We sincerely appreciate the reviewer’s constructive feedback. We hope the following responses will fully address your concerns and further clarify our contributions.

W1:

We would like to clarify the contribution and novelty of our work as follows:

1. First work to explore cross-task length generalization
   • We fully acknowledge that multi-task training is a well-established concept across many domains. However, our work introduces a novel perspective by being the first to explore cross-task transfer of length generalization through multi-task training. Length generalization presents a unique challenge due to its inherent out-of-distribution (OOD) nature—models are trained on short sequences but must generalize to much longer ones. We show through experiments that traditional multi-task methods like instruction tuning (e.g., Tulu3 in Table 3) fail under such conditions, since the reasoning steps required at test time go far beyond those seen during training.
2. Meta rule-following through multi-task training
   • While multi-task training itself is not new, our key insight is that training on a large number of (rule, execution trace) pairs teaches the model to internalize transferable, rule-based reasoning patterns through shared computation primitives, such as loop maintainence. This results in a meta rule-following capability that supports length generalization across diverse tasks. For example, our RF-pretrained 32B model achieves 95% accuracy on 30-digit addition, even though it has never seen that task during training—dramatically outperforming much larger models like DeepSeek-R1-671B (72%) and QwQ-32B (32%).
3. Why training on many rules matters
   • Humans have developed an extensive array of rules throughout history, encompassing both natural laws and regulatory frameworks. For instance, the rules for integer addition are clearly outlined in textbooks, on wikis, and within computer programs. Although these rules may be present within the large training corpus during pretraining for LLMs, current training methods fail to fully leverage them. The relationships between the “rules” and their corresponding “instances” remain inadequately modeled. As a result, while recalling rules is relatively straightforward for models, they struggle to apply these rules to specific instances. This results in failures to generalize in length on seemingly simple problems. Meta-RFFT addresses this by explicitly linking rules and step-by-step executions across many tasks, encouraging cross-task rule-based reasoning. The idea of modeling the relationship between rules and rule-execution traces is novel beyond RFFT.
4. Key technical contribution beyond RFFT
   • We collect 86 diverse tasks spanning code execution, number processing, logic, and symbolic reasoning—far beyond the 3 tasks used in RFFT—and generate 310k rule-following samples for RF-pretraining across 74 of these tasks.
   • Through this, the model learns a meta rule-following ability: it can solve unseen tasks with only 1-shot prompting, as shown in Section 4.3 (Figures 5 & 9). This enables in-context transfer of rule-following behavior, reducing or even eliminating the need for downstream fine-tuning—greatly enhancing the practicality and usability of our approach over RFFT.
   • Besides, the RF-pretrained model demonstrates superior performance in various downstream tasks to vanilla RFFT.
5. Beyond prior length generalization literature
   • Previous studies on length generalization focus on single-task, small-scale transformers trained from scratch. These models, despite generalizing well in certain tasks, have little generic language ability. Our work aligns with LLM's core multi-task advantage and explore length generalization in a multi-task, post-training setting, using pretrained LLMs.

W2:

Indeed, learning transferable patterns aids generalization is a well-established principle in areas such as Domain Generalization and Instruction Tuning, but what are the "transferrable patterns" and how to find them for specific scenarios such as length generalization, matter much more than the principle itself. In this regard, we respectfully argue that our work innovatively introduces a new insight specific to the problem of length generalization in large language models: that learning explicit, transferable rule-following patterns via multi-task training significantly enhances OOD generalization on unseen tasks, which is a direction not addressed in prior work. In other words, our work answers it is the "rules" and their underlying loop structure that make the transfer happen.

By explicitly teaching rules and execution traces across many tasks, Meta-RFFT enables models to internalize meta-level computation strategies, such as loop maintenance, that generalize both across lengths and tasks. This is not merely multi-task learning—it is the first demonstration of cross-task transfer in length generalization, enabled by explicit rule-based supervision at scale.

We believe this is a meaningful insight with practical implications for building LLMs that generalize more robustly in reasoning-intensive scenarios.

W3:

We appreciate the reviewer for pointing out this important and practical concern.

Meta-RFFT involves substantial RF-pretraining, which indeed can affect the model’s general capabilities due to distribution shift, known as catastrophic forgetting. But typically this is easily addressed by mixing some pretraining corpus during fine-tuning.

To verify this, we conduct a supplementary experiment. As we don't have access to the pretraining data, we mix GSM8K training data into downstream finetuning alongside the original meta-rule-following data to verify that the reasoning ability on GSM8K can be kept after RFFT. More specifically, for each training example in GSM8K, we use Qwen2.5-7B-Instruct to generate 10 candidate answers and filter the corrrect traces as the training set, forming a filtered GSM8K dataset of 7182 samples.

