Summary GRACE Discriminator-Guided Chain-of-Thought Reasoning arxiv.org
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GRACE improves the performance of pre-trained language models by incorporating a Correctness Discriminator, leading to better accuracy and sample efficiency in complex reasoning tasks.
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Slide Presentation (12 slides)
Key Points
- GRACE is a stepwise decoding approach that addresses the limitations of pre-trained language models in complex multi-step reasoning tasks.
- GRACE uses a Correctness Discriminator to guide the decoding process towards producing correct reasoning steps.
- GRACE outperforms baselines, including greedy decoding and self-consistency, in terms of final answer accuracy and intermediate reasoning correctness.
- The proposed method does not require LM training and only relies on sampling from the LM distribution.
- GRACE achieves higher accuracy in final answers and intermediate reasoning steps compared to baselines.
- Discriminator size and discriminator score coefficient have an impact on model performance.
- GRACE is more sample-efficient compared to vanilla self-consistency.
- The study explores the use of discriminators in training language models for math word problem solving.
Summaries
21 word summary
GRACE enhances pre-trained language models with a Correctness Discriminator, outperforming baselines in complex reasoning tasks. It improves accuracy and sample efficiency.
53 word summary
GRACE (Discriminator-Guided Chain-of-Thought Reasoning) improves pre-trained language models in complex reasoning tasks. It introduces a Correctness Discriminator and outperforms baselines like greedy decoding, verifiers, and self-consistency. GRACE involves negative sampling, alignment, and learning. It demonstrates higher accuracy in final answers and intermediate reasoning steps, surpassing greedy decoding and self-consistency while being more sample-efficient.
148 word summary
GRACE (Discriminator-Guided Chain-of-Thought Reasoning) is a decoding approach that enhances the performance of pre-trained language models in complex multi-step reasoning tasks. It introduces a Correctness Discriminator and does not require LM training or fine-tuning. GRACE outperforms baselines such as greedy decoding, verifiers, and self-consistency, improving final answer accuracy and reasoning chain correctness. The method involves negative sampling, alignment, and learning. During guided stepwise decoding, a pool of candidate next steps is sampled using nucleus sampling. Each candidate is scored using LM probability and the discriminator score, and the top-scored step is selected. The paper provides detailed information on training, evaluation, and results. GRACE demonstrates higher accuracy in final answers and intermediate reasoning steps, surpassing greedy decoding and self-consistency while being more sample-efficient. The paper discusses related work, limitations, and future directions of GRACE. Overall, GRACE shows promise in enhancing the correctness and quality of reasoning in language models.
432 word summary
GRACE (Discriminator-Guided Chain-of-Thought Reasoning) is a decoding approach that improves pre-trained language models' performance in complex multi-step reasoning tasks. It introduces a Correctness Discriminator to guide the decoding process and does not require LM training or fine-tuning. GRACE was evaluated on various reasoning tasks and demonstrated significant performance gains compared to baselines such as greedy decoding, verifiers, and self-consistency.
The proposed method involves three steps: negative sampling, alignment, and learning. Negative sampling collects incorrect solutions by sampling from the LM and keeping only solutions with incorrect final answers. Alignment aligns these incorrect solutions with reference solutions using the Needleman-Wunsch algorithm. Learning involves training the discriminator to distinguish between correct and incorrect steps.
During guided stepwise decoding, a pool of candidate next steps is sampled using nucleus sampling from the LM distribution. Each candidate is scored using LM probability and the discriminator score, and the top-scored step is selected and added to the prefix until a final answer is generated.
GRACE outperformed baselines on multiple benchmarks, improving final answer accuracy and reasoning chain correctness. It does not require LM training and solely relies on sampling from the LM distribution.
The paper provides detailed information on the training and evaluation processes, as well as the results and analysis of using discriminators in training language models for math word problem solving. GRACE's effectiveness is verified on two language models, FLAN-T5 Large and LLaMA, in various reasoning tasks. Results show higher final answer accuracy, especially when combined with self-consistency.
