Reason from Future: Reverse Thought Chain Enhances LLM Reasoning
Authors: Yinlong Xu, Yanzhao Zheng, Shuoshuo Sun, Shuaihan Huang, Baohua Dong, Ran Lin, Ruohui Huang, Gang Yu, Hongxia Xu, Jian Wu
Accepted at: acl25

Reason from Future: Reverse Thought Chain Enhances LLM Reasoning

Yinlong Xu1,2, Yanzhao Zheng2, Shuoshuo Sun2, Shuaihan Huang2, Baohua Dong2, Hangcheng Zhu2, Ruohui Huang2, Gang Yu2, Hongxia Xu3,4*, Jian Wu1,5*
1 College of Computer Science and Technology, Zhejiang University, Hangzhou, China
2 Alibaba Group, Hangzhou, China
3 State Key Laboratory of Transvascular Implantation Devices and TIDRI, Hangzhou, China
4 Liangzhu Laboratory and WeDoctor Cloud, Hangzhou, China
5 Zhejiang Key Laboratory of Medical Imaging Artificial Intelligence, Hangzhou, China
{xuyinlong,s.huang,Einstein,Wujian2000}@zju.edu.cn {zhengyanzhao.zyz,sunshuoshuo.sss,baohua.dbh,linran.lr09}@taobao.com

Abstract

It has been demonstrated that carefully designed reasoning paradigms, like Chain-of-Thought (CoT) and Tree-of-Thought (ToT), can enhance the reasoning capabilities of small language models by detailed thinking and extensive thought searching, unbounded branching factors in the searching space create prohibitive reasoning consumption. However these methods fall into the trap of local optimum reasoning, which means the model lacks a global perspective while solving problems. We propose a novel reasoning paradigm called Reason from Future (RFF), which generates reasoning paths by bidirectional reasoning that combines top-down planning with bottom-up reasoning accumulation. The essence of RFF lies in its reverse reasoning mechanism, which prioritizes core logical relationships and imposes goal-oriented constraints on intermediate steps, thereby reducing the searching space and mitigating error accumulation inherent in sequential forward reasoning. Empirical evaluations across diverse experiments demonstrate that RFF outperforms conventional paradigms with higher accuracy and less searching space to solve complex tasks.

1 Introduction

The rapid evolution of large language models (LLMs), fueled by breakthroughs in deep learning architectures and unprecedented datasets, has demonstrated remarkable potential across natural language processing (NLP) and interdisciplinary applications (Lee and Toutanova, 2018; Radford, 2018; Team et al., 2023; Sel et al., 2023). LLMs like ChatGPT (Achiam et al., 2023) and Llama (Dubey et al., 2024) exhibit human-like text generation, multilingual task execution, and emerging logical reasoning. Current scholarly investigations identify their reasoning capacity for problem decomposition as the critical determinant of functional boundaries, enabling industrial automation and academic research applications.

Recent studies demonstrate that well-designed reasoning paradigms can significantly enhance LLMs’ reasoning ability without additional costly and time-consuming post-training. A seminal work in this area is Chain-of-Thought (CoT) (Wei et al., 2022), which pioneered the novel view that reasoning ability can be improved by designing reasoning prompts, paradigms, and examples. Tree-of-Thought (ToT) (Yao et al., 2024) provides a searching view to enhance the ability of complex reasoning. Progressive-Hint Prompting (PHP) (Zheng et al., 2023) and Cumulative Reasoning (CR) (Zhang et al., 2023) asks the model to generate hints for the question before generating the answer.

Although, these reasoning paradigms, breaking down the solution into multiple steps through

![Comparison between simple forward reasoning (left) and forward reasoning guided by back reasoning (right).](page_1012_670_382_382.png)

Figure 1: Comparison between simple forward reasoning (left) and forward reasoning guided by back reasoning (right).
prompts or spatial search, can enhance the reasoning ability and coherence of the model. They tend to make the model focus on the current state, resulting in lacking explicit guidance from a global understanding of the problem and excessive exploration of redundant information, overthinking, or errors during inference (Boix-Adsera et al., 2023).

In contrast, the way human approaches problem-solving is different. Researches have shown that humans begin by building holistic mental modeling when solving complex problems, allowing problem solvers to form a topological framework before focusing on specific details (Spreng et al., 2009; Koban et al., 2021). This kind of cognitive prediction provides dual guidance for the subsequent solution process: forming a "cognitive road map" of the solution path at the macro-level, helping to exclude obviously unrelated branches; evaluation criteria are established at the micro-level so that each specific operation remains dynamically calibrated to the end goal. This global awareness allows us to avoid blindly combining superficial details and instead prioritize purposeful, contextually grounded deductions. This suggests that modeling this local-global consistency thinking paradigm might be able to enable LLMs to strategically synthesize information, minimize irrelevant exploration, and align intermediate steps with the overarching goal.

Inspired by the maze-solving strategy of backward reasoning, where reversing the path from the endpoint accelerates discovering the solution, we propose a novel reasoning paradigm called Reason-from-Future (RFF) to enhance the reasoning ability of LLMs by adding reverse thinking process to guide the forward reasoning as shown in Figure 1.

RFF integrates bidirectional reasoning by alternating between reverse and forward thinking to maintain solution states: the reverse reasoning generates the potential last state of the target state and sets the last state as the new target, then the forward reasoning takes a step toward the new target. The target state serves as a guide to precisely lead the forward reasoning, and the forward reasoning in turn produces more useful information to make the reverse reasoning more reasonable. We evaluate RFF in five datasets: Game of 24 (Yao et al., 2024), GSM8K (Cobbe et al., 2021), ASDiv (Miao et al., 2021), SVAMP (Patel et al., 2021) MATH-500 (Lightman et al., 2023), and demonstrate significant improvements in accuracy over baseline methods. Additionally, RFF reduces the search space by constraining reasoning to target-driven states, demonstrating good efficiency. Our results highlight the potential of bidirectional, goal-aware reasoning to unlock more robust and systematic problem-solving in LLMs.

In summary, We introduce RFF, a novel self-planning reasoning paradigm to enhance the reason ability of LLMs. In which, reverse thinking and forward-thinking alternately to obtain a future perspective and narrow the solution-searching space. We conduct experiments involving four datasets to demonstrate the great performance and efficiency of RFF. And we employ two extra experiments by complicating the questions in Game of 24 and GSM8K. The results represent RFF less consuming in larger search spaces and robust thinking in variant problems.

