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Awesome-AI-Examples🖼️ Digital Image Processing
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11.0 Introduction
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OpenAI ChatGPT Progression🔗9.4.1.3 ReCEval: Evaluating Reasoning Chains via Correctness and Informativeness
Paper link: https://arxiv.org/abs/2304.10703
Release date: April 21, 2023
This paper aims to evaluate the quality of reasoning chains. They propose RECEVAL, a reference-free evaluation framework based on two properties: correctness (logical validity of each step) and informativeness (whether each step actually helps predict the final answer):
- Correctness is measured with Natural Language Inference (NLI)-based entailment and contradiction checks
- Informativeness is measured using Pointwise V-Information (PVI) based on language-model likelihoods.
The method is evaluated using the same Somer’s D meta-evaluation protocol as Section 9.4.1.2 ROSCOE, showing improved detection of synthetic and human-labeled reasoning errors and small gains in downstream accuracy when used for reranking.
Important note: RECEVAL assumes one sentence ≈ one reasoning step, and operates purely on natural-language chains. It is not suitable for modern LLM outputs with compressed symbolic reasoning, equations, tool use, or ultra-terse derivations.
Introduction
Recent LLMs exhibit multi-step reasoning ability via Chain-of-Thought (CoT) prompting, and their performance is typically evaluated based on final answer accuracy. However, correct answers do not guarantee correct or faithful reasoning, as models may rely on shortcuts, hallucinated steps, or spurious patterns.
ROSCOE introduced a reference-free reasoning evaluation framework, but it primarily relies on semantic similarity and alignment. This paper explicitly defines what constitutes a good reasoning chain and introduces explicit metrics for correctness and informativeness.
Preliminaries
Reasoning Chains
A reasoning chain is a sequence of steps
used to derive a final answer for a question. In RECEVAL, each sentence in the model’s output paragraph is treated as one reasoning step. The framework does not attempt to discover logical steps beyond sentence splitting.
Reasoning Content Units (RCUs)
Each reasoning step is further decomposed into Reasoning Content Units (RCUs), which represent atomic factual claims. RCUs are extracted automatically using a Semantic Role Labeling (SRL) model, where each predicate–argument frame becomes one RCU.
Reasoning Step segmentation: The paper does not define how logical steps are detected. In practice, the reasoning chain is first split into sentences, and each sentence is treated as one step.
Within each sentence-step:
- If multiple RCUs exist:
- The last RCU is treated as the conclusion
- Earlier RCUs are treated as premises
- If only one RCU exists, it is treated as a conclusion-only step
This process is fully automatic and heuristic-based, without manual annotation. While RCUs enable fine-grained logical checks inside each sentence, the approach is not stable for symbolic, compressed, or equation-heavy reasoning.
Pointwise V-Information (PVI)
PVI measures how much a piece of text helps a language model predict another piece of text. It is defined as the change in the log-likelihood of an output after adding additional conditioning information.
In RECEVAL:
- : current reasoning step
- : final answer
- : previous reasoning steps
Probabilities are computed using a seq2seq language model (T5) with full sequence log-likelihood. Example:
Suppose the question is:
What is the result of 3 × 4?Let:
- z =
What is the result of 3 × 4
- x =
?
- y =
12(Here, the output 12 has two tokens,1and2)
The model computes:
If adding “equals” makes both tokens more confident, then:
Thus, PVI directly measures how much the reasoning step increases the likelihood of the full multi-token answer, not just a single token.
In RECEVAL, a large positive PVI indicates that a step is informative, while near-zero or negative PVI indicates that the step is redundant or irrelevant.
Properties of a Good Reasoning Chain
The paper defines two core properties:
Correctness
- Intra-step correctness: the conclusion of a step should logically follow from its premises.
- Inter-step correctness: each step should be consistent with all previous steps and the original input.
Informativeness
- Each step should provide new, useful information toward the final answer.
- Redundant, paraphrased, or irrelevant steps should be penalized.
RECEVAL evaluates reasoning quality using these two properties.
