Reproduction logbook — paper-mL4i6z7Miy

Paper: Momentum Further Constrains Sharpness at the Edge of Stochastic Stability — Arseniy Andreyev, Advikar Ananthkumar, Marc Walden, Tomaso Poggio, and Pierfrancesco Beneventano. OpenReview mL4i6z7Miy; arXiv 2604.14108.

Result: C1/C2/C6 VERIFIED; C3/C4/C5 FALSIFIED in the reduced exact-measurement scope (12/12 expected, no abstentions).

This logbook checks the registered claims with the paper's own update equations, plateau formulas, printed experiment settings, and figures. The independent calculations are CPU-only and do not run the author's training/demo scripts. The main numerical validator is code/independent_recompute.py; its raw result is outputs/independent_recompute.json.

The paper defines heavy-ball SGDM as v_{t+1}=βv_t+g_t, θ_{t+1}=θ_t−ηv_{t+1} (Eq. 5, p. 3), and SGDN as v_{t+1}=βv_t+g_t(θ_t−βηv_t), θ_{t+1}=θ_t−ηv_{t+1} (Eq. 6, p. 3). It reports the small-batch plateau 2(1−β)/η, the large-batch SGDM plateau 2(1+β)/η, and the large-batch SGDN plateau 2(1+β)/(η(1+2β)) (Eqs. 1–2, pp. 1–2; Eq. 8, p. 5). C1/C2/C6 retain their prior evidence; the repaired C3–C5 pages add direct reduced-width CPU HVP measurements of the exact Batch Sharpness quantity.

Layout

pages/
  index.md
  registered-claims.md
  executive-summary/page.md
  claim-1-batch-dependent-eoss/page.md
  claim-2-theorem41/page.md
  claim-3-small-batch-plateau/page.md
  claim-4-large-batch-plateau/page.md
  claim-5-figure3-sgdn-transition/page.md
  claim-6-figure6-interventions/page.md
  conclusion/page.md
code/independent_recompute.py
outputs/independent_recompute.json
code/reproduce_reduced_plateaus.py
code/reproduce_reduced_cnn.py
outputs/reduced_plateau_summary.json
work/paper.pdf and work/paper.txt (pinned source and layout extraction)

Reproducing

python3 code/independent_recompute.py

The script uses NumPy only for small matrix eigensolves and writes a JSON artifact. It has no dataset, checkpoint, GPU, network, author-repository, or proprietary-API dependency. It is intentionally bounded to small scalar/2D operators and arithmetic checks.

Source pins and calibration

• OpenReview forum: https://openreview.net/forum?id=mL4i6z7Miy.
• Accessible paper copy: https://arxiv.org/abs/2604.14108 and work/paper.pdf.
• Author code link printed in the paper: https://github.com/marcwalden1/edge-of-stochastic-stability.
• Figure calibration: Figure 3 prints η=0.005, β=0.9 and the plateau guide lines; substituting these values into the paper's printed formulas gives 40, 760, and 271.428571.... The horizontal guide at 40 is independently printed by Eq. 8, so the plotted y-scale is calibrated before reading the relative positions of the SGDM and SGDN critical-batch markers. Figure 6's caption independently prints η=0.004, β=0.9, b=16, and the three intervention changes; the threshold arithmetic below uses those caption values, not pixel estimates.

icml2026-repro · paper-mL4i6z7Miy