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Rethinking Generalization in Reasoning SFT: A Conditional Analysis on Optimization, Data, and Model Capability
Qihan Ren, Peng Wang, Ruikun Cai, Shuai Shao, Dadi Guo, Yuejin Xie, Yafu Li, Quanshi Zhang, Xia Hu, Jing Shao, Dongrui Liu
TL;DR
The paper asks whether reasoning SFT inherently fails to generalize across domains, and studies this question by varying optimization, data, and base-model capability under long-CoT supervision. It finds that cross-domain generalization is conditional: extended optimization and suitable traces can enable transfer, but the same procedural supervision can degrade safety.
Problem
Prior evidence leaves unclear whether SFT’s reported generalization failures are intrinsic or artifacts of optimization, data, model capability, and starting-checkpoint conditions.
Method
The study systematically varies optimization, training data, and base-model capability in math-only reasoning SFT on pretrained models, evaluating transfer across reasoning, general capabilities, and safety.
Results
Cross-domain generalization is conditional rather than absent: performance can dip before recovering with extended training, while data quality, trace structure, and model capability shape transfer.
Takeaways & Limitations
Reasoning SFT should be evaluated across training trajectories and conditions, because short checkpoints or weak data and models can misrepresent its generalization potential.
Takeaways & Limitations
The recovery also depends on data quality and model capability, so the optimization finding is not independent of these factors.
Abstract
from arXiv · showhide
A prevailing narrative in LLM post-training holds that supervised finetuning (SFT) memorizes while reinforcement learning (RL) generalizes. We revisit this claim for reasoning SFT with long chain-of-thought (CoT) supervision and find that cross-domain generalization is not absent but conditional, jointly shaped by optimization dynamics, training data, and base-model capability. Some reported failures are under-optimization artifacts: cross-domain performance first degrades before recovering and improving with extended training (a dip-and-recovery pattern), so shorttraining checkpoints can underestimate generalization. Data quality and structure both matter: low-quality solutions broadly hurt generalization,while verified long-CoT traces yield consistent cross-domain gains. Model capability is essential: stronger models internalize transferable procedural patterns (e.g., backtracking) even from a toy arithmetic game, while weaker ones imitate surface verbosity. This generalization is asymmetric, however: reasoning improves while safety degrades, reframing the question from whether reasoning SFT generalizes to under what conditions and at what cost.
1 Introduction
The paper revisits the claim that SFT memorizes while RL generalizes, arguing that reasoning-SFT generalization is conditional on optimization, data, and model capability. It studies these factors with long-CoT supervision and evaluates both gains and trade-offs across domains and safety.
- Motivation: Reported SFT generalization failures may reflect differing optimization, data, model-capability, and checkpoint conditions rather than an intrinsic limitation.Prior studies vary in CoT supervision, training duration, response quality, base-model capability, and starting checkpoint.
- Motivation: Long-CoT reasoning SFT is especially suitable for studying these factors because its traces are structurally different, harder to fit, and more capability-demanding than short targets.
- Approach: The study systematically varies optimization, training data, and model capability using math-only SFT on pretrained base models, then evaluates in-domain, OOD, general-capability, and safety outcomes.
- Findings: Cross-domain transfer can first deteriorate and later recover during long-CoT SFT, while repeated exposure, verified traces, and procedural structure support generalization.
- Conclusion: The paper reframes “does SFT generalize?” as a conditional question because optimization sufficiency, data quality and structure, and base-model capability determine outcomes.
2 Experimental Setup
The experiments use pretrained base models, verified long-CoT reasoning data, standard SFT, and a broad evaluation suite spanning in-domain reasoning, OOD reasoning, general capabilities, and safety. Early figures establish the contrast between short-training limitations and longer-training dynamics.
- Models: The default experiments use pretrained Qwen3 base models, with InternLM2.5 and Qwen2.5 models added to test whether trends extend beyond one model family.
- Training data: Math-CoT-20k contains 20,480 verified long-CoT math examples generated with thinking enabled, with responses capped at 16,384 tokens.
