cs.LGOct 19, 2026

NADS: Navigator-Guided Data Selection for Mitigating Catastrophic Forgetting in Fine-Tuning

Authors: Jianhao Zhang, Ou Wu, Yi Du

Organizations: Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, China · Computer Network Information Center, Chinese Academy of Sciences, Beijing, China

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Abstract

Catastrophic forgetting is a central obstacle in single-stage fine-tuning of large language models (LLMs) on a new task, especially when the original pretraining data are unavailable. Synthetic data offers a practical mitigation path, but candidate pools are often noisy and redundant, making effective selection essential. Existing methods often rely on indirect proxy signals whose alignment with actual training benefit can be limited, while utility--diversity selection over large candidate pools remains computationally demanding. To address these challenges, we propose NAvigator-guided Data Selection (NADS), a fine-tuning framework for LLMs. NADS first follows the target fine-tuning recipe without preservation regularization to obtain a navigator model, whose deviation from the pretrained model exposes recipe-induced capability drift. It then uses the predictive divergence between the navigator and the pretrained model to score forgetting-aware utility for each synthetic candidate, and constructs a constraint set through an efficient utility--diversity selection strategy. Finally, NADS fine-tunes on the new-task data while distilling pretrained behavior on the selected constraints to preserve general capabilities. Experiments show that NADS delivers a stronger balance between new-task performance and general capability preservation, while reducing utility--diversity selection overhead. Code at: https://github.com/zjh-vinky/NADS.

Figures & tables

Figure 1: The overall framework of NADS. First, we train a navigator MnavM_{\text{nav}} from MpretrainM_{\text{pretrain}} on Dnew\mathcal{D}_{\text{new}} without regularization. Next, we score sample utility from the predictive divergence between MnavM_{\text{nav}} and MpretrainM_{\text{pretrain}} , and construct Dconstraint\mathcal{D}_{\text{constraint}} via utility–diversity selection with DPPs. Finally, we train MfinalM_{\text{final}} on Dnew\mathcal{D}_{\text{new}} with distillation on Dconstraint\mathcal{D}_{\text{constraint}} to preserve general capabilities during new-task adaptation.
Figure 2: (a–b) Utility versus response-only NLL degradation and full-sequence loss increase, with Pearson and Spearman measuring sample correlation and ranking consistency, respectively. (c–d) Mean response-only NLL degradation and full-sequence loss increase across utility deciles. Higher-utility samples exhibit larger increases, indicating strong correlation with samples’ forgetting risk.
ModelMethodGeneral Capability ↑\uparrowTarget ↑\uparrowOverall ↑\uparrow
HASWOBQAMMLUGSM8KAvg.HEAvg.
 Pre-trained55.83±0.00\text{55.83}_{\pm\text{0.00}}31.20±0.00\text{31.20}_{\pm\text{0.00}}56.92±0.00\text{56.92}_{\pm\text{0.00}}27.90±0.00\text{27.90}_{\pm\text{0.00}}42.96±0.00\text{42.96}_{\pm\text{0.00}}28.16±0.00\text{28.16}_{\pm\text{0.00}}35.56±0.00\text{35.56}_{\pm\text{0.00}}
 Standard FT52.12±0.52\text{52.12}_{\pm\text{0.52}}28.40±0.69\text{28.40}_{\pm\text{0.69}}48.61±0.40\text{48.61}_{\pm\text{0.40}}20.75±0.74\text{20.75}_{\pm\text{0.74}}37.47±0.30\text{37.47}_{\pm\text{0.30}}45.13±0.32\text{45.13}_{\pm\text{0.32}}41.30±0.22\text{41.30}_{\pm\text{0.22}}
 LoRA53.38±0.55\text{53.38}_{\pm\text{0.55}}29.47±0.64\text{29.47}_{\pm\text{0.64}}51.98±0.42\text{51.98}_{\pm\text{0.42}}21.18±0.79\text{21.18}_{\pm\text{0.79}}39.00±0.31\text{39.00}_{\pm\text{0.31}}41.92±0.30\text{41.92}_{\pm\text{0.30}}40.46±0.21\text{40.46}_{\pm\text{0.21}}
 Random52.03±0.54\text{52.03}_{\pm\text{0.54}}28.13±0.64\text{28.13}_{\pm\text{0.64}}49.21±0.43\text{49.21}_{\pm\text{0.43}}21.83±0.73\text{21.83}_{\pm\text{0.73}}37.80±0.30\text{37.80}_{\pm\text{0.30}}41.77±0.46\text{41.77}_{\pm\text{0.46}}39.79±0.27\text{39.79}_{\pm\text{0.27}}
 InsCL53.95±0.54\text{53.95}_{\pm\text{0.54}}29.27±0.70\text{29.27}_{\pm\text{0.70}}{\color[rgb]{0,0,1}\text{54.86}_{\pm\text{0.43}}}25.40±0.76\text{25.40}_{\pm\text{0.76}}40.87±0.31\text{40.87}_{\pm\text{0.31}}42.02±0.82\text{42.02}_{\pm\text{0.82}}41.45±0.44\text{41.45}_{\pm\text{0.44}}
Table 1: Performance comparison with methods selecting Dconstraint\mathcal{D}_{\text{constraint}} for replay on Magicoder (%). The best results are highlighted in red , and the second-best results are highlighted in blue .
