Diversity in Multi-Objective GFlowNets

A systematic study investigating what drives diversity in Multi-Objective Generative Flow Networks (MOGFNs), featuring novel GFlowNet-specific diversity metrics and comprehensive factorial experiments across four benchmark tasks.

Based on: "Multi-Objective GFlowNets" by Jain et al. (ICML 2023) - https://proceedings.mlr.press/v202/jain23a.html

---

Overview

This project explores how architectural choices, sampling strategies, and loss functions affect diversity in multi-objective optimization using GFlowNets. Through 405 factorial experiments and rigorous validation, we identify task-specific optimal configurations and demonstrate that diversity is highly dependent on hyperparameter tuning.

Key Findings

• Temperature is task-specific: HyperGrid requires τ=5.0, Molecules requires τ=1.0, N-grams requires τ=2.0
• Smaller models often perform better: 64×2 architectures prevent mode collapse on molecular/discrete tasks
• Trajectory Balance consistently outperforms alternatives for quality-diversity balance
• Novel QDS metric discovered a bug: Hypervolume calculation inflated scores ~4× for 3D objectives (fixed)

---

Environments

Four benchmark tasks with varying characteristics:

Environment	State Space	Objectives	Key Challenge
HyperGrid	32×32 grid	2 (corners)	Spatial exploration, mode collapse
Molecules	Fragment assembly	3 (QED, SA, logP)	Chemical validity, precision
N-grams	8-char sequences	16 (bigrams)	Discrete combinatorics
Sequences	20-base RNA	3 (energy, pairs, length)	High variance, complex structure

---

Metrics

Implemented 4 categories of diversity metrics (10 total):

1. Traditional (from MOEA/D, NSGA-II)

• Hypervolume, R2 Indicator, Spacing, Spread

2. GFlowNet-Specific

• Trajectory Diversity Score (TDS): Path uniqueness in state space
• Mode Coverage Entropy (MCE): DBSCAN-based spatial diversity
• Quality-Diversity Score (QDS): Composite metric (fixed bug: now uses correct HV)

3. Preference-Aware

• Pareto Front Smoothness (PFS): Preference alignment quality
• Preference-Aligned Spread (PAS): Diversity along preference directions

---

Experiments

Factorial Studies (405 total experiments)

Three 2-way factorial designs per task (135 experiments × 3 tasks):

1. Capacity × Sampling: Model size (small/medium/large) × Temperature (low/high/very high)
2. Capacity × Loss: Model size × Loss function (TB/SubTB/SubTB+entropy)
3. Sampling × Loss: Temperature × Loss function

All experiments: 5 random seeds, full metrics suite

Validation

Best configurations identified by average QDS across seeds (not cherry-picked):

Task	Config	Architecture	Temperature	QDS	MCE	Status
N-grams	small_tb	64×2	τ=2.0	0.576±0.005	0.606	✅ Validated (+2.3% vs factorial)
Molecules	small_low_tb	64×2	τ=1.0	0.165±0.001*	0.294	✅ Validated (matched factorial)
Sequences	medium_veryhigh_tb	64×3	τ=5.0	0.219±0.014*	0.439	✅ Validated (-5% vs factorial)
HyperGrid	medium_veryhigh_tb	64×3	τ=5.0	0.567±0.066	0.274	⚠️ Mode collapse (1/5 seeds)

*QDS values corrected after fixing hypervolume bug

---

Project Structure

diversity-mogfn/
├── src/
│   ├── environments/        # HyperGrid, Molecules, Sequences, N-grams
│   ├── models/              # MOGFN-PC, conditioning mechanisms
│   ├── metrics/             # 7 categories of diversity metrics
│   └── utils/               # Tensor/NumPy conversion utilities
├── configs/
│   ├── factorials/          # Factorial experiment configs
│   └── ablations/           # Legacy ablation configs
├── scripts/
│   ├── factorials/          # Per-task factorial experiment runners
│   ├── ablations/           # Analysis and plotting scripts
│   └── baselines/           # Baseline comparisons
└── results/
    ├── factorials/          # 405 factorial experiments
    └── validation/          # Best config validation runs

