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Exploring Diverse Generation Paths via Inference-time Stiefel Activation Steering

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Proposes STARS, a training-free inference-time method that steers hidden activations of concurrent generation runs with orthogonal additive vectors optimized on the Stiefel manifold (volume maximization), with a closed-form one-step update for per-token latency.

Problem

Language model generations collapse onto homogeneous high-probability outputs, so multiple concurrent sampled runs (e.g., for best-of-N or test generation) lack diversity; sampling-based fixes do not guarantee diversity across runs.

Approach

At each token, jointly compute orthogonal, fixed-norm additive steering vectors for all N concurrent runs by maximizing the log-determinant (volume) of the steered activation matrix on the scaled Stiefel manifold; a closed-form SVD-based one-step update with greedy stepsize replaces iterative Riemannian gradient descent for real-time use.

Key results

• On TESTEVAL with Qwen3-1.7B at T=1.0, STARS_0.5 raises overall line coverage from 59.95% (sampling) to 91.05%, and branch coverage from 55.05% to 86.81%.
• On LiveIdeaBench with Qwen2.5-3B-Instruct at T=0.2, STARS_0.5 improves fluency from 2.68 (sampling) to 5.09 and average score from 5.01 to 5.59.
• Reported one-step update reaches about 2% optimality gap using about 3% of the runtime of full Riemannian gradient descent (appendix claim).

Surprising findings

• Standard temperature sampling on Gemma-1.1-2b-it gives near-zero execution and assertion correctness scores that STARS improves only marginally, while on Qwen3-1.7B STARS raises correctness substantially at all temperatures.
• Per-question runtime overhead is small on most settings but reaches about 2 seconds (Qwen2.5-3B: 3.02s to 5.01s), which the authors call negligible.

Limitations

• No theoretical convergence guarantee for the one-step heuristic update; only empirical optimality gap evidence.
• Evaluated only on two benchmarks (test case generation and idea generation) with small models (1.7B-3B).
• Steering hyperparameter alpha and layer choice require tuning on a subset of data.

Experimental setup

Datasets: TESTEVAL LiveIdeaBench

Benchmarks: TESTEVAL LiveIdeaBench

Metrics: syntax correctness execution correctness assertion correctness line coverage branch coverage cov@k originality feasibility clarity fluency

Baselines: temperature sampling

Builds on: activation steering polar retraction temperature sampling

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