The results on length generalization (averaged across 8 LeetCode tasks) and GSM8K test accuracy are shown below. We observe that merely mixing 7k samples (compared to 310k Meta-RFFT data) effectively recovers the model’s reasoning performance on GSM8K, while maintaining the strong multi-task length generalization ability. Notably, Meta-RFFT still significantly outperforms vanilla RFFT, demonstrating that general capabilities can be preserved with minimal additional data.

W4:

We’d like to clarify a key point: the evaluation tasks are entirely distinct from the training tasks, and the focus of this paper is precisely on generalizing to unseen tasks and unseen lengths, not merely expanding training coverage. Besides, we conduct additional experiments on a real-world task the Airline Baggage Cost Estimation task, which is very different from the tasks in our paper and show the results below.

• As shown in Figure 2, the 12 evaluation tasks (8 from LeetCode, 4 from NUPA in Figure 3) have no overlap with the 74 tasks used during RF-pretraining. We will make this clearer in the revision.
• In particular, the NUPA tasks, used solely for evaluation, are completely held out during RF-pretraining—yet the model generalizes well to these tasks after minimal adaptation.
• In the downstream adaptation setting, the model is fine-tuned only on lengths 1–5 and then tested on unseen lengths 6–30, to assess true OOD length generalization.
• Beyond that, we also evaluate the model’s ability to handle unseen tasks via 1-shot in-context learning, without any fine-tuning. As shown in Figure 5 (7B) and Figure 9 (32B, Appendix E.1), the RF-pretrained model can directly adapt to new tasks with only a single example, achieving strong performance and robust length generalization.

In short, Meta-RFFT is explicitly designed and evaluated for generalization to tasks and lengths never seen during training—in stark contrast to simply expanding dataset coverage. We show that it enables LLMs to:

• (a) extrapolate to longer input lengths (length generalization); and
• (b) adapt to entirely unseen tasks through minimal examples (cross-task transfer).

---

Further Results on Real-World Task

To validate the practical value of Meta-RFFT beyond symbolic tasks, we additionally conduct experiments on a real-world scenario: the Airline Baggage Cost Estimation task from [1].

This task asks the model to compute the total travel cost for passengers according to American Airlines' policy. Solving it requires understanding and applying natural language regulations, which go beyond what can be fully captured in formal code. Current LLMs perform poorly on it, and even strong models like Claude-3.5 and o1-preview degrade rapidly with input length (see the table below).

We train models on samples with length 1-8, and report test accuracy on OOD lengths 10-16. As shown below, Meta-RFFT significantly outperforms vanilla RFFT in the practical domain:

[1] Zhou et al., RULEARENA: A Benchmark for Rule-Guided Reasoning with LLMs in Real-World Scenarios, 2025.

Thanks for your instructive feedback! We hope that we can address the remaining concerns as follows:

W1 (3) & (4)

The central weakness remains: the paper does not offer a unified or principled methodology for constructing such a dataset.

The contribution currently reads as, "We created a successful dataset," rather than, "We are proposing a novel and principled method for creating such datasets."

We would like to clarify that the core contribution of our paper is that, we for the first time demonstrate that length generalization can be transferred across tasks through the Meta-RFFT method. Constructing this large-scale dataset is a necessary step to prove this claim, but definitely not our whole contribution. Moreover, we have a clear motivation and principled insight to construct such a rule-following dataset for cross-task length generalization transfer. We believe this insight is beneficial and inspirational for other domains and goals requiring nontrivial OOD generalization. Below, we detail our logic for constructing this dataset:

1. First, we hope to reach a consensus: Cross-task length generalization is a challenging and important problem.
2. However, merely expanding training data coverage or standard multi-task learning methods, such as instruction tuning, are not capable of achieving out-of-distribution (OOD) generalization, as evidenced by our experiments of Tulu3 on length generalization tasks (Table 3 in the original paper).
3. Our method, Meta-RFFT, enables cross-task OOD generalization. The core reason we have such a belief and thus constructing the necessary dataset is, we observe that tasks requiring infinite generalization on the "length" dimension all need to master a common ability—"looping". But how can we teach models to master the underlying looping ability instead of overfitting the specific rules for a task (what RFFT does)? Our solution is to manually construct a dataset of diverse length-generalization tasks and prepare extensive training data across different lengths with strict (rule, execution) format. Such extensive data force the model to learn the underlying common structure across tasks, thus mastering the meta ability of looping which allows cross-task length generalization.
4. Broadly speaking, we are attempting to model the relationship between rules and instances, which is a crucial insight for other domains as well. In OOD scenarios, the key is first identifying shared meta rules (looping here) and then fine-tuning the model across diverse tasks sharing such meta rules. This enables the model to perform well on unseen tasks and unseen complexity. Humans have developed a vast array of rules throughout history, including both natural laws and regulatory frameworks. For example, the rules for integer addition are clearly laid out in textbooks, wikis, and computer programs. While these rules may be present in the large training corpus used for pretraining LLMs, current training methods fail to fully utilize them, i.e., LLMs can recite them but cannot faithfully execute them. The relationship between these rules and their corresponding instances is often inadequately modeled, which causes models to struggle to apply these rules to specific instances, leading to poor generalization on tasks involving length. Meta-RFFT addresses this by explicitly modeling the relationship between rules and rule-execution traces across tasks, fostering OOD rule-based reasoning, as evidenced by our impressive one-shot performance on unseen tasks. This is analogous to experienced human learners -- the more tasks they learn, the faster they are capable of learning a new task. Ultimately, human experts can directly execute a rule they see for the first time, faithfully across lengths, with few or even zero examples. Such important ability is missing from current LLMs/agents and our work alleviates this gap.
5. Regarding inspiration for other domains, as shown in the original paper, Meta-RFFT proves beneficial in downstream tasks that involve natural language rules, not just formal language rules (Figure 6). This greatly expands the applicability of Meta-RFFT to real-world rule-following domains, such as agentic workflow execution and reading and executing manuals or instructions. To further validate the method on practical tasks, we conducted additional experiments on the Airline Baggage Cost Estimation task, with detailed results shared in the previous response. We believe that the results involving natural language rules and real-world tasks demonstrate that the meta rule-following capability gained by training on vast (rule, execution) pairs can inspire the construction of similar (rule, execution) pairs for other tasks that require rule-following, which is a critical capability involving a wide range of practical applications.

W4

I encourage the authors to highlight this in the experimental setup by clearly listing out what tasks are used for training what are used for validation.

We apologize for any confusion. In the original paper, we emphasized in Figure 2 that the tasks used during the RF-pretraining phase do not overlap with those used in the downstream adaptation phase. Additionally, Table 1 further illustrates the task distribution across domains for both RF-pretraining and downstream adaptation. We will make sure to highlight this distinction more clearly in the revised version.

how are the held-out validation tasks determined? The held-out validation tasks were determined as follows:

First, we retained the NUPA dataset for validation, as it covers numeric processing tasks, which present a significant domain shift compared to the other three datasets. This makes it an ideal choice for evaluating performance transfer across different task domains.

Secondly, for the LeetCode tasks, we manually selected challenging tasks that also reflect practical real-world scenarios. For example, the LC Crawler Log Folder task involves determining the final folder after operations like ../ (move up) and x/ (enter folder), which simulates real-world file system navigation—a common problem in software development. The LC Hamming Distance task calculates the difference between two integers' binary representations, which mirrors practical applications in areas such as data comparison, error detection, and cryptography. These tasks demonstrate that our downstream tasks involve reasoning applicable to real-world computational problems.

Finally, for all downstream tasks, we strictly checked—both manually and using LLMs—that there were no data overlaps with the tasks used in the RF-pretraining phase to avoid any potential data contamination.

It seems that a more rigourous approach would be performing something like cross-validation - randomly splitting a certain ratio of tasks for validation and average over multiple seeds.

Thank you for the suggestion. We agree that a more rigorous approach, such as cross-validation with random task splits and averaging over multiple seeds, would be beneficial. However, due to limited computation resources, we were unable to complete multiple runs of RF-pretraining during the discussion period. That said, we conduct a preliminary evaluation as follows:

We re-run the RF-pretraining with only LeetCode tasks. Due to resource constraints, we evaluate the model on 4 downstream tasks from the original paper: 2 from LeetCode (Move Zeros & Valid Palindrome) and 2 from NUPA (Add Integer & Digit Max Integer). Additionally, we test the model on 3 tasks (2 from Symbolic Reasoning and 1 from Big-Bench Hard), which have been included in the original RF-pretraining but excluded in this new run. All these tasks are unseen during the RF-pretraining phase.