ModelMethodGeneral Capability ↑\uparrowTarget ↑\uparrowOverall ↑\uparrow
HASWOBQAMMLUGSM8KAvg.HEAvg.
 LESS{\color[rgb]{0,0,1}\text{54.12}_{\pm\text{0.49}}}{\color[rgb]{0,0,1}\text{30.67}_{\pm\text{0.61}}}{\color[rgb]{0,0,1}\text{54.38}_{\pm\text{0.40}}}23.73±0.62\text{23.73}_{\pm\text{0.62}}{\color[rgb]{0,0,1}\text{40.73}_{\pm\text{0.27}}}{\color[rgb]{0,0,1}\text{43.01}_{\pm\text{0.84}}}{\color[rgb]{0,0,1}\text{41.87}_{\pm\text{0.44}}}
 FisherSFT54.03±0.49\text{54.03}_{\pm\text{0.49}}29.80±0.60\text{29.80}_{\pm\text{0.60}}52.89±0.41\text{52.89}_{\pm\text{0.41}}23.15±0.62\text{23.15}_{\pm\text{0.62}}39.97±0.27\text{39.97}_{\pm\text{0.27}}41.85±0.74\text{41.85}_{\pm\text{0.74}}40.91±0.39\text{40.91}_{\pm\text{0.39}}
 SPICE53.58±0.50\text{53.58}_{\pm\text{0.50}}29.60±0.60\text{29.60}_{\pm\text{0.60}}53.39±0.40\text{53.39}_{\pm\text{0.40}}{\color[rgb]{0,0,1}\text{24.92}_{\pm\text{0.73}}}40.37±0.29\text{40.37}_{\pm\text{0.29}}42.61±0.66\text{42.61}_{\pm\text{0.66}}41.49±0.36\text{41.49}_{\pm\text{0.36}}
LLaMA3.2NADS (Ours){\color[rgb]{1,0,0}\text{55.17}_{\pm\text{0.49}}}{\color[rgb]{1,0,0}\text{31.07}_{\pm\text{0.58}}}{\color[rgb]{1,0,0}\text{56.45}_{\pm\text{0.41}}}{\color[rgb]{1,0,0}\text{27.37}_{\pm\text{0.67}}}{\color[rgb]{1,0,0}\text{42.52}_{\pm\text{0.27}}}{\color[rgb]{1,0,0}\text{44.39}_{\pm\text{0.40}}}{\color[rgb]{1,0,0}\text{43.46}_{\pm\text{0.24}}}
 LESS55.56±0.52\text{55.56}_{\pm\text{0.52}}31.80±0.69\text{31.80}_{\pm\text{0.69}}57.26±0.39\text{57.26}_{\pm\text{0.39}}35.08±0.83\text{35.08}_{\pm\text{0.83}}44.93±0.31\text{44.93}_{\pm\text{0.31}}{\color[rgb]{0,0,1}\text{57.07}_{\pm\text{0.91}}}{\color[rgb]{0,0,1}\text{51.00}_{\pm\text{0.48}}}
Table 2: Cross-paradigm reference comparison with methods selecting Dnew\mathcal{D}_{\text{new}} on Magicoder (%).
