From Noise to Diversity: Random Embedding Injection in LLM Reasoning
Authors: Heejun Kim, Seungpil Lee, Jewon Yeom, Jaewon Sok, Seonghyeon Park, Jeongjae Park, Taesup Kim, Sundong Kim
Organizations: 1Gwangju Institute of Science and Technology · 3Microsoft Research · 2Seoul National University
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.
Reinforcement learning with verifiable rewards, particularly Group Relative Policy Optimization (GRPO), has significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, in complex tasks, GRPO frequently suffers from the ``zero-advantage problem'': when all sampled rollouts for a query fail, the relative advantage collapses to zero. Consequently, the model loses effective training signals for these questions, wasting the training data and computational budget. While simply increasing the sampling budget for these questions is a common remedy, the static sampling policy inherently constrains reasoning exploration, limiting the success rate. In this paper, we propose Lorem Perturbation for Exploration (LoPE), a simple yet effective training framework to break this exploration bottleneck. We posit that task-irrelevant prompt-space perturbations can shift the model's output distribution enough to unlock orthogonal reasoning pathways for hard questions. Specifically, LoPE prepends sequences stochastically assembled from Lorem Ipsum vocabulary (a pseudo-Latin placeholder text) to the prompts before resampling. Experiments across 1.7B, 4B, and 7B models demonstrate that LoPE significantly outperforms resampling with the original prompts. Further analysis reveals that other Latin-based random sequences with low perplexity are also effective perturbations. Our results establish LoPE as a strong baseline for broadening exploration in LLM reinforcement learning.
Existing reinforcement learning methods for LLM reasoning implicitly assume that the policy generating training trajectories should coincide with the one producing inference responses. We argue that this is a misleading inductive bias: the optimization-optimal trajectory distribution favors informative gradients, whereas the inference-optimal response distribution emphasizes accuracy and consistency. Forcing both into a single policy entangles their gradients and suppresses exploration. We propose R2PO (Residual Rollout Policy Optimization), which attaches a lightweight Residual Rollout-Head atop the policy to decouple training trajectories from inference responses, diversifying rollouts during training while keeping inference generation intact. Experiments show that R2PO consistently outperforms baselines, with average accuracy gains of 3.4% on MATH-500 and 1.3% on APPS, alongside more diverse rollouts and reduced length bias. Our code is available at https://github.com/RRPO-ARR/Code.
Reinforcement learning (RL) has become the dominant paradigm for improving the reasoning capabilities of large language models, but it requires expensive training, curated data, and reward signals. Recent work shows that sampling from sharpened base-model distributions at test time recovers much of the RL gain, yet existing methods rely solely on output-layer likelihoods and ignore the transformer's internal forward-pass dynamics. We introduce Depth-Entropy Guided Sampling (DEGS), a training-free, test-time method that exploits layer-wise entropy collapse as an intrinsic quality signal. We observe that stronger reasoners -- including RL-posttrained variants -- exhibit a distinctive "late collapse": logit-lens decoded entropy stays elevated until deeper layers before converging. We define a per-sequence collapse depth D(x) and a joint objective π(x)∝p(x)αexp(βD(x)) that combines sequence likelihood with this depth-entropy structure, instantiated inside an MCMC power-sampling framework (DEGS-MCMC). Across three open-weight models and four reasoning benchmarks, this near-chance per-candidate signal compounds over the sampling trajectory into state-of-the-art training-free accuracy, with gains largest out of domain and on the harder splits -- exactly where likelihood alone falls short -- at single-digit-percent wall-clock overhead. DEGS narrowly trails an in-house GRPO reference on the math splits GRPO was trained for, yet surpasses it out of domain on GPQA for all three models, without any training, reward model, or labeled data.