4arXiv cs.AI (Artificial Intelligence)·
Analysis challenges 'free lunch' narrative for Hyperball-style optimizers in deep network training
A new arXiv preprint investigates why Hyperball-style optimizers (which fix matrix parameter norms and normalize updates) outperform alternatives in large-scale training, finding that their advantage stems primarily from effective learning-rate schedule dynamics rather than an intrinsically superior update direction. The authors introduce an angular effective learning rate framework, decompose updates into radial and tangential components, and show that radial updates have limited direct effect on angular displacement. Experiments with MuonH and MuonWD reveal that careful learning-rate scheduling remains essential even under Hyperball constraints, contradicting the implicit assumption that norm-fixing eliminates scheduling sensitivity.
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Radial suppression of hidden representations accelerates grokking by up to 6x on algorithmic tasks
A new arXiv preprint presents a geometric analysis of the memorization-to-generalization delay (grokking) in neural networks, attributing it to radial inflation of hidden representations under cross-entropy optimization. The authors formalize a radial-angular decomposition of activation-space dynamics and derive three testable propositions about the effects of penalizing radial growth. Empirically, a single-hyperparameter norm penalty that constrains activations to a sqrt(d)-radius hypersphere accelerates grokking up to 6x on modular arithmetic tasks across MLPs and Transformers, and halves training steps for a 10M-parameter nanoGPT on 3-digit addition.
Analysis-driven transformer linearization outperforms prior baselines on LLaMA and Qwen up to 32B
A new arXiv paper analyzes why post-hoc linearization of causal self-attention degrades model quality, identifying key-dependent rank-1 orthogonal projections as the mechanism softmax relies on and explaining why delta-style networks outperform gated accumulation. The authors introduce structural interventions—sink tokens, short convolutions, and fixed-budget cache routing—applied in a frozen-backbone regime. Scaling across LLaMA and Qwen models up to 32B parameters, the approach outperforms prior post-hoc linearization baselines on MMLU and matches long-context retrieval of adaptive-caching frameworks.
Quantifying Hyperparameter Transfer: Embedding Layer Learning Rate as Key Driver of μP Benefits
This paper develops a three-metric framework to quantify hyperparameter transfer quality across model scales, targeting the problem of extrapolating optimal hyperparameters from small to large LLMs. The central empirical finding is that the well-known advantage of Maximal Update Parameterization (μP) over standard parameterization (SP) with AdamW largely reduces to a single factor: the embedding layer learning rate. In SP, the embedding layer acts as a training bottleneck causing instabilities; scaling its learning rate by model width to match μP substantially stabilizes training and improves transfer. The paper also characterizes how weight decay affects scaling law fit quality versus extrapolation robustness in opposite directions.
Muon optimizer shows large gains over AdamW in sparse-reward agentic RL on ALFWorld
A new arXiv preprint investigates the Muon optimizer for reinforcement learning post-training of language model agents, comparing it to AdamW on the ALFWorld benchmark using Qwen2.5-0.5B-Instruct. Under Group-in-Group Policy Optimization (GiGPO), applying Muon to hidden weight matrices raises validation success from 0.290 to 0.546 (+88%), with further gains at lower learning rates reaching 0.901 success. The results are exploratory (single-seed, single-task) but suggest that optimizer choice, advantage estimator, and learning rate interact significantly in agentic RL settings.
Asynchronous pipeline parallelism for LLM pretraining made viable with Muon optimizer and error feedback correction
A new arXiv paper challenges the assumption that gradient staleness in asynchronous pipeline parallelism (specifically PipeDream-2BW) is fundamentally unstable, showing the degradation is optimizer-dependent rather than intrinsic. The authors demonstrate that the Muon optimizer is robust under one-step gradient delay where AdamW fails, and introduce an optimizer-agnostic Error Feedback correction to further close the gap with synchronous training. Experiments on models up to 10B parameters confirm the approach matches synchronous training performance, potentially unlocking higher GPU utilization by eliminating pipeline bubbles.
Open problem paper questions whether AdamW converges under heavy-tailed gradient noise
A preprint from arXiv frames as an open problem whether AdamW, the dominant optimizer for LLM pretraining, can achieve rigorous convergence guarantees under heavy-tailed stochastic gradient noise. The authors note that sign-based optimizers like Lion and Muon already have sharp heavy-tailed convergence rates, while AdamW's second-moment accumulator may create a fundamental obstruction by hiding large gradients. The paper proves a positive weighted-metric benchmark and introduces a corridor lower-bound mechanism to characterize the potential failure mode.
Hamiltonian Probability Gradient Flow Analysis of the Muon Optimizer
This paper develops a rigorous theoretical framework for the Muon optimizer by interpreting its regularized orthogonalization map as the gradient of a Fenchel-dual smoothing of the nuclear norm, identifying Muon updates as mirror/prox steps with momentum as dual coordinates. The authors lift this structure to probability measures over matrix-valued parameters, deriving a mean-field phase-space equation that constitutes a damped Hamiltonian probability dynamics with monotonically decreasing Hamiltonian energy. Exponential convergence rates are established under gradient-dominance and curvature assumptions, and propagation-of-chaos guarantees are provided for the interacting particle system. The framework extends to transformer mixture-of-experts architectures via blockwise Muon probability flows.
AdamO optimizer and dynamical isometry regularization preserve plasticity in continual learning
A new arXiv preprint connects plasticity loss in continual learning to the empirical Neural Tangent Kernel and identifies dynamical isometry—keeping layer-wise Jacobian singular values near one—as a key mechanism for maintaining learning capacity under non-stationarity. The authors propose an isometry-promoting regularization scheme that can reactivate dormant ReLU units and introduce AdamO, an Adam-style optimizer that decouples isometry regularization from gradient updates analogously to AdamW. The methods are evaluated on supervised and reinforcement-learning continual-learning benchmarks, consistently matching or outperforming prior approaches. The work also reinterprets existing plasticity-preserving methods as targeting only partial isometry measures.