Figure 3: (a) Training dynamics of the navigator model on the Magicoder dataset. (b) Dynamics of individual general-capability benchmarks during navigator training. (c) NADS performance with navigators selected at different training stages on Magicoder with LLaMA3.2-3B.
Figure 4: Controlled comparison with a fixed KD objective on Magicoder with LLaMA3.2.
ModelHASWOBQAMMLUGSM8KHE
MpretrainM_{\text{pretrain}}55.8331.2056.9227.9028.16
MnavM_{\text{nav}}52.8029.2050.6022.0945.50
Table 3: Performance comparison between MpretrainM_{\text{pretrain}} and MnavM_{\text{nav}} .
MethodGeneralTargetOverall
Random37.9641.9139.94
PPL-based38.7642.0240.39
DPP-based38.0441.2739.66
NADS42.5244.3943.46
Table 4: Controlled constraint-selection comparison on Magicoder.
Figure 5: (a) Quantitative diversity diagnostics of selected data. (b) t-SNE visualizations of selected data. (c) Data-selection cost in terms of selection time and peak GPU memory usage.
MethodGeneralTargetOverall
NADS42.5244.3943.46
- w/o KL drift37.6442.3139.98
- w/o Diversity40.2142.8341.52
- w/o Entropy Gate41.2643.1742.22
Table 5: Ablation of NADS components.
Figure 6: (a) Performance comparison under different utility signals. (b) Hyperparameter sensitivity of NADS. (c) Comparison with catastrophic forgetting mitigation methods on the Pareto frontier.
Appendix figures & tables23 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Trajectory mismatch and ordering fidelity under different KD strengths on Magicoder with LLaMA3.2-3B. The dashed line marks the default setting λ=5\lambda=5 used in the main experiments. Increasing λ\lambda enlarges the predictive-behavior mismatch between the unconstrained navigator and the constrained final model, while the navigator preserves high ordering fidelity in the practical regime.
Checkpoint pairSpearmanTop- KK overlap
Mnav−1M_{\text{nav}}-1 vs. Mnav−2M_{\text{nav}}-20.670.56
Mnav−2M_{\text{nav}}-2 vs. Mnav−3M_{\text{nav}}-30.720.61
Mnav−1M_{\text{nav}}-1 vs. Mnav−3M_{\text{nav}}-30.470.39
Appendix
Table 6: Utility ranking stability across navigator checkpoints.
Constraint sourceGeneral Avg.TargetOverall
Low-utility37.8241.7839.80
Middle-utility39.3842.5240.95
High-utility41.7843.8142.80
Full NADS42.5244.3943.46
Appendix
Table 7: Utility-range analysis under the same final KD objective on Magicoder with LLaMA3.2-3B.
Figure 8: Scalable selection surrogate consistency on Magicoder with LLaMA3.2. (a) reports the off-diagonal ratio and relative diagonal approximation gap. (b) reports Spearman rank correlation between the full log-det diversity term and its diagonal surrogate over same-size candidate subsets.
Figure 9: Split-spectrum certificate for the diagonal log-determinant bound on the final selected constraint set. The stacked bar gives Bsplit=B++B−=1206.65B_{\text{split}}=B_{+}+B_{-}=1206.65 . The dashed red line marks the observed gap Δdiag=64.45\Delta_{\text{diag}}=64.45 . The certificate ratio is Δdiag/Bsplit=0.053\Delta_{\text{diag}}/B_{\text{split}}=0.053 , and the observed relative approximation gap is 2.40%2.40\% .
Figure 10: Approximation consistency under the original discrete objective. Each point corresponds to one random trial under one greedy comparison. The x-axis denotes the objective value of the subset selected by Fast Greedy or Lazy-Fast Greedy, and the y-axis denotes that of NADS. Points near the diagonal indicate that the scalable NADS procedure remains close to greedy optimization when all subsets are evaluated under the original utility–diversity objective.
DatasetsAspectNums
Magicoder [ 80 ]Code Generation111K
MetaMathQA [ 81 ]Math Reasoning395K
Magpie-Qwen2.5-Pro-300K-Filtered [ 82 ]\300K
Appendix
Table 8: Summary of training datasets used in our experiments.
