nmaher/icml2026-repro-l35QweVxgn-code

Reproduction code — On the Theory of Continual Learning with Gradient Descent for Neural Networks

Clean-room NumPy reimplementation and full sweep harness for the ICML 2026 submission l35QweVxgn (arXiv:2510.05573v2), Taheri, Ghosh & Mazumdar.

The write-up lives in the Trackio logbook: 🚀 nmaher/repro-on-the-theory-of-continual-learning-with-gradient-descent-for-neural-networks. This repo is the code and the raw numbers behind it.

Layout

code/      the reimplementation and all eight sweep drivers
results/   one JSON per driver — every logged run, plus summary.json (all fitted slopes)
figs/      every figure as standalone HTML + PNG + the CSV it was drawn from
poster/    the 60"×36" conference poster (HTML source, print PDF, preview PNG)

File	Claims	What it does
code/clcore.py	—	The model, the XOR-cluster data generator, full-batch GD, and the closed-form linear-loss solver. Everything else imports this.
code/exp1_scalings.py	1	Plain full-batch GD; forgetting vs $n$, $m$, $K-k$, $\eta$, $T$
code/exp2_mechanism.py	1, 2	Closed-form solver; splits forgetting into first_order / remainder / fo_fluct / fo_mean, plus the mean-overlap control
code/exp3_regime.py	2, 3, 6	Prescribed-path sweep + 3 condition-breaking arms; the $\eta T$ horizon grid; the $4\times4$ $(n,m)$ joint grid
code/exp4_gengap.py	4, 5	Measured delayed generalization gap vs both bound right-hand sides
code/exp5_etaT_needed.py	2	Bisection for the smallest $\eta T$ that fits one task, over $(d,m)$
code/exp6_noise.py	3	Cluster-noise control, $\sigma_c \in [0.1, 4.0]$
code/exp7_decomp_mc.py	6	Monte-Carlo control on the term the decomposition drops
code/exp8_nonvacuous.py	4, 5	The low-$\eta$ corner where the exponential prefactors fall to $O(1)$
code/analyze.py	all	Reads every results/exp*.json, fits every log–log slope, writes results/summary.json
code/figures.py	all	Reads summary.json, writes figs/*.html and figs/*.csv (set CL_FIG_PNG=1 for PNGs)
code/runall.sh	—	Runs the drivers in order, skipping any whose JSON already exists

The poster in poster/ is a posterly (MIT, © 2026 Ruishuo Chen) landscape 4-column build; poster/BUILD_NOTES.md records the canvas, palette and gate decisions, and poster/poster.pdf is the print-ready file. It clears preflight, style, measure and polish --strict (column spread 0.00 px).

Reproducing

pip install numpy plotly
cd code
OMP_NUM_THREADS=1 CL_NPROC=3 ./runall.sh    # ~2.8 h on one CPU box
python analyze.py && python figures.py

Every driver seeds from an integer and is deterministic. No GPU, no trained weights to download: the network state is a float64 $m\times d$ matrix regenerated from its seed in under a second, so the seed is the checkpoint.

Memory. clcore.out() and clcore.gd_step() multiply in row blocks of CL_ZBLOCK (default 4096) rows so peak RSS stays under ~160 MB per worker even at $m=10^5$. This was not a premature optimization — the unblocked version exhausted 16 GB twice. Lower CL_ZBLOCK if you are tighter on memory; raise it for speed.

What was checked

Six claims, each with an audit and at least one control that breaks a stated hypothesis:

1. Theorem 1's closed-form forgetting bound — term structure and all eight exponents. Supported.
2. The parameter regime $n=\widetilde\Theta(d^2K)$, $m=\widetilde\Omega(d^8K^4)$, $\eta T=\Theta(d^2)$ — two of three conditions load-bearing; the width condition is loose by ~$10^{14}$.
3. Theorem 2's uniform misclassification error — error half yes (0 errors in 32/32 runs); loss half needs the full horizon.
4. Theorem 3's delayed generalization gap — holds, but vacuously everywhere reachable ($10^{826}$ vs $1.7\times10^{-4}$).
5. Theorem 4's improvement for self-bounded losses — supported; $10^{756}$ tighter at the base point.
6. The test-time forgetting decomposition — $n$ controls forgetting, $m$ does not; the dropped term is unresolved.

Full reasoning, figures and caveats are on the corresponding pages of the logbook.

Provenance

The authors release three Jupyter notebooks at hosseinta2/continual-learning-with-neural-nets (audited at commit 5e73290). They contain no reusable module, no config or seed files and no sweep driver, so nothing here is derived from them except the data generator and model definition, which were cross-checked line-by-line against continual_learning_codes-XOR.ipynb.