IvanMiao/icml2026-layer-lr-repro

Two-step learning-rate symmetry transition — reproduction

Independent, low-cost reproduction of the central two-layer result in Balancing Learning Rates Across Layers: Exact Two-Step Dynamics and Optimal Scaling in Linear Neural Networks (arXiv:2606.00340; OpenReview 4vztmTrGhd).

Scope and verdict

This is a formula-grid reproduction of the displayed random-orthogonal two-layer test-loss equations in Theorem 5.3 and the qualitative conclusion in Corollary 5.4. It is not a reimplementation of the authors' full simulation code or a proof of the theorem.

Following the paper's Figure 2 setting, the run uses width h=1000 and scans 2001 allocations constrained to eta_1 + eta_2 = 2 h^1.5.

Updates	Symmetric allocation (eta_1=eta_2)	Neighbour loss − symmetric loss	Result
1 GD step	0.879510894	-8.0064e-7	not a local minimum
2 GD steps	0.590067574	+4.9976e-5	local minimum on the grid

So the predicted asymmetry-to-balance transition is reproduced. The one-step global grid minimum occurs at a boundary allocation; the claim tested here is the local behavior at the symmetric allocation.

Compute and audit trail

The actual GPU run used one t4-small Hugging Face Job and performed the tensor scan on CUDA in about 0.34 seconds after environment setup:

• Job: https://huggingface.co/jobs/IvanMiao/6a5d37dfd216bd6f3a201fab
• Raw job-derived values: outputs/gpu_job/results.json
• Interactive plot and raw curve: outputs/local/reproduction_plot.html, outputs/local/curve.csv

Re-run

The script is self-contained with PEP 723 dependencies:

uv run repro.py --h 1000 --alpha 1.5 --points 2001 --output-dir outputs/run
python -m unittest discover -s . -p test_repro.py

repro.py chooses CUDA automatically when available, otherwise CPU. The calculations use float64 because the curvature signal around the symmetric point is small.

Files

• repro.py: independent formula implementation and SVG/HTML report generator.
• test_repro.py: formula finiteness, grid alignment, and claim-direction tests.
• outputs/gpu_job/: GPU-job result and machine-readable job record.
• outputs/local/: full 2001-point CSV and standalone interactive report.