From Noise to Diversity: Random Embedding Injection in LLM Reasoning

TL;DR

This paper introduces Random Soft Prompts (RSPs), which are untrained, randomly generated embeddings that improve reasoning accuracy and diversity in large language models, both during inference and training.

Contribution

RSPs provide a training-free, simple method to enhance reasoning and diversity in LLMs, isolating the structural effect of prompt injection without learned content.

Findings

RSPs achieve comparable accuracy to trained prompts on math reasoning benchmarks.

RSPs increase early-stage token diversity and widen Pass@N during inference.

Applying RSPs during training yields practical performance gains.

Abstract

Recent soft prompt research has tried to improve reasoning by inserting trained vectors into LLM inputs, yet whether the gain comes from the learned content or from the act of injection itself has not been carefully separated. We study Random Soft Prompts (RSPs), which drop the training step entirely and append a freshly drawn sequence of random embedding vectors to the input. Each RSP vector is sampled from an isotropic Gaussian fitted to the entrywise mean and variance of the pretrained embedding table; the sequence carries no learned content, and yet reaches accuracy comparable to optimized soft prompts on math reasoning benchmarks in several settings. The mechanism unfolds in two stages: because attention has to absorb a never-seen-before random position, the distribution over the first few generated tokens flattens and reasoning trajectories branch, and as generation continues this influence dilutes naturally so the response commits to a single completion. We show that during inference RSPs lift early-stage token diversity and, combined with temperature sampling, widen Pass@N, the probability that at least one out of N attempts is correct. Beyond inference, we carry the same effect into DAPO training and demonstrate practical gains. Our contributions are: (i) RSP isolates the simplest form of soft prompt -- training-free, freshly resampled -- providing a unified lens for the structural effect of injection that variants otherwise differing in training and form all share; (ii) a theoretical and empirical validation of the underlying mechanism; and (iii) an extension from inference to training.