2 Related Work

2.1 Chain of Thought Reasoning

In the study of complex reasoning tasks, Chain-of-Thought (CoT) (Wei et al., 2022; Wang et al., 2022) prompting has emerged as a pivotal technique for significantly improving the performance of large language models (LLMs) by explicitly generating intermediate reasoning steps. This approach enables the decomposition of problems into structured, stepwise reasoning pathways, demonstrating particular efficacy in mathematical and logical domains. Recent advancements extend CoT through symbolic formalization (e.g., Symbolic CoT (Xu et al., 2024)), which incorporates formal logic systems to enhance both reliability and interpretability by grounding reasoning in rigorous symbolic frameworks. Critical analyses, however, reveal potential limitations where models may exploit computational redundancy rather than genuine reasoning in extended CoT steps, prompting discussions about mechanistic transparency.

2.2 Search Reasoning

In the domain of search-based reasoning for large language models, the Tree-of-Thought (ToT) (Yao et al., 2024) framework introduces backtracking capabilities within multi-path decision structures, enabling systematic exploration of diverse solution trajectories. This approach proves particularly effective for complex tasks requiring iterative hypothesis generation and validation. Monte Carlo Tree Search (MCTS) (Świechowski et al., 2023) strengthens online decision-making robustness through simulating and evaluating long-term re-
Figure 2: Schematic illustrating various approaches to problem-solving with LLMs, and each rectangle box represents a thought. Figure2(d) only shows the basic framework about RFF; see the concrete pipeline of two types of RFF in Algorithm 1 (RFF-T) and Algorithm 2 (RFF-G).

wards of candidate paths, demonstrating strengths in reinforcement learning and dynamic programming scenarios. AOT (Sel et al., 2023) improves TOT by introducing a step-evaluation mechanism into the reasoning process, which helps LLM to prune the less likely searching route thus reduce the searching space. AOT+ (Sel et al., 2025), as the upgrade of AOT, adds a fine-grained backtracking mechanism by labeling each steps, which further reduces the reasoning consumption on an error searching route. However, both AOT and AOT+ get their global perspectives by continue exploring reasoning and degrade to normal TOT when exploring their first reasoning route, which may lead to a random search in each step and may miss the correct searching route.

Recent innovations also bridge reasoning with executable action, exemplified by frameworks like LATs (Language Agent Tree Search) (Zhou et al., 2023). By unifying hierarchical planning, probabilistic reasoning, and environment interaction within language models, LATs extends the dynamic capabilities of ReAct (Reasoning + Acting) (Yao et al., 2022) paradigms, enabling adaptive agent behavior in multi-step problem-solving scenarios. While these approaches show complementary advantages in addressing combinatorial optimization and long-range dependency challenges, computational efficiency and path-pruning strategies remain critical areas for improvement.

2.3 Progressive Hint Prompting Reasoning

In the realm of progressive prompting for complex reasoning, the LLMs solve a problem through multiple rounds of messages. Least-to-Most (Zhou et al., 2022) first breaks a problem into several sub-problems and then solve them sequentially. Progressive-Hint Prompting (PHP) (Zheng et al., 2023) advances dynamic problem-solving by fostering iterative, multi-turn interactions between users and LLMs. This method leverages feedback-driven prompts informed by historical outputs to systematically refine reasoning accuracy and coherence. Parallel to this, Cumulative Reasoning (CR) (Zhang et al., 2023) emulates human-like incremental cognition by decomposing tasks into structured subtasks and aggregating intermediate results through stepwise integration. Both PHP and CR synergize with foundational frameworks like CoT and its derivatives, collectively strengthening the generation and validation of adaptive reasoning pathways.

Recent advancements further explore hybrid architectures that combine PHP with retrieval-augmented mechanisms and task-specific distillation. These frameworks aim to balance computational efficiency with robust reasoning fidelity, addressing challenges such as error propagation and context scalability. By integrating iterative feedback loops with external knowledge retrieval, such approaches optimize performance in multi-step rea-
Algorithm 1 RFF-T
Require: LM \( p_\theta \), input \( x \), max Steps \( L \), last step generator \( G() \), stepwise reasoner \( R() \), state checker \( C() \), current state \( \{S\} \), target state \( \{T\} \), avoid attempts \( \{A\} \), verifier \( V() \), Output function \( O() \)
1: \( S_0 \leftarrow x, T_0 \leftarrow t, A_0 \leftarrow \{\}, i \leftarrow 0 \)
2: while \( i <= L \) do
3:     \( i \leftarrow i + 1 \)
4:     \( A_i \leftarrow \{\} \)
5:     \( T_i \leftarrow G(p_\theta, S_{i-1}, T_{i-1}) \)
6:     \( S_i \leftarrow R(p_\theta, S_{i-1}, T_i, A_{i-1}) \)
7:     if \( C(S_i, T_i) == True \) then
8:         \( j \leftarrow V(S_i, T_i) \)
9:         if \( j == i \) then
10:             break
11:         end if
12:         \( A_j \leftarrow A_j \cup \{S_j, T_j\} \)
13:         \( i \leftarrow j \)
14:     end if
15: end while
16: return \( O(p_\theta, x, t|S_i) \)

soning tasks while maintaining generalizability.

3 Methods

Reason from Future (RFF) is a reasoning paradigm that allows models to solve a question by using forward and backward reasoning alternately. We use \( p_\theta \) to denote a LLM with parameters \( p_\theta \), and \( x, t \) to denote the input and question. The \( \{S\} \sim \{S_0, S_1...S_i\}, \{T\} \sim \{T_0, T_1...T_i\} \) denote the list of current states and the list of target states in each step \( i \). We define \( O(p_\theta, x, t|S_i) \) as the output of the LLM with parameters \( p_\theta \) using a prompt consisting of input \( x \), target \( t \), and hints \( S_i \). In the \( i-th \) step, the model identifies the preceding step closest to the current target state \( T_{i-1} \) and considers it as the new target state \( T_i \) and provides the calculation relationship between the two. Then the model takes the \( T_{i-1} \) as the new target for one-step forward reasoning. The model then repeats this step until the latest target state has been achieved (\( S_i = T_i \)). A specific RFF pipeline should consist of three components: 1: Last Step Generator \( G() \); 2: Stepwise Forward Reason \( R() \); 3: State Check \( C() \).