DatasetsAspectsMetricsNumsEvaluate
HellaSwag [ 87 ]Commonsense ReasoningAccuracy10,0420-shot
OpenBookQA [ 89 ]Commonsense ReasoningAccuracy5000-shot
MMLU [ 86 ]Multi Task UnderstandingAccuracy14,0425-shot
GSM8K [ 88 ]Math ReasoningExact Match1,3195-shot
HumanEval [ 85 ]Code GenerationPASS@11640-shot
Appendix
Table 9: Evaluation benchmarks and detailed settings.
ModelMethodGeneral Capability ↑\uparrowTarget ↑\uparrowOverall ↑\uparrow
HASWOBQAMMLUHEAvg.GSM8KAvg.
 Pre-trained55.83±0.00\text{55.83}_{\pm\text{0.00}}31.20±0.00\text{31.20}_{\pm\text{0.00}}56.92±0.00\text{56.92}_{\pm\text{0.00}}28.16±0.00\text{28.16}_{\pm\text{0.00}}43.03±0.00\text{43.03}_{\pm\text{0.00}}27.90±0.00\text{27.90}_{\pm\text{0.00}}35.47±0.00\text{35.47}_{\pm\text{0.00}}
 Standard FT50.02±0.50\text{50.02}_{\pm\text{0.50}}28.40±0.53\text{28.40}_{\pm\text{0.53}}48.49±0.41\text{48.49}_{\pm\text{0.41}}15.27±0.49\text{15.27}_{\pm\text{0.49}}35.55±0.24\text{35.55}_{\pm\text{0.24}}65.93±0.81\text{65.93}_{\pm\text{0.81}}50.74±0.42\text{50.74}_{\pm\text{0.42}}
 LoRA52.06±0.50\text{52.06}_{\pm\text{0.50}}28.60±0.53\text{28.60}_{\pm\text{0.53}}52.34±0.40\text{52.34}_{\pm\text{0.40}}25.31±0.52\text{25.31}_{\pm\text{0.52}}39.58±0.25\text{39.58}_{\pm\text{0.25}}61.03±0.83\text{61.03}_{\pm\text{0.83}}50.31±0.43\text{50.31}_{\pm\text{0.43}}
 Random50.38±0.50\text{50.38}_{\pm\text{0.50}}28.47±0.58\text{28.47}_{\pm\text{0.58}}49.54±0.40\text{49.54}_{\pm\text{0.40}}17.35±0.46\text{17.35}_{\pm\text{0.46}}36.44±0.24\text{36.44}_{\pm\text{0.24}}62.70±0.79\text{62.70}_{\pm\text{0.79}}49.57±0.41\text{49.57}_{\pm\text{0.41}}
 InsCL52.85±0.50\text{52.85}_{\pm\text{0.50}}28.93±0.58\text{28.93}_{\pm\text{0.58}}55.17±0.40\text{55.17}_{\pm\text{0.40}}26.34±0.21\text{26.34}_{\pm\text{0.21}}40.82±0.22\text{40.82}_{\pm\text{0.22}}62.77±0.87\text{62.77}_{\pm\text{0.87}}51.80±0.45\text{51.80}_{\pm\text{0.45}}
Appendix
Table 10: Performance comparison with methods selecting Dconstraint\mathcal{D}_{\text{constraint}} for replay on MetaMathQA (%). The best results are highlighted in red , and the second-best results are highlighted in blue .
ModelMethodGeneral Capability ↑\uparrowTarget ↑\uparrowOverall ↑\uparrow
HASWOBQAMMLUHEAvg.GSM8KAvg.
