Towards Understanding Momentum Acceleration in River-Valley Loss Landscape P5YB6R0RK3

URI	`m2://res/P5YB6R0RK3`
Kind	preprint
Creators	Miao Lu, Zeyu Bian, Kaiyue Wen, Beining Wu, Siyu Chen, Tianhao Wang, Zhiyuan Li
Date	2026-09-25
Subjects	arxiv cs.LG, arxiv math.OC
Scope	border

Expressions

e1: version, preprint

Date	2026-09-25
Ids	arXiv 2609.30957

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
Gradient norm in the flat direction dominates	statement	lemma E.2	arxiv
Time index grows almost linearly with learning rate	statement	lemma C.14	arxiv
3ABZGMZ4NR	definition	definition	arxiv
Existence of projection onto the river \& further properties	statement	lemma D.4	arxiv
Informal, GD in river-valley landscape (improved version of Theorem 3.3	statement	theorem 3.1	arxiv
River-valley landscape	definition	definition 2.3	arxiv
Davis--Kahan $\sin(\theta)$ theorem	statement	lemma D.12	arxiv
Change of projection matrix	statement	lemma D.6	arxiv
GD-momentum in river valley loss landscape (formal version	statement	theorem C.1	arxiv
Auxiliary inequality 1	statement	lemma C.12	arxiv
Eigenvalue perturbation of symmetric matrices (Corollary 4.3.15	statement	lemma D.11	arxiv
Auxiliary inequality 2	statement	lemma D.8	arxiv
One-step variation of the flat-direction gradient	statement	lemma C.8	arxiv
Induction argument 1	statement	lemma C.9	arxiv
F4JZR108F2	statement	lemma 5.1	arxiv
Spectral radius of matrix $\boldsymbol{T}$	statement	proposition D.2	arxiv
Tangent vector and gradient in the flat direction	statement	lemma D.9	arxiv
Analysis of the sharp directions	statement	lemma C.7	arxiv
Tangent direction of the river	statement	lemma D.7	arxiv
GD in river-valley loss landscape (improved version of Theorem 3.2	statement	theorem E.1	arxiv
Induction argument 2	statement	lemma C.10	arxiv
K8SWRVY7XQ	statement	lemma 5.2	arxiv
River spinning	statement	lemma D.5	arxiv
Jacobian of projection to the river	statement	lemma D.10	arxiv
Induction argument 3	statement	lemma C.11	arxiv
Dominance of the flat direction	statement	lemma C.4	arxiv
TFA0NHY2HA	statement	lemma 5.3	arxiv
Schur unit-disk stability test for a quadratic	statement	lemma D.1	arxiv
Uniform momentum bound	statement	lemma C.6	arxiv
XRTC9Z79AG	statement	theorem 4.1	arxiv
Sensitivity of Lyapunov equation solution $\boldsymbol{P}$	statement	proposition D.3	arxiv
The trajectory tracks the river closely	statement	lemma C.13	arxiv

Catalogue records

arxiv: 2609.30957 (work)