3.1 Last Step Generator

RFF implements backward reasoning by generating the last previous step. To be specific, RFF decomposes one target state \( T_i \) with current state \( S_i \) into a pre-target state \( T_{i+1} = G(p_\theta, S_i, T_i) \) at a time, the form of the specific sub-target state depends on the on the target of the task, such as a set of numbers (Game of 24), the variables to be found (mathematical problems). It is worth noticing that the transition step between pre-target state \( T_{i+1} \) to target \( T_i \) should be output explicitly to guarantee the correctness of the target decomposition to a certain extent.

3.2 Stepwise Forward Reason

We consider two different strategies: RFF-T in Algorithm 1 and RFF-G in Algorithm 2, to generate the next forward reasoning step for different types of target:

(a) RFF-T: For problems like Game of 24 or Maze game, whose solution is one branch of a searching tree, the model should avoid repeating the wrong attempts in the same layer of the searching tree. We use \( \{A\} \sim \{A_0, A_1...A_i\} \) to denote the attempts should be avoid in step \( i \), thus the next state should be \( S_i \leftarrow R(p_\theta, S_{i-1}, T_i, A_{i-1}) \).

(b) RFF-G: For the problem like mathematical problems, whose solution is a directed acyclic graph, all the information calculated by the previous states are either useful or redundant but not harmful, so the reasoning path should consider all the information calculated by the previous states, which is \( S_i \leftarrow S_{i-1} \cup R(p_\theta, x, S_{i-1}, T_i) \).

Algorithm 2 RFF-G
Require: LM \( p_\theta \), input \( x \), max Steps \( L \), last step generator \( G() \), stepwise reasoner \( R() \), state checker \( V() \), current state \( \{S\} \), target state \( \{T\} \), Output function \( O() \)
1: \( S_0 \leftarrow x, T_0 \leftarrow t_0 \)
2: for \( i = 1 \) to \( L \) do
3:     \( T_i \leftarrow G(p_\theta, S_{i-1}, T_{i-1}) \)
4:     \( S_i \leftarrow S_{i-1} \cup R(p_\theta, S_{i-1}, T_i) \)
5:     if \( V(S_i, T_i) == True \) then
6:         break
7:     end if
8: end for
9: return \( O(p_\theta, x, t|S_i) \)

3.3 State Check

State Check \( C() \) maintains an inference boundary that determines the termination conditions of the inference paradigm. Similar to Stepwise Forward
Reason, we set two different strategies to check whether the reasoning comes to the boundary:

(a) RFF-T: For the reason only the correct reasoning path will be saved in the end, the \( C(p_\theta, S_i, T_i) \) only considers whether the current state \( S_i \) coincides with the latest target state \( T_i \), or whether the current state requires only one mathematical or logical operation to reach the target state(e.g. present state:(2 3 4), target state:(4 6) in Game of 24). Meanwhile, because RFF-T need to revisit the previous state to explore the thought space, a Verifier \( V(S_i, T_i) \) is set to verify whether this path is the correct path when the reasoning comes to the boundary. If the path is a wrong path \( V() \) will return the previous state \( j \) which should be revisited and record the wrong attempt \((S_j, T_j)\).

(b) RFF-G: Different from the RFF-T, each step of reasoning generates a useful node of the directed acyclic graph, so \( C(p_\theta, S_i, T_i) \) considers whether the information the target state needs has already been solved or is noted in the background.

4 Experiment

We evaluate the effectiveness of RFF on some widely used LLM reasoning benchmarks, like GAME of 24 and GSM8k. Considering that successful paradigm may be due to the strength of the model itself rather than the strength of the paradigm, leading to difficulty in migrating them to weak models or small models, we carry out our experiments using Llama3-8B-Instruct (Dubey et al., 2024) and Qwen2.5-7B-Instruct (Yang et al., 2024) as the base models, and more detailed parameters will be shown in specific tasks setup.

4.1 Game of 24

The task of Game of 24 originates from (Yao et al., 2024), where the goal is to use four numbers with basic arithmetic operations (+-*/) to obtain 24, and each number can be used only once.

Task Setup

We conduct Game of 24 on Llama3-8B-Instruct with a temperature of 0.7 (consistent with the setup of CoT (Wei et al., 2022) and ToT (Yao et al., 2024)). We apply RFF-T because Game of 24 is usually viewed as fetching a branch of the searching tree and is consistent with the paradigm of RFF-T. A solving example can be seen in Figure 3. We conduct 100 times about the middle hard 100 puzzles from 901 to 1000 (Yao et al., 2024). We also consider each branch of the searching tree as a visit state and record the average visit states of different paradigms, which is proportional to the search space and the consumption of computation.

<table>
  <tr>
    <th>Model</th>
    <th>Method</th>
    <th>ACC</th>
    <th>Visited States</th>
  </tr>
  <tr>
    <td rowspan="5">GPT-4</td>
    <td>CoT</td>
    <td>3%</td>
    <td>1.0</td>
  </tr>
  <tr>
    <td>ToT(n=1)</td>
    <td>45%</td>
    <td>-</td>
  </tr>
  <tr>
    <td>ToT(n=5)</td>
    <td>74%</td>
    <td>61.2</td>
  </tr>
  <tr>
    <td>AoT</td>
    <td>71%*</td>
    <td>-</td>
  </tr>
  <tr>
    <td>CR(n=1)</td>
    <td>84%</td>
    <td>11.7</td>
  </tr>
  <tr>
    <td>CR(n=5)</td>
    <td>94%</td>
    <td>13.7</td>
  </tr>
  <tr>
    <td rowspan="1">RFF(n=5)</td>
    <td><b>RFF(n=5)</b></td>
    <td><b>95%</b></td>
    <td><b>9.3</b></td>
  </tr>
  <tr>
    <td rowspan="2">Llama3-8B</td>
    <td>CR(n=1)</td>
    <td>9%</td>
    <td>30.9</td>
  </tr>
  <tr>
    <td>CR(n=5)</td>
    <td>19%</td>
    <td>89.8</td>
  </tr>
  <tr>
    <td rowspan="2">Llama3-8B</td>
    <td><b>RFF(n=5)</b></td>
    <td><b>89%</b></td>
    <td><b>9.9</b></td>
  </tr>
  <tr>
    <td><b>RFF(n=10)</b></td>
    <td><b>96%</b></td>
    <td><b>15.0</b></td>
  </tr>
</table>

Table 1: The results of the Game of 24, where n denotes the width of the searching tree. * denotes the result is from (Sel et al., 2023).

