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arxiv: 2605.11936 · v1 · submitted 2026-05-12 · 💻 cs.AI

Recognition: no theorem link

From Noise to Diversity: Random Embedding Injection in LLM Reasoning

Heejun Kim, Jaewon Sok, Jeongjae Park, Jewon Yeom, Seonghyeon Park, Seungpil Lee, Sundong Kim, Taesup Kim

Pith reviewed 2026-05-13 05:39 UTC · model grok-4.3

classification 💻 cs.AI
keywords random soft promptsLLM reasoningtoken diversitysoft promptingmath reasoningPass@NDAPO trainingembedding injection
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The pith

Appending fresh random embedding vectors to LLM inputs matches the accuracy of trained soft prompts on math reasoning by flattening early token probabilities.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that Random Soft Prompts, created by sampling new sequences of vectors from a Gaussian matched to the model's embedding statistics and appending them without any training, reach accuracy levels comparable to optimized soft prompts across several math reasoning benchmarks. This happens because the attention layers must incorporate an entirely unfamiliar position, which spreads out the probability distribution over the first few output tokens and opens up multiple reasoning branches before the influence fades and the model commits to one path. When paired with temperature sampling, the added early diversity raises the chance that at least one of N sampled responses is correct, an effect the authors also transfer into the DAPO training loop to obtain practical improvements. A reader would care because the result separates the structural benefit of simply adding an extra position from any learned content in the prompt vectors.

Core claim

Random Soft Prompts consist of a freshly sampled sequence of random embedding vectors drawn from an isotropic Gaussian fitted to the mean and variance of the pretrained embedding table; these vectors carry no task-specific information yet produce accuracy on math reasoning tasks that matches optimized soft prompts in multiple settings. The mechanism works in two stages: the unseen random position forces attention to flatten the distribution over the initial generated tokens, causing reasoning trajectories to branch, after which the effect naturally dilutes so the model settles on a single completion. During inference the prompts increase early-stage token diversity and, together with higher-

What carries the argument

Random Soft Prompts (RSPs): a training-free sequence of random embedding vectors freshly sampled from the model's embedding statistics and appended to the input, whose only role is to occupy an unseen position.

If this is right

  • RSPs isolate the structural effect of injection that all soft-prompt variants share regardless of training.
  • Early token diversity rises during generation, which widens Pass@N when temperature sampling is applied.
  • The same injection effect transfers from inference into DAPO training and yields measurable gains there.
  • The influence of the random position dilutes naturally as generation proceeds, allowing the model to converge on a coherent answer.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the benefit is purely structural, then simpler forms of position noise such as random padding tokens or fixed but unseen vectors might produce similar diversity increases without sampling new vectors each time.
  • The two-stage pattern (early branching followed by commitment) suggests the method could be tuned by varying the number of appended vectors to control how long the exploration phase lasts.
  • Extending the approach to non-math domains would test whether the flattening effect generalizes beyond the structured step-by-step nature of mathematical reasoning.

Load-bearing premise

The accuracy and diversity gains are produced by the attention mechanism processing an unfamiliar random position rather than by any accidental statistical resemblance between the random vectors and the actual task.

What would settle it

Run the same benchmarks with random vectors whose entrywise statistics are deliberately altered to remove any possible match to task-related embeddings while still keeping them unseen; if performance remains equal to trained soft prompts the claim holds, but if the gains disappear the structural-injection account is falsified.

Figures

Figures reproduced from arXiv: 2605.11936 by Heejun Kim, Jaewon Sok, Jeongjae Park, Jewon Yeom, Seonghyeon Park, Seungpil Lee, Sundong Kim, Taesup Kim.

