Reverse Thinking Makes LLM s Stronger Reasoners (2025)

Abstract: Reverse thinking plays a crucial role in human reasoning. Humans can reason not only from a problem to a solution but also in reverse, i.e., start from the solution and reason towards the problem. This often enhances overall reasoning performance as it enables consistency checks between their forward and backward thinking. To enable Large Language Models (LLMs) to perform reverse thinking, we introduce Reverse-Enhanced Thinking (RevThink), a framework composed of data augmentation and learning objectives. In RevThink, we augment the dataset by collecting structured forward-backward reasoning from a teacher model, consisting of: (1) the original question, (2) forward reasoning, (3) backward question, and (4) backward reasoning. We then employ three objectives to train a smaller student model in a multi-task learning fashion: (a) generate forward reasoning from a question, (b) generate a backward question from a question, and (c) generate backward reasoning from the backward question. Experiments across 12 datasets covering commonsense, math, and logical reasoning show an average 13.53% improvement over the student model’s zero-shot performance and a 6.84% improvement over the strongest knowledge distillation baselines. Moreover, our method demonstrates sample efficiency – using only 10% of the correct forward reasoning from the training data, it outperforms a standard fine-tuning method trained on 10x more forward reasoning. RevThink also exhibits strong generalization to out-of-distribution held-out datasets.

## introduction if emma has two, we can ask: how many does jack have? the result is three, which matches the original problem and confirms the solution is correct. however, if forward reasoning mistakenly predicts the answer as six, reverse reasoning would reveal a conflict: they have six apples, emma has two, so jack must have four, which contradicts the original problem. this discrepancy signals the need to reassess and improve the solution. prior work has shown that large language models (llms) benefit from forward-backward reasoning in math @xcite . this is largely due to two factors: (1) the highly structured nature of math, which facilitates a clear inverse relationship between forward and backward reasoning, and (2) the ability to create new math problems by simply replacing variables like names or numbers. these factors lead to the first research question: can reverse thinking be applied to broader, less structured domains? moreover, these methods operate at test time, serving as a verification purpose: given solution, we can ask the llm to think backward and see whether the forward reasoning is correct or not. while they show moderate improvements over other test-time methods such as self-consistency @xcite , it prompts the second question: instead of using backward reasoning for verification at test time, can we train a model to inherently think backward, thereby improving its forward reasoning? to address these research questions, we propose revthink, a framework that consists of data augmentation and novel learning objectives designed to instill reverse thinking in language models. we begin by augmenting the dataset using a larger, more capable teacher model. reasoning benchmark data typically consists of a question and answer. we extend this by generating (1) forward reasoning, (2) a backward question, and (3) backward reasoning, all through few-shot prompting from the teacher model. both forward and backward reasoning are chain-of-thought @xcite . we retain only those data points where the forward reasoning is accurate (verified against ground truth) and where the backward reasoning aligns with the original question (validated by prompting the teacher model). after augmenting the dataset, we propose three key objectives for training the smaller student model. specifically, the student learns to: (1) generate correct forward reasoning from the question, (2) generate a backward question from the original question, and (3) generate backward reasoning from the backward question. the rationale for these objectives is threefold. first, generating correct reasoning from a question is a standard method of knowledge distillation @xcite . second, producing a reverse question encourages the student model to "think" about how to invert a problem and determine the right question to ask. lastly, solving the backward question reinforces the student's ability to reason backward. at test time, the student model is prompted with the question, and it generates only forward reasoning, similar to standard zero-shot inference. in essence, our pipeline internalizes the ability to reason backward during training, while keeping test-time computation as efficient as zeroshot approaches. as shown in fig. 1 , conventional supervised fine-tuning focuses on unidirectional reasoning, from the question to the answer. in contrast, revthink introduces bidirectional thinking by learning to reason in both directions through our data augmentation method and proposed objectives, resulting in greater improvements. we evaluate revthink on 12 diverse datasets across commonsense reasoning, mathematical reasoning, logical reasoning, and natural language inference, using two models: mistral-7b-instruct @xcite and gemma-7b-instruct @xcite . our results demonstrate that learning to think backward through our pipeline consistently improves performance, with an average gain of 13.53% over the student's zero-shot performance and 6.84% over the widely-used symbolic knowledge distillation (skd) method. revthink also shows similar 4.52% -7.99% gains compared to other data augmentation baselines. our analysis further highlights that revthink exhibits sample efficiency, where in a low-resource regime, using just 10% of the training instances (augmented by our method) surpasses the performance of skd applied to the full training set (using forward reasoning). moreover, revthink scales positively with the student model size from 2b to 176b, achieving better results on a 7b model than a 176b model's zero-shot performance, despite the latter having 25× more parameters. furthermore, revthink generalizes well to unseen datasets and complements existing data augmentation techniques. ## method revthink mainly consists of two stages. in section 3.1, we provide a formal description of the problem setup. section 3.2 then describes the details of training data creation. lastly, in section 3.3, we introduce the learning objectives. ## experimental setup we use gemini-1.5-pro-001 @xcite as the teacher model t , with mistral-7b-instruct-v0.3 and gemma-7b-instruct as the student model s. for training, we use lora fine-tuning (hu et al., 2022) with rank 32. we use vllm @xcite and greedy decoding (with @xmath0. the student model is fine-tuned for 3 epochs on math reasoning tasks (math and gsm8k) and 10 epochs for all other domains. for mistral-7b-instruct-v0.3, we set the learning rate to 5e-6, while for gemma-7b-instruct, we use a learning rate of 2e-4. these configurations remain consistent across all baseline comparisons. we evaluate our method on a wide range of tasks: commonsense reason-ing: strategyqa (sqa; @xcite , com-monsenseqa (csqa; @xcite , arcchallenge (arc; @xcite . math reasoning: math @xcite , gsm8k @xcite . tabular data reasoning: tabmwp @xcite . natural language inference: anli @xcite . logical reasoning: date understanding (bench authors, 2023). we compare with three categories of baselines as follows. ## conclusion we introduce revthink, a framework that improves llm by enabling backward reasoning. we propose an effective data augmentation method that generates well-structured forward-backward data from a teacher model, and we also propose an effective learning objective with auxiliary tasks that make full use of this augmented data. experimental results not only show that revthink is effective across 12 datasets on a wide range of tasks, but also reveal additional benefits, including sample efficiency, generalization, and the complementary strength to existing methods.