Looped linear transformers with LN provably converge via GD to implement the power method on principal component prediction.
Toward understanding why adam converges faster than sgd for transform- ers.arXiv preprint arXiv:2306.00204
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
years
2026 7representative citing papers
Adam achieves a δ^{-1/2} high-probability convergence rate while SGD requires at least δ^{-1} due to second-moment normalization, established via stopping-time/martingale analysis under bounded variance.
Muon outperforms Adam by reducing curvature penalty via lower Normalized Directional Sharpness, as shown via Taylor approximation on LLM training and proven on stylized quadratic problems with heterogeneous curvature.
Multi-layer transformers can implement in-context logistic regression by performing normalized gradient descent steps layer by layer, obtained via supervised training of a single attention layer followed by recurrent application with convergence and OOD guarantees.
The Adam-SGD gap in large-batch LLM pre-training arises mainly from SGD's restricted effective learning rates caused by small gradients and output-layer spikes; clipping lets SGD recover nearly all of Adam's performance.
Muon learns more robust and transferable features than Adam and SGD, shown via corruption robustness tests, transfer experiments, layer-wise probes, effective rank measurements, and a theoretical proof on margins in a multi-component classification problem.
citing papers explorer
-
Looped Transformers with Layer Normalization Provably Learn the Power Method
Looped linear transformers with LN provably converge via GD to implement the power method on principal component prediction.
-
Why Adam Can Beat SGD: Second-Moment Normalization Yields Sharper Tails
Adam achieves a δ^{-1/2} high-probability convergence rate while SGD requires at least δ^{-1} due to second-moment normalization, established via stopping-time/martingale analysis under bounded variance.
-
Why Muon Outperforms Adam: A Curvature Perspective
Muon outperforms Adam by reducing curvature penalty via lower Normalized Directional Sharpness, as shown via Taylor approximation on LLM training and proven on stylized quadratic problems with heterogeneous curvature.
-
Transformers Efficiently Perform In-Context Logistic Regression via Normalized Gradient Descent
Multi-layer transformers can implement in-context logistic regression by performing normalized gradient descent steps layer by layer, obtained via supervised training of a single attention layer followed by recurrent application with convergence and OOD guarantees.
-
Revisiting the Adam-SGD Gap in LLM Pre-Training: The Role of Large Effective Learning Rates
The Adam-SGD gap in large-batch LLM pre-training arises mainly from SGD's restricted effective learning rates caused by small gradients and output-layer spikes; clipping lets SGD recover nearly all of Adam's performance.
-
Muon Learns More Robust and Transferable Features than Adam
Muon learns more robust and transferable features than Adam and SGD, shown via corruption robustness tests, transfer experiments, layer-wise probes, effective rank measurements, and a theoretical proof on margins in a multi-component classification problem.
- Convergence of difference inclusions: a diameter criterion and step-size conditions