Evaluation of intermediate step correctness demonstrates that GRACE surpasses greedy decoding and self-consistency, indicating improved reasoning chain correctness. Trace error evaluation reveals a reduction in major mistakes compared to greedy decoding, demonstrating improved reasoning quality.
Further analysis explores the efficiency and performance of GRACE. It requires fewer samples than vanilla self-consistency to achieve the same accuracy and increasing the discriminator score coefficient improves final answer accuracy. The size of the discriminator model is also investigated, showing that smaller discriminators can still achieve high accuracy.
The related work in controlled generation and multi-step reasoning is discussed, emphasizing the novelty of GRACE in its fine-grained control over solution decoding and its novel training process for the discriminator model. The paper addresses the limitations and future directions of GRACE, including potential overhead and extension to commercial APIs.
In conclusion, GRACE is an effective approach for improving multi-step reasoning in language models. It achieves higher accuracy in final answers and intermediate reasoning steps compared to baselines, outperforming greedy decoding and self-consistency while being more sample-efficient. The proposed method shows promise in enhancing the correctness and quality of reasoning in language models.
522 word summary
GRACE (Discriminator-Guided Chain-of-Thought Reasoning) is a stepwise decoding approach that addresses the limitations of pre-trained language models (LMs) in complex multi-step reasoning tasks. It proposes the use of a Correctness Discriminator to guide the decoding process towards producing correct reasoning steps. GRACE does not require LM training or fine-tuning and relies solely on sampling from the LM distribution. The approach was evaluated on various reasoning tasks and demonstrated substantial performance gains compared to baselines such as greedy decoding, verifiers, and self-consistency. When combined with self-consistency, GRACE outperformed all baselines by sizable margins. It improved both the final answer accuracy and the correctness of intermediate reasoning.
The proposed method involves three steps: negative sampling, alignment, and learning. Negative sampling collects solutions with incorrect steps by sampling from the LM and keeping only solutions with incorrect final answers. Alignment aligns these incorrect solutions with reference solutions using the Needleman-Wunsch algorithm. Learning involves training the discriminator to distinguish between correct and incorrect steps using a max-margin loss objective.
During guided stepwise decoding, a pool of candidate next steps is sampled using nucleus sampling from the LM distribution. Each candidate is scored using a combination of LM probability and the discriminator score. The top-scored step is selected and added to the prefix until a final answer is generated.
GRACE outperformed greedy decoding, self-consistency, and verifiers on multiple benchmarks, significantly improving final answer accuracy and reasoning chain correctness. It does not require LM training and only relies on sampling from the LM distribution.
The paper provides detailed information on the training and evaluation processes, as well as the results and analysis of using discriminators in training language models for math word problem solving. The effectiveness of GRACE is verified on two language models, FLAN-T5 Large and LLaMA, in various reasoning tasks. Results show that GRACE outperforms baselines, achieving higher final answer accuracy. When combined with self-consistency, GRACE produces even better results. It improves the correctness of both final answers and intermediate reasoning steps.
Evaluation of intermediate step correctness shows that GRACE surpasses both greedy decoding and self-consistency, indicating improved reasoning chain correctness. Trace error evaluation indicates a reduction in major mistakes compared to greedy decoding, demonstrating improved reasoning quality.
The paper includes further analysis, exploring the efficiency and performance of GRACE. It requires fewer samples than vanilla self-consistency to achieve the same accuracy and shows that increasing the discriminator score coefficient improves final answer accuracy. The size of the discriminator model is also investigated, revealing that smaller discriminators can still achieve high accuracy.
The related work in controlled generation and multi-step reasoning is discussed, highlighting the novelty of GRACE in its fine-grained control over solution decoding and its novel training process for the discriminator model. The paper addresses the limitations and future directions of GRACE, including potential overhead and extension to commercial APIs.
In conclusion, GRACE is an effective approach for improving multi-step reasoning in language models. It achieves higher accuracy in final answers and intermediate reasoning steps compared to baselines. It outperforms greedy decoding and self-consistency while being more sample-efficient. The proposed method shows promise in enhancing the correctness and quality of reasoning in language models.
