Score $\times$ Decoder: A Unified View of Unsupervised Inference-Time Scaling for Hallucination Mitigation

Large language models hallucinate even when the answer lies within their parameters. While inference-time scaling can surface this latent knowledge, the most effective methods require supervision: a trained verifier or reward model. We ask what can be done with only a base language model: which intrinsic signal best identifies correct outputs, and how should it be decoded? We cast this as a score~$\times$~decoder grid pairing four scores (perplexity, contrastive, power-distribution likelihood, and self-verification) with three decoding families (optimization, sampling, consensus), and evaluate every cell on MATH500 with the base and instruction-tuned Qwen3-1.7B. While self-verification, which prompts the model to judge its own answer and is sharpened by a training-free virtual-thinking prefix, works well in most settings, no score has a fixed quality: its value depends on the decoder that consumes it and on model capability. When no supervision is available, the score and the decoding family must be chosen together.