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IOP: An Idempotent-Like Optimization Method on the Pareto Front of Hypernetwork
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Proposes IOP, a Pareto hypernetwork method that drops human-crafted preference inputs, uses an idempotent-like loss on sample/weight manifolds and a hypervolume-based MOO loss, optimized with a dual gradient strategy.
Problem
Pareto Hypernetwork (PHN) methods rely on human-crafted preference vectors or chunk embeddings rather than data samples, making them sensitive to distribution shift and optimizing only one solution per round, so the learned Pareto front is poor.
Approach
Train the hypernetwork with an idempotent-like objective (H(H(x))≈H(x) plus self-mapping and a manifold contraction term controlled by λide) so it takes raw samples as inputs, while simultaneously maximizing the hypervolume of all generated solutions, combined via a gradient-based dual optimization strategy.
Key results
- IOP outperforms MOO and PHN baselines by an average of 5.3% and 4.0% in accuracy on multi-task datasets, and 5.2% and 3.9% in hypervolume.
- On domain adaptation datasets, IOP (λide=0.75) reaches 86.25% on PACS and 85.46% on Office-Home cross-domain average accuracy, versus 80.12% and 80.43% for PHN-HVI.
- Applied to VLLMv2, IOP improves VQAv2 from 81.2 to 82.5 and VCR Q-AR from 79.1 to 82.1.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use IOP instead of PHN-HVI | Pareto front learning · Multi-MNIST | Acc: 92.81 ± 0.54 -> 95.34 ± 0.81 | Helped |
| use IOP instead of PHN-HVI | Pareto front learning · Multi-Fashion | HV: 2.71 ± 0.09 -> 2.78 ± 0.08 | Helped |
| use IOP (λide=0.75) instead of PHN-EPO | domain adaptation · PACS | CDAA: 80.22 ± 0.13 -> 86.25 ± 0.85 | Helped |
| use IOP (λide=0.75) instead of PHN-EPO | domain adaptation · DomainNet | CDAA: 60.09 ± 0.31 -> 62.07 ± 1.32 | Helped |
| use IOP (λide=0.75) instead of PHN-EPO | domain adaptation · Office-Home | CDAA: 81.56 ± 1.03 -> 85.46 ± 0.36 | Helped |
| apply IOP to VLLMv2 | VLLMv2 · VQAv2 | score: 81.2 -> 82.5 | Helped |
| add Hypervolume and idempotent-like loss to cosine loss (ablation) | IOP · Multi-MNIST | Acc: 83.12 ± 0.4 -> 95.19 ± 1.5 | Helped |
| add cosine and idempotent-like loss to Hypervolume loss (ablation) | IOP · Multi-MNIST | Acc: 85.35 ± 0.2 -> 95.19 ± 1.5 | Helped |
| add idempotent-like loss to cosine and Hypervolume loss (ablation) | IOP · Multi-MNIST | Acc: 95.17 ± 0.2 -> 95.19 ± 1.5 | No clear effect |
| add cosine and Hypervolume loss to idempotent-like loss (ablation) | IOP · PACS | accuracy: 83.41 ± 1.6 -> 86.18 ± 1.2 | Helped |
| add idempotent-like loss to cosine and Hypervolume loss (ablation) | IOP · PACS | accuracy: 79.78 ± 1.6 -> 86.18 ± 1.2 | Helped |
| vary λide from 0.35 to 0.75 (ablation) | IOP · PACS | CDAA: 83.23 ± 1.31 -> 86.25 ± 0.85 | Helped |
Surprising findings
- Adopting the idempotent-like loss alone is ineffective; it only helps when combined with the cosine and hypervolume terms.
- Too small or too large contraction coefficient λide (0.35 or 0.95) weakens the adaptability gain, with peak near 0.75.
Limitations
- Training cost grows with the number of objectives or hypernetwork input/output dimension.
- Reported gains rely on a reference point chosen empirically (2,2) and on a hyperparameter λide that must be tuned.
Experimental setup
Datasets: Multi-MNIST Multi-Fashion Fashion-MNIST PACS DomainNet Office-Home 2OP 3OP Bi-CVRP Bi-KP Tri-TSP Tri-CVRP
Benchmarks: Multi-MNIST Multi-Fashion Fashion-MNIST PACS DomainNet Office-Home 2OP 3OP Bi-CVRP Bi-KP Tri-TSP Tri-CVRP
Metrics: accuracy hypervolume training cost (GFlops) cross-domain average accuracy number of optimal solutions
Baselines: MGD UW LS PMTL COSMOS DWA NashMTL EPO FAMO PNG CPMTL PHN-LS
Builds on: Pareto Hypernetwork PNG PHN-HVI Shocher et al. idempotent manifold mapping EPO
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