The results, shown below, indicate a slight performance drop on the tasks that were used in the original paper, likely due to reduced task diversity in this new pretraining run. Nevertheless, Meta-RFFT still significantly outperforms vanilla RFFT, further validating the effectiveness of our approach. Furthermore, we test the model trained on LeetCode-only tasks on the Big-Bench Hard and Symbolic Reasoning tasks, and Meta-RFFT continues to outperform vanilla RFFT, confirming that our method is robust across tasks.

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We are eager to continue addressing any additional questions or concerns you may have. We sincerely appreciate your review and look forward to hearing whether our rebuttal has sufficiently addressed your concerns.

continuing W1 (3) & (4)

The emergent abilities observed appear to be a post-hoc discovery resulting from this specific data artifact, not from a novel, principled methodology.

the observed "meta rule-following", "in-context transfer" abilities are results from improved datasets, but not novel methodlogies or any principled approaches.

Based on the clarifications above, we would like to emphasize that the creation of the dataset was driven by a clear insight and methodological necessity. Specifically, we strongly believe that Meta-RFFT is essential for enabling cross-task length generalization transfer. The dataset was not created arbitrarily, but rather it was carefully designed following a principle (modeling common structure underlying rule-execution pairs) to validate our core claim that length generalization can be transferred across tasks. The observed empirical results were not coincidental, but a direct consequence of our principled approach.

W3

I am looking for results on common knowledge (ARC, MMLU), and preference alignment (Alpaca-Eval, MT-Bench) as well.

Thanks for your constructive advice! We have extended our evaluation to include common knowledge and preference alignment.

Similar to our previous experiments on GSM8K, we mix general data into the downstream fine-tuning alongside the original rule-following data to ensure that general ability is preserved. The results of the model's general ability and length generalization are shown below. Regarding length generalization results, due to tight time constraint, we test on 2 downstream task: LC Valid Palindrome and NUPA Add Integer. We observe that by mixing 6,872 training samples for ARC and 8,000 for Alpaca, the model’s general ability is effectively restored, while still maintaining strong multi-task length generalization.

Specifically, for Alpaca-Eval, we observe that the model’s win rate improves significantly. This improvement is due to the model generating longer outputs, which is preferred in the win rate calculation. So we add another metric length control win rate introduced by [1] to provide a more comprehensive result.

• General ability results:

• Length generalization results:

---

[1] Dubois et al., Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators, 2025.

We sincerely appreciate the reviewer’s insightful and constructive feedback! We hope the following responses will further address your concerns.

W1, Q2:

We find the reviewer’s suggestion to explore RL for rule-following tasks highly insightful, and in fact, we have conducted preliminary investigations along this line.

In our current work, we explore a baseline using RL with outcome rewards through experiments. While outcome-reward RL has achieved success in general reasoning, we find it less suited for strict rule-following. Unlike supervised fine-tuning (SFT), which directly maximizes the likelihood of generating rule-compliant intermediate steps, outcome-based RL optimizes only for the final answer. For tasks with explicit human-defined rules, we believe explicitly teaching the rule is more effective than relying on model's exploration.

Empirically, as shown in Figure 7, the RL-trained model underperforms Meta-RFFT. Without supervision of intermediate steps, it struggles to follow rules reliably (see Table 9 for an error case). Besides, Meta-RFFT significantly outperforms long-CoT models like DeepSeek-R1-671B and QwQ-32B on length generalization tasks (see R1's error case in Table 8).

That said, we strongly agree with the reviewer tbVk (and reviewer VnFA) that RL, especially multi-task RL with process-level rewards is a promising future direction.

Q1:

Yes, we appreciate your interest! The data construction code is already included in the supplementary material, and we will release the full codebase, including task generation scripts and training pipelines, to support future research and adoption.

Q3:

We appreciate your insightful suggestion and have conducted the following ablation study.

In the current paper, the RF-pretraining stage includes tasks from three datasets: LeetCode, Big-Bench Hard, and Symbolic Reasoning. To assess the impact of the number of composed tasks, we conduct an ablation where the model is RF-pretrained only on the LeetCode subset.

Due to resource constraints, we evaluate on 4 downstream tasks, including 2 LeetCode tasks (Move Zeros & Valid Palindrome) and 2 NUPA tasks (Add Integer & Digit Max Integer), all of which are unseen during RF-pretraining.

The results are shown below. We observe a slight performance drop when excluding Big-Bench Hard and Symbolic Reasoning, likely due to reduced task diversity during pretraining:

We sincerely thank the reviewer for recognizing our key contributions, including cross-task generalization, strong empirical results, and practical scalability. We hope the following responses help address your remaining concerns.