---

Quick Start

Setup

# Clone repository
git clone https://github.com/yourusername/diversity-mogfn.git
cd diversity-mogfn

# Create virtual environment
python3 -m venv .venv
source .venv/bin/activate

# Install dependencies
pip install -r requirements.txt

Run Validation Experiments

# N-grams (best performing)
python scripts/factorials/ngrams/run_factorial_experiment_ngrams.py \
    --config configs/factorials/ngrams_best_config.yaml \
    --output_dir results/validation/ngrams_best

# Molecules (with corrected QDS calculation)
python scripts/factorials/molecules/run_factorial_molecules.py \
    --config configs/factorials/molecules_best_config.yaml \
    --output_dir results/validation/molecules_best

# Sequences (corrected config: medium_veryhigh_tb)
python scripts/factorials/sequences/run_factorial_sequences.py \
    --config configs/factorials/sequences_best_config.yaml \
    --output_dir results/validation/sequences_best

# HyperGrid (note: mode collapse issue)
python scripts/factorials/hypergrid/run_factorial_hypergrid.py \
    --config configs/factorials/hypergrid_best_config.yaml \
    --output_dir results/validation/hypergrid_best

Run Factorial Studies

# Example: Molecules capacity × sampling factorial
python scripts/factorials/molecules/run_factorial_molecules.py \
    --config configs/factorials/molecules_capacity_sampling_2way.yaml \
    --output_dir results/factorials/molecules_capacity_sampling

---

Key Implementation Details

Fixed QDS Bug (2025-12-12)

Issue: QDS calculation used incorrect hypervolume implementation for 3D objectives, inflating scores ~4×

Fix: Updated src/metrics/composite.py to use proper hypervolume from traditional.py

Impact: Molecules validation QDS changed from 0.455 (buggy) to 0.165 (correct), now matching factorial baseline

Temperature Tuning is Critical

Different tasks require different exploration levels:

• Molecules (τ=1.0): Chemical validity requires precision
• N-grams (τ=2.0): Balanced discrete exploration
• HyperGrid/Sequences (τ=5.0): Broad exploration needed

Lesson: Temperature cannot be a fixed hyperparameter across tasks!

Mode Collapse in HyperGrid

Spatial exploration tasks show high seed sensitivity:

• small_veryhigh_tb: 3/5 seeds collapsed to <5 modes
• medium_veryhigh_tb: 1/5 seeds collapsed
• Open problem: Requires further investigation

---

Results Summary

Validation Success Rate: 3/4 Tasks

✅ N-grams: Improved over factorial (+2.3% QDS, +9.4% MCE) ✅ Molecules: Matched factorial (after QDS fix), +38% MCE, 4× more modes ✅ Sequences: Nearly matched factorial (-5% MCE, -8% HV) with excellent stability ⚠️ HyperGrid: Mode collapse persists, needs investigation

Cross-Seed Stability

Validated configurations show excellent generalization:

• N-grams: CV < 3% across all metrics
• Molecules: CV < 8% across all metrics
• Sequences: MCE CV = 1.3% (exceptionally stable)

---

Citation

If you use this code or findings, please cite:

@misc{diversity-mogfn-2025,
  author = {Demers, Katherine},
  title = {Diversity in Multi-Objective GFlowNets: A Systematic Study},
  year = {2025},
  publisher = {GitHub},
  url = {https://github.com/yourusername/diversity-mogfn}
}

Original MOGFN paper:

@inproceedings{jain2023multi,
  title={Multi-Objective GFlowNets},
  author={Jain, Moksh and Raparthy, Sharath Chandra and Hernandez-Garcia, Alex and others},
  booktitle={ICML},
  year={2023}
}

---

License

MIT License - See LICENSE file for details

---

Contact

For questions or issues, please open a GitHub issue or contact katherine.demers@umontreal.ca.

Last Updated: December 12th 2025