Baselines

We employ CoT, ToT, AoT and cumulative reasoning (CR) with different parameters as the baselines. The setup of CoT is consistent with (Wei et al., 2022) and (Yang et al., 2024), who employ the intermediate calculation process as the reasoning step. As for ToT and CR, we adapt the settings and prompts from (Zhang et al., 2023). All methods are tested 100 times to get the average result, and unless otherwise specified, the temperature of the model is set to 0.7. We also use GPT-4 as the base-

![An example of how RFF-T works in Game of 24. Different reasoning paths represent the backtracking mechanism of RFF-T](page_1012_180_410_312.png)

Figure 3: An example of how RFF-T works in Game of 24. Different reasoning paths represent the backtracking mechanism of RFF-T
Jon runs a triathlon. It takes him 40 minutes for the swim, an hour and 20 minutes for the bike ride and 50 minutes for the run. Compared to Jon, James finishes the swim 10% faster but takes 5 minutes longer on the bike. If Jon won by 10 minutes, how long did it take James to do the run?

Jon's total time is 40 + 80 + 50 = 170 minutes. James' swim time is 40 * 0.9 = 36 minutes. His bike time is 80 + 5 = 85 minutes. So his total time is 36 + 85 + x = 121 + x. Since he lost by 10 minutes, \(121 + x - 170 = 10 \rightarrow 160\). So x = 160 - 121 = 39. The answer is 39.

Let's break it down step by step.
1. Jon's total time is: 40 minutes (swim) + 80 minutes (bike ride) + 50 minutes (run) = 170 minutes
2. James finishes the swim 10% faster than Jon, which means James' swim time is: Jon's swim time - 10% of Jon's swim time = 40 - 4 = 36 minutes
3. James takes 5 minutes longer on the bike than Jon, so James' bike time is: Jon's bike time + 5 minutes = 80 + 5 = 85 minutes
4. Since James won by 10 minutes, his total time is 10 minutes less than Jon's total time:
   James' total time = 170 - 10 = 160 minutes
5. James' total time is the sum of his swim time, bike time, and run time: 160 minutes = 36 minutes (swim) + 85 minutes (bike) + ?
6. To find James' run time, subtract the swim and bike times from his total time: ? minutes = 160 - 36 - 85 = 39 minutes So, it took James 39 minutes to complete the run.

Step 1:
Back Reason:
To know how long did it take James to do the run, we can do:
the time James finishes – the time James swim-the time James rides = the time James runs.
What we need to know is: the time James finishes, the time swims, the time James rides.

Forward Reason:
the time James rides is: 1 hour+ 20 minutes = 80 minutes

Step 2:
Back Reason:
To know the time James finishes: Since Jon won, we can do:
the time Jon finishes + the time Jon won

Forward Reason:
the time James finishes is:
40 minutes + 80 minutes+ 50 minutes + 10 minutes = 180 minutes

Step 3:
Back Reason:
To know the time James swims: Since James swims 10% faster, we can do:
the time James swims – the time Jon swims faster = the time Jon swims

Forward Reason:
The time Jon swims = 40 minutes – 40 minutes*10% = 36 minutes

Step 4:
Back Reason:
To know the time James rides: Since James rides 5 minutes later, we can do:
the time James rides + 5 minutes = the time Jon rides

Forward Reason:
The time Jon rides is: 1 hour + 20 minutes + 5minutes = 85 minutes

Step 5:
Back Reason:
We have known all the information, now we can solve the problem:
the time James finishes – the time James swim-the time James rides = the time James runs

Forward Reason:
The time James runs is: 180 minutes – 36 minutes – 85 minutes = 59 minutes
Final Answer:
The time James runs is 59 minutes

Figure 4: An example from the GSM8K dataset, with solution generated by Direct, CoT, and RFF paradigms. The former two paradigms tend to connect with "win" to positive operation "more", while RFF will first analyze the background of the "win" and then generate the operation.

line model. Due to the different space exploring paradigms, we treat those with a similar number of search spaces as a same class for comparison instead of similar branches of searching trees.

Results
As shown in Table 1, RFF with Llama3-8B exhibits outstanding performance even compared to GPT-4. CoT performs badly on this task for the searching-tree-like tasks need the model to explore wide solution space. Searching paradigms like ToT and CR achieve better scores than CoT, meanwhile, the ToT method visits more states because of blind searching. RFF reaches the highest accuracy and least visit-states at the same level: when the visit-state is around 10, RFF reaches the best accuracy of 89% compared to CR with GPT-4 at 84%; when the visit-state is around 14, RFF reaches an accuracy of 96% compared to CR with GPT-4 at 94%. The fewer visit-states and higher accuracy are due to the searching space in RFF being much smaller and reasonable than simply forward searching (e.g. for "1 2 12 12", with the target "12+12=24", LLM will less likely explore ways like "2+12=14").