W1:

This is a valid and important concern. While our current evaluation focuses on structured tasks, the goal is to establish a foundation for robust generalization that can eventually transfer to more complex and unstructured real-world settings. Below, we explain the rationale behind our task choices and how they connect to broader applications.

1. Additional experiments on more complex tasks

   • To validate the practical value of Meta-RFFT beyond symbolic tasks, we additionally conduct experiments and evaluate it on a real-world scenario: the Airline Baggage Cost Estimation task from [1].

   • This task asks the model to compute the total travel cost for one or more passengers, including flight fare and baggage fees. The rules which are based on American Airlines' policy are complex, depending on cabin class, flight route, number of bags, and bag dimensions. Solving it requires understanding and applying natural language regulations, which go beyond what can be fully captured in formal code. We use pseudo-code rules in this task and test whether the model can perform length generalization.

   • This task illustrates a practical setting for length generalization, where the model must apply multiple interrelated rules over long reasoning chains. Current LLMs perform poorly on it, and even strong models like Claude-3.5 and o1-preview degrade rapidly with input length (see the table below).

   • We train models on samples with length 1–8, and test on OOD lengths 10–16. As shown below, Meta-RFFT significantly outperforms vanilla RFFT in the practical domain:

   length	2	4	6	8	10	12	14	16
   Vanilla RFFT	0.94	0.72	0.78	0.56	0.44	0.16	0.00	0.08
   Meta-RFFT	1.00	1.00	0.92	0.90	0.74	0.38	0.24	0.26

   length	5	8	11
   Qwen-2.5-72B (0-shot)	0.01	0.01	0.00
   Qwen-2.5-72B (1-shot)	0.19	0.10	0.01
   Claude-3.5 Sonnet (0-shot)	0.04	0.00	0.01
   Claude-3.5 Sonnet (1-shot)	0.29	0.30	0.11
   o1-preview (0-shot)	0.54	0.37	0.21
   o1-preview (1-shot)	0.63	0.55	0.46

2. Why we choose symbolic tasks in our paper

   • We agree that extending our method to real-world, complex tasks is a valuable future direction. In this paper, we intentionally focus on controlled tasks to clearly isolate the challenges of length generalization, independent of task complexity of each step. This setup follows the standard in prior studies [2–5]. Notably, even when individual steps are simple, length generalization remains highly challenging for LLMs. For example, DeepSeek-R1-671B achieves only 72% accuracy on 30-digit addition, despite the task’s apparent simplicity to humans. This demonstrates that length generalization is a fundamental and non-trivial ability, separate from broader reasoning complexity.
   • Furthermore, we also acknowledge the challenge of defining "length" in unstructured real-world tasks. Extending our framework to such domains is a key direction we plan to pursue.

3. Our contribution towards real-world settings

   • Our work bridges the gap between prior small-scale, single-task studies and practical LLMs. We show that multi-task rule-following training enables transferable length generalization, including to unseen tasks. This provides a scalable path toward improving reliability in multi-step, real-world reasoning.

W2:

Thank you for highlighting this important practical consideration. We’d like to address your concern as follows:

1. Reducing pretraining cost with fewer steps: As shown in Figure 15 (Appendix E.5), the model’s performance improves steadily with more RF-pretraining steps, but even partial pretraining (e.g., fewer steps) yields notable gains over vanilla RFFT. This provides a flexible trade-off for users with limited resources: by reducing pretraining steps, one can still achieve meaningful improvements in length generalization.

2. Cost amortization across tasks: While Meta-RFFT incurs an upfront cost (144 GPU-hours for 7B; 713.6 for 32B), it becomes significantly more efficient than vanilla RFFT when applied across multiple tasks. Since Meta-RFFT enables positive transfer via 1-shot prompting on unseen tasks, it reduces the need for downstream fine-tuning altogether. For example, with downstream adaptation costing just 2.4–4.4 GPU-hours per task (7B), the pretraining cost is amortized after only ~42 tasks—a threshold quickly exceeded in practice. For the 32B model, the breakeven point is ~72 tasks. This makes Meta-RFFT cost-effective for large-scale multi-task deployment. We will also open-source the Meta-RFFT checkpoints for efficient downstream applications.

W3:

We would like to clarify how multi-task rule transfer and length generalization are closely connected in our work.

As identified in [5], poor length generalization in LLMs stems from reliance on case-based reasoning, where models memorize shallow patterns instead of learning genuine rules. For example, models memorize addition results within 5-digit numbers by seeing a large number of training examples in this range, but do not capture the underlying digit-by-digit with carry-over addition rules (which are the key for generalization to infinite lengths), thus fail to solve 10-digit addition problems. RFFT addresses this by providing explicit rules and execution traces, enabling the model to adopt rule-based reasoning, which significantly improves out-of-distribution (OOD) generalization.

