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Conditional Optimal Bridge for Riemannian Activation Steering

NeurIPS 2026 · Learning theory and algorithms › Optimal transport · approach: Neural optimal transport · 0 citations (OpenAlex)

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Casts LLM activation steering as a Schrödinger Bridge on the residual-stream hypersphere, derives a query-adaptive log-density-ratio steering field (COBRAS), and reports gains on helpfulness, truthfulness, and detoxification with better OOD preservation on MMLU and GSM8K.

Problem

Existing activation steering methods implicitly optimize a log-density-ratio objective heuristically and use query-independent directions that degrade performance on out-of-distribution inputs.

Approach

Frame steering as a Schrödinger Bridge between negative and positive activation distributions on a hypersphere, solve it via entropic OT with Sinkhorn potentials, and integrate the probability flow ODE with potentials evaluated at the current query via spherical KDE, plus vMF-strength and abstain gates for query-adaptive, OOD-safe steering.

Key results

• COBRAS achieves the highest UltraFeedback win rate on all four models, e.g., 59.7% on LLaMA3.1-8B versus 56.3% for the next best (ODESteer).
• On TruthfulQA True×Info, COBRAS reaches 85.2% on Mistral-7B (vs. 65.2% for ODESteer) and 68.1% on LLaMA3.1-8B.
• COBRAS reduces toxicity by 46%–53% relative to the original models across the four models.

Surprising findings

• Increasing the abstention percentile to 99.5 sharply lowers LLaMA3.1-8B GSM8K accuracy to 11.59%, showing a trade-off between in-distribution steering and OOD preservation.
• Several baselines such as SphericalSteer raise TruthfulQA substantially but severely increase perplexity (e.g., 68.5 on Qwen2.5-7B).

Limitations

• O(N+·N−) cost of pairwise geodesic distances and Sinkhorn may be prohibitive for large contrastive sets.
• Reliance on fixed spherical geometry may not hold for all architectures or layers.
• Steering results are reported on a single layer with hyperparameters chosen on the evaluated models; the abstention trade-off requires tuning.

Experimental setup

Datasets: TruthfulQA UltraFeedback RealToxicityPrompts Jigsaw Unintended Bias in Toxicity Classification MMLU GSM8K

Benchmarks: TruthfulQA UltraFeedback RealToxicityPrompts MMLU GSM8K

Metrics: Truthfulness x Informativeness win rate reward model mean and P90 toxicity score (Perspective API) perplexity Dist-2 accuracy

Baselines: RepE ITI CAA MiMiC Linear-AcT ODESteer SphericalSteer

Builds on: Contrastive Activation Addition ODESteer Spherical Steering Linear Activation Transport Sinkhorn algorithm

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