arxiv: 2605.04638 · v1 · submitted 2026-05-06 · 💻 cs.CL · cs.AI

Recognition: unknown

Gradients with Respect to Semantics Preserving Embeddings Tell the Uncertainty of Large Language Models

Mingda Li, Rundong Lv, Ting Liu, Weinan Zhang, Xinyu Li

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:19 UTC · model grok-4.3

classification 💻 cs.CL cs.AI

keywords uncertainty quantificationlarge language modelsgradient-based methodssemantic embeddingsfree-form generationhallucination detectionsampling-free UQ

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The pith

Gradients with respect to semantics-preserving embeddings quantify uncertainty in LLM free-form generation.

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

The paper develops SemGrad, a sampling-free method to estimate uncertainty in large language models' free-form outputs by examining gradients in semantic space. It rests on the observation that confident models produce consistent responses even when inputs are slightly rephrased while keeping meaning the same. A Semantic Preservation Score helps select the embeddings best suited for these gradient calculations. This is important for practical use because it avoids the high cost and variability of sampling-based uncertainty methods, and works well when multiple answers are possible.

Core claim

The central claim is that uncertainty quantification for free-form generation in LLMs can be achieved through gradients computed with respect to semantics-preserving embeddings, as identified by the Semantic Preservation Score. This approach interprets output stability under semantic perturbations as a measure of model confidence, contrasting with parameter-space gradients used in classification. The method SemGrad implements this idea efficiently without sampling, and when combined with parameter gradients in HybridGrad, it outperforms state-of-the-art sampling methods especially in scenarios with multiple valid responses.

What carries the argument

The Semantic Preservation Score (SPS) that selects embeddings for computing semantic-space gradients to assess output distribution stability.

Load-bearing premise

Confident large language models exhibit stable output distributions under semantically equivalent input perturbations, and the Semantic Preservation Score reliably identifies the embeddings that capture this stability for gradient computation.

What would settle it

A direct test would involve generating multiple semantically equivalent inputs for both high-confidence and low-confidence LLM responses and verifying whether the computed semantic gradients are consistently lower for the high-confidence cases.

Figures

Figures reproduced from arXiv: 2605.04638 by Mingda Li, Rundong Lv, Ting Liu, Weinan Zhang, Xinyu Li.

**Figure 1.** Figure 1: Illustration of output distribution shift under small input semantic perturbations and the semantic gradients. x represents the original input, and x + ∆x denotes a perturbed input with a small semantic change on x in the semantic space. y ∗ denotes the response generated from p(y|x). For an input that the model is certain about, a small semantic perturbation should not significantly alter the output distr… view at source ↗

**Figure 2.** Figure 2: Semantic Preservation Score (SPS) of hidden states across different layers and tokens. We experiment on the last 10 input tokens, where “last #t token” denotes the last t-th token from the end of the user query (corresponding token is different for different queries). We observe that the token position carrying the most semantic information is consistent for the same model across different datasets. 3.3. S… view at source ↗

**Figure 3.** Figure 3: Comparison of SemGrad UQ performance (AUROC) and semantic preservation capability (SPS) of different hidden states across layers and tokens. Experiments are conducted on the last 5 input tokens of Llama3.1-Instruct8B and Qwen3-Instruct4B. A strong correlation is observed: hidden states with higher semantic preservation capability yield better SemGrad performance view at source ↗

**Figure 4.** Figure 4: Semantic Preservation Score (SPS) of hidden states across different layers and tokens. We experiment on the last 10 input tokens, where “last #t token” denotes the last t-th token from the end of the user query (corresponding token is different for different queries). We observe that the token position carrying the most semantic information is consistent for the same model across different datasets. M.I. (… view at source ↗

**Figure 5.** Figure 5: Upper: The upper panels show the histogram of the average per-token entropy ω¯ of responses generated by Llama3.1-Instruct8B on TruthfulQA, SciQ, and TriviaQA (left to right). The darker blue histogram corresponds to ω¯ for correct generations, while the lighter blue histogram corresponds to ω¯ for all generations. The two vertical dashed lines indicate the 50th and 75th percentiles of the ω¯ distribution … view at source ↗

read the original abstract

Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.

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.

Desk Editor's Note private letter to a colleague

The paper gives a sampling-free gradient method for LLM uncertainty by moving to semantic embeddings via a new SPS score, but the superiority claims over sampling baselines rest on thin experimental description.

read the letter

The key point is that this work tries to do uncertainty quantification for free-form LLM generation using gradients computed in semantic space instead of by sampling outputs or looking at parameter gradients. They introduce SemGrad, which picks embeddings via a Semantic Preservation Score that measures how stable the output stays under meaning-preserving changes, then takes gradients with respect to those. HybridGrad just adds the usual parameter-space gradients on top. That is the actual novelty: prior gradient UQ was classification-only, and sampling methods pay a high cost for multiple generations. The intuition is straightforward and practical for settings where you cannot afford repeated sampling. If the SPS reliably flags semantically stable directions, the method could give cheap uncertainty signals, especially when several answers are valid. The abstract positions the results as better than SOTA, particularly in multi-answer cases. That would be useful if it holds. The soft spots are in the evidence. The abstract gives no numbers, no dataset list, no error bars, and no clear description of how they constructed or validated the SPS itself. Without those, it is hard to know whether the claimed gains come from the semantic gradient idea or from other choices in the setup. The stability assumption could also be fragile if the SPS correlates poorly with actual semantic equivalence on harder prompts. No code or data release is mentioned, which makes independent checks harder. This is for researchers who need low-cost UQ for open-ended generation and are willing to test new proxies. A reader focused on efficient trustworthiness methods would find the direction worth following even if the current results are preliminary. It deserves a serious referee because the core idea is distinct from existing lines and the claims are falsifiable with standard benchmarks, though the paper will need tighter experimental reporting to stand up.