 LESS{\color[rgb]{0,0,1}\text{53.09}_{\pm\text{0.49}}}{\color[rgb]{0,0,1}\text{30.47}_{\pm\text{0.58}}}53.62±0.40\text{53.62}_{\pm\text{0.40}}26.27±0.52\text{26.27}_{\pm\text{0.52}}40.86±0.25\text{40.86}_{\pm\text{0.25}}{\color[rgb]{0,0,1}\text{63.63}_{\pm\text{0.87}}}{\color[rgb]{0,0,1}\text{52.25}_{\pm\text{0.45}}}
 FisherSFT53.01±0.49\text{53.01}_{\pm\text{0.49}}29.60±0.60\text{29.60}_{\pm\text{0.60}}55.07±0.40\text{55.07}_{\pm\text{0.40}}26.94±0.61\text{26.94}_{\pm\text{0.61}}41.16±0.26\text{41.16}_{\pm\text{0.26}}61.46±0.87\text{61.46}_{\pm\text{0.87}}51.31±0.45\text{51.31}_{\pm\text{0.45}}
 SPICE52.50±0.50\text{52.50}_{\pm\text{0.50}}29.13±0.58\text{29.13}_{\pm\text{0.58}}{\color[rgb]{0,0,1}\text{55.57}_{\pm\text{0.40}}}{\color[rgb]{0,0,1}\text{27.48}_{\pm\text{0.59}}}{\color[rgb]{0,0,1}\text{41.17}_{\pm\text{0.26}}}62.55±0.85\text{62.55}_{\pm\text{0.85}}51.86±0.44\text{51.86}_{\pm\text{0.44}}
LLaMA3.2NADS (Ours){\color[rgb]{1,0,0}\text{54.86}_{\pm\text{0.50}}}{\color[rgb]{1,0,0}\text{30.80}_{\pm\text{0.60}}}{\color[rgb]{1,0,0}\text{56.23}_{\pm\text{0.41}}}{\color[rgb]{1,0,0}\text{28.21}_{\pm\text{0.42}}}{\color[rgb]{1,0,0}\text{42.53}_{\pm\text{0.24}}}{\color[rgb]{1,0,0}\text{65.18}_{\pm\text{0.83}}}{\color[rgb]{1,0,0}\text{53.86}_{\pm\text{0.43}}}
 LESS54.93±0.49\text{54.93}_{\pm\text{0.49}}32.00±0.60\text{32.00}_{\pm\text{0.60}}56.24±0.40\text{56.24}_{\pm\text{0.40}}30.97±0.89\text{30.97}_{\pm\text{0.89}}43.54±0.32\text{43.54}_{\pm\text{0.32}}{\color[rgb]{0,0,1}\text{65.23}_{\pm\text{0.77}}}54.39±0.42\text{54.39}_{\pm\text{0.42}}
Appendix
Table 11: Cross-paradigm comparison with methods selecting Dnew\mathcal{D}_{\text{new}} on MetaMathQA (%).
MethodGeneral Capability ↑\uparrowTarget ↑\uparrowOverall ↑\uparrow
HASWOBQAMMLUGSM8KAvg.HEAvg.
LESS54.12±0.49\text{54.12}_{\pm\text{0.49}}30.67±0.61\text{30.67}_{\pm\text{0.61}}54.38±0.40\text{54.38}_{\pm\text{0.40}}23.73±0.62\text{23.73}_{\pm\text{0.62}}40.73±0.27\text{40.73}_{\pm\text{0.27}}43.01±0.84\textbf{43.01}_{\pm\textbf{0.84}}41.87±0.44\text{41.87}_{\pm\text{0.44}}
LESS + Random + KD53.21±0.49\text{53.21}_{\pm\text{0.49}}29.73±0.61\text{29.73}_{\pm\text{0.61}}53.52±0.39\text{53.52}_{\pm\text{0.39}}22.31±0.64\text{22.31}_{\pm\text{0.64}}39.69±0.27\text{39.69}_{\pm\text{0.27}}42.15±0.81\text{42.15}_{\pm\text{0.81}}40.92±0.43\text{40.92}_{\pm\text{0.43}}
LESS + Navigator + KD55.39±0.49\textbf{55.39}_{\pm\textbf{0.49}}31.13±0.61\textbf{31.13}_{\pm\textbf{0.61}}55.74±0.41\textbf{55.74}_{\pm\textbf{0.41}}25.35±0.64\textbf{25.35}_{\pm\textbf{0.64}}41.90±0.27\textbf{41.90}_{\pm\textbf{0.27}}42.76±0.86\text{42.76}_{\pm\text{0.86}}42.33±0.45\textbf{42.33}_{\pm\textbf{0.45}}
FisherSFT54.03±0.49\text{54.03}_{\pm\text{0.49}}29.80±0.60\text{29.80}_{\pm\text{0.60}}52.89±0.41\text{52.89}_{\pm\text{0.41}}23.15±0.62\text{23.15}_{\pm\text{0.62}}39.97±0.27\text{39.97}_{\pm\text{0.27}}41.85±0.74\text{41.85}_{\pm\text{0.74}}40.91±0.39\text{40.91}_{\pm\text{0.39}}
FisherSFT + Random + KD52.44±0.49\text{52.44}_{\pm\text{0.49}}29.33±0.61\text{29.33}_{\pm\text{0.61}}51.71±0.40\text{51.71}_{\pm\text{0.40}}21.86±0.64\text{21.86}_{\pm\text{0.64}}38.84±0.27\text{38.84}_{\pm\text{0.27}}41.26±0.82\text{41.26}_{\pm\text{0.82}}40.05±0.43\text{40.05}_{\pm\text{0.43}}
Appendix
Table 12: Effect of constraint-set quality under the same KD objective. Random + KD uses randomly selected constraint data, while Navigator + KD uses navigator-selected constraint data.
