arXiv:2608. 02991v1 Announce Type: new Abstract: Matrix spectral optimizers reshape weight-update spectra but usually delegate vector-valued biases to a separate optimizer.
arXiv:2603. 28921v3 Announce Type: replace-cross Abstract: The critical damping condition of the damped harmonic oscillator model of SGD with momentum (Qian, 1999) yields a momentum schedule with no tuned hyperparameters: mu(t) = 1 - 2*sqrt(alpha(t)).
arXiv:2607. 22927v1 Announce Type: new Abstract: Weights and biases are normally optimized as separate parameter tensors, yet they do not represent separate functions when the input to an affine layer has nonzero mean.
arXiv:2607. 19331v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood.
arXiv:2607. 14516v1 Announce Type: new Abstract: Interpreting optimizers as gradient-flow discretizations has motivated applying higher-order Runge-Kutta (RK) integrators to neural networks.
arXiv:2608. 04407v1 Announce Type: cross Abstract: Memory-efficient matrix optimizers such as Sinkhorn gradient descent remove most AdamW optimizer state for dense Transformer matrices, but direct application to Mixture-of-Experts (MoE) training is unreliable.
arXiv:2607. 23711v1 Announce Type: new Abstract: LoRA fine-tuning can create intruder dimensions: new leading singular vectors of the updated weight matrix $W+BA$ that are nearly orthogonal to all pretrained singular vectors and that drive catastrophic forgetting.
arXiv:2606. 12921v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) significantly reduces compute and memory costs for finetuning Deep Learning models but is often harder to tune than dense training: when using factor-wise optimizers such as AdamW, it is sensitive to initialization choices, its optimal learning rates transfer poorly across ranks, and it often fails to beat dense baselines.
arXiv:2608. 05136v1 Announce Type: new Abstract: Gradient descent on a factored model $W = UV^\top$ is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not.
arXiv:2607. 18343v1 Announce Type: cross Abstract: Federated fine-tuning is bottlenecked by communication: FedAvg and pseudo-gradient schemes transmit a payload that scales with the model, and gradient compression shrinks it by only a constant factor.
arXiv:2608. 02829v1 Announce Type: new Abstract: Model families train every size from scratch.
arXiv:2605. 17109v3 Announce Type: replace-cross Abstract: In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly.
arXiv:2606. 25971v1 Announce Type: new Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object.