- Optimization: Standard SFT minimizes response-token negative log-likelihood under a default AdamW schedule with learning rate 5e-5, batch size 256, cosine decay, and 8 epochs.
- Evaluation: The evaluation suite covers in-domain math, OOD code and scientific reasoning, general capabilities such as instruction following and truthfulness, and safety against harmful queries.
- Reference dynamics: Short-epoch SFT substantially improves math but yields limited or negative gains on OOD reasoning and general capabilities, while longer training exhibits dip-and-recovery dynamics.
3 Optimization Dynamics of Reasoning SFT
Optimization dynamics explain why short-training evaluations can understate reasoning-SFT transfer: performance often dips before recovering, while aggressive schedules can eventually produce overfitting-like degradation.
- Replication: Under the short-epoch protocol, in-domain math improves substantially while OOD gains remain limited or become negative on some benchmarks.
- Dip-and-recovery: Several OOD benchmarks show deeper dips, slower recovery, and eventual improvement beyond the base model after extended training.
- Interpretation: These trajectories suggest that some reported generalization limits are under-optimization artifacts because long-CoT data is difficult to internalize.
- Mechanism: Early training produces sharply longer responses, whereas performance recovery coincides with shorter, more concise responses and increased self-verification.
- Exposure pattern: At a fixed 640-step budget, repeated exposure to a smaller dataset outperforms one-pass coverage, while larger data diversity adds further value.
- Overfitting regime: Pronounced overfitting-like symptoms mainly require a combined aggressive schedule of high learning rate, no decay, and long training.
4 How Training Data Shapes Generalization
Training data shapes cross-domain reasoning generalization through both trace structure and solution quality, with benefits depending on model capability and task type.
- Experimental setup: Table 2 compares four data configurations using final-checkpoint performance, with intermediate-checkpoint results reported separately.The configurations include Math-CoT-20k, Math-NoCoT-20k, NuminaMath-20k, and Countdown-CoT-20k.
- Long-CoT structure: Long-CoT supervision yields stronger generalization on reasoning-intensive tasks, especially mathematics, while no-CoT data can perform better on instruction-following and alignment benchmarks.The advantage is weaker for Qwen3-8B and is not uniform across tasks.
- Data quality: Math-NoCoT-20k consistently outperforms NuminaMath-20k, whose mixed-quality short solutions produce broad OOD degradation and little in-domain math improvement.NuminaMath also shows little or no recovery in the dip-and-recovery training dynamics.
- Procedural transfer: Countdown-CoT-20k improves reasoning performance for both Qwen3 models and can outperform narrow-domain Math-NoCoT-20k on math tasks.Its traces provide search, backtracking, and verification procedures despite limited broad mathematical knowledge.
- Procedural transfer: Procedural transfer from Countdown is not automatic: it is marginal for the weaker-reasoning InternLM2.5-20B and can degrade IFEval scores.The result links transfer to the interaction between trace structure, prior representations, and task demands.
5 How Model Capability Affects Generalization
Under matched data and training, model capability strongly affects reasoning SFT generalization: larger models recover more effectively and show broader cross-domain gains.
- Experimental setup: The controlled comparison trains Qwen3 1.7B, 4B, 8B, and 14B models on identical Math-CoT-20k data and protocol.This design attributes differences in generalization behavior to model capability.
- Capability-dependent generalization: The 14B model shows pronounced dip-and-recovery dynamics and broad late gains, while the 1.7B model has marginal or negative gains across benchmarks.The 4B and 8B models recover but improve less than the 14B model.
- Response length: Smaller models retain longer responses after extended training, whereas larger models contract and stabilize at shorter lengths.Persistent prolonged responses are treated as a coarse indicator of surface-pattern imitation rather than internalized reasoning.
6 Asymmetric Generalization: Safety Under Long-CoT SFT
Long-CoT reasoning SFT transfers across domains but weakens safety and refusal behavior, with matched CoT comparisons implicating procedural patterns in the traces.
