Showing incorrect answers to Large Language Models (LLMs) is a popular strategy to improve their performance in reasoning-intensive tasks.It is widely assumed that, in order to be helpful, the incorrect answers must be accompanied by comprehensive rationales, explicitly detailing where the mistakes are and how to correct them.However, in this work we present a counterintuitive finding: we observe that LLMs perform better in math reasoning tasks when these rationales are eliminated from the context and models are left to infer on their own what makes an incorrect answer flawed.This approach also substantially outperforms chainof-thought prompting in our evaluations.These results are consistent across LLMs of different sizes and varying reasoning abilities.To gain an understanding of why LLMs learn from mistakes more effectively without explicit corrective rationales, we perform a thorough analysis, investigating changes in context length and answer diversity between different prompting strategies, and their effect on performance.We also examine evidence of overfitting to the in-context rationales when these are provided, and study the extent to which LLMs are able to autonomously infer high-quality corrective rationales given only incorrect answers as input.We find evidence that, while incorrect answers are more beneficial for LLM learning than additional diverse correct answers, explicit corrective rationales over-constrain the model, thus limiting those benefits.

The capabilities of Large Language Models (LLMs) are routinely evaluated by other LLMs trained to predict human preferences. This framework—known as *LLM-as-a-judge*—is highly scalable and relatively low cost. However, it is also vulnerable to malicious exploitation, as LLM responses can be tuned to overfit the preferences of the judge. Previous work shows that the answers generated by a candidate-LLM can be edited *post hoc* to maximise the score assigned to them by a judge-LLM. In this study, we adopt a different approach and use the signal provided by judge-LLMs as a reward to adversarially tune models that generate text preambles designed to boost downstream performance. We find that frozen LLMs pipelined with these models attain higher LLM-evaluation scores than existing frameworks. Crucially, unlike other frameworks which intervene directly on the model's response, our method is virtually undetectable. We also demonstrate that the effectiveness of the tuned preamble generator transfers when the candidate-LLM and the judge-LLM are replaced with models that are not used during training. These findings raise important questions about the design of more reliable LLM-as-a-judge evaluation settings. They also demonstrate that human preferences can be reverse engineered effectively, by pipelining LLMs to optimise upstream preambles via reinforcement learning—an approach that could find future applications in diverse tasks and domains beyond adversarial attacks.

Linyong Nan, Dragomir Radev, Rui Zhang, Amrit Rau, Abhinand Sivaprasad, Chiachun Hsieh, Xiangru Tang, Aadit Vyas, Neha Verma, Pranav Krishna, Yangxiaokang Liu, Nadia Irwanto, Jessica Pan, Faiaz Rahman, Ahmad Zaidi, Mutethia Mutuma, Yasin Tarabar, Ankit Gupta, Tao Yu, Yi Chern Tan, Xi Victoria Lin, Caiming Xiong, Richard Socher, Nazneen Fatema Rajani. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

Nazneen Fatema Rajani, Rui Zhang, Yi Chern Tan, Stephan Zheng, Jeremy Weiss, Aadit Vyas, Abhijit Gupta, Caiming Xiong, Richard Socher, Dragomir Radev. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 2020.

Tao Yu, Rui Zhang, Michihiro Yasunaga, Yi Chern Tan, Xi Victoria Lin, Suyi Li, Heyang Er, Irene Li, Bo Pang, Tao Chen, Emily Ji, Shreya Dixit, David Proctor, Sungrok Shim, Jonathan Kraft, Vincent Zhang, Caiming Xiong, Richard Socher, Dragomir Radev. Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. 2019.

Tao Yu, Rui Zhang, Heyang Er, Suyi Li, Eric Xue, Bo Pang, Xi Victoria Lin, Yi Chern Tan, Tianze Shi, Zihan Li, Youxuan Jiang, Michihiro Yasunaga, Sungrok Shim, Tao Chen, Alexander Fabbri, Zifan Li, Luyao Chen, Yuwen Zhang, Shreya Dixit, Vincent Zhang, Caiming Xiong, Richard Socher, Walter Lasecki, Dragomir Radev. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.

Social bias in machine learning has drawn significant attention, with work ranging from demonstrations of bias in a multitude of applications, curating definitions of fairness for different contexts, to developing algorithms to mitigate bias. In natural language processing, gender bias has been shown to exist in context-free word embeddings. Recently, contextual word representations have outperformed word embeddings in several downstream NLP tasks. These word representations are conditioned on their context within a sentence, and can also be used to encode the entire sentence. In this paper, we analyze the extent to which state-of-the-art models for contextual word representations, such as BERT and GPT-2, encode biases with respect to gender, race, and intersectional identities. Towards this, we propose assessing bias at the contextual word level. This novel approach captures the contextual effects of bias missing in context-free word embeddings, yet avoids confounding effects that underestimate bias at the sentence encoding level. We demonstrate evidence of bias at the corpus level, find varying evidence of bias in embedding association tests, show in particular that racial bias is strongly encoded in contextual word models, and observe that bias effects for intersectional minorities are exacerbated beyond their constituent minority identities. Further, evaluating bias effects at the contextual word level captures biases that are not captured at the sentence level, confirming the need for our novel approach.