arXiv AI

Which Optimizer Leaks Most? Optimizer Implicit Bias as a Training-Data Privacy Controller

arXiv AI
Jul 23

In-Run Data Shapley for Adam Optimizer

arXiv:2602. 00329v4 Announce Type: replace-cross Abstract: Reliable data attribution is essential for mitigating bias and reducing computational waste in modern machine learning, with the Shapley value serving as the theoretical gold standard.

By Meng Ding, Zeqing Zhang, Di Wang, Lijie Hu
arXiv Machine Learning
Jun 9

Convergence Bound and Critical Batch Size of Muon Optimizer

arXiv:2507. 01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW.

By Naoki Sato, Hiroki Naganuma, Hideaki Iiduka
arXiv Machine Learning
Sep 24

A lift for input-convex neural net training

The paper introduces the "lift" technique for training input‑convex neural networks, replacing the traditional non‑negative weight constraint enforced by projected gradient descent or a softplus map. By adding a learnable slack variable and an unconstrained network that processes a permutation‑invariant batch summary, the lift couples batch‑dependent latent weights to the gradient, increasing update variance and enabling faster escape from the softplus shoulder. Experiments show that when the softplus method stalls at the shoulder, the lift achieves tighter fits and reconstructs targets roughly three times faster, while both methods agree when the shoulder is rarely reached.

By Ali Siahkoohi
arXiv Machine Learning
Oct 5

The Conflict Between Logic and Memory: Training Conditions for Optimizer-Dependent Rule Acquisition

The paper investigates how different optimizers acquire distinct generalizing relations in single‑hidden‑layer ReLU networks. By manipulating nuisance‑connected weights and performing a strict‑parity sweep, the authors show that training conditions reshape both shared failures and relative optimizer advantages, with specific interventions improving accuracy on hard stages. The study also compares optimizer behavior across tasks and an external architecture (CIFAR‑10).

By Gongyue Zhang, Honghai Liu
arXiv Machine Learning
Aug 27

Spectral Allocation: Why Muon Outperforms Adam, and How to Improve Muon

The paper investigates why the orthogonal optimiser Muon outperforms Adam in large language model pretraining by analysing the spectral properties of Transformer loss landscapes. It finds that Muon’s momentum buffers exhibit an anisotropic spectral profile with a volatile head and a tolerant bulk, enabling larger effective step sizes. Building on this insight, the authors propose Spectral‑Aware Muon (SAMuon) and a lightweight variant, which adjust the bulk scaling while keeping the head unchanged, achieving 13–24 % fewer training tokens than Muon without extra FLOPs.

By Xiaodong Wu, Wenyi Yu, Chao Zhang, Philip Woodland
arXiv Machine Learning
Sep 4

Activation-Keyed Momentum: An Anisotropic Momentum Update via the Delta Rule

The paper introduces Activation-Keyed Momentum (AK‑Momentum), a momentum update that uses the input activation of a linear layer as a key to apply a delta‑rule update, allowing each direction to decay at a rate proportional to its frequency of appearance. AK‑Momentum is proven to be a valid momentum, incorporates input‑side curvature correction without matrix inversion, and clears stale directions faster than traditional exponential moving average (EMA) under both fixed and drifting optima. It can replace the momentum buffer of any optimizer, scales with width under μP, adds only 22–25% extra compute, and demonstrates significant step‑count reductions in FineWeb‑Edu pretraining and other benchmarks. whyItMatters":"AK‑Momentum offers a principled, efficient way to adapt momentum decay to anisotropic training dynamics, improving convergence speed and stability across a range of models and datasets."

By Euijin Hong, Guannan Qu