ModelTarget DatasetNavigatorTargetGeneralOverall
LLaMA3.2-3BMetaMathQANav-164.7541.2152.98
Nav-265.3542.7154.03
Nav-365.0541.7353.39
Gemma3-4BMagicoderNav-157.3245.0551.19
Nav-258.5446.5352.54
Nav-357.9345.5151.72
Appendix
Table 13: Comparison of three Navigator checkpoints across five additional model–dataset combinations. Results (%) are obtained using a single seed.
Figure 11: t-SNE visualization of the selected data under different selection methods.
ValidationUtility SpearmanTop- KK OverlapTargetGeneralOverall
Original1.001.001.001.0044.39±0.40\text{44.39}_{\pm\text{0.40}}42.52±0.27\text{42.52}_{\pm\text{0.27}}43.46±0.24\text{43.46}_{\pm\text{0.24}}
20% label noise0.830.830.720.7244.11±0.35\text{44.11}_{\pm\text{0.35}}41.72±0.31\text{41.72}_{\pm\text{0.31}}42.92±0.26\text{42.92}_{\pm\text{0.26}}
40% label noise0.690.690.580.5843.29±0.61\text{43.29}_{\pm\text{0.61}}40.94±0.35\text{40.94}_{\pm\text{0.35}}42.12±0.30\text{42.12}_{\pm\text{0.30}}
Template shifted0.760.760.640.6443.70±0.35\text{43.70}_{\pm\text{0.35}}41.20±0.33\text{41.20}_{\pm\text{0.33}}42.45±0.28\text{42.45}_{\pm\text{0.28}}
Appendix
Table 14: Navigator selection sensitivity to validation perturbations on Magicoder with LLaMA3.2.
Figure 12: Quantitative diversity diagnostics of the selected data under different selection methods. Higher values indicate stronger diversity under the corresponding metric.
Figure 13: Performance and cost visualization of different selection paradigms on Magicoder with LLaMA3.2-3B. Target-data selection methods select from Dnew\mathcal{D}_{\text{new}} , whereas replay-based methods and NADS select constraints from the synthetic pool C\mathcal{C} .
NavigatorSpearmanOverlap@KRel. TimeRel. Mem.
LoRA navigator0.890.820.74 ×\times0.16 ×\times
Full navigator1.001.001.00 ×\times1.00 ×\times
Appendix
Table 15: Comparison between full-parameter and LoRA-based navigators.
MethodGeneral Capability ↑\uparrowTarget ↑\uparrowOverall ↑\uparrow
HASWOBQAMMLUGSM8KAvg.HEAvg.
NADS + LoRA navigator55.0330.9356.2427.2242.3644.2843.32
NADS + Full navigator55.1731.0756.4527.3742.5244.3943.46
Appendix
Table 16: Comparison between LoRA-based and full-parameter navigators under the same final training objective. Both use the same synthetic candidate pool and KD objective.
ModelMethodNavigator Training (LoRA)Utility ComputationSubset OptimizationFinal TrainingTotal Cost (LoRA)Overall (LoRA)
LLaMA3.2-3BInsCL––12.6922.8535.5441.45
 LER––7.9622.8530.8141.81
 Mix-cd––18.2322.8541.0842.01
 NADS15.83 (11.72)5.190.0223.7844.82 (40.71)43.46 (43.32)
Gemma3-4BInsCL––12.6927.6140.3050.34
 LER––9.6727.6137.2850.76
Appendix
Table 17: Stage-wise computational costs (GPU-hours) and overall performance (%) on Magicoder. Parenthesized values correspond to LoRA-based Navigator training.