1753 word summary
GRACE (Discriminator-Guided Chain-of-Thought Reasoning) is a stepwise decoding approach that addresses the limitations of pre-trained language models (LMs) in complex multi-step reasoning tasks. LMs struggle with problems that require multi-step reasoning because they often assign high likelihoods to incorrect steps. This leads to incorrect solutions when decoding strategies optimize for solution likelihood. To overcome this issue, GRACE proposes the use of a Correctness Discriminator, trained with a contrastive loss over correct and incorrect steps, to guide the decoding process towards producing correct reasoning steps.
GRACE does not require LM training or fine-tuning. It only relies on sampling from the LM distribution. The approach was evaluated using models from the FLAN-T5 and LLaMA families on four math and two symbolic reasoning tasks. GRACE demonstrated substantial performance gains compared to greedy decoding, verifiers, and self-consistency in most settings. When combined with self-consistency, GRACE outperformed all baselines by sizable margins. Human and LLM evaluations on GSM8K showed that GRACE improved both the final answer accuracy and the correctness of intermediate reasoning.
The proposed method involves three steps: negative sampling, alignment, and learning. Negative sampling involves collecting solutions with incorrect steps by sampling from the LM and keeping only solutions with incorrect final answers. Alignment aligns these incorrect solutions with reference solutions using the Needleman-Wunsch algorithm to create examples with correct and incorrect steps. Learning involves training the discriminator with a max-margin loss objective to distinguish between correct and incorrect steps.
During guided stepwise decoding, a pool of candidate next steps is sampled using nucleus sampling from the LM distribution. Each candidate is then scored using a combination of LM probability and the discriminator score. The top-scored step is selected and added to the prefix, and this process is repeated until a final answer is generated.
The approach was evaluated on various reasoning tasks, including math word problems and symbolic reasoning tasks. GRACE outperformed greedy decoding, self-consistency, and verifiers on multiple benchmarks. It significantly improved final answer accuracy and reasoning chain correctness. The proposed method does not require LM training and only relies on sampling from the LM distribution.
In conclusion, GRACE is a stepwise decoding approach that addresses the limitations of pre-trained LMs in complex multi-step reasoning tasks. It employs a Correctness Discriminator to guide the decoding process towards producing correct reasoning steps. The approach outperforms baselines and improves both final answer accuracy and intermediate reasoning correctness. It does not require LM training and only relies on sampling from the LM distribution.
The GRACE Discriminator-Guided Chain-of-Thought Reasoning method is proposed in this paper to improve multi-step reasoning in language models. The approach involves training a step-level discriminator model that guides the decoding process towards correct reasoning steps. The effectiveness of GRACE is verified on two language models, FLAN-T5 Large and LLaMA, in various reasoning tasks. Results show that GRACE outperforms baselines such as greedy decoding and self-consistency, achieving higher final answer accuracy on math reasoning tasks. When combined with self-consistency, GRACE produces even better results, outperforming vanilla self-consistency with random sampling. Similar trends are observed in few-shot prompted tasks. The accuracy boost achieved by GRACE is significant, demonstrating its ability to improve the correctness of both final answers and intermediate reasoning steps.
Evaluation of intermediate step correctness is also conducted to assess the quality of the reasoning chains produced by GRACE. The prefix correctness (PC) metric is used to measure the correctness of the reasoning steps so far. Results show that GRACE surpasses both greedy decoding and self-consistency in PC, indicating improved reasoning chain correctness. Furthermore, trace error (TE) evaluation is performed to identify major mistakes in solutions with correct final answers. GRACE demonstrates a reduction in TE compared to greedy decoding, indicating improved reasoning quality.
Several analyses are conducted to explore the efficiency and performance of GRACE. It is found that GRACE requires fewer samples than vanilla self-consistency to achieve the same accuracy, making it more sample-efficient. The effect of the discriminator score coefficient is also studied, showing that increasing the coefficient improves final answer accuracy up to a certain level. The size of the discriminator model is investigated, revealing that smaller discriminators can still achieve high accuracy.
