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This paper introduces SemGrad, a novel sampling-free, gradient-based uncertainty quantification (UQ) method for free-form LLM generation that operates in semantic space rather than parameter space. SemGrad leverages the intuition that confident LLMs should exhibit stable output distributions under semantically equivalent input perturbations, quantified via gradients with respect to "semantic preserving score" (SPS) embeddings. Experiments demonstrate SemGrad and its hybrid variant (HybridGrad) outperform existing sampling-based UQ methods, especially when multiple valid responses exist.
LLM uncertainty can be efficiently estimated *without* sampling by measuring the stability of output distributions under semantically equivalent input perturbations.
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.