Figure 14: NADS performance under different synthetic datasets across seven evaluation metrics on the Magicoder dataset with LLaMA3.2-3B. Each group of bars compares the results obtained with different synthetic data pools under the same setting.
KKGeneral CapabilityTargetOverall
HASWOBQAMMLUGSM8KAvg.HEAvg.
1%52.8428.7352.5422.8739.2544.9342.09
3%53.9730.1354.6225.4041.0344.5042.77
5%55.1731.0756.4527.3742.5244.3943.46
10%55.3431.1356.7327.4242.6644.3843.52
15%55.1530.8756.2427.1442.3543.8643.11
Appendix
Table 18: Target performance and general capability of NADS under different constraint-set sizes KK .
TasksPre-trainedStandard FTInsCLLERMix-cdNADS
General Capability ↑\uparrow
ARC-Challenge42.9242.9244.3744.3744.7144.7145.0545.0545.6545.6546.6746.67
ARC-Easy74.5874.5873.4873.4875.3475.3475.1375.1375.2575.2575.9375.93
PIQA76.2876.2875.4175.4176.5076.5076.7176.7177.5877.5877.3777.37
HellaSwag55.8355.8357.4257.4257.0557.0557.5557.5558.1058.1059.0059.00
OpenBookQA31.2031.2033.2033.2033.0033.0033.8033.8033.6033.6034.6034.60
Appendix
Table 19: Performance comparison on general capability and IFEval benchmarks (%). Results are obtained using a single random seed. Pre-trained and Standard FT are excluded from the ranking. The best results are highlighted in red , and the second-best results are highlighted in blue .
MethodGeneral Capability ↑\uparrowTarget ↑\uparrowOverall ↑\uparrow
HASWOBQAMMLUGSM8KAvg.HEAvg.
LLaMA3.2-3B
Pre-trained55.83±0.00\text{55.83}_{\pm\text{0.00}}31.20±0.00\text{31.20}_{\pm\text{0.00}}56.92±0.00\text{56.92}_{\pm\text{0.00}}27.90±0.00\text{27.90}_{\pm\text{0.00}}42.96±0.00\text{42.96}_{\pm\text{0.00}}28.16±0.00\text{28.16}_{\pm\text{0.00}}35.56±0.00\text{35.56}_{\pm\text{0.00}}
Standard FT52.12±0.52\text{52.12}_{\pm\text{0.52}}28.40±0.69\text{28.40}_{\pm\text{0.69}}48.61±0.40\text{48.61}_{\pm\text{0.40}}20.75±0.74\text{20.75}_{\pm\text{0.74}}37.47±0.30\text{37.47}_{\pm\text{0.30}}45.13±0.32\text{45.13}_{\pm\text{0.32}}41.30±0.22\text{41.30}_{\pm\text{0.22}}
LoRA \venuebox ICLR 2253.38±0.55\text{53.38}_{\pm\text{0.55}}29.47±0.64\text{29.47}_{\pm\text{0.64}}51.98±0.42\text{51.98}_{\pm\text{0.42}}21.18±0.79\text{21.18}_{\pm\text{0.79}}39.00±0.31\text{39.00}_{\pm\text{0.31}}41.92±0.30\text{41.92}_{\pm\text{0.30}}40.46±0.21\text{40.46}_{\pm\text{0.21}}
STM \venuebox NIPS 2553.02±0.49\text{53.02}_{\pm\text{0.49}}29.67±0.61\text{29.67}_{\pm\text{0.61}}53.24±0.41\text{53.24}_{\pm\text{0.41}}23.81±0.75\text{23.81}_{\pm\text{0.75}}39.94±0.29\text{39.94}_{\pm\text{0.29}}42.04±0.82\text{42.04}_{\pm\text{0.82}}40.99±0.44\text{40.99}_{\pm\text{0.44}}
Appendix
Table 20: Comparison with catastrophic forgetting mitigation methods on Magicoder dataset (%). The best results are highlighted in red , and the second-best results are highlighted in blue .
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