- Figure guide: Figure 6 tracks ASR across checkpoints and presents a case study of self-rationalization during thinking that eventually produces harmful content.ASR is defined in the caption so that lower values indicate safer behavior.
- Safety degradation: Long-CoT SFT substantially increases HEx-PHI attack success rate across all three evaluated models, while matched no-CoT SFT causes much smaller safety degradation.Because the datasets share queries and final solutions, the comparison points to long-CoT procedures rather than math content.
- Refusal behavior: After long-CoT SFT, models shift from short refusals to warnings, self-rationalization, and harmful details presented with caveats.The case study describes a progression in refusal behavior on the same harmful queries.
- Quantitative analysis: Self-rationalization appears in 67.3% of Math-CoT responses, versus 31.0% after matched Math-NoCoT training and 6.3% for the base model.Its prevalence correlates strongly with ASR across Math-CoT checkpoints: Pearson r = 0.979 and Spearman ρ = 0.857.
- Interpretation: The authors hypothesize that long-CoT SFT strengthens a persistent problem-solving prior that can search for ways around refusal policies.For harmful queries, extended reasoning may treat the safety guardrail as an obstacle to work around.
7 Related Work
Related work frames an SFT–RL generalization gap and explores data, objective, and trace-structure explanations; this study instead examines their interaction within reasoning SFT.
- SFT–RL framing: Prior studies commonly frame SFT as memorizing and RL as generalizing, while short-training math SFT studies report limited cross-domain transfer.The paper reports replicating the limited-transfer finding under the same short-training protocol but obtaining a different outcome with longer optimization.
- Objective-based approaches: Alternative work modifies SFT through RL or distribution-matching interpretations and proposes different weighting strategies, whereas this study retains vanilla SFT.Its focus is the conditions under which generalization emerges rather than changing the objective.
- Data and interaction effects: Concurrent research shows that data source and composition materially affect the observed SFT–RL gap, while this paper studies optimization, data, and capability jointly.The distinction is broader interaction analysis within reasoning SFT rather than data alone as an explanation for objective differences.
- Trace structure: Other work finds that branch-heavy correct traces can yield inefficient exploration, whereas more convergent traces transfer better, supporting the importance of trace structure.This study additionally examines trace structure alongside optimization stage and base-model capability.
- Safety: Prior studies link extended reasoning to self-jailbreaking and safety degradation; this paper uses matched CoT and no-CoT supervision to attribute the drop to procedural patterns.The comparison holds queries and answers constant while varying the exploratory reasoning process.
8 Discussion and Conclusion
The study concludes that cross-domain generalization in reasoning SFT is conditional, and that SFT can outperform GRPO on five ID/OOD reasoning benchmarks under a matched-query comparison, while general-capability results are mixed.
- Under the matched-query setting, SFT performs better than GRPO on five ID/OOD reasoning benchmarks, while general-capability results are mixed.The comparison does not match total FLOPs, and GRPO is sensitive to reward design and evaluation budget.
- Cross-domain generalization in reasoning SFT is conditional rather than absent, depending on optimization, data quality and structure, and base-model capability.
Reproducibility Statement
The authors release the training and evaluation artifacts to support reproduction and future research.
- The authors open-sourced all training code, evaluation code, datasets, and models, including intermediate checkpoints.
A Discussion and Limitation
The discussion argues that generalization depends on co-designing model, data, algorithm, and schedule, while the study remains bounded by its domains, model coverage, comparisons, factorial analysis, and behavioral detectors.
- Discussion: Base-model capability and pretraining representations shape what models extract from identical SFT data, making the starting checkpoint an important design choice.Comparable-size models from different pretraining pipelines can exhibit different generalization trajectories.
- Discussion: No single factor determines generalization: strong models can fail with poor data, high-quality data can appear ineffective under insufficient optimization, and weak models gain little from extended training.
- Limitations: The study primarily controls math reasoning, with Code-CoT providing an additional domain replication; broader scientific, multimodal, and reasoning validation remains open.
