Research map / Large language models / Reasoning and chain of thought

From Noise to Diversity: Random Embedding Injection in LLM Reasoning

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

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Shows that training-free random soft prompts (isotropic Gaussian embeddings appended to input) match optimized soft prompts on math reasoning, explains the effect via attention-mass branching and KV-cache decay, and shows gains in Pass@N and DAPO training.

Problem

Soft prompt methods improve LLM reasoning by inserting trained vectors, but it is unclear whether gains come from the learned content or from the act of injection itself.

Approach

Replace learned soft prompts with Random Soft Prompts: fresh isotropic Gaussian embedding vectors (fitted to the embedding table's mean and variance) appended per rollout with no training; argues early attention to random tokens branches reasoning trajectories, which later stabilize as the KV cache grows, and that independent resampling yields Pass@N gains.

Key results

• On Qwen2.5-Math-1.5B-Instruct, RSP reaches 20.00% on AIME24 vs 10.00% baseline and comparable MATH-500 accuracy (75.20 vs 73.00).
• On ChatML-mismatched Qwen2.5-Math-1.5B base, prefix RSP lifts MATH-500 from 34.40% to 63.40% (+29.0 pp).
• DAPO+RSP reaches 54.36% five-benchmark average at step 90 vs 53.20% for DAPO on Qwen2.5-Math-7B.

Surprising findings

• Random embeddings recover up to +29 pp on format-mismatched base models instead of degrading accuracy.
• Single shared RSP across samples gives no Pass@N gain over baseline; only independent per-sample RSPs help.

Limitations

• Gains are mixed on well-aligned instruct models, staying within a few points of baseline.
• Results use single runs or limited seeds; the authors note multi-seed evaluation is needed for tighter claims.
• Mechanism theory covers only sequence-axis attenuation; layer-axis behavior is empirical.

Experimental setup

Datasets: MATH-500 MATH Level 3-5 subset GSM8K AIME24 College Math Minerva Math

Benchmarks: MATH-500 GSM8K AIME24 College Math Minerva Math

Metrics: accuracy Pass@N Avg@32 entropy top-1 probability varentropy Spearman rho JS divergence semantic cosine distance

Baselines: TTSV SoftCoT LTPO Temperature sampling baseline

Builds on: DAPO GRPO SimpleRL-Zoo NEFTune NoisyNet

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