Research map / Learning theory and algorithms / Fairness
On Optimal Steering to Achieve Exact Fairness
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Defines "ideal" data distributions where the Bayes-optimal cost-sensitive classifier is exactly fair, and finds the nearest such distribution in KL divergence for Gaussian/log-normal families, with applications to steering LLM representations for fair occupation prediction and joy steering.
Problem
Fair machine learning suffers from bias in data; existing pre-processing methods (e.g., reweighing) lack provable exact fairness guarantees for Bayes-optimal downstream classifiers, and finding the nearest fair data distribution is intractable in general.
Approach
Defines an "ideal" distribution as one whose Bayes-optimal classifier for any cost-sensitive risk is exactly fair; for parametric (Gaussian, log-normal) families this reduces to parametric conditions, enabling a KL-minimization program to find the nearest ideal distribution, which is then used to steer LLM representations.
Key results
- On Bias in Bios with Llama-2 7b embeddings, EF Affirmative reduces per-profession TPR-gaps across classes while keeping accuracy in the 0.77-0.79 range, comparable to MiMiC and LEACE.
- In the univariate Gaussian case study, EF-All Subgroups achieves perfect demographic parity and equal opportunity and the Bayes error of the original distribution while staying close to the original distribution in KL.
- For joy steering of horror reviews on Llama-3 8B, moderate nudging parameter alpha improves joyfulness, while excessive nudging reduces steering effectiveness.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply EF Affirmative affine steering toward ideal target moments | Llama-2 7B representations · Bias in Bios | TPR-gap | Helped |
| Apply EF Affirmative affine steering toward ideal target moments | Llama-2 7B representations · Bias in Bios | accuracy: 0.77-0.79 | No clear effect |
| Use EF Affirmative rather than MiMiC or LEACE | Llama-2 7B representations · Bias in Bios | TPR-gap | Mixed |
| Nudge the horror group's joyful steering vectors with EF Affirmative | GCS steering · Movie reviews: horror | Δ-Joyful | Helped |
| Use excessive EF nudging (ablation) | GCS steering · Movie reviews: horror | Δ-Joyful | Hurt |
| Change all subgroups using EF-All Subgroups instead of leaving the original distribution unchanged | Gaussian distribution case study · High ΔDP setting | Bayes Error | Helped |
| Use EF Affirmative to transform the under-privileged subgroups | Gaussian distribution case study · High ΔDP setting | Bayes Error | Helped |
| Match group means | Gaussian distribution case study · High ΔDP setting | KL/JS-divergence | Hurt |
| Set nudging parameter α to 0, retaining the original steering vectors (ablation) | GCS steering · Movie reviews: horror | Δ-Joyful: α = 0 | No clear effect |
Surprising findings
- The optimal ideal distribution can improve both accuracy and fairness simultaneously, not just trade them off.
- Excessive nudging of steering vectors distorts them and reduces steering effectiveness.
Limitations
- Theoretical results rely on parametric (Gaussian/log-normal) assumptions that may not fit real data.
- Non-convex all-subgroup intervention requires line search over a grid.
- Bayes-optimal ideality is sufficient but not always necessary for the 0-1 loss case.
Experimental setup
Datasets: Bias in Bios synthetic Gaussian distributions
Benchmarks: Bias in Bios
Metrics: TPR-gap demographic parity equal opportunity KL divergence Jensen-Shannon divergence Bayes error accuracy Delta-Joyful
Baselines: MiMiC LEACE reweighing Mean Matching
Builds on: MiMiC LEACE Gaussian Concept Steer
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