Method - RECEVAL
RECEVAL evaluates reasoning chains by scoring each step along two dimensions: correctness and informativeness, and then aggregating these step-level scores to the chain level. The reasoning chain is first split into sentences, and each sentence is treated as one reasoning step. RECEVAL relies on a standard Natural Language Inference (NLI) classifier to test the correctness of the reasoning chain:
NLI Model Interface (Used for Correctness Scoring)
The NLI model takes as input a premise sentence and a hypothesis sentence, and outputs a 3-way probability distribution:
with:
- Entailment: the hypothesis logically follows from the premise
- Neutral: the premise neither supports nor contradicts the hypothesis
- Contradiction: the hypothesis conflicts with the premise
These are softmax probabilities, so they sum to 1. RECEVAL uses:
- for intra-step correctness
- for inter-step correctness
Three aspects are then used to check the performance of a reason chain:
Aspects 1. Intra-Step Correctness (NLI-Based and PVI-Based)
Intra-step correctness measures whether the conclusion RCU logically follows from the premise RCUs within a single step.
- Entailment-based: The premise RCUs are concatenated and used as the premise input, and the conclusion RCU is used as the hypothesis input to an NLI model. The entailment probability is directly used as the intra-step correctness score. A low entailment score indicates unsupported or hallucinated inference.
- PVI-based: Uses sequence log-likelihood to measure how much the premise increases the probability of generating the conclusion. This allows weaker, implicit inferences that may not satisfy strict logical entailment.
Aspect 2: Inter-Step Correctness (Contradiction-Based)
Inter-step correctness checks whether the current step contradicts any previous knowledge. For the conclusion RCU of step , the method:
- Compares it against:
- The original input context
- All previous conclusion RCUs
- For each comparison, an NLI model outputs a contradiction probability
- The maximum contradiction probability is selected
- The inter-step correctness score is defined as:
Thus:
- High contradiction probability means low inter-step correctness
- No strong contradictions means high inter-step correctness
Aspect 3: Informativeness via PVI
Informativeness measures how much a step helps predict the final answer.
For each step , RECEVAL computes:
using the full sequence log-likelihood from a language model.
A large positive value indicates that the step is helpful, while near-zero or negative values indicate redundancy or irrelevance.
The 3 scores from the 3 aspects are aggregated using a minimum operator:
- Chain correctness = minimum intra- or inter-step score
- Chain informativeness = minimum step informativeness
This reflects the assumption that a reasoning chain is only as good as its weakest step.
Experiments and Results
Error Detection Performance
Using the same Somer’s D meta-evaluation protocol as Section 9.4.1.2 ROSCOE, RECEVAL is evaluated on EntailmentBank with synthetic reasoning errors. The task is to test whether a metric can distinguish clean reasoning chains from corrupted ones, not whether the final answer is correct.
- For correctness-related errors (hallucination, negation, swap):
- RECEVAL achieves much higher correlation than ROUGE, BERTScore, and ROSCOE.
- In particular, hallucination detection improves substantially (≈0.89 vs ≈0.62 with ROSCOE).
- For informativeness-related errors (repetition, paraphrase, redundancy):
- RECEVAL-informativeness performs best on paraphrasing and redundancy.
- ROSCOE still performs slightly better on verbatim repetition, which is surface-text driven.
RECEVAL is more sensitive to logical and structural reasoning errors, while traditional metrics mainly capture surface-level overlap. Note that these results rely heavily on synthetically perturbed errors, which may not fully reflect natural model failures.
Downstream Accuracy Improvement
RECEVAL is also used as a reranking metric for sampled reasoning chains on GSM-8K. Basically, it samples multiple answers from an LLM, then evaluates each answer using RECEVAL, and selects the answer with the highest score.
RECEVAL can serve as a useful heuristic for selecting better reasoning chains, not only as an evaluation metric. However, the accuracy gain is small and requires multiple sampled chains. Also, the benefit is demonstrated only on GSM-8K, not across diverse modern reasoning settings.
Limitations & Conclusion
Limitations: RECEVAL assumes one sentence equals one reasoning step and relies on heuristic RCU extraction, making it unstable for symbolic, compressed, or tool-based reasoning used by modern LLMs. Its scores depend heavily on NLI and language model calibration, and much of the evaluation is based on synthetic error perturbations, limiting ecological validity.
Conclusion: RECEVAL introduces a step-level, reference-free framework for evaluating reasoning via correctness and informativeness, outperforming ROSCOE in controlled meta-evaluation and giving modest gains in reranking for GSM-8K. It is best viewed as a method designed for early natural-language CoT reasoning rather than modern LLM reasoning, useful mainly as a structured baseline.
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