Our key contribution builds on this by scaling rule-based reasoning to the multi-task setting. By training on a large number of (rule, execution trace) pairs from diverse tasks, Meta-RFFT equips the model with a meta rule-following ability—allowing it to transfer rule-following behavior across tasks. Crucially, this enables the model to generalize not only to longer inputs but also to unseen tasks.

Thus, while Meta-RFFT introduces multi-task rule transfer, its primary goal remains to improve length generalization in a more generalizable and scalable way. We also provide a mechanistic explanation: this transferability emerges from learning shared computational primitives (e.g., loop maintenance), which are essential for both length generalization and cross-task generalization.

In this sense, multi-task rule transfer is not a departure from our focus on length generalization, but a natural and scalable extension of it.

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[1] Zhou et al., RULEARENA: A Benchmark for Rule-Guided Reasoning with LLMs in Real-World Scenarios, 2025.

[2] Anil et al., Exploring length generalization in large language models, 2022.

[3] Zhou et al., What algorithms can transformers learn?, 2023.

[4] Zhou et al., Transformers can achieve length generalization but not robustly, 2024.

[5] Hu et al., Case-Based or Rule-Based: How Do Transformers Do the Math?, 2024.

We sincerely appreciate the reviewer’s insightful and constructive feedback! We hope our responses below address your concerns and help clarify our key contributions.

W1,2; Q2:

We thank the reviewer for raising this important point. We agree that going beyond symbolic or formally codable tasks is crucial for evaluating real-world reasoning. Below, we clarify our task choices and how our work sets the stage for broader generalization.

1. Additional experiments on more complex tasks

   • To validate the practical value of Meta-RFFT beyond symbolic tasks, we additionally conduct experiments and evaluate it on a real-world scenario: the Airline Baggage Cost Estimation task from [1].

   • This task asks the model to compute the total travel cost for one or more passengers, including flight fare and baggage fees. The rules which are based on American Airlines' policy are complex, depending on cabin class, flight route, number of bags, and bag dimensions. Solving it requires understanding and applying natural language regulations, which go beyond what can be fully captured in formal code. We use pseudo-code rules in this task and test whether the model can perform length generalization.

   • This task illustrates a practical setting for length generalization, where the model must apply multiple interrelated rules over long reasoning chains. Current LLMs perform poorly on it, and even strong models like Claude-3.5 and o1-preview degrade rapidly with input length (see the table below).

   • We train models on samples with length 1–8, and report test accuracy on OOD lengths 10-16. As shown below, Meta-RFFT significantly outperforms vanilla RFFT in the practical domain:

   length	2	4	6	8	10	12	14	16
   Vanilla RFFT	0.94	0.72	0.78	0.56	0.44	0.16	0.00	0.08
   Meta-RFFT	1.00	1.00	0.92	0.90	0.74	0.38	0.24	0.26

   length	5	8	11
   Qwen-2.5-72B (0-shot)	0.01	0.01	0.00
   Qwen-2.5-72B (1-shot)	0.19	0.10	0.01
   Claude-3.5 Sonnet (0-shot)	0.04	0.00	0.01
   Claude-3.5 Sonnet (1-shot)	0.29	0.30	0.11
   o1-preview (0-shot)	0.54	0.37	0.21
   o1-preview (1-shot)	0.63	0.55	0.46

2. Why we choose symbolic tasks in our paper

   • We agree that extending our method to real-world, complex tasks is a valuable future direction. In this paper, we intentionally focus on controlled tasks to clearly isolate the challenges of length generalization, independent of task complexity of each step. This setup follows the standard in prior studies [2–5]. Notably, even when individual steps are simple, length generalization remains highly challenging for LLMs. For example, DeepSeek-R1-671B achieves only 72% accuracy on 30-digit addition, despite the task’s apparent simplicity to humans. This demonstrates that length generalization is a fundamental and non-trivial ability, separate from broader reasoning complexity.
   • Furthermore, defining "length" in complex real-world tasks is non-trivial. Our framework does not yet include large-scale real-world tasks, but we view this as a critical next step.

3. Our contribution towards real-world settings

   • Our work bridges the gap between prior small-scale, single-task studies and practical LLMs. We demonstrate, for the first time, that multi-task rule-following training enables cross-task transfer of length generalization, marking an essential step toward scaling to more realistic, multi-step tasks.

[1] Zhou et al., RULEARENA: A Benchmark for Rule-Guided Reasoning with LLMs in Real-World Scenarios, 2025.