The related work in controlled generation and multi-step reasoning is discussed, highlighting the novelty of GRACE in its fine-grained control over solution decoding and its novel training process for the discriminator model. The limitations and future directions of GRACE are also addressed, including the overhead incurred by sampling and computing discriminator scores, reliance on reference solutions for alignment, and the potential for extending GRACE to commercial APIs.
In conclusion, GRACE is an effective approach for improving multi-step reasoning in language models. By training a step-level discriminator model and guiding the decoding process, GRACE achieves higher accuracy in final answers and intermediate reasoning steps compared to baselines. It demonstrates better performance than greedy decoding and self-consistency, while also being more sample-efficient. The proposed method shows promise in enhancing the correctness and quality of reasoning in language models.
The study explores the use of discriminators in training language models to solve math word problems. The authors reference several related papers that have investigated similar topics. They discuss the importance of faithful reasoning and interpretable logical reasoning in language models. The authors also mention the use of plug and play language models and large language models as reasoning teachers.
The paper provides implementation details, including hyperparameters and training methods. For example, the authors describe the use of discriminators in step scoring and the training process for the discriminator. They also explain the decoding process, which involves sampling reasoning steps and using a calculator for math operations.
The authors discuss the solution alignment algorithm used to align sampled solutions with the ground-truth solution. They filter out low-quality samples based on alignment cost. The algorithm utilizes embeddings obtained from ROSCOE or SimCSE to compute the alignment.
The paper includes information about the few-shot prompt used to evaluate the model's ability to predict prefix correctness. They manually annotate 100 model-generated solutions from GSM8K to assess the model's performance. The few-shot prompt achieves a high macro F1 score in predicting prefix correctness.
The authors provide details about human evaluation, including datasets used and reference generation for step-by-step solutions. They explain how reference solutions are generated and how they filter out solutions that do not reach the correct final answer. The dataset statistics are also presented.
The paper presents further analysis, including the impact of discriminator size on model performance. Larger discriminators tend to perform better, especially for more complex tasks like GSM8K. The authors show that G RACE outperforms self-consistency and greedy decoding on GSM8K and SVAMP datasets.
Finally, the authors provide statistics on the annotator agreement for human evaluation. They achieved high agreement and used one annotator to annotate all 400 solutions.
Overall, the paper provides detailed information on the training and evaluation processes, as well as the results and analysis of using discriminators in training language models for math word problem solving.
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D Few-shot prompts Tables 8, 9, and 10 show the 6-shot prompt used with LLaMA 7B with GSM8K, SVAMP, and MultiArith, respectively. Tables 11 and 12 show the 6-shot prompt used with LLaMA 13B for the Coin Flip and Tracking Shuffled Objects, respectively.
H Sample Outputs Tables 13, 14, 15, 16, 17, 18, 19, 20, 21 show compared sampled solutions from both GRACE and self-consistency where GRACE reached the correct answer but self-consistency did not.
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Q: 1/3 of the townspeople have received the full COVID vaccine. 1/3 are immune because they already recovered from COVID. If 1/6 of the townspeople are both vaccinated and already had COVID, what percent of the town is immune in some way? A: 50% of the town is immune in some way.
Q: James was doing some shopping in his favorite shop and he saw an offer on shoes that give him a second pair of shoes for half off the original price. He took the offer and took the first pair of shoes for $40 and the second one for $60. At the cashier, the lady told him that the offer applies strictly to the cheaper pair of shoes, and also that he was selected for an extra discount of a fourth off the total amount. How much money did James end up paying for both pairs of shoes? A: James ended up paying $60 for both pairs of shoes.
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Table 8 shows the 6-shot prompt used with LLaMA 7B for GSM8K.
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Q: White t-shirts can be purchased in packages of 13. If mom buys 39 white t-shirts, how many packages will she have? A: Mom will have 3 packages of t-shirts.
Q: There are 384 oranges and 192 bananas in Philip's collection. If the bananas are organized into 345 groups and oranges are organized into 16 groups, how big is