4.2 Math Problem Benchmark
This task contains four datasets: GSM8K, SVAMP, AsDiv and MATH-500. GSM8K is a mathematical dataset with 1319 test data, each question requires 3-10 steps of reasoning and calculation. SVAMP and AsDiv are two simple math problem datasets
<table>
  <tr>
    <th>Model</th>
    <th>Method</th>
    <th>GSM8K</th>
    <th>SVAMP</th>
    <th>ASDiv</th>
    <th>MATH</th>
    <th>AVG</th>
  </tr>
  <tr>
    <td rowspan="4">Llama3-8B-Instruct</td>
    <td>CoT</td>
    <td>75.6%</td>
    <td>80.5%</td>
    <td>82.3%</td>
    <td>32.8%</td>
    <td>67.8%</td>
  </tr>
  <tr>
    <td>Least-to-Most</td>
    <td>79.5%</td>
    <td>86.8%</td>
    <td>84.4%</td>
    <td>38.8%</td>
    <td>72.4%</td>
  </tr>
  <tr>
    <td>Give-me-Hint</td>
    <td>77.3%</td>
    <td>87.9%</td>
    <td>86.0%</td>
    <td>37.0%</td>
    <td>72.1%</td>
  </tr>
  <tr>
    <td>CR</td>
    <td>77.0%</td>
    <td>71.2%</td>
    <td>84.8%</td>
    <td>40.2%</td>
    <td>68.3%</td>
  </tr>
  <tr>
    <td></td>
    <td>RFF</td>
    <td><b>83.8%</b></td>
    <td><b>89.7%</b></td>
    <td><b>86.7%</b></td>
    <td><b>41.4%</b></td>
    <td><b>75.4%</b></td>
  </tr>
  <tr>
    <td rowspan="3">Qwen2.5-7B-Instruct</td>
    <td>CoT</td>
    <td>87.2%</td>
    <td>92.1%</td>
    <td>88.0%</td>
    <td>74.6%</td>
    <td>85.5%</td>
  </tr>
  <tr>
    <td>CR</td>
    <td>87.7%</td>
    <td>83.7%</td>
    <td>91.9%</td>
    <td>78.2%</td>
    <td>85.4%</td>
  </tr>
  <tr>
    <td>RFF</td>
    <td><b>89.5%</b></td>
    <td><b>95.1%</b></td>
    <td><b>92.2%</b></td>
    <td><b>79.8%</b></td>
    <td><b>89.1%</b></td>
  </tr>
</table>

Table 2: The results of the math problems. The score represents the accuracy of the benchmarks. The best results in each column is highlighted in bold. The AVG represents the average value of the four benchmarks.

with 1000 and 2096 data respectively, each question requires 1-2 steps of reasoning and calculation. MATH-500 is a subset of 500 mathematical problem from the MATH (Hendrycks et al., 2021) benchmark, which is a much more harder benchmark than GSM8K.

Task Setup

We conduct this task on Llama3-8B-Instruct and Qwen2.5-7B-Instruct with a greedy search to exclude the influence of random numbers on textual reasoning. We apply RFF-G for the mathematical puzzle as its solution can be seen as a directed acyclic graph from the question to the answer. We employ 1 shot as the example to lead the model to perform formatted reasoning.

Baselines

Considering the nature of the math problems, CoT and CR are chosen as baselines for their excellent ability for complex thinking and multi-jump reasoning either. CoT and CR are set with one shot to balance the influence of the same setup in RFF-G. CoT generates a continuous chain of thoughts until the model answers the question while CR generates a few hints first, then generates simple questions and answers until the model thinks it’s enough to answer the question. We also conducted two extra baseline not showing in the Game of 24: Least-to-Most (Zhou et al., 2022), which generates the sub-problem pipeline first and then follow the pipeline to solve the problem and Give-me-Hint (Agrawal et al., 2024), which generates helpful hints to help LLM solve the problem. Both baselines are recent and typical to serve as convincing control groups.

Results

Table 2 shows the accuracy of Llama3-8B-Instruct and Qwen-2.5-7B-Instruct on four datasets and our method RFF shows great advantages over the other methods. Meanwhile, there is another an interesting phenomenon: since the methods present great improvement of accuracy to CoT on GSM8K, ASDiv and MATH datasets, contributing to the better focus on details and relations about progressive prompting methods. However, CR fails to reach the average level of other methods on simple task SVAMP with 71.2% compared to 85.1%, and demonstrates better performance on hard task MATH with 40.2% to 36.2%. We carefully check the output of the CR and our RFF to and find that the detailed hints and question-answer pairs can be helpful in hard problems like MATH, but they lead to a harmful phenomenon of overthinking when facing simple problems like SVAMP. And our method RFF, benefiting from the State Checker, can avoid overthinking when the State Checker thinks the reasoning should be stopped. We also notice the gap between RFF and CoT is increasing with the base ability of the model decreasing (from Qwen to Llama), demonstrating a significant complementary effect on the model’s reasoning ability.

4.3 Commonsense Problem Benchmark

To further explore the effectiveness of RFF in different NLP tasks, we have conducted experiments on commonsense problem benchmarks. Commonsense problems usually refer to those that require basic knowledge and reasoning ability in human daily life to solve. These problems rely on background knowledge, which is usually not explicitly stated in the problems. we have conducted experiments on two widely used commonsense
benchmarks: CommonQA (Talmor et al., 2018) and LogiQA (Liu et al., 2020) using RFF-G. Both two benchmarks are multiple-choice, which contains 12102 and 8678 questions respectively, each with one correct answer and four choices.

Task Setup
We conduct this task on Llama3-8B-Instruct to test on this benchmark. Considering the nature of the commonsense tasks, we choose RFF-G to solve the question. We judge the accuracy of the answer by observing whether the model outputs the correct option, any other forms of answers will be viewed as wrong.

Baselines
For commonsense tasks, it will be much helpful if the model is given background informations before answering the question, so the hints based and progressive prompt reasoning paradigms will serve as effective references. Same as math benchmark, we choose COT, CR, Least-to-Most and CR as our experiment baselines.

Results
As shown in Table 3, all the reasoning paradigms achieve a better accuracy on CommonQA, demonstrating the complex prompting can easily improve the performance on it. However, the differences among these methods are not so apparent (all distributed at around 76%), so the sole result of CommonQA is not sufficient to express the superiority of our method. In LogiQA, the differences shows a greater gap among these baselines: the results of Least-to-Most and Give-me-Hint are close to COT while the results of RFF and CR shows a significant improvement over COT.

<table>
  <tr>
    <th>Method</th>
    <th>CommonQA</th>
    <th>LogiQA</th>
    <th>AVG</th>
  </tr>
  <tr>
    <td>COT</td>
    <td>73.1%</td>
    <td>41.8%</td>
    <td>57.5%</td>
  </tr>
  <tr>
    <td>CR</td>
    <td>75.4%</td>
    <td><b>45.5%</b></td>
    <td><b>60.5%</b></td>
  </tr>
  <tr>
    <td>Least-to-Most</td>
    <td>74.3%</td>
    <td>42.9%</td>
    <td>58.6%</td>
  </tr>
  <tr>
    <td>Give-me-Hint</td>
    <td>76.6%</td>
    <td>42.0%</td>
    <td>59.3%</td>
  </tr>
  <tr>
    <td><b>RFF</b></td>
    <td><b>77.1%</b></td>
    <td><u>45.2%</u></td>
    <td><u>61.2%</u></td>
  </tr>
</table>

Table 3: The results of commonsense reasoning benchmarks. The best result in each column is highlighted in bold, and the second best in each column is added an underline.