Referee Report

2 major / 2 minor

Summary. The paper proposes SemGrad, the first gradient-based uncertainty quantification (UQ) method for free-form LLM generation. It operates in semantic space (rather than parameter space) by computing gradients with respect to embeddings selected via a new Semantic Preservation Score (SPS) that identifies semantics-preserving perturbations. The core intuition is that confident models produce stable output distributions under such perturbations. A hybrid variant (HybridGrad) is also introduced that combines semantic and parameter gradients. Experiments claim that both methods are sampling-free, computationally efficient, and outperform state-of-the-art sampling-based UQ baselines, especially when multiple valid responses exist.

Significance. If the empirical results hold under rigorous validation, the work offers a meaningful efficiency improvement for UQ in generative settings by eliminating sampling variance and cost. The semantic-space gradient formulation is a substantive departure from prior classification-oriented gradient UQ methods and directly targets the multi-valid-answer regime common in free-form generation. The introduction of SPS and the hybrid combination are concrete technical contributions that could be adopted or extended by the community.

major comments (2)

[Experimental Evaluation] Experimental Evaluation section: the superiority claims over SOTA methods rest on performance numbers whose supporting details (exact metrics, full list of baselines, number of runs, error bars, statistical significance) are not provided. Without these, it is impossible to assess whether the reported gains are robust or whether they specifically hold in the multiple-valid-response regime highlighted in the abstract.
[Method] Method section (SPS definition): the Semantic Preservation Score is constructed directly from the same semantic-stability intuition used to motivate the gradients. No independent validation, ablation against alternative embedding-selection heuristics, or proof that SPS reliably isolates semantics (as opposed to other surface features) is supplied, leaving the central modeling choice under-justified.

minor comments (2)

[Abstract] Abstract: the sentence 'both of our methods' is slightly ambiguous on first reading; explicitly naming SemGrad and HybridGrad would improve immediate clarity.
[Introduction] Notation: the distinction between semantic-space gradients and parameter-space gradients would benefit from an early, compact equation or diagram in the introduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential contributions of SemGrad and HybridGrad. We agree that additional experimental details and justification for the Semantic Preservation Score are needed to strengthen the paper. We will revise the manuscript accordingly and provide point-by-point responses below.

read point-by-point responses

Referee: [Experimental Evaluation] Experimental Evaluation section: the superiority claims over SOTA methods rest on performance numbers whose supporting details (exact metrics, full list of baselines, number of runs, error bars, statistical significance) are not provided. Without these, it is impossible to assess whether the reported gains are robust or whether they specifically hold in the multiple-valid-response regime highlighted in the abstract.

Authors: We agree that the current experimental section lacks sufficient supporting details to allow full assessment of robustness and performance in the multiple-valid-response regime. In the revised manuscript, we will expand this section to explicitly list all evaluation metrics (e.g., AUROC, AUPRC), provide the complete set of baselines with citations, report the number of runs and random seeds, include error bars (standard deviation across runs), and add statistical significance tests (e.g., paired t-tests or Wilcoxon tests). We will also add a dedicated analysis or table isolating results on subsets or datasets emphasizing multiple valid responses to directly address this regime. revision: yes
Referee: [Method] Method section (SPS definition): the Semantic Preservation Score is constructed directly from the same semantic-stability intuition used to motivate the gradients. No independent validation, ablation against alternative embedding-selection heuristics, or proof that SPS reliably isolates semantics (as opposed to other surface features) is supplied, leaving the central modeling choice under-justified.

Authors: We acknowledge that SPS is motivated by the semantic-stability intuition and that the original submission provides limited independent validation. To address this, the revised manuscript will include an ablation study comparing SPS to alternative heuristics (e.g., random embedding selection and lexical-overlap-based selection). We will also add empirical validation showing that SPS-selected embeddings better preserve semantics, measured via independent metrics such as embedding cosine similarity in a held-out space and a small-scale human evaluation of semantic equivalence. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's core derivation starts from the stated intuition that confident LLMs exhibit stable output distributions under semantically equivalent perturbations, then introduces SPS as a score to select embeddings for computing semantic-space gradients in SemGrad (and HybridGrad). No equations, definitions, or steps in the abstract or summary reduce the final uncertainty estimate to a fitted parameter renamed as a prediction, a self-citation chain, or a definitional loop (e.g., SPS is not shown to be computed from the gradients it enables). The method remains self-contained against external benchmarks, with the central claim of sampling-free gradient UQ for free-form generation carrying independent content beyond its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 3 invented entities

The central claim rests on a domain assumption about model stability under semantic perturbations and introduces new constructs without external evidence in the abstract.

axioms (1)

domain assumption A confident LLM should maintain stable output distributions under semantically equivalent input perturbations.
This is stated as the key intuition underlying the gradient interpretation in semantic space.

invented entities (3)

SemGrad no independent evidence
purpose: Sampling-free gradient-based UQ method operating in semantic space
New method proposed as the core contribution.
Semantic Preservation Score (SPS) no independent evidence
purpose: Score to identify embeddings that best preserve semantics for gradient computation
Invented to support selection of perturbation directions.
HybridGrad no independent evidence
purpose: Hybrid method combining semantic and parameter gradients
Proposed extension to leverage strengths of both approaches.

pith-pipeline@v0.9.0 · 5494 in / 1437 out tokens · 52114 ms · 2026-05-08T16:19:59.980650+00:00 · methodology

discussion (0)

Reference graph

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