Only Project Once: Projection-Adaptive Loss for Exact Constraint Satisfaction

Tim Aebersold, Soheyl Massoudi, Mark Fuge

ETH Zürich

Methods that repair neural predictions to satisfy hard constraints usually unroll many repair steps per training iteration and softly penalize whatever violation is left. PAL (Projection-Adaptive Loss) shows that a single detached projection step suffices in training. The constraint residual after that one step drives adaptive penalty weights $\bar w_c$ on the raw prediction, so the network itself learns to be feasible and the repair only cleans up.

This repository contains the method (pal/method, pal/projection), the baselines (pal/baselines), the synthetic and engineering benchmarks (pal/benchmarks), the experiment runner (pal/runner) and the scripts and results behind the paper tables.

Install

python -m venv .venv && source .venv/bin/activate
pip install -e .
python scripts/download_artifacts.py --benchmark e2   # WinDiNet weights, only for e2

With uv, uv sync --extra bo installs the locked versions from uv.lock into .venv/ instead.

On first use e2 also downloads the Lightricks/LTX-Video base weights from Hugging Face, which the WinDiNet surrogate fine-tunes. The Bayesian optimisation tuning in scripts/bo/ needs the optional bo extra (pip install -e '.[bo]', exact pins in scripts/bo/requirements-bo.txt). IPOPT is optional and installed separately (conda install -c conda-forge cyipopt, see pal/baselines/ipopt/README.md). PAL_DATA_DIR (default ~/.pal_data) sets where downloaded artifacts are cached.

Benchmarks

Paper	Code id
S1-S6	s1_sphere_track, s2_active_set_switch, s3_illcond_tube, s4_qv_coupling, s5_overdetermined, s6_redundant_ineq	synthetic, CPU
curvature sweep	curvature_warp_k0 ... curvature_warp_k13	synthetic, CPU
E1	e1/bwb	aircraft design, GPU
E2	e2/urban_wind	urban layout with a diffusion wind surrogate, GPU
E3	e3/acopf_ieee57	AC optimal power flow
E4	e4/chip_layout	macro placement, CPU

rosenbrock_eq, two_basins and equality_dominated (small test fixtures), curvature_hinge_k* and curvature_sine_k* (control families of the curvature sweep) and e3/acopf_ieee30, e3/acopf_ieee118 are additional benchmarks that are not used in the paper.

Running

# one synthetic benchmark, PAL and two baselines, three seeds
pal run --method pal_loggap,alm,fsnet --benchmarks s1_sphere_track --seeds 0,1,2 --device cpu

# one engineering benchmark
pal run --method pal_loggap --benchmarks e1/bwb --seeds 0 --device cuda

Methods: pal_loggap (PAL), pal_sqp and pal_ip (PAL with SQP or interior-point repair steps), alm, alm_bolton, dc3, enforce_orig, enforce_v4, fsnet, snarenet, slsqp, ipopt. Hand-set defaults for ALM, ALM+Bolt-On, DC3 and FSNet are read from pal/baselines/hparams/, and the other methods define theirs in their config classes. The paper's tuned configurations are the BO winners listed below. Each run writes config.json, final.json (objective, maximum violation and feasibility before and after projection), metrics.jsonl and model.pt to runs/<timestamp>_<method>_<bench>_seed<N>_<id>/. pal eval --run-id <prefix> re-runs inference on a saved model. See quickstart.md for a minimal check of an installation.

Reproducing the paper

results/README.md lists every results directory, the paper table it feeds and the command that produces it. The main entry points are:

• scripts/bo/ Bayesian optimisation of each method's hyperparameters on S1-S6. The selected configurations are in results/2026-07-26_bo_tuned_table/winners/ (ENFORCE v4: results/2026-09-11_enforce_v4_no_warmup/winners/).
• scripts/run_ablation.py --ablation pal/configs/ablations/s1_s6.yaml for the PAL ablation.
• scripts/bp_campaign/driver.py for the curvature sweep on curvature_warp.
• scripts/fp64_repair_sweep.py for the repair-precision table.
• slurm/engineering/*.sbatch for the engineering runs, and scripts/aggregate.py, scripts/aggregate_engineering.py and scripts/render_engineering.py to turn run directories into tables.

The Slurm files assume a GPU cluster with a container runtime (docker/, edf/) and need the account and paths adapted.

Tests

python -m pytest tests -q

Citation

@article{aebersold2026onlyprojectonce,
  title   = {Only Project Once: Projection-Adaptive Loss for Exact Constraint Satisfaction},
  author  = {Aebersold, Tim and Massoudi, Soheyl and Fuge, Mark D.},
  journal = {arXiv preprint arXiv:2610.04572},
  year    = {2026}
}