Research map / Large language models / Reasoning and chain of thought
Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation
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Proposes Chain-of-Embedding (CoE), a training-free, output-free self-evaluation method that scores LLM response correctness from magnitude and angle changes across layer-wise hidden states.
Problem
Label-free self-evaluation of LLM response correctness without relying on output text, output probabilities, sampling, labels, or external tools.
Approach
Treat the sequence of layer-wise averaged hidden states as a latent "chain-of-embedding" trajectory; correct and incorrect responses show different magnitude and angle changes along it. Two combinations of these features (CoE-R real-space sum, CoE-C complex-plane magnitude) give a correctness score with no training or labels.
Key results
- CoE achieves average improvements of 8.30%, 5.55%, and 5.52% in AUROC, FPR95, and AUPR over the optimal baseline across four domains.
- CoE-C reaches 75.22 average AUROC in the Mathematics domain with Qwen-family and Llama models, versus 65.39 for the best baseline (PSA pipeline).
- CoE computation takes about 1.12e-03 s versus 12.59 s for base LLM inference with Llama3-8B on GSM8K.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| combine magnitude and angle features rather than use either alone (ablation) | CoE self-evaluation · Four domains across four 7B+ models | AUROC: 14 out of 16 settings | Helped |
| use complex-space combination (CoE-C) rather than real-space combination (CoE-R) (ablation) | CoE self-evaluation · Four domains; anomalies in Mathematics and Knowledge with Qwen1.5-7B | AUROC | Mixed |
| add the angle component to magnitude-only CoE (ablation) | CoE-R, Llama3-8B-Instruct · Mathematics | AUROC: 74.50 -> 72.54 | Hurt |
| add the angle component to magnitude-only CoE (ablation) | CoE-R, Llama3-8B-Instruct · Reasoning | AUROC: 55.57 -> 63.12 | Helped |
| add the magnitude component to angle-only CoE (ablation) | CoE-R, Llama3-8B-Instruct · Mathematics | AUROC: 71.69 -> 72.54 | Helped |
| add the magnitude component to angle-only CoE (ablation) | CoE-R, Llama3-8B-Instruct · Understanding | AUROC: 64.27 -> 64.81 | Helped |
| use CoE-C rather than CoE-R | CoE self-evaluation · Four domains, average across models | AUROC | Mixed |
| use CoE-R rather than the strongest baseline | LLM self-evaluation · Mathematics, Reasoning, Knowledge, and Understanding averages | AUROC: 9.83%, 8.36%, 7.78%, 7.23% | Helped |
Surprising findings
- Magnitude-only or angle-only features can underperform the combined CoE score, and CoE-R is unstable on some models (e.g., Qwen1.5-7B in Mathematics at 38.44 AUROC).
- Supervised hidden-state probes ITI and MIND drop to near-chance AUROC (about 46-51) on GSM8K, MATH and TheoremQA, despite strong in-distribution TruthfulQA results.
Limitations
- Requires access to internal hidden states, so it cannot be applied to closed-source black-box models such as GPT-4.
- CoE-R lacks clear physical meaning and is sensitive to outliers; CoE-C is more robust but still not uniformly best.
- Evaluated only on instruction-tuned models of 7B-72B and on four domains; results are not uniform across all models (e.g., Mistral and Qwen1.5 in some settings).
Experimental setup
Datasets: GSM8K MATH CommonsenseQA TheoremQA MMLU Belebele MGSM TruthfulQA
Benchmarks: GSM8K MATH CommonsenseQA TheoremQA MMLU Belebele MGSM TruthfulQA
Metrics: AUROC FPR95 AUPR execution time
Baselines: Verbal Confidence (P(true)) PSA pipeline Maximum Softmax Probability Perplexity Entropy Temperature Scaling Energy MC Dropout LN-Entropy EigenScore ITI MIND
Builds on: Eigenscore P(true) Perplexity Semantic entropy
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