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Representation Consistency for Accurate and Coherent LLM Answer Aggregation
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Proposes representation consistency (RC), which reweights self-consistency answer aggregation by the similarity of the LLM's cached internal activations (dense or SAE-sparse) across responses that reach the same answer.
Problem
Test-time scaling via answer aggregation over multiple LLM responses (from prompt rephrasings and sampling) ignores internal model activations, and self-consistency treats all responses to the same answer equally, which can reward incoherent reasoning.
Approach
Score each candidate answer by a weighted sum of its frequency and the cosine consistency of the model's residual-stream activations (raw or SAE-encoded) across the responses supporting it, using only cached activations and no extra model queries.
Key results
- RC-S improves over self-consistency by +1.10 to +1.84 points on average across four models (e.g., RC-D +1.84 and RC-S +1.73 on Llama3.1-8B-IT), with per-setting gains up to about 4%.
- RC-S agrees with deepseek-R1 coherence labels in most cases (e.g., 94.6% on CSQA for Llama3.1-8B-IT), while RC-D and RC-E are near or modestly above 50%.
- The best-performing setting was CSQA on Llama at 6 responses, where RC-S reached a 4.00% accuracy gain over SC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use dense internal activations for answer aggregation instead of self-consistency | Llama-3.1-8B-Instruct · Four reasoning datasets, averaged | accuracy: +1.84 | Helped |
| Use sparse SAE activations for answer aggregation instead of self-consistency | Gemma-2-2B-IT · Four reasoning datasets, averaged | accuracy: +1.10 | Helped |
| Use sparse SAE activations for answer aggregation instead of self-consistency | Gemma-2-9B-IT · Four reasoning datasets, averaged | accuracy: +1.40 | Helped |
| Use sparse SAE activations for answer aggregation instead of self-consistency | Gemma-2-27B-IT · Four reasoning datasets, averaged | accuracy: +0.89 | Helped |
| Use external NLI consistency for answer aggregation instead of self-consistency | Four LLMs · Four reasoning datasets, averaged | accuracy: +1.06; +0.84; +1.07; +0.55 | Helped |
| Replace external response entailment with internal activation consistency (ablation) | RC-style answer aggregation · Four reasoning datasets, averaged | accuracy: RC-D: +1.84 vs RC-E: +1.06; +0.89 vs +0.84; +1.32 vs +1.07; +0.76 vs +0.55 | Helped |
| Use sparse SAE activations rather than dense raw activations (ablation) | RC answer aggregation · Four reasoning datasets, averaged | accuracy: Llama-3.1-8B-Instruct: +1.84 vs +1.73; Gemma-2-2B-IT: +0.89 vs +1.10; Gemma-2-9B-IT: +1.32 vs +1.40; Gemma-2-27B-IT: +0. | Mixed |
| Set λ to a moderate positive value rather than zero (majority vote) (ablation) | RC-D and RC-S · Six-response configurations, across four reasoning datasets and models | accuracy: 0.25 ≤λ≤0.85 | Helped |
| Increase λ into the region where frequency no longer plays an important role (ablation) | RC-D and RC-S · Six-response configurations, across four reasoning datasets and models | accuracy | Hurt |
| Use SAE-sparse rather than external entailment consistency to identify coherent reasoning (ablation) | RC-S versus RC-E · CSQA, HSwag, MedMCQA, and MMLU | agreement with coherence labels: RC-S surpassing 90% in most cases | Helped |
| Use sparse internal activations rather than textual embedding entailment (ablation) | Answer-group consistency scoring · CSQA, HSwag, MedMCQA, and MMLU | correct answer has higher consistency: Sparse: 53.9%/46.1%, 54.7%/45.3%, 58.4%/41.6%, 56.4%/43.6%; Embedding: 50.9%/49.1%, 49.5%/50.5%, 47.8%/52.2%, 50.3%/49.7 | Helped |
| Choose activation layer based on depth (ablation) | RC-D and RC-S · Four reasoning datasets, averaged | accuracy | No clear effect |
Surprising findings
- Dense activation consistency and external NLI embedding consistency align with coherence labels only near chance (around 50%), while sparse SAE consistency aligns strongly.
- Sparse SAE consistency with cosine similarity gives the largest coherence agreement, though dense RC gives the more consistent accuracy gain on Llama.
Limitations
- Requires access to model internal activations, so only open-weight models can use it.
- Intuition fails when an LLM is confidently and systematically wrong, yielding consistent but incorrect activations.
- Evaluated only on multiple-choice QA; hyperparameters (lambda, layer) are model- and dataset-specific and tuned on 50% of data.
Experimental setup
Datasets: CommonsenseQA MMLU MedMCQA HellaSwag
Benchmarks: CommonsenseQA MMLU MedMCQA HellaSwag
Metrics: accuracy relative accuracy vs self-consistency agreement rate with coherence labels
Baselines: Self-consistency Non-selective Expectation RC-E (external NLI embedding variant)
Builds on: self-consistency chain-of-thought GemmaScope LlamaScope
Closest papers by meaning
- Latent Self-Consistency for Reliable Majority-Set Selection in Short- and Long-Answer Reasoning (AAAI 2026 · similarity 0.91)
- A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning (NeurIPS 2025 · similarity 0.91)
- Optimal Self-Consistency for Efficient Reasoning with Large Language Models (ICML 2026 · similarity 0.90)
- Calibrating Reasoning in Language Models with Internal Consistency (NeurIPS 2024 · similarity 0.89)
- Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for LLM Problem-Solving (ICLR 2025 · similarity 0.89)
- Sample Smart, Not Hard: Correctness-First Decoding for Better Reasoning in LLMs (ICLR 2026 · similarity 0.89)
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