Figure 1
Figure 1. Figure 1: Conceptual overview of RSP-induced trajectory diversity. The hidden states shown are [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Per-token attention mass on Qwen2.5-Math-7B ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mean entropy, top-1 probability, and varentropy during the first 5% of generation steps [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Pass@N scaling on (a) MATH-500 and (b) AIME24 with Qwen2.5-Math-1.5B-Instruct, 16 samples per problem. Baseline: temperature sampling only. RSP (single seed): single RSP shared across samples combined with temperature. RSP (indep. seed): a different RSP per sample, with or without temperature. 4.5 Application: DAPO Training with RSP Beyond inference (§4), does the same effect transfer to training? DAPO [Yu… view at source ↗
Figure 5
Figure 5. Figure 5: Five-benchmark average accu￾racy on Qwen2.5-Math-7B. DAPO + RSP reaches a higher peak (step 90) and stays stable through step 100 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mean entropy (top), top-1 probability (middle), and varentropy (bottom) over the full [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Per-token RSP attention mass under suffix injection for the remaining two models (500 MATH-500 samples each). Axes and preprocessing match [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript claims that appending sequences of random embedding vectors—sampled from an isotropic Gaussian fitted once to the entrywise mean and variance of the pretrained embedding table—to LLM inputs, without any training, yields accuracy on math reasoning benchmarks comparable to optimized soft prompts. The mechanism is that attention must absorb a never-seen-before random position, flattening early-token distributions, increasing reasoning-trajectory diversity, and widening Pass@N under temperature sampling; the same injection is carried into DAPO training.

Significance. If the results hold after controls, the work supplies a clean training-free baseline that isolates the structural effect of injection itself, offering a unified lens on soft-prompt variants and a practical route to diversity gains in reasoning. The reported empirical comparability on math benchmarks and the extension to DAPO training are concrete strengths.

major comments (1)
  1. [mechanism validation and experimental results] § on mechanism validation and experimental results: the central claim that gains arise from the structural novelty of an unseen position (rather than residual statistical match) is load-bearing, yet no ablations are reported that keep injection format and length fixed while breaking the first- and second-moment match (e.g., zero vectors, shifted-mean Gaussians, or uniform sampling). Without these, the two-stage flattening-and-dilution account cannot be isolated from distributional compatibility.
minor comments (2)
  1. [Abstract and results] Abstract and results: accuracy comparisons are stated as 'comparable' without error bars, statistical tests, or explicit length-matched random-token baselines, making quantitative assessment of the claim difficult.
  2. [experimental results] No ablation on RSP vector length or sampling-distribution parameters is described, leaving the robustness of the reported gains unclear.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address the single major comment on mechanism validation below and will revise the manuscript to incorporate the requested controls.

read point-by-point responses
  1. Referee: § on mechanism validation and experimental results: the central claim that gains arise from the structural novelty of an unseen position (rather than residual statistical match) is load-bearing, yet no ablations are reported that keep injection format and length fixed while breaking the first- and second-moment match (e.g., zero vectors, shifted-mean Gaussians, or uniform sampling). Without these, the two-stage flattening-and-dilution account cannot be isolated from distributional compatibility.

    Authors: We agree that the suggested ablations are necessary to rigorously separate the structural effect of an unseen position from any residual first- or second-moment compatibility. The current manuscript shows that moment-matched isotropic Gaussian sampling yields performance comparable to trained soft prompts and empirically increases early-token entropy, but does not report the exact controls listed. In the revised manuscript we will add a dedicated ablation subsection that keeps injection length and format identical while using (i) zero vectors, (ii) Gaussians whose mean is shifted by 2–4 standard deviations, and (iii) uniform sampling over the observed embedding range. These results will be placed alongside the existing RSP curves to test whether the flattening-and-dilution mechanism persists when moment matching is deliberately broken. We expect the diversity gains to remain driven primarily by positional novelty, but will report the data transparently regardless of outcome. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results independent of fitted sampling distribution

full rationale

The paper's core claims rest on empirical measurements of RSP performance on math reasoning benchmarks and observed changes in token diversity/Pass@N, rather than any closed-form derivation. The Gaussian parameters are fitted once to the fixed embedding table and then used only to draw fresh vectors at inference time; downstream accuracy and diversity metrics are evaluated on separate tasks and are not algebraically forced by the moment-matching step. No self-citation chain, uniqueness theorem, or ansatz is invoked to justify the central mechanism, and the proposed attention-flattening account is presented as an interpretation of the measurements rather than a reduction to the input distribution by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard transformer attention mechanism plus the assumption that the embedding table statistics are a reasonable isotropic prior; no new entities are postulated.

free parameters (1)
  • embedding mean and variance
    Used to define the isotropic Gaussian from which RSP vectors are sampled; these are taken from the pretrained model rather than fitted to the downstream task.
axioms (1)
  • domain assumption Transformer attention allocates capacity to every input position regardless of content
    Invoked to explain why an unseen random position flattens the next-token distribution.

pith-pipeline@v0.9.0 · 5590 in / 1219 out tokens · 66461 ms · 2026-05-13T05:39:17.961602+00:00 · methodology

discussion (0)

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