supply only part of that triad. SelPI trains interval, value and two abstention heads jointly under one loss, with a Fréchet penalty tying the two gates' budgets to the joint acceptance rate they deliver. Across 18 tabular benchmarks, interval width predicts large point errors well but is anti-correlated with interval misses, so abstaining on wide intervals discards inputs the interval got right; with the base predictor held fixed, the learned gate beats width thresholding on a proper interval score on all 18 tabular datasets, and the advantage grows with task heteroscedasticity.

High-stakes regression decisions need a point estimate, a risk interval and an option to abstain, yet interval methods and selective prediction each supply only part of that triad. SelPI trains interval, value and two abstention heads jointly under one loss, with a Fréchet penalty tying the two gates' budgets to the joint acceptance rate they deliver. Across 18 tabular benchmarks, interval width predicts large point errors well but is anti-correlated with interval misses, so abstaining on wide intervals discards inputs the interval got right; with the base predictor held fixed, the learned gate beats width thresholding on a proper interval score on all 18 tabular datasets, and the advantage grows with task heteroscedasticity.

Probabilistic time-series forecasting must capture temporal structure, express uncertainty and infer quickly; diffusion and flow-matching methods buy flexibility with multi-step iterative sampling whose cost grows with the number of steps. KGO treats prediction as the evolution of structured uncertainty in a Koopman latent space: KoPE extrapolates latent trajectories with a learned linear operator, KoFM transports noise to the future in one step via a matrix exponential, and AUG adapts the deterministic and stochastic mix per variable and horizon. Across 17 ProbTS settings, KGO reports the lowest CRPS on 13 and the lowest NMAE on 16, with at least a 25-fold inference speedup over iterative generative models.

Probabilistic time-series forecasting must capture temporal structure, express uncertainty and infer quickly; diffusion and flow-matching methods buy flexibility with multi-step iterative sampling whose cost grows with the number of steps. KGO treats prediction as the evolution of structured uncertainty in a Koopman latent space: KoPE extrapolates latent trajectories with a learned linear operator, KoFM transports noise to the future in one step via a matrix exponential, and AUG adapts the deterministic and stochastic mix per variable and horizon. Across 17 ProbTS settings, KGO reports the lowest CRPS on 13 and the lowest NMAE on 16, with at least a 25-fold inference speedup over iterative generative models.

Organizations checking whether an LLM reply breaks internal policy have relied on fine-tuned detectors or a second LLM judging each exchange, both costly to train and to run. The new approach recasts violation detection as out-of-distribution detection in activation space: a whitening transform estimated from policy text and a few examples standardizes compliant hidden states, and the Euclidean norm of the whitened vector is compared with a calibrated threshold. On the DynaBench test set with a Qwen2.5-7B-Instruct backbone, F1 reaches 86.0%, above the fine-tuned detectors and LLM-as-a-judge baselines listed in the comparison table.

Organizations checking whether an LLM reply breaks internal policy have relied on fine-tuned detectors or a second LLM judging each exchange, both costly to train and to run. The new approach recasts violation detection as out-of-distribution detection in activation space: a whitening transform estimated from policy text and a few examples standardizes compliant hidden states, and the Euclidean norm of the whitened vector is compared with a calibrated threshold. On the DynaBench test set with a Qwen2.5-7B-Instruct backbone, F1 reaches 86.0%, above the fine-tuned detectors and LLM-as-a-judge baselines listed in the comparison table.

With architecture and data held fixed, a checkpoint-only reconstruction attack recovers training images best from Muon-trained models and worst from Adam-trained models, making the optimizer choice a control axis for training-data privacy.

With architecture and data held fixed, a checkpoint-only reconstruction attack recovers training images best from Muon-trained models and worst from Adam-trained models, making the optimizer choice a control axis for training-data privacy.