The results also indicate that in commonsense tasks, especially in easy task (CommonQA), simple prompting method (Give-me-Hint) achieves better scores than complex prompting methods (Least-to-Most and CR), which we think it’s for the over thinking of these methods. Meanwhile, RFF can still maintain a high score due to its step-evaluation mechanism: when facing simple questions, the forward reasoning can quickly meets the backward reasoning, then the RFF turns to simple COT to solve the problems instead of over thinking.

4.4 Studies of Redundant Thinking
We investigate the limitations of traditional algorithms for solving Game of 24. While conventional breadth-first searching methods perform well in low-dimensional solution spaces, their unguided exploration mechanisms may lead to significant computational resource waste and efficiency degradation when handling higher-dimensional problems.

To validate this theoretical hypothesis, we constructed an experimental dataset comprising 100 enhanced problems (IDs 901-1000) by strategically adding the constant "1" to original four-number combinations, creating five-number variants. Theoretically, this operation preserves the solvability of problems (based on arithmetic identity transformations) and is expected to decrease the difficulty by introducing a redundant variant.

<table>
  <tr>
    <th>Model</th>
    <th>Method</th>
    <th>ACC</th>
    <th>Visited States</th>
  </tr>
  <tr>
    <td rowspan="3">GPT-4</td>
    <td>CR(n=5)</td>
    <td>76%</td>
    <td>7.06</td>
  </tr>
  <tr>
    <td><b>RFF(n=5)</b></td>
    <td><b>89%</b></td>
    <td><b>5.96</b></td>
  </tr>
  <tr>
    <td><b>RFF(n=10)</b></td>
    <td><b>93%</b></td>
    <td>9.13</td>
  </tr>
  <tr>
    <td rowspan="3">Llama3-8B</td>
    <td>CR(n=5)</td>
    <td>26%</td>
    <td>96.56</td>
  </tr>
  <tr>
    <td><b>RFF(n=5)</b></td>
    <td><b>85%</b></td>
    <td><b>28.62</b></td>
  </tr>
  <tr>
    <td><b>RFF(n=10)</b></td>
    <td><b>92%</b></td>
    <td>56.13</td>
  </tr>
</table>

Table 4: The results of 5 numbers of the Game of 24.

As shown in Table 4, after adding a redundant "1", the performance of CR decreased significantly with GPT-4 (from 94% to 76%). In contrast, RFF achieves a higher success rate with fewer visit states compared with CR. When we further expand the search space, the model’s performance continues to improve. At the same time, we observe the smaller model requires more attempts to achieve performance comparable to the original data. However, RFF consistently surpasses CR in terms of success rate and resource consumption. The result demonstrates the effective prospective state space pruning in RFF and validates the superiority of the searching space convergence mechanisms of RFF.
Figure 5: The result of CoT and RFF on GSM-Symbolic dataset. The score in the upper right of the chart is the average accuracy score of the 50 subsets. RFF shows more stable and better distributed at high accuracy.

4.5 Studies of Robust Thinking
To address the data leakage risks associated with the widespread adoption of the GSM8K, researchers (Mirzadeh et al., 2024) proposed the GSM-Symbolic benchmark through semantic-preserving transformations. This dataset generates derivative problems via entity/quantity substitution (GSM-SYM) and the addition of single (GSM-P1) or dual (GSM-P2) conditional constraints to the original question. Despite theoretical expectations that surface-level modifications (e.g., name/quantity changes) should not impact reasoning capabilities, empirical observations reveal significant accuracy degradation across all models. Following the standard evaluation protocol of GSM8K, we systematically assess the reasoning generalization of RFF models using the publicly available SYM, P1, and P2 subsets (each subset contains 50 variants from an original dataset). We employ Llama3-8B-Instruct with CoT and RFF methods to conduct this task.

Figure 5 shows the accuracy distribution of the 50 variants datasets in three subsets. The result exhibits that the accuracy of both methods drops on these three datasets, representing the fragility of the reasoning ability of models.

However, RFF still has advantages in the average accuracy and shows a more concentrated and more accurate distribution. The result emphasizes that the form of forward reasoning guided by backward reasoning is quite robust in the face of variant problems.

5 Conclusion
In this paper, we introduce Reason from Future (RFF), a novel reasoning paradigm aiming at enhancing the reasoning ability of LLMs for complex problems. RFF leverages a bidirectional reasoning framework integrates top-down planning with bottom-up reasoning accumulation to generate a solution path. This aids in the convergence of the search space for the model, thereby enhancing inference efficiency. Simultaneously, it allows the model to focus on critical information, which improves the accuracy of reasoning. RFF has demonstrated superior performance across both searching tree tasks (Game of 24) and directed acyclic graph tasks (math problems and commonsense problems), showing the potential to enhance the model’s reasoning capabilities.

Limitations
The effectiveness of RFF relies on the model’s ability for reverse thinking. Since the model has not been trained with specialized data, there can be rare instances where errors in the final step of reverse reasoning lead to failure. In future work, we will introduce fine-tuning or reinforcement learning to further enhance the generalizability of this reasoning paradigm.

Acknowledgments
This research was partially supported by National Natural Science Foundation of China under Grant No.12326612, No.82202984, Zhejiang Key R&D Program of China under Grant No.2024SSYS0026, Zhejiang Key Laboratory of Medical Imaging Artificial Intelligence, and the Transvascular Implantation Devices Research Institute (TIDRI).

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A Detailed Difference between Baselines

Although most progressive prompting methods employ the reasoning paradigms by dividing a hard problem into several simple subproblems, the mechanism for decomposing the problem and the mechanism for how to solve the subproblems are different and serves as the core of the reasoning paradigms. We carefully compare the two typical baselines we used in our work (Least-to-Most and CR), and analyzed their characteristics and difference with RFF.