- Limitations: The experiments cover dense model families up to 27B parameters but omit substantially larger dense models and mixture-of-experts architectures.
- Limitations: The GRPO comparison matches several training quantities but not total generated tokens or FLOPs, so conclusions may vary with algorithm, reward design, and budget definition.
- Limitations: The study isolates optimization, data, and capability in controlled settings but does not quantify all main and interaction effects through a full factorial design.
B.3 Additional experiment details
Additional experiments test reproducibility across seeds, domains, teachers, model families, and training schedules, confirming dip-and-recovery dynamics while identifying conditions associated with overfitting.
- Additional experiment details: DeepSeek-R1-generated data preserves the dip-and-recovery pattern and better gains with sufficient training despite modest differences in absolute benchmark scores.
- Additional experiment details: Qwen2.5 models show early OOD and general-capability dips followed by slow recovery, whereas in-domain math improves more steadily.
- Additional experiment details: Three-seed reruns preserve the early dip, subsequent recovery, and response-length rise-and-fall, with late-stage gains generally exceeding seed-level variation.
- Additional experiment details: Code-CoT produces a similar dip-and-recovery trajectory and response-length contraction, with the strongest final gain shifting toward the code-domain benchmark.
- Additional experiment details: Granite replicates dip-and-recovery across families, while Gemma exhibits substantial late-stage gains with a less uniform intermediate trajectory.
- Additional experiment details: Later checkpoints replace prolonged thinking-like imitation with backtracking, cross-validation, error correction, and re-verification before reaching the correct answer.The earlier checkpoint exhausts its token limit without producing an answer, while the later checkpoint demonstrates transferable reasoning behavior.
- Additional experiment details: More aggressive schedules produce broader degradation: high learning rate, no decay, and long epochs yield OOD drops and can also reduce in-domain math performance.
C.8 Full results on model capability experiment
The full model-capability results preserve the paper’s qualitative conclusions across Qwen3 and Qwen2.5 benchmarks: generalization depends on optimization, data, and capability. Higher-capability models better capture transferable reasoning patterns, while low-capability models more often imitate surface verbosity.
- Full-benchmark validation: Full-benchmark results preserve the relative ordering across settings for most Qwen3 checkpoints, reinforcing the data-factor conclusions.The corresponding response-length curves show similar trends to the main text.
- Full-benchmark validation: The performance trend also holds for the Qwen2.5 model family, with response-length dynamics aligned with the main observations.
- Capability-dependent behavior: Qwen3-1.7B imitates deliberative form through repetitive loops, whereas the larger model internalizes reasoning patterns and maintains clearer, more reliable responses.The contrast appears in both number-theory and badminton-learning cases, where the smaller model shows repetition, topic drift, and factual errors.
- Capability-dependent behavior: Across approximately 122K tokens, 14B assigns higher log probability to 89.2% of tokens, with a mean gap of +0.252 over 1.7B.At Δlogprob > 1.0, the advantage ratio is 8.0×, rising to 18.7× at Δlogprob > 3.0.
- Capability-dependent behavior: The larger model’s strongest token advantages concentrate on reasoning transitions, mathematical terms, and decision-point verbs rather than uniformly improved word prediction.Examples include therefore, alternatively, wait, backtracking-related transitions, sqrt, equation, compute, and divisible.
- Capability-dependent transfer: Capability determines transfer from procedurally rich but knowledge-poor Countdown-CoT: InternLM2.5-20B gains little despite more parameters and lower starting math performance.Qwen3-14B starts at 77.8% on MATH500 and 14.7% on AIME24, compared with 53.7% and 1.7% for InternLM2.5-20B.
D Full Result Tables for All Experiments
The appendix collects full result tables covering benchmark baselines and training dynamics across datasets, model families, optimization schedules, and auxiliary analyses. It also documents limited LLM assistance with polishing, plotting, and formatting, while authors retained responsibility for the research and claims.
- Research process: LLMs assisted with language polishing, plotting scripts, and figure/table formatting, while authors determined and validated the core research components and claims.