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Mitigating Overthinking in Large Reasoning Models via Manifold Steering
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Proposes Manifold Steering, which projects an overthinking steering direction onto a low-dimensional PCA activation subspace to reduce LRM overthinking, cutting output tokens by up to 71% on DeepSeek-R1 distilled models while keeping or improving math accuracy.
Problem
Large reasoning models often overthink, producing excessive validation loops and redundant deliberation that inflate inference cost. Single-direction activation steering to fix this plateaus and collapses at higher strengths due to interference noise from high-dimensional steering directions.
Approach
Extract a difference-in-means overthinking direction, then project it onto the top-k PCA subspace of layer activations (the estimated low-dimensional activation manifold) to remove the orthogonal interference component, enabling stronger steering without collapse.
Key results
- On GSM8K, manifold steering reduces tokens by 41% to 71% across R1 models while keeping Pass@1 within about +0.5 points of Vanilla (e.g., R1-1.5B 77.2 vs 76.7 with 593 vs 2035 tokens).
- On MATH500 with R1-7B, the method achieves 42% token reduction with Pass@1 88.4 vs 88.2 Vanilla, outperforming Dynasor and SEAL in token reduction.
- Cross-domain results show 12% to 27% token reduction on LiveCodeBench and GPQA-Diamond while maintaining accuracy; on AdvBench the cross-task variant reaches 100% JSR vs 74% for the baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| manifold steering (projecting steering direction onto low-dim PCA manifold) vs. raw difference-in-means direction | DeepSeek-R1-Distill-Qwen models · GSM8K, MATH500, AMC2023, AIME2024 | #Tokens and Pass@1: up to 71% token reduction with accuracy maintained or improved | Helped |
| manifold steering vs. Dynasor and SEAL baselines | DeepSeek-R1-Distill-Qwen models · GSM8K, MATH500, AMC2023, AIME2024 | #Tokens reduction: manifold steering reduces more tokens than Dynasor/SEAL in most model-dataset pairs | Helped |
| manifold steering on cross-domain tasks | DeepSeek-R1 distilled models · LiveCodeBench, GPQA-Diamond | #Tokens: 12% to 27% token reduction while maintaining accuracy | Helped |
| manifold steering on AIME2024 for R1-7B | DeepSeek-R1-Distill-Qwen-7B · AIME2024 | Pass@1: +3.3 points | Helped |
| Dynasor early stopping | DeepSeek-R1-Distill-Qwen-7B · MATH500 latency | Time latency (s): 39.89 s vs 1.74 s original | Hurt |
| Manifold steering on Layer-wise (later layers) selection (ablation) | DeepSeek-R1-Distill-Qwen-1.5B and 7B · MATH500 | Pass@1 and #Tokens: Layer 1-10 steering yields accuracy near vanilla with fewer tokens; layers 15-25 sharply reduce accuracy | Mixed |
| Raw steering direction intervention strength increased beyond 1.5 (naive direction, without manifold projection) (ablation) | DeepSeek-R1-Distill-Qwen-7B · MATH500 | #Tokens: token count rebounds beyond alpha=1.5 | Hurt |
| Increasing intervention strength alpha for manifold steering from 0.1 to 0.5 (ablation) | DeepSeek-R1-Distill-Qwen-7B · MATH500 | #Tokens and Pass@1: token reduction up to 77.1% at alpha=0.5, but accuracy declines at high strength; alpha=0.3 chosen | Mixed |
| Manifold steering projection on cross-task refusal ablation | Qwen2.5-7B-Instruct · AdvBench jailbreak | JSR: 100% JSR vs baseline 74% (alpha=2.0) | Helped |
| Model scale increase (R1-1.5B to R1-14B) | DeepSeek-R1-Distill-Qwen family · MATH500 vanilla | #Tokens: vanilla tokens 4762 (1.5B) to 3496 (14B); overthinking diminishes with scale | No clear effect |
Surprising findings
- Plain single-direction steering reaches a plateau and then loses effectiveness at larger intervention strength, with token counts rebounding beyond alpha of about 1.5 and model collapse observed.
- Dynasor's early stopping often omits the final solution, so the authors modified it to require a complete answer, which changes its reported behavior.
Limitations
- Applicability to multimodal LLMs is unexplored.
- Sensitivity to intervention strength; the optimal alpha is chosen per model and dataset by tuning on MATH500.
- Method evaluated only on DeepSeek-R1 distilled models, with limited exploration of specialized domains such as legal or medical reasoning.
Experimental setup
Datasets: OpenMathInstruct-2 MATH500 GSM8K AMC2023 AIME2024 LiveCodeBench GPQA-Diamond AdvBench
Benchmarks: GSM8K MATH500 AMC2023 AIME2024 LiveCodeBench GPQA-Diamond AdvBench
Metrics: Pass@1 #Tokens time latency jailbreak success rate
Baselines: Vanilla Dynasor SEAL
Builds on: difference-in-means steering Dynasor SEAL
Closest papers by meaning
- Do NOT Think That Much for 2+3=? On the Overthinking of Long Reasoning Models (ICML 2025 · similarity 0.90)
- Efficient Reasoning with Balanced Thinking (ICLR 2026 · similarity 0.90)
- Let LRMs Break Free from Overthinking via Self-Braking Tuning (NeurIPS 2025 · similarity 0.90)
- Mitigating Overthinking in Large Reasoning Language Models via Reasoning Path Deviation Monitoring (NeurIPS 2026 · similarity 0.89)
- Decoding the Critique Mechanism in Large Reasoning Models (NeurIPS 2026 · similarity 0.88)
- Efficient Reasoning via Constrained Optimization in Latent Space (NeurIPS 2026 · similarity 0.88)
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