A.1 Difference between Least-to-Most
For Least-to-Most, it generates its sub-problems of the final problem in the very beginning, then the LLM follows the pipeline of the sub-problems to generate its reasoning. It’s a two-stage plan-solve reasoning and the sub-problems never change during the solution, so the sub-problems may be wrong or insufficient because of a lack of the intermediate information generated by the reasoning process.

The biggest difference between RFF and Least-to-Most is that process of RFF starts from the end state of the problem, RFF doesn’t plan just at the beginning but to continue to generate questions or hints or guidance by backward reasoning to lead LLM to better reason forward.

A.2 Difference between CR
For CR, it generates several hints for the problem first, the hints are helpful to solve the questions. Then the LLM continues to generate subproblem which based on the hints and then answer it until the LLM can solve the problem.

Differ from CR, which generates guidances from the previous visiting states to reduce hallucinations, our method (RFF) generates guidance from the backward reasoning to give the model a full-perspective of the problem. Additionally, the detailed hints and nonstop subproblems may lead CR to overthinking, meanwhile, the full-perspective and State Check ensure the ability of RFF to stop overthinking quickly when facing simple questions with complex prompting.

B Extra Experiments on Reasoning Paradigms

We compare two different backward reasoning strategies on Math Problems called Pair Reasoning (same as RFF in 2) and Single Reasoning as shown in Figure 6, we conduct experiments on GSM8K dataset using Llama3-8B-Instruct with greedy search.

<table>
  <tr>
    <th>Model</th>
    <th>Method</th>
    <th>ACC</th>
  </tr>
  <tr>
    <td rowspan="3">Llama3-8B</td>
    <td>CoT</td>
    <td>75.6%</td>
  </tr>
  <tr>
    <td>Pair Reasoning RFF</td>
    <td><b>83.8%</b></td>
  </tr>
  <tr>
    <td>Single Reasoning RFF</td>
    <td>69.8%</td>
  </tr>
</table>

Table 5: The results of different back reasoning strategies.

As shown in Table 5, the performance of Single Reasoning RFF drops badly on GSM8K dataset and even worse than CoT, we assume that the weakness of the strategy of Single Reasoning is that when deducing the whole chain of backward thought, the situations of multi-hop seriously affects the backward reasoning without new information generated by the forward reasoning. So when employing backward reasoning paradigms, a continuous generation of new information is needed.

C Appendix for Prompts

The design of prompts is critical to lead the model to reason exactly according to the paradigm we have planned. We design these prompts deliberately to ensure the model reason and output according to the format we give it.
System: Suppose you are one of the greatest AI scientists, logicians, and mathematicians. Let’s play a game.
The Input is the current state, which contains four or three numbers.
The Target is the state we want to get, which contains one or two numbers.
The Last Step is how to get the Target with Input in the last step.
The Avoid is tested to be a wrong Last step, you need to generate another different step.
What you need to do is to think how to use Input to get Target use some steps, just output the most likely Last Step you think.
Notice:
1 Now do not calculate the game, you need to rely on your instincts to give the most likely Last Step directly, and do not output other thinking process.
2 The Last Step should contains two parts: "calculation" and "left".
3 The number used in "calculation" may not appear in Input, and the result of "calculation" must appear in "left".
4 The numbers in "left" must be the same as Target.
5 You are forbidden to output Steps, you should output Last Step only.

User:
Input: 1 3 6 11
Target: 24
Avoid: 3 x 8 = 24 (left: 24)
Avoid: 4 x 6 = 24 (left: 24)

Assistant:
Last Step: 2 x 12 = 24 (left: 24)
System: Now you are given few examples about the game:
Input is the current state of the game.
Target is the final state you need try to satisfy using basic arithmetic operations (+ - * /) with the Input.
Steps are how to get Target with Input through basic operations.
Next Step is the how to get the Target with Input in the next step.
The Avoid is tested to be a wrong Next step, you need to generate another different step.
You need to choose two numbers from Input and use one basic arithmetic operations (+ - * /) to generate a new number.
Notice:
1 Output the Next Step directly and do not output the other thinking process.
2 The Next Step contains and only contain two parts: "calculation" and "left".
3 The "left" should be close to Target but not asked to be the totally same.
4 Your calculation must be correct.
5 Do not output Steps.

User:
Input: 8 8 10 12
Target: 8 16
Avoid: 8 + 8 = 16

System:
Next Step: 12 - 10 = 2 (left: 2 8 8)

Figure 8: Prompts of Stepwise Forward Reason for Game of 24

System: You are one of the GREATEST mathematicians, logicians, programmers, and AI scientists. You are intelligent and rational. You are prudent and cautious. You THINK NATURAL, BROAD AND DEEP.
Let's think step by step.
You will be given a mathematical problem, a question about it and the information we have calculated.
Notice:
1 You are not permitted to solve the question from the beginning.
2 You need to analyse the question and figure out what will be the last step to solve the question.
3 Make sure your analysis are used to calculate the result of the question not the intermediate result.
4 Output the calculation process, and the information we need.

User:
Problem: {problem}
Question: {question}
Information: {information}

Assistant:
To know {question}: Since {information}, we can do: {calculation process}
Need Information: {need information}

Figure 9: Prompts of Last Step Generator for math problems
System: You are one of the GREATEST mathematicians, logicians, programmers, and AI scientists. You are intelligent and rational. You are prudent and cautious. You THINK NATURAL, BROAD AND DEEP. Let's think step by step.
You will be given a mathematical problem, a question about the problem, and the information we have calculated.
Notice:
1 You are not permitted to solve the question directly.
2 You need to analyse the question and figure out next step we get to solve the question.
3 Make sure your analysis are used to calculate the result of the question not the intermediate result.
4 Output the calculation process, and the new information we get.

User:
Problem: {problem}
Question: {question}
Information: {information}

Assistant:
Next Step: {calculation process}
New Information: {new information}

Figure 10: Prompts of Stepwise Forward Reason for math problems

System: You are one of the GREATEST mathematicians, logicians, programmers, and AI scientists. You are intelligent and rational. You are prudent and cautious. You THINK NATURAL, BROAD AND DEEP. Let's think step by step.
You will be given a mathematical problem, a question about it and information we have calculated.
Notice:
1 You are not permitted to solve the question.
2 You need to analyse the question and information, then figure out whether we have already solved the question.
3 Make sure your analysis do not consist of calculation process.
4 If we have solved the question, you should output [True], else you should output [False].