[2] Anil et al., Exploring length generalization in large language models, 2022.

[3] Zhou et al., What algorithms can transformers learn?, 2023.

[4] Zhou et al., Transformers can achieve length generalization but not robustly, 2024.

[5] Hu et al., Case-Based or Rule-Based: How Do Transformers Do the Math?, 2024.

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Q1:

We apologize for the lack of clarity. In Figure 4(b), we report the relative error in loop counts, defined as:

$$\text{relative-error} = \frac{\left|\text{ground-truth-loop-num} - \text{model-loop-num}\right|}{\text{ground-truth-loop-num}}$$

For each task, the reported value is the average relative error computed over test cases of input lengths from 2 to 30 (in increments of 2), with 50 samples per length.

We will revise the text to include this definition for clarity.

Q3:

Thank you for the insightful question.

Yes, in our task design, the length parameter can be roughly interpreted as the input size $n$ in algorithmic complexity terms. For example, in the word sorting task, length corresponds to the number of words ($O(n^2)$), while in coin flip, it denotes the number of flips ($O(n)$).

However, during training, we do not provide the model with explicit length values. As shown in the RFFT input format (e.g., Figure 1, right), the model is not required to be aware of the value of $n$. Instead, it learns to manage loop entry and exit based on conditions, not on fixed input lengths. This design encourages length-agnostic reasoning and prevents overfitting to specific lengths seen during training.

Empirically, despite training on tasks of mixed complexity, the model generalizes well across downstream tasks of varying complexity, outperforming all baselines. This suggests that the mixed training does not bias the model in practice.

We sincerely appreciate the reviewer’s insightful and positive feedback! We hope the following responses will fully address your concerns and further clarify our contributions.

W1:

We fully acknowledge that multi-task training is a well-established concept across many domains. However, our work introduces a novel perspective by being the first to explore cross-task transfer of length generalization through multi-task training. Length generalization presents a unique challenge due to its inherent out-of-distribution (OOD) nature—models are trained on short sequences but must generalize to much longer ones. We show through experiments that traditional multi-task methods like instruction tuning (e.g., Tulu3 in Table 3) fail under such conditions, since the reasoning steps required at test time go far beyond those seen during training.

Besides, while the original RFFT framework showed that explicitly providing rules improves rule-based reasoning in single-task settings, our contribution is to scale this approach to multi-task training across a large number of (rule, rule-execution trace) pairs. This enables the model to acquire a meta rule-following capability, allowing it to generalize to unseen tasks by transferring reasoning skills across tasks. We are, to the best of our knowledge, the first to systematically study this form of cross-task OOD generalization in LLMs. We also provide a mechanistic explanation: the transferability stems from the model’s ability to learn shared computational primitives, such as loop maintenance, which are essential across tasks.

Moreover, previous studies on length generalization [2–5] has largely been restricted to single-task, small-scale settings, often using transformers trained from scratch. However, a key strength of large language models lies in their ability to handle a wide range of diverse tasks within a single model. Our work aligns with this core advantage: we explore length generalization in a multi-task, post-training setting, using pretrained LLMs. Our method enables generalization across tasks and lengths, making it far more practical and scalable for real-world use.

W2:

We thank the reviewer for raising this important point. We agree that going beyond symbolic or formally codable tasks is crucial for evaluating real-world reasoning.

1. Additional experiments on more complex tasks

   • To validate the practical value of Meta-RFFT beyond symbolic tasks, we additionally conduct experiments and evaluate it on a real-world scenario: the Airline Baggage Cost Estimation task from [1].

   • This task asks the model to compute the total travel cost for one or more passengers, including flight fare and baggage fees. The rules which are based on American Airlines' policy are complex, depending on cabin class, flight route, number of bags, and bag dimensions. Solving it requires understanding and applying natural language regulations, which go beyond what can be fully captured in formal code. We use pseudo-code rules in this task and test whether the model can perform length generalization.

   • This task illustrates a practical setting for length generalization, where the model must apply multiple interrelated rules over long reasoning chains. Current LLMs perform poorly on it, and even strong models like Claude-3.5 and o1-preview degrade rapidly with input length (see the table below, the results are from [1]).

   • We train models on samples with length 1–8, and report test accuracy on OOD lengths 10-16. As shown below, Meta-RFFT significantly outperforms vanilla RFFT in the practical domain:

   length	2	4	6	8	10	12	14	16
   Vanilla RFFT	0.94	0.72	0.78	0.56	0.44	0.16	0.00	0.08
   Meta-RFFT	1.00	1.00	0.92	0.90	0.74	0.38	0.24	0.26

   length	5	8	11
   Qwen-2.5-72B (0-shot)	0.01	0.01	0.00
   Qwen-2.5-72B (1-shot)	0.19	0.10	0.01
   Claude-3.5 Sonnet (0-shot)	0.04	0.00	0.01
   Claude-3.5 Sonnet (1-shot)	0.29	0.30	0.11
   o1-preview (0-shot)	0.54	0.37	0.21
   o1-preview (1-shot)	0.63	0.55	0.46

2. Why we choose symbolic tasks in our paper

   • We agree that extending our method to real-world, complex tasks is a valuable future direction. In this paper, we intentionally focus on controlled tasks to clearly isolate the challenges of length generalization, independent of task complexity of each step. This setup follows the standard in prior studies [2–5]. Notably, even when individual steps are simple, length generalization remains highly challenging for LLMs. For example, DeepSeek-R1-671B achieves only 72% accuracy on 30-digit addition, despite the task’s apparent simplicity to humans. This demonstrates that length generalization is a fundamental and non-trivial ability, separate from broader reasoning complexity.
   • Furthermore, defining "length" in complex real-world tasks is non-trivial. Our framework does not yet include large-scale real-world tasks, but we view this as a critical next step.

3. Our contribution towards real-world settings

   • Our work bridges the gap between prior small-scale, single-task studies and practical LLMs. We demonstrate, for the first time, that multi-task rule-following training enables cross-task transfer of length generalization, marking an essential step toward scaling to more realistic, multi-step tasks.

[1] Zhou et al., RULEARENA: A Benchmark for Rule-Guided Reasoning with LLMs in Real-World Scenarios, 2025.

[2] Anil et al., Exploring length generalization in large language models, 2022.

[3] Zhou et al., What algorithms can transformers learn?, 2023.

[4] Zhou et al., Transformers can achieve length generalization but not robustly, 2024.

[5] Hu et al., Case-Based or Rule-Based: How Do Transformers Do the Math?, 2024.

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Q1,3:

We find the reviewer’s suggestion to explore RL for rule-following tasks highly insightful, and in fact, we have conducted preliminary investigations along this line.

1. On computational primitives: While loop maintenance is indeed a core challenge for length generalization, our model also learns other common primitives such as if-else logic and operations on lists and strings. These structures are broadly shared across tasks and essential for handling symbolic and algorithmic reasoning. Meta-RFFT leverages these shared patterns to improve cross-task generalization.

2. On reinforcement learning:

   • Outcome reward: We find SFT more effective than outcome-based RL for rule-following tasks. RL optimizes only for final correctness, while SFT directly trains the model to generate rule-compliant intermediate steps. As shown in Figure 7, RL fails to capture the process structure and underperforms Meta-RFFT (see error case of R1 in Table 9). Moreover, Meta-RFFT outperforms advanced long-CoT models like DeepSeek-R1-671B and QwQ-32B (Table 2), despite being smaller (see error case of R1 in Table 8).
   • Process reward: We strongly agree that this is a valuable idea. Supervising rule execution with process-level rewards could enhance improve rule adherence and generalization, and we consider it a promising direction for future research.

Q2:

We appreciate the reviewer for pointing out this important and practical concern.

Meta-RFFT involves substantial RF-pretraining, which indeed can affect the model’s general capabilities due to distribution shift, known as catastrophic forgetting. But typically this is easily addressed by mixing some pretraining corpus during fine-tuning.

To verify this, we conduct a supplementary experiment. As we don't have access to the pretraining data, we mix GSM8K training data into downstream finetuning alongside the original meta-rule-following data to verify that the reasoning ability on GSM8K can be kept after RFFT. More specifically, for each training example in GSM8K, we use Qwen2.5-7B-Instruct to generate 10 candidate answers and filter the corrrect traces as the training set, forming a filtered GSM8K dataset of 7182 samples.

The results on length generalization (averaged across 8 LeetCode tasks) and GSM8K test accuracy are shown below. We observe that merely mixing 7k samples (compared to 310k Meta-RFFT data) effectively recovers the model’s reasoning performance on GSM8K, while maintaining the strong multi-task length generalization ability. Notably, Meta-RFFT still significantly outperforms vanilla RFFT, demonstrating that general capabilities can be preserved with minimal additional data.

Q4:

While we have seen references included in some abstracts, we look into the convention and find that abstracts are generally expected to be self-contained and citation-free. We will revise our abstract accordingly to remove the reference.