User:
Problem: {problem}
Question: {question}
Information: {information}

Assistant:
Analyse: {analyse}
Answer: [True, False]

Figure 11: Prompts of State Check for math problems

Reviewer paper summaries: The paper introduces a novel reasoning paradigm called Reason from Future (RFF), aimed at enhancing the problem-solving capabilities of language models by combining bidirectional reasoning, reverse reasoning, and goal-oriented constraints. By prioritizing core logical relationships and reducing the search space, RFF addresses the shortcomings of traditional reasoning paradigms like Chain-of-Thought and Tree-of-Thought. The empirical evaluations show that RFF not only improves accuracy but also enhances computational efficiency

This work proposes a reasoning method that combines both bidirectional reasoning including top-down planning and bottom-up reasoning. Experimental results demonstrate improved reasoning performance. The method exhibits some novelty but also suffers from several issues.

Authors introduce a novel reasoning paradigm called "Reason from Future" (RFF) that enhances the reasoning capabilities of large language models through bidirectional reasoning. Unlike conventional approaches like Chain-of-Thought and Tree-of-Thought that focus on forward reasoning and can fall into local reasoning traps, RFF combines top-down planning with bottom-up reasoning by alternating between reverse and forward thinking. This approach prioritizes goal-oriented constraints, reduces search space, and mitigates error accumulation. The authors evaluate RFF across multiple datasets including Game of 24, GSM8K, ASDiv, and SVAMP, demonstrating improvements in both accuracy and efficiency compared to baseline methods.
Summary of strengths: 1. RFF is a novel paradigm for the LLM reasoning, incorporating bidirectional reasoning, which blends top-down planning with bottom-up reasoning accumulation. 
2. The paper is written clearly and easy to follow.  
3. experiments on game and math show the effectiveness of the method.

1. The reasoning process resembles human cognitive patterns, offering a degree of innovation.  
2. The schematic diagrams are clear and illustrative.  
3. The proposed method requires no training.  
4. Experimental results show significant performance improvements.

- Demonstrates significant performance gains on reasoning tasks with smaller models (8B parameters)
- Reduces computational resources by efficiently pruning search space
- Shows robustness when handling variations of problems (e.g., GSM-Symbolic dataset)
Summary of weaknesses: 1. Game of 24 and GSM8K are easy, it would be important to evaluate RFF across a wider array of NLP tasks—particularly those that involve diverse reasoning challenges.

1. Novelty: The method resembles early question decomposition-based reasoning approaches such as Least-to-Most[1] and DecomP[2], which decompose problems into subproblems solved sequentially. While the paper claims to integrate reverse and forward reasoning, its implementation aligns closely with prior methods. For instance, the reverse thought decomposes the original problem into subproblems e.g., planning James’s end time, swimming time, and cycling time in the first step, followed by sequential resolution of these subproblems, as illustrated in Figure 4. Thus, the proposed method appears to reinterpret existing reasoning workflows (e.g., Least-to-Most) rather than introducing fundamentally new mechanisms. 
2. Writing:  
   1. The literature review is insufficient, with the latest cited work dated 2023. More recent and relevant studies on planning + reasoning should be included.  
   2. Numerous typographical errors exist, e.g.,  
      - Line 213: Ambiguous definition of $p(x,t|S_i)$.  
      - Line 232: Duplicated "on the."  
      - Line 273: Inconsistent notation $V(Si,Ti)$ (missing subscripts).  
   3. The methodology description in Section 3 is vague, particularly the "Last Step Generator" subsection, despite half a page of space still available for clarification. For example, I am not clear about the term "last previous step" in Line 228.
   4. Inconsistent symbolic definitions:  
      - Line 211 defines the target state at step i as {T}={T_0,T_1,...,T_i}, conflicting with subsequent descriptions of $T_i$ as a singular target state.  
3. Experiments:  
   1. Insufficient baseline comparisons, especially in mathematical reasoning (only two baselines, with the latest from 2023).  
   2. Evaluations rely on overly simple tasks. Mathematical reasoning works should be tested on more challenging benchmarks like MATH. For example, CR also include experiments on MATH.


[1] Least-to-Most Prompting Enables Complex Reasoning in Large Language Models
[2] Decomposed Prompting: A Modular Approach for Solving Complex Tasks

I don't see any major weaknesses in the paper except that the discussions in the introduction can be greatly improved. For instance, RFF is not the only method aimed at overcoming the ToT's lack of global perspective, comparisons to other such methods such as AoT [1] (although cited in the paper, no discussions) / AoT+ [2] is required to distinguish the method in the paper. I'm happy to reconsider my score after more discussions are added.

[1] Algorithm of Thoughts: Enhancing Exploration of Ideas in Large Language Models
[2] LLMs Can Plan Only If We Tell Them
Comments, suggestions and typos: NA

Please see the weaknesses.

See weaknesses.
Overall assessment scores: 2.5

3

3
Metareview score: 3
Metareview: This paper introduces "Reason from Future"(RFF), a novel reasoning paradigm designed to improve large language model performance by incorporating bidirectional reasoning. RFF combines reverse thinking with forward reasoning to achieve more efficient and accurate reasoning outcomes, especially in mathematical and symbolic tasks. The proposed approach is evaluated across several benchmarks including Game of 24, GSM8K, ASDiv, and SVAMP, and shows notable improvements over established baselines. The method is particularly compelling for smaller models, achieving gains in both reasoning performance and computational efficiency.

While the overall idea is innovative and well-executed, the novelty of RFF relative to prior work—especially recent advances in decomposition and planning-based methods—is underexplored. The paper would benefit from deeper discussions and comparisons to approaches like Algorithm of Thoughts (AoT), AoT+, Least-to-Most Prompting, and Decomposed Prompting. Additionally, the methodology section could be clarified further to ensure accessibility, and broader benchmark evaluations are needed to strengthen the generalizability of the results. The work is promising but needs refinement and broader context to fully realize its impact.
Summary of reasons to publish: 1. Proposes a compelling bidirectional reasoning paradigm that mimics human cognitive processes.

2. Demonstrates clear empirical gains on several reasoning datasets with a lightweight and training-free method.

3. Offers practical value by reducing search space and computation, particularly useful for smaller models.

4. The paper is generally well-written, with